CE 220 ADVANCED SURVEYING

TOPICS

ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM) First introduced by Swedish physicist Erik Bergstrand (Geodimeter) in 1948. Used visible light at night to accurately measure distances of up to 40km. In 1957, the first Tellurometer, designed by South African, Dr. T.L. Wadley, was launched. The Tellurometer used microwaves to measure distances up to 80km during day or night. Although the first models were very bulky and power hungry, they revolutionized survey industry which, until their arrival, relied on tape measurements for accurate distance determinations. The picture above shows the slave (or remote) unit of the Tellurometer CA1000, a model which was extensively used in the 70’s and 80’s.

INITIAL IMPACTS OF EDM SCALE DETERMINATION IN TRIGONOMETRICAL CONTROL NETWORKS Trigonometric Base Line Extension EDM Traverses (and Trilateration) TRAVERSES TO EXPAND AND DENSIFY NATIONAL CONTROL NETWORKS

Propagation of Electromagnetic Energy Velocity of EM energy, V = ƒ λ ƒ is the frequency in hertz (cycles/second) λ is the wavelength In vacuum the velocity of electromagnetic waves equals the speed of light. V = c/n n >1, n is the refractive index of the medium through which the wave propagates c is the speed of light = 299 792 458 m/sec f λ = c/n or λ = cf/n (i.e. λ varies with n !) Note that n in any homogeneous medium varies with the wavelength λ. White light consists of a combination of wavelengths and hence n for visible light is referred to as a group index of refraction. For EDM purposes the medium through which electromagnetic energy is propagated is the earths atmosphere along the line being measured. It is therefore necessary to determine n of the atmosphere at the time and location at which the measurement is conducted.

Propagation of Electromagnetic Energy The refractive index of air varies with air density and is derived from measurements of air temperature and atmospheric pressure at the time and site of a distance measurement. For an average wavelength λ: na= 1 + ( ng-1 ) x p - 5.5e x 10-8 1 + 0.003661T 760 1 + 0.003661T Where ng is the group index of refraction in a standard atmosphere (T=0°C, p=760mm of mercury, 0.03% carbon dioxide) ng = 1+ ( 2876.04 + 48.864/λ2 +0.680/ λ4 ) x 10-7 p is the atmospheric pressure in mm of mercury (torr) T is the dry bulb temperature in °C and e is the vapor pressure Where e= e’+de and e’=4.58 x 10a, a=(7.5T’)/(237.3+T’), de=-(0.000660p (1+0.000115T’) (T-T’) and T’ is the wet-bulb temperature Hence measuring p, T and T’ will allow for the computation of n for a specific λ

THE FRACTION OF A WAVELENGTH AND THE PHASE ANGLE 90° λ + r θ ½λ ½λ 0° 180° Amplitude - r ¼λ ¼λ ¼λ ¼λ 270° θ λ 360 A fraction of a wavelength can be determined from a corresponding phase angle θ Note: For θ = 0° the fraction is 0 For θ = 90° the fraction is ¼ For θ = 180° the fraction is ½ For θ = 270° the fraction is ¾ For θ = 360° the fraction is 1 EDM INSTRUMENTS CAN MEASURE PHASE ANGLES

Principles of Electronic Distance Measurement If an object moves at a constant speed of V over a straight distance L in a time interval ∆t, then L= V∆t = (c/n)∆t Knowing the speed of light c and being able to determine the refractive index, we could measure the time interval it takes for an electromagnetic wave to move from A to B to determine the distance L between A and B. But since c, the speed of light, is very high, the time interval ∆t would need to be measured extremely accurately. Instead, the principle of EDM is based on the following relationship: L = (m + p) λ 1 2 3 4 5 6 7 8 9 10 11 12 p λ A B L m is an integer number of whole wavelengths, p is a fraction of a wavelength Thus L can be determined from λ, m and p

Solving for the integer number (m) of whole wavelengths (Resolving the ambiguity in the number of whole wave lengths) p3 λ2 p2 10 1 4 7 8 9 11 2 3 12 5 6 B A λ p1 λ λ λ λ λ λ λ λ λ λ λ L Additional waves of known lengths λ3= kλ2 and λ2= k λ1 (k is a constant), are introduced to measure the same distance L: L = (m3 + p3) λ3 L =(m2 + p2) λ2 L =(m1 + p1) λ1 Determining p1 p2 and p3 by measuring phase angles θ1 θ2 and θ3 and solving the above equations simultaneously yields L ( Note: For L < λ3 , m3 = 0). For example, if λ1 = 10.000m, k= 10.000 and p1 = 0.2562, p2 = 0.2620 and p3 = 0.0125 Then λ2= 10.000m x 10.000 = 100.000m and λ3= 100.000 x 10.000 = 1000.000 L= (m3 + p3) λ3 = (0+0.1250)x 1000.000 = 125.000m approximately m2= 125/ λ2=125/100=1 and hence L = (1+0.2620)x100.000 = 126.200m approximately m1= 126.2/ λ1=126.2/10=12 and hence L = (12+ 0.2562)x10 = 122.562m

Receiver Optics and phase-difference circuits Basic Components of an EDM Instrument Reflector Reflector L Beam Splitter Length of measured path is 2xL Variable Filter Interference Filter L Transmitter F1 F4 F2 F3 Receiver Optics and phase-difference circuits Measurement signal Reference signal Frequency Generator Display Phase Meter To obtain the phase angle the reflected signal phase is compared to the reference signal phase. Note also that the measured distance equals 2 x L.

General Remarks on EDM The original Tellurometer models, using microwaves, consisted of two units, the master and the remote, both of which had to be manned. The carrier wave was used to establish a voice channel between the operators who had to coordinate the manual switching of the frequencies. The measuring signals were directed (bundled) by means of metal cones. For long lines careful measurements of pressure and the wet- and dry-bulb temperatures were made at each end of the line. Measurements were very susceptible to multipath reflections (ground swing). Developments in electronics reduced the size of the components drastically so that EDM instruments could be mounted on top of theodolites for convenient simultaneous measurements of distances as well as directions. Nowadays EDM components are completely integrated into total stations. Total stations allow for the direct input of temperature and pressure and automatic application of meteorological corrections. Most of the current EDM instruments use LASER beams and passive optical reflectors, thus reducing the possibility of multipathing considerably. The latest models provide for reflector-less measurements, thus improving efficiency for certain applications drastically.

Sources of Error in EDM: Personal: Careless centering of instr. and/or reflector Faulty temperature and pressure measurements Incorrect input of T and p Instrumental Instrument not calibrated Electrical center Prism Constant (see next slide) Natural Varying ‘met’ along line Turbulence in air Remember: L = (m + p) λ

Sources of Error in EDM: Determination of System Measuring Constant A B C Mistakes: Incorrect ‘met’ settings Incorrect scale settings Prism constants ignored Incorrect recording settings (e.g. horizontal vs. slope) Measure AB, BC and AC AC + K = (AB + K) + (BC + K) K = AC- (AB + BC) If electrical center is calibrated, K rep- resents the prism constant. Good Practice: Never mix prism types and makes on same project!!! Calibrate regularly !!!

CURVES

SIMPLE CURVES

Circular Curves TYPES OF CURVES: Simple Curve Compound Curve Reverse Curve spiral R R R R Easement or Transitional Curve spiral

Definitions “Degree of Curve” Central angle subtended by a circular ARC of 100 ft (highways) 100 ft R R D/100’ = 360/ 2p r = full circle angle / circumference PI PC PI = Point of Intersection PC = Point of Curvature PT = Point of Tangency L = Length of Curve L PT

Formulae T = R Tan I/2 L = 100 I0/D0 = R I rads LC = 2 R Sin I/2 LC = Long Chord M = Middle Ordinate E = External Distance T = Tangent Distance I = Intersection Angle T E T L M PC PT LC R T = R Tan I/2 R I/2 L = 100 I0/D0 = R I rads I LC = 2 R Sin I/2 R/ (R+E) = Cos I/2 => E = R [(1/Cos (I/2)) - 1] (R - M)/R = Cos I/2 => M = R [1 - (Cos (I/2)]

Stationing (usually every 100 feet) PC 4+86.75 4+00.00 0+00.00 1+00.00 2+00.00 3+00.00 5+00.00 T PI L 6+00.00 7+00.00 PC sta = PI sta – T PT sta = PC sta + L PT 7+27.87 8+00.00 9+00.00 10+00.00 11+00.00

Curve Layout Need to stake at “full stations” (XX+00.00) Set up on PC, backsight PI, turn deflection angle (d), measure chord distance (c) PI d PC chord

Vertical Curves Crest Curve Crest Curve Provides a smooth transition between different grades Parabola - constant rate of change of grade GRADE: Grade = +4.00% + rising grad - falling grade 4.00’ 100’

Vertical Curve Geometry Back tangent (g1) Forward tangent (g2) BVC EVC Xp Yp X L/2 L/2 L = curve length

Constant rate of change of Grade r r = (g2 – g1) / L R should be low (long L) for rider comfort and sight distance Equation of Curve (parabola): Y = YBVC + g1 X + ((g2 – g1)/2L) X2 Units: g in %, L and X in stations, Y in ft/meters Or G in fractions (0.04), L, X, Y in ft/meters

COORDINATE GEOMETRY

COORDINATE GEOMETRY Except for Geodetic Control Surveys, most surveys are referenced to plane rectangular coordinate systems. Frequently State Plane Coordinate Systems are used. The advantage of referencing surveys to defined coordinate systems are: Spatial relations are uniquely defined. Points can be easily plotted. Coordinates provide a strong record of absolute positions of physical features and can thus be used to re-construct and physically re-position points that may have been physically destroyed or lost. Coordinate systems facilitate efficient computations concerning spatial relationships. In many developed countries official coordinate systems are generally defined by a national network of suitably spaced control points to which virtually all surveys and maps are referenced. Such spatial reference networks form an important part of the national infrastructure. They provide a uniform standard for all positioning and mapping activities.

THE TRIANGLE x = -b ±  b2 – 4ac is also often used. The geometry of triangles is extensively employed in survey calculations. B For any triangle ABC with sides a, b and c: a = b = c (LAW OF SINES) sin A sin B sin C AND a2 = b2 + c2 -2ab cosA b2 = a2 + c2 -2ac cosB (LAW OF COSINES) c2 = a2 + b2 -2ab cosC c a A b C A + B + C = 180° The solution of the quadratic equation ax2 + bx + c = 0 x = -b ±  b2 – 4ac is also often used. 2a

THE STRAIGHT LINE Y ∆XAB = XB-XA AND ∆YAB = YB-YA ∆XAB = XB-XA AND ∆YAB = YB-YA LAB =  ∆XAB2 + ∆YAB2 AzAB = atan(∆XAB / ∆YAB ) + C C=0° for ∆XAB >0 and ∆YAB >0 C=180° for ∆YAB <0 and C=360° for ∆XAB <0 and ∆YAB >0 B(XB,YB) P(XP,YP) AzAB For P on line AB: YP = mXp + b where the slope m = ((∆yAB / ∆xAB ) = cot(AzAB ) AzAB = atan (1/m) + C A(XA,YA) b

THE CIRCLE Y P(XP,YP) R R2 = ∆XOP2 + ∆YOP2 O(XO,YO) P(XP,YP) R R2 = ∆XOP2 + ∆YOP2 XP2+YP2 – 2XOXP – 2YOYP + f = 0 R =  XO2 + YO2 - f O(XO,YO) f

THE PERPENDICULAR OFFSET Y X Given known points A,B and P, compute distance PC (LPC) C=0° for ∆XAB >0 and ∆YAB >0 C=180° for ∆YAB <0 and C=360° for ∆XAB <0 and ∆YAB >0 P(XP,YP) B(XB,YB) AzAP = atan(∆XAP / ∆YAP ) + C LAP =  ∆XAP2 + ∆YAP2 AzAB = atan(∆XAB / ∆YAB ) + C LAB =  ∆XAB2 + ∆YAB2 AzAP C a AzAB A(XA,YA) a = AzAB – AzAP LPC = LAB sin LAC = LAB cos a b

THE INTERSECTION Y X Given A(XA,YA), B(XB,YB), AzAP and AzBP compute P(XP,YP) AzAB = atan(∆XAB / ∆YAB ) + C LAB =  ∆XAB2 + ∆YAB2 a = AzAB – AzAP β = AzBA – AzBP γ = 180° – a – β LAP = LAB (sin rule) sin β sin γ LAP = LAB (sin β / sin γ ) XP = XA + LAP sin AzAP YP = YA + LAP cos AzAP C=0° for ∆XAB >0 and ∆YAB >0 C=180° for ∆YAB <0 and C=360° for ∆XAB <0 and ∆YAB >0 B(XB,YB) AzBP AzAP β Outside Orientation AzBA Similarly (as a check on the calculations): LBP = LAB (sin rule) sin a sin γ LBP = LAB (sin β / sin γ ) XP = XA + LBP sin AzBP YP = YA + LBP cos AzBP AzAB a γ A(XA,YA) P(XP,YP) WARNING: USE A THIRD KNOWN POINT TO CHECK ORIENTATIONS

INTERSECTION OF A LINE WITH A CIRCLE Y X Given A,B and C and radius R, compute P1 and P2 Note a = AzAC – AzAB and LBP1 = LBP2 = R Apply the cos rule to triangle ABP1: LBP12 = LAB2+ LAP12-2(LAB)(LAP1)cos a or LAP12 –(2LABcos a) LAP1 + (LAB2 - LBP12) = 0 which is a quadratic equation with LAP1 as unknown C(XC,YC) B(XB,YB) R Note that since LBP1 = LBP2 = R the above equation also applies to triangle ABP2. Hence the two solutions of the quadratic equation are AP1 and AP2. P2(XP2,YP2) a P1(XP1,YP1) AP= 2LABcos a ± (2LABcos a)2-4(LAB2 - LBP12) 2 A(XA,YA) Now use AzAC and the solutions of AP to compute P1(XP1,YP1) and P2(XP2,YP2)

INTERSECTION OF TWO CIRCLES Y X Given A,B and C and radius R, compute P1 and P2 Note LAP1 = LAP2 = RA and LBP1 = LBP2 = RB Compute AzAB and LAB from given coordinates of A and B Apply the cos rule to triangle ABP1: a = acos ((LAB2+ LAP12-LBP12)/(2LABLAP1)) = acos ((LAB2+ RA2-RB2)/(2LABRA)) B(XB,YB) AzAP1 = AzAB – a and AzAP2 = AzAB + a P1(XP1,YP1) RB P2(XP2,YP2) a a XP1 = XA + RAsin (AzAP1) YP1 = YA + RAcos(AzAP1) and XP2 = XA + RAsin (AzAP2) YP2 = YA + RAcos(AzAP2) RA A(XA,YA) WARNING Trilatertion of a point with only two distances yields two positions!!!!!

HOMEWORK: LECTURE 13 (CHAPTER 11 SEC 1-6) 11.1, 11.9, 11.13, 11.15, 11.17

RESECTION

THE RESECTION Determine Coordinates of P from observations to known points A, B and C. Note: Since P is un-known, the raw observations at P need to be oriented. Use the Q-Point Method to orient the observations at P and then intersect P with the oriented forward directions from A and B. Compute α and β from observations a = 180° - α , b = 180° - β Compute AzAB from XA, YA, XB,YB AzAQ = AzAB – b, AzBQ = AzBA + a Compute XQ and YQ with AzAQ and AzBQ from A and B (forward intersection) Compute AzQC (= AzPC) from XQ, YQ, XC,YC AzAP = AzPC + α ± 180°, AzBP = AzPC - β ± 180° 8. Compute XP and YP with AzAQ and AzBQ Q A b a α P b a Note: The solution is ambiguous when A,B,C and P all lie on a circle (the danger circle) β B C For best orientation results use the furthest point for Orientation.

THE INACCESSIBLE POINT AP = AB sin (B) = AB sin (B) sin(180-(A+B) sin (A+B) BP = AB sin (A) sin (A+B) ∆hA = AP tan (vA) ∆hB = BP tan (vB) Elev.PA = Elev.A + ∆hA + hiA Elev.PB = Elev.B + ∆hB + hiB Elev P = Elev.PA + Elev.B 2 Can be applied in reverse to determine height of A (or B) from known height of P. Provided sufficient outside orientation is given, this model is also used to close traverses on inaccessible points with known coords. (e.g. church spire) ∆hA ∆hB vA B p hiA Outside Orientation A Caution: Steep sights – observe on both faces and level instrument carefully.

THE ‘DOG’S LEG’ CHECK When fixing or placing a point from only one known station by means of a ‘single polar’, the ‘dog’s leg’ is often applied to obtain an independent check. O U From known point B observe two orientation points to ensure correct orientation. Measure direction and distance to unknown point U Place auxiliary point A in such a way that at least one known point in addition to B is visible and that the angle at U is greater than 30°. Measure direction and distance to A Move instrument to A and observe outside orientation point O and B and measure direction and distance to U. Compute Coordinates of A and U to obtain independent coordinates for U A B To strengthen the check A is sometimes placed on line from B to an orientation point.

THE 2D CONFORMAL COORDINATE TRANSFORMATION Given A(E,N) and B(E,N) and A(X,Y) and B(X,Y) compute C(E,N) from C(X,Y) 1. Compute the Swing Az(XY)AB = atan (∆XAB/∆YAB) Az(EN)AB = acot (∆NAB/∆EAB) ‘Swing’ θ = Az(XY)AB - Az(EN)AB Az(EN)AB Az(XY)AB B C ∆NAB θ X D 2. Compute the Scale  ∆EAB2 + ∆NAB2 Scale s =  ∆XAB2 + ∆YAB2 Y A XAB YAB ∆XAB ∆YAB ∆EAB E

THE 2D CONFORMAL COORDINATE TRANSFORMATION Given A(E,N) and B(E,N) and A(X,Y) and B(X,Y) compute C(E,N) from C(X,Y) 1. Compute the Swing Az(XY)AB = atan (∆XAB/∆YAB) Az(EN)AB = acot (∆NAB/∆EAB) ‘Swing’ θ = Az(XY)AB - Az(EN)AB 2. Compute the Scale  ∆EAB2 + ∆NAB2 Scale s =  ∆XAB2 + ∆YAB2 3. Compute the Translations TX and TY a = sYAsin θ, b=sXAcos θ Hence X’A = s(XAcos θ - YAsin θ) c = sXAsin θ, d=sYAcos θ Hence Y’A = s(XAsin θ + YAcos θ) EA = X’A + TX hence TX = EA – X’A and NA = Y’A + TY hence TY = NA – Y’A C NC Y’ B D Y A X A YA d θ Y’A XA 4. Apply the transformation parameters EC = s(XCcos θ - YCsin θ) + TX NC = s(XCsin θ + YCcos θ) + TY c θ θ TY X’ X’A a b E Tx EA EC

Ø ✔ Ø ✔ ✔ Ø SOME ‘GOLDEN RULES’ Unless traversing, always observe two orientation rays to control correct orientation of instrument. Long observation rays give better orientation than short rays. Orientation rays should always be longer than fixing rays. The formulae derived for trilateration, intersection and resection use the minimum number of observations to determine one unchecked set of coordinates for unknown points. Additional independent observations should be made to provide sufficient redundancy and control of the quality of coordinates. Pay attention to the strength in the geometry – keep intersection angles larger than 30°. Be aware of situations that yield multiple solutions. (Intersection/Trilateration). Add value to your survey by connecting it to the most widely used coordinate system in the area. If possible, avoid local coordinate systems. Interpolate – do NOT extrapolate! Connect to nearest available known points Orientation B A Mirror image due to orientation mistake of 180° Geometry Ø ✔ Interpolation Ø ✔ Neighborhood Principle ✔ Ø

GEODESY

Geodesy, Map Projections and Coordinate Systems Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data

Types of Coordinate Systems (1) Global Cartesian coordinates (x,y,z) for the whole earth (2) Geographic coordinates (f, l, z) (3) Projected coordinates (x, y, z) on a local area of the earth’s surface The z-coordinate in (1) and (3) is defined geometrically; in (2) the z-coordinate is defined gravitationally

Global Cartesian Coordinates (x,y,z) Greenwich Meridian Equator •

Global Positioning System (GPS) 24 satellites in orbit around the earth Each satellite is continuously radiating a signal at speed of light, c GPS receiver measures time lapse, Dt, since signal left the satellite, Dr = cDt Position obtained by intersection of radial distances, Dr, from each satellite Differential correction improves accuracy

Global Positioning using Satellites Dr2 Dr3 Number of Satellites 1 2 3 4 Object Defined Sphere Circle Two Points Single Point Dr4 Dr1

Geographic Coordinates (f, l, z) Latitude (f) and Longitude (l) defined using an ellipsoid, an ellipse rotated about an axis Elevation (z) defined using geoid, a surface of constant gravitational potential Earth datums define standard values of the ellipsoid and geoid

Shape of the Earth It is actually a spheroid, slightly larger in radius at the equator than at the poles We think of the earth as a sphere

Ellipse Z b O a X  F1  F2 P An ellipse is defined by: Focal length =  Distance (F1, P, F2) is constant for all points on ellipse When  = 0, ellipse = circle Z b O a X F1   F2 For the earth: Major axis, a = 6378 km Minor axis, b = 6357 km Flattening ratio, f = (a-b)/a ~ 1/300 P

Ellipsoid or Spheroid Rotate an ellipse around an axis Z b O a a Y X Rotational axis

Standard Ellipsoids Ref: Snyder, Map Projections, A working manual, USGS Professional Paper 1395, p.12

Horizontal Earth Datums An earth datum is defined by an ellipse and an axis of rotation NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non geocentric axis of rotation NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83

Definition of Latitude, f m S p n O f q r (1) Take a point S on the surface of the ellipsoid and define there the tangent plane, mn (2) Define the line pq through S and normal to the tangent plane (3) Angle pqr which this line makes with the equatorial plane is the latitude f, of point S

Cutting Plane of a Meridian Equator plane Prime Meridian

Definition of Longitude, l l = the angle between a cutting plane on the prime meridian and the cutting plane on the meridian through the point, P 180°E, W -150° 150° -120° 120° 90°W (-90 °) 90°E (+90 °) -60° P l -60° -30° 30° 0°E, W

Latitude and Longitude on a Sphere Z Meridian of longitude Greenwich meridian N Parallel of latitude =0° P • =0-90°N  - Geographic longitude  - Geographic latitude  W O E • Y  R R - Mean earth radius • =0-180°W Equator =0° •  O - Geocenter =0-180°E X =0-90°S

Length on Meridians and Parallels (Lat, Long) = (f, l) Length on a Meridian: AB = Re Df (same for all latitudes) R Dl 30 N R D C Re Df B 0 N Re Length on a Parallel: CD = R Dl = Re Dl Cos f (varies with latitude) A

Example: What is the length of a 1º increment along on a meridian and on a parallel at 30N, 90W? Radius of the earth = 6370 km. Solution: A 1º angle has first to be converted to radians p radians = 180 º, so 1º = p/180 = 3.1416/180 = 0.0175 radians For the meridian, DL = Re Df = 6370 * 0.0175 = 111 km For the parallel, DL = Re Dl Cos f = 6370 * 0.0175 * Cos 30 = 96.5 km Parallels converge as poles are approached

Representations of the Earth Mean Sea Level is a surface of constant gravitational potential called the Geoid Earth surface Ellipsoid Sea surface Geoid

Geoid and Ellipsoid Gravity Anomaly Earth surface Ellipsoid Ocean Geoid Gravity Anomaly Gravity anomaly is the elevation difference between a standard shape of the earth (ellipsoid) and a surface of constant gravitational potential (geoid)

Definition of Elevation Elevation Z P z = zp • z = 0 Land Surface Mean Sea level = Geoid Elevation is measured from the Geoid

Vertical Earth Datums A vertical datum defines elevation, z NGVD29 (National Geodetic Vertical Datum of 1929) NAVD88 (North American Vertical Datum of 1988) takes into account a map of gravity anomalies between the ellipsoid and the geoid

Converting Vertical Datums Corps program Corpscon (not in ArcInfo) http://crunch.tec.army.mil/software/corpscon/corpscon.html Point file attributed with the elevation difference between NGVD 29 and NAVD 88 NGVD 29 terrain + adjustment = NAVD 88 terrain elevation

http://www.csr.utexas.edu/ocean/mss.html

http://www.csr.utexas.edu/ocean/egs04.html

Geodesy and Map Projections Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data

Earth to Globe to Map Map Projection: Map Scale: Scale Factor Representative Fraction Globe distance Earth distance = Scale Factor Map distance Globe distance = (e.g. 1:24,000) (e.g. 0.9996)

Geographic and Projected Coordinates (f, l) (x, y) Map Projection

Projection onto a Flat Surface

Types of Projections Conic (Albers Equal Area, Lambert Conformal Conic) - good for East-West land areas Cylindrical (Transverse Mercator) - good for North-South land areas Azimuthal (Lambert Azimuthal Equal Area) - good for global views

Conic Projections (Albers, Lambert)

Cylindrical Projections (Mercator) Transverse Oblique

Azimuthal (Lambert)

Albers Equal Area Conic Projection

Lambert Conformal Conic Projection

Universal Transverse Mercator Projection

Lambert Azimuthal Equal Area Projection

Projections Preserve Some Earth Properties Area - correct earth surface area (Albers Equal Area) important for mass balances Shape - local angles are shown correctly (Lambert Conformal Conic) Direction - all directions are shown correctly relative to the center (Lambert Azimuthal Equal Area) Distance - preserved along particular lines Some projections preserve two properties

Geodesy and Map Projections Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data

Coordinate Systems Universal Transverse Mercator (UTM) - a global system developed by the US Military Services State Plane Coordinate System - civilian system for defining legal boundaries California State Mapping System - a statewide coordinate system for California

Coordinate System A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin Y X Origin (xo,yo) (fo,lo)

Universal Transverse Mercator Uses the Transverse Mercator projection Each zone has a Central Meridian (lo), zones are 6° wide, and go from pole to pole 60 zones cover the earth from East to West Reference Latitude (fo), is the equator (Xshift, Yshift) = (xo,yo) = (500000, 0) in the Northern Hemisphere, units are meters

UTM Zone 21 &22 -123° -102° -96° 6° Origin Equator -120° -90 ° -60 °

State Plane Coordinate System Defined for each State in the United States East-West States (e.g. Texas) use Lambert Conformal Conic, North-South States (e.g. California) use Transverse Mercator Texas has five zones (North, North Central, Central, South Central, South) to give accurate representation Greatest accuracy for local measurements

California Mapping System Designed to give State-wide coverage of Texas without gaps Lambert Conformal Conic projection with standard parallels 1/6 from the top and 1/6 from bottom of the State Adapted to Albers equal area projection for working in hydrology

Standard Hydrologic Grid (SHG) Developed by Hydrologic Engineering Center, US Army Corps of Engineers Uses USGS National Albers Projection Parameters Used for defining a grid over the US with cells of equal area and correct earth surface area everywhere in the country

Coordinate Systems Geographic coordinates (decimal degrees) Projected coordinates (length units, ft or meters)

Summary Concepts Two basic locational systems: geometric or Cartesian (x, y, z) and geographic or gravitational (f, l, z) Mean sea level surface or geoid is approximated by an ellipsoid to define an earth datum which gives (f, l) and distance above geoid gives (z)

Summary Concepts (Cont.) To prepare a map, the earth is first reduced to a globe and then projected onto a flat surface Three basic types of map projections: conic, cylindrical and azimuthal A particular projection is defined by a datum, a projection type and a set of projection parameters

Summary Concepts (Cont.) Standard coordinate systems use particular projections over zones of the earth’s surface Types of standard coordinate systems: UTM, State Plane, California State Mapping System, Standard Hydrologic Grid Reference Frame in ArcInfo 8,& Geomedia requires projection and map extent

GPS

Introduction to the NAVSTAR Global Positioning System (GPS) The NAVSTAR is a satellite-based radio navigation system and was invented by the United States Department of Defense (DoD) in 1973. Although there are thousands of civilian users of the NAVSTAR system, the system was designed for and is operated by the U.S. military. The Global Positioning System (GPS) provides specially coded satellite signals that are processed by a receiver. This receiver interprets the signals to give position, velocity, and time. The range between a user antenna and four satellites is measured by correlating a general signal with the received ones from the satellites, which have known coordinates, and then the user coordinates and the time offset in the receiver clock, clock bias, can be determined.

Agenda GPS Lineage What is GPS How Does It Work Errors and Accuracy's in the GPS system Future Initiatives

GPS Lineage Phase 1: 1973-1979 CONCEPT VALIDATION 1978- First Launch of Block 1 SV Phase 2: 1979-1985 FULL DEVELOPMENT AND TESTS Phase 3: 1985-Present PRODUCTION AND DEPLOYMENT 1993-IOC 1995-FOC The important thing to note is that GPS is a type of radio navigation, and that it was specifically designed to eliminate the disadvantages of all the other radio systems we've used for the last 50 years or so. All of the others have at least one weakness, such as interference in bad weather, limited local coverage, etc. The reason we are so interested in GPS at DMS is that it represents a dramatic change in the way people find their way around the world.

What is GPS Space Segment Control Segment User Segment The Global Positioning System (GPS) is a Constellation of Earth-Orbiting Satellites Maintained by the United States Government for the Purpose of Defining Geographic Positions On and Above the Surface of the Earth. It consists of Three Segments: There are three major components that make up the GPS system. These three components will be discussed in-depth in the following slides. Space Segment Control Segment User Segment

Space Segment Description 24+ satellites 6 planes with 55° Inclination Each plane has 4 or 5 satellites Broadcasting position and time information on 2 frequencies Constellation has Spares Very high orbit 20,200 km 1 revolution in approximately 12 hrs For accuracy Survivability Coverage The first segment is the Space Segment, and this refers to the actual satellites (officially, they're called Satellite Vehicles, or SVs) in orbit. The constellation consists of 24 satellites arranged in 6 orbital planes. There are 4 satellites in each plane and the system was designed so that there would always be at least 4 SVs visible from anywhere in the world at all times. Each satellite orbits the earth in 12 hours. Actually, a satellite will pass over the same location every 23 hours and 56 minutes. This also means that the SVs are not geostationary - they are constantly moving overhead, rising and falling from the perspective of someone on the ground. The orbit is fairly high, making it is a little harder to attack the SVs than if they were in a Low Earth Orbit (LEO). The higher altitude gives broader ground coverage than satellites in a LEO, and allows each SV to pass over an Upload Station twice in every 24 hour period. The life time design of the Block II/IIA is 7.5 years and costs about 53.8 million dollars per satellite. All of the SVs broadcast on the same 2 L-band frequencies - we'll talk more about them later.

Control Segment Monitor and Control Colorado Springs Kwajalein Ascension Islands Hawaii Kwajalein The second segment we'll talk about is the Operational Control Segment. This segment consists of 5 Monitor Stations on islands near the equator (Hawaii, Ascension, Diego Garcia, and Kwajelin) and one Master Control Station located at Falcon AFB, CO. All of these stations track the GPS signals, and send them back to the Master Control Station at Falcon. A backup MCS exists at Loral Federal System in Gaithersburg, MD. The four stations track and monitor the where-abouts of each GPS satellite each day. Then land-based and space-based communications are used to connect the monitoring stations with MCS. Diego Garcia Master Control Station Monitor Station Ground Antenna

Control Segment Correct Orbit and clock errors Observe Create new navigation message Observe ephemeris and clock The MCS, at Falcon AFB, is responsible for the overall command and control, which includes maintaining the exact orbits of each satellite and determining any timing errors that may be present in the highly accurate atomic clocks. The errors are corrected by Falcon with updated orbits and clock corrections relayed once a day to each satellite via four ground antennas. In the future, more monitor stations will be added to further refine the system. Military customers get better than required accuracy as a result. It is important to note that even though the Air Force operates the constellation of satellites on a day-to-day basis, the overall GPS program is jointly managed. The unit that develops the hardware (both military receivers and the actual satellites) is the GPS Joint Program Office (JPO) at Los Angeles AFB. There are, among others, Army, Navy, DoT, and even DMA Deputy Program Managers. Upload Station (5) Monitor Stations Falcon AFB

User Segment Over $19 Billion invested by DoD Dual Use System Since 1985 (civil & military) Civilian community was quick to take advantage of the system Hundreds of receivers on the market 3 billion in sales, double in 2 years 95% of current users DoD/DoT Executive Board sets GPS policy PLGR The final segment is the User Segment and this refers to anybody, anywhere using a GPS receiver. DoD has invested billions in receiver development, and they are now used by all kinds of U.S. military forces. The official name for military receivers is User Equipment (UE) Sets. The JPO estimates that 95% of the current users, though, are civilians. Included in this category are also potential enemies. There are hundreds of receivers available on the open market, from wrist watch sized, to huge rack mounted receivers on airliners. Ranging in price from $400 to $30,000 (Garmin GPS II). GPS receivers normally track more than one signal at a time using multiple channels or multiple signals on a time sharing single channel. Most common use of GPS is for navigation, examples including helicopter search and rescue, munitions guidance such as the NAVY’s Stand off Attack Missile (SLAM).

Common Uses for GPS Military Specific: Navigation Surveying Target acquisition and destruction Missile Guidance Systems Joint Direct Attack Munition (JDAM) Tomahawk III Joint Stand Off Weapon (JSOW) Data Collection Integration with INS for High dynamic environment Search & Rescue Ops Summary Using GPS for mapping allows for the quick and effective capture of data in the field. Summary Complete definition of features and attributes prior to field work, means no time is wasted capturing the wrong information. GPS can be used not only for data capture, but also for navigation and GIS update. Different products are available for different applications.

How the system works Monitor Stations GPS Control Space Segment 24+ Satellites The Current Ephemeris is Transmitted to Users Monitor Stations Diego Garcia Ascension Island Kwajalein Hawaii Colorado Springs End User GPS Control Colorado Springs

Distance Measuring The whole system revolves around time!!! Distance = Rate x Time Rate = 186,000 miles per second (Speed of Light) Time = time it takes signal to travel from the SV to GPS receiver Since GPS is based on knowing your distance to satellites in orbit, a method must be devised to figure out how far we are from the satellites. The GPS system works by timing how long it takes a radio signal to reach us from a satellite and then calculating the distance from that time. We calculate this by measuring distance or the velocity times travel time. Radio waves travel at the speed of light: 186,000 miles per second. If we can then compute the exactly when the signal started at the satellite and ended at the receiver then we have our required distance. We then multiply the time by the velocity to derive the distance. The time is differential is computed by synchronizing the satellites and receivers so they are generating the same code at exactly the same time

Triangulation Satellite 1 Satellite 2 Satellite 3 Satellite 4 For simplicity sake, we calculate our position by understanding where a satellites is in orbit and then further computing how far we are from those satellites. If we know we are a certain distance from satellite A (11,000 miles). This narrows down where we are in the whole universe. This one range tells us we are located somewhere on the sphere of the range of this one satellite. If at the same time we also know that we are 12,000 miles away from a second satellite. This narrows where we are in the universe even more. The only place we can be 11,000 miles from A and 12,000 miles from B is on a circle where those two spheres intersect. Then if we measure to a third satellite we can pinpoint our location. If we know that we are 13,000 miles from satellite C then there are only two points in the universe that this can be true. One point is where the sphere enters into the circle formed by satellites A and B and the second is where the sphere of satellite C exits the circle formed by satellites A and B. By ranging from three satellites we can narrow our location down to one of two points. We decide between these two points typically by one of two methods. In some cases the software built into the GPS receivers have various techniques to determine which point is correct and which point is ridiculous. Technically, trigonometry says we really need four satellites to range to unambiguously locate ourselves. In other words the fourth satellite can be used to determine which of the two points derived from three satellites is the correct choice. The fourth satellite has other functions that relate to time that will be discussed later.

Distance Measuring Satellite Receiver Transmission Time The Carrier... combined with Satellite The PRN code... produces the This is a diagram that shows how radio signals work in general. Each SV generates a plain sine wave called the Carrier 1575.42Mhz and 1227.6Mhz. This carrier is Modulated (altered) by adding three signals to it. (The C/A code, P-Code and the Navigation message). In this case, it is that particular SV's Pseudo-Random Noise (PRN) Code this is essentially the P-Code and the C/A code for each SV. The PRN code looks like a square wave because it's just 1's and 0's; digital information that is Phase Modulated (PM). Then what the SV actually broadcasts is that modulated signal. Your receiver picks this up, subtracts the carrier (it can generate a copy of the carrier on its own), and is left with a copy of the original signal. All radios works this way. The significance for GPS is that the signal that is produced in the receiver is delayed by a small amount of time. For GPS, the information in the signal is not the only important part - as we've seen, it's the time delay that we really care about. In fact, GPS receivers already have to have a copy of the signal (most of it anyway) just to pick it up in the first place. Remember, all the SVs are talking on the same frequency, so we can't pick them out of the chatter without knowing what to expect ahead of time. Modulated carrier signal which is transmitted... demodulated... Receiver Producing the same code at the user, but delayed... Time delay

Signal Structure L1 Carrier Wave 1575.42MHz C/A Code 1.023 MHz Precise Code 10.23 MHz C/A Code 1.023 MHz Navigation Message 50Hz There is a navigation message which is a 50Hz signal consisting of bits of data that describe the GPS satellite ephemerides, system time, satellite clock corrections, almanac and system status. GPS signals are based on the fundamental L band frequency of 10.23MHz that generate two carrier phases which are L1 and L2. The signals are received on one or both of these frequencies by the GPS user. The coarse acquisition code is modulated on the L1 carrier wave and broadcast at a chipping rate of 1.023 MHz. The C/A code is a repeating 1 MHz PRN code and a wavelength of 300cm. There is a different code PRN for each satellite. The precise code is modulated on both the L1 and L2 carrier and broadcasts at a chipping rate of 10.23MHz with a smaller wavelength (30cm). The P-Code is encrypted into the Y-Code. The encrypted code requires a classified Anti Spoofing module for each receiver and is for use by an authorized user group only with use of a crypto key.

Signal Structure L2 Carrier Wave 1227.6MHz Navigation Message 50 Hz Precise Code 10.23 MHz

Measuring Travel Time SV Clocks 2 Cesium & 2 Rubidium in each SV Receiver Clocks Clocks similar to quartz watch Always an error between satellite and receiver clocks (  t) Require 4 satellites to solve for x, y, z, and  t We're not too worried about the clocks on the SVs. Each platform carries a $500,000 set of 4 atomic clocks. These are stable and accurate enough to lose a second only about once every 160,000 years or 1 nanosecond per day. Additionally, the clocks are corrected by 2 SOPS twice each day. The reason we get so concerned with SV clock accuracy is that the signals travel a foot in about a billionth of a second. So if the SV clocks were off by just 1 millionth of second, our position solution would be off by 1000 feet. The clocks in receiver are normally a quartz crystal which can lose a second a day. Time is very crucial to achieve success with GPS.

Measuring Travel Time Time Adjustment 1 2 4 3 8 nano seconds XX (wrong time) 9 nano seconds YY ZZ 8 nano seconds 7 nano seconds 4 X We saw in ranging that a fourth satellite can be used to determine which of the two points in a three satellite range is the correct point and which is the ridiculous point. When software is not complex enough to perform this function there is another important use of a fourth satellite…..correcting for time offset. Trigonometry says that three perfect measurements locate a point in 3-dimensional space, then four imperfect measurements can eliminate any timing offsets as long as the offset is consistent with the other three. The pseudorange is measured by receiver a,b, and c while four unknowns need to be solved for. The four unknowns are the coordinates of the receiver a,b, and c (3) and the receiver clock offset (1). In order to solve for these four unknowns, measurements must be taken to a minimum of four satellites to triangulate the position and solve for the unknowns. In practice, the coordinates and satellite clock offset for the satellites are broadcast in the navigation message and the atmospheric delays are modelled for. The pseudorange observation equation is what derives the three dimensional position for the receiver. 3

3 vs 4 Satellites This slide depicts how the effects of only three satellites show that either the timing is off (directly relates to position inaccuracy) or that the software did not have the capability of distinguishing between the actual point and the rediculous point on the ground. The fourth satellite brings the points back on the road and corrects for the error or ambiguity.

Cartesian Coordinate System Satellite Locations Cartesian Coordinate System Three dimensional right coordinate system with an origin at the center of the earth and the X axis oriented at at the Prime Meridian and the Z at the North Pole X Axis Coordinate Distance in meters from the the prime meridian at the origin; positive from 90º E Long to 90º W Long Y Axis Coordinate Distance in meters from 90º E longitude at the origin; positive in the eastern hemisphere and negative in the western Z Axis Coordinate Distance in meters from the plane of the equator; positive in the northern Hemisphere negative in the southern Z (X,Y,Z) Like the moon, which has reliably spun around the earth for millions of years without any significant change, the GPS satellites are orbiting the earth very predictably as well. The orbits are known in advance and in fact, some GPS receivers have an “almanac” programmed in them to tell where in the sky each satellite will be at any given moment. Each satellite is known where it is in space via Cartesian Coordinates. These known coordiantes are used to triangulate the position of the receiver. GPS satellites are consistently monitored by the Department of Defense to ensure that each satellite is travelling along its mathematically modeled orbit. This is the reason that the satellites are put in a non geo-synchronous orbit. This allows each satellite to pass over the monitoring station twice a day. This gives the DoD the chance to precisely measure their altitude, position and speed. Any variations are called ephemeris errors. These are typically minor and are caused from anomolies such as gravitational pulls from the moon and sun, and from pressure of solar radiation on the satellite.Once any ephemeris errors are detected, the correction is relayed to the satellite and the corrected information or ephemeris is then incorporated onto the timing information sent from the satellite. Y 90°E X 0º Long Prime Meridian

Common Problems - Errors Satellite Reflected Signal Direct Signal Hard Surface Reflected Signal GPS Antenna

Selective Availability (S/A) Implemented on Block II satellites, but turned off 2 May 2000 for the foreseeable future: Requires military to develop Direct Y Code receivers and local jamming capability Introduces deliberate errors into satellite ephemeris (SV location) and clock parameters on the C\A code Degrades horizontal positional accuracy to 100m 2DRMS (95% of the time.) SA is a purposeful degradation in GPS navigation and timing accuracy that is accomplished by intentionally varying the precise time of the clocks on board the satellites and providing incorrect orbital positioning. This is how DoD controls the accuracy for non-DoD users. They aren't altered very much - President Reagan promised in 1985 that the U.S. would allow anyone in the world to use GPS free of charge for 10 years, and that we would never make it worse than 100 m. He did this in response to the Soviet downing of KAL 007, the idea being that GPS would have prevented such a horrible navigation error. The 100 m is therefore the required C/A-code accuracy, and it is expressed in 2DRMS. This is equal to about 40 m CEP Accuracy lesson if you're not clear what these terms mean. Even though we had experimented with SA before the Gulf War, we actually turned it off for that engagement. There were 3 reasons: 1. Iraq didn't have any GPS-guided weapons. 2. The U.S. Army had bought about 8,000 Small Lightweight GPS Receivers (SLGRs) that could not read the P code, so SA would have caused degraded accuracy for our own troops. 3. People had such a tough time navigating in the desert that they were buying their own civilian units (USSPACECOM tracked over 300 coming in with the care packages from home). SA has been on continuously ever since, except for 2 weeks around the time of the Haiti invasion (for the same 3 reasons). Politically, SA is very unpopular. Many organizations hostile to defense interests want the government to force DoD not to degrade the signal. Most of their reasoning is flawed, but that will probably not matter. SA will probably go away in the next two years or so. The important thing to remember is that even with SA on, GPS is by far the most accurate source of radio navigation in the world.

Anti-Spoofing (A-S) P-Code +W-Key Y-Code Protects military receivers from receiving a “fake” P-Code P-Code modulation on both L1 and L2 No plans to phase out Continuously on since January 31, 1994 Anti-Spoofing (A-S) is done not to prevent others from reading the P-code, but to prevent them from broadcasting a fake P-code. Ever since Feb 94, A-S has been on continuously. At the SV, the P-codes are encrypted with a W-code, and broadcast as Y-codes. Numerous DoD directives say that U.S. military forces will not operate on the battlefield with receivers that are not capable of reading and un-encrypting the Y-code. To do this, the receiver needs a special circuit that is only available in military UE sets, and a current crypto key. There are several types of keys, but they all allow the military UE set to read the encrypted codes, and remove the effects of SA. Every once in awhile, A-S is turned off for short periods for testing and other classified purposes. Two types of keys are Group Unique Variable and the Crypto Variable Weekly GUV key lasts 54 weeks and is transmitted from the transmitters every 12 1/2 minutes. A GUV key decrypts the daily key sent by the satellites. CVW automatically generate daily keys in the PLGR and don’t require the daily key from the satellites.

Resistance to Jamming Low power signal is vulnerable to jamming Intentional or unintentional jamming Theater wide jamming Local area jamming The P-Code is phase modulated to provide better resistance to jamming DoD working on electronic warfare enhancements to deny disruption and spoofing. Direct Y-Code Receivers Theater jamming capability Electronic interference is transmitted power that impairs reception of GPS satellite signals. The power can be from natural or man made sources. It consists of interfering, typically noise like, signals being transmitted at frequencies in the frequency band of the receiver. Jamming signals are generally only effective along “Lines of Sight” depending upon the strength of the jammed signal. The positional accuracy usually decreases as electronic interference increases. An SPS receiver will have difficulty locking on to and tracking satellite signals at low jamming levels. At medium or high jamming levels this C/A code will not be able to lock on or track at all. A PPS receiver will be effected ranging from not being effected to greatly reducing the accuracy and satellite tracking capability of the receiver. Having the encryption loaded, a PPS receiver can track and decode Y code signals enabling your receiver to remove the selective availability (SA) errors, implement its anti-spoofing (A/S) function, and provide minimal protection against jamming. This is a direct cause of the encrypted receiver having the capability of demodulating the Y code that was modulated on the signal at the satellite.

Common Problems - Errors Pseudo-Ranging Errors Satellite clock (S/A) Ephemeris/orbit (S/A) Atmospheric delays Ionosphere Troposphere Receiver computation & noise There is a host of errors that are inherent with a GPS system. The accuracy of a GPS is influenced by this budget. Collectively these factors combine to induce the 100m plan position error, at 2 deviations root mean square (2drms) at 98% probability experienced by Standard Positioning System (SPS) users, and 17.8m at 2 deviations root mean square (2drms) at 98% probability experienced by the Precise Positioning System (PPS) users. The sum of all the errors or biases, is referred to as bias range or “pseudorange.” Principal contributors to the final range error that also contribute to the overall GPS error are ephemeris error, satellite clock error, electronic inaccuracies, tropospheric and ionospheric refraction, atmospheric absorption, receiver noise and multipath effects. In addition to these errors, GPS also contains other interruptions to the service that can be introduced by the U.S. DoD are Selective Availability and Anti-Spoofing.

Common Problems - Errors Errors Caused By GPS Multipath Reflections Use Ground Plane On Antenna Move Away From Reflective Surfaces Influences on the GPS Signal Radar Microwave ILS or Radio NDB Equipment ATC Radio Traffic Misidentification of Thresholds and Other Features

Effects of Multipath on the GPS Signal GPS Multipath Errors Effects of Multipath on the GPS Signal Direct Signal Reflected Signal GPS Antenna Hard Surface Satellite Avoid Reflective Surfaces Use A Ground Plane Antenna Use Multipath Rejection Receiver Another potential, though relatively minor, source of signal error is Multi-Path. Multi-Path is simply the reception of a reflected satellite signal. With multi-path reception, the receiver collects both the direct signal from the satellite and a fractionally delayed signal that has bounced off of some nearby reflective surface then reached the receiver. This is the same kind of thing seen in television "ghosts”. The problem is that the path of the signal that has reflected off some surface is longer than the direct line to the satellite. This can "confuse" some lower-end receivers resulting in an incorrect range measurement and, consequently, an incorrect position. There are several ways to deal with this problem. Most receivers have some way of "seeing" and comparing the correct and incorrect incoming signal. Since the reflected multi-path signal has traveled a longer path, it will arrive a fraction of a second later, and a fraction weaker than the direct signal. By recognizing that there are two signals, one right after another, and that one is slightly weaker than the other, the receiver can reject the later, weaker signal, minimizing the problem. This ability is referred to as the receiver's multi-path rejection capability. Mapping and survey quality receivers also use semi-directional, ground-plane antennas to reduce the amount of multi-path that the receiver will have to deal with. Semi-directional antennas are designed to reject any signal below a tangent to the surface of the Earth, meaning that they are preferentially directional upward. This is usually seen as a large (up to 20 to 30 centimeters across) flat metal plate (usually aluminum) with the actual, much smaller, receiver antenna attached on top. The metal plate interferes with any signals that may be reflected off of low reflective surfaces below them, such as bodies of water.

Dilution Of Precision (DOP) A Measure of The Geometry Of The Visible GPS Constellation Good DOP Poor DOP Dilution of Precision (DOP) The cumulative UERE (User Equivalent Range Error) totals are multiplied by a factor of usually I to 6, which represents a value of the Dilution of Precision, or DOP. The DOP is, in turn, a measure of the geometry of the visible satellite constellation. The ideal orientation of four or more satellites would be to have them equally spaced all around the receiver, including one above and one below. Because we're taking our position from only one side of the Earth that’s really not possible since the planet itself blocks that part of space. The upper diagram at left illustrates the next best orientation. That is, to have one satellite directly above and the other three evenly spaced around the receiver and elevated to about 25 to 30 degrees (to help minimize atmospheric refraction). This would result in a very good DOP value. The lower diagram illustrates poor satellite geometry. In this case, all of the satellites are clustered together. This would result in a poor DOP value. A low numeric Dilution of Precision value represents a good satellite configuration, whereas a higher value represents a poor satellite con- figuration. The DOP at any given moment will change with time as the satellites move along their orbits.

Dilution Of Precision (3) PDOP = Position Dilution Of Precision (Most Commonly Used) VDOP = Vertical Dilution Of Precision GDOP = Geometric Dilution Of Precision HDOP = Horizontal Dilution Of Precision TDOP = Time Dilution Of Precision Dilution of Precision (DOP) There are a number of Dilution of Precision components. The overall GDOP, or Geometric Dilution of precision includes: PDOP, or Precision Dilution of precision, probably the most commonly used, which is the dilution of precision in three dimensions. Some- times called the Spherical DOP. HDOP, or Horizontal Dilution of Precision, is the dilution of precision in two dimensions horizontally. This value is often lower (meaning "better") than the PDOP because it ignores the vertical dimension. VDOP, or Vertical Dilution of precision, is the dilution of precision in one dimension, the vertical. TDOP, or Time Dilution of Precision, is the dilution of precision with respect to time. A DOP value of less than 2 is considered excellent-about as good as it gets, but it doesn't happen often, usually requiring a clear view of the sky all the way to the horizon. DOP values of 2 to 3 are considered very good. DOP values of 4 or below are frequently specified when equipment accuracy capabilities are given. DOP values of 4 to 5 are considered fairly good and would normally be acceptable for all but the highest levels of survey precision requirements. A DOP value of 6 would be acceptable only in low precision conditions, such as in coarse positioning and navigation. Position data generally should not be recorded when the DOP value exceeds 6, QUALITY DOP Very Good 1-3 Good 4-5 Fair 6 Suspect >6 Mission Planning Is Critical to Obtain Good DOP

Standard Positioning Service (SPS) System Accuracy Standard Positioning Service (SPS) Available to all users Accuracy was degraded by Selective Availability until 2 May 2000 Horizontal Accuracy: 100 meters 2 DRMS (40 meters CEP) Now has roughly the same accuracy as PPS Used by military receivers before Y-code lock is established Standard Positioning Service (SPS) is the actual formal name given to the GPS service that is available to everybody. We have already covered most of the points here, but you do need to point out again that all current military receivers use SPS when you first turn them on, and then switch to Y-code when they have a good locked-down time. The JPO is designing enhancements for all of our military UE sets so that they can go directly to Y-code when turned on, without bothering with SPS. This program is called, not surprisingly, Direct Y. It should be in place within 2 years.

Scatter plot of horizontal accuracy 2 May 2000 A similar slide to the previous in that shows S/A before and after it was turned off on 2 May, 2000. The figure on the left is a scattergram displaying the horizontal error of a point over multiple epochs of time. The horizontal error shows a figure of about ±75m. Th figure on the right shows a similar amount of epochs of data collected at the same point following the removal of S/A. The difference is now displayed at about ±12m.

Precise Positioning Service (PPS) System Accuracy Precise Positioning Service (PPS) Only available to authorized DoD users Decryption device and crypto key are required to decode A-S and remove SA GUV Key (1 year) CVW Key (1 week) Accurate to 21m 2DRMS (8 m CEP) 95% of the time, a receiver's computed horizontal position will be within 21 meters of its actual location The Precise Positioning Service was designed by the U.S. DoD to allow a select user group to be able to achieve a higher accuracy with GPS than that of their counter part SPS users. The authorised users with cryptographic equipment and keys and specially equipped receivers comprise this select group. This group of users is proimarily made up of U.S military and its Allies, U.S. Governmental agencies and selected civilian user groups approved by the U.S. DoD. The predictable accuracies that can be achieved using this service are: 22 meter horizontal accuracy 27.7 meter vertical accuracy 100 nanoseconds time accuracy PPS still must content with Errors

Specifications and Derived Values GPS Accuracy - PPS Specifications and Derived Values PPS CEP/50 % DRMS 2DRMS/95% Position Horizontal 8 m 10.5 m 21 m Vertical 9 m 14 m 28 m This chart shows the military accuracy requirements. Notice that there is a PPS requirement for both velocity and time, in addition to position. In reality, the numbers are even better than shown here, because 2 SOPS does a better than required job with the Control Segment. There are a lot of assumptions involved in these derivations as well. For instance, this chart applies to dual frequency receivers (those that can pick up both L1 and L2) only. The PLGR cannot read L2, so it could get away with less accuracy than shown here and still meet spec. In fact, tests have shown that the PLGR does pretty well, in spite of not being able to do ionosphere corrections. Both of these accuracy charts came right out of the ARINC book - do not use numbers found in civilian documents, they are almost always wrong! Spherical 16 m 18 m 36 m Velocity Any Axis 0.07 m/sec 0.1 m/sec 0.2 m/sec Time GPS 17 nsec 26 nsec 52 nsec UTC 68 nsec 100 nsec 200 nsec

Error and Map Problems X X 50 m Map Error Map coordinate determined by terrain association X It is important to understand the sources that coordinates are derived from and the intent behind what those coordinates will be used for. In the case of this slide, the PLGR was used to acquire coordinates with a measurement of precision of +/- 21m @95%. If these coordinates were applied to a 1:50,000 map product, that maintains an accuracy statement of +/- 50m @ 90%, then the accuracy drops to the less precise statement of the two products . A point plotted to this map can be measured as accurately as humanly possible but once plotted to the map it carries all the propagated error that is inherent with that map product. The only exception to this is if the coordinates are labeled or a recorded and the map is merely a representation of that point. If the point is plotted directly to a map, the statement of accuracy of that point has now changed from +/-21m@ 95% to +/-50m @ 90% by virtue of the application of those coordinates. X GPS coordinate plotted on map 21m GPS Error

Types of Differential Coverage Differential GPS Types of Differential Coverage Coverage: Local Area (Coast Guard) Wide Area (INMARSAT) Methods: Real-Time (navigation/mapping) Post Processing (survey) Surveyors have been using GPS for several years now to calculate positions right down to the last centimeter. Their techniques are extensions of differential GPS. With a GPS survey receiver, one surveyor can do the work of a whole team in a fraction of the time required by conventional techniques. The two primary types of Differential coverages are the local and wide area systems. Each of these systems will be discussed in depth on the next few slides. The two primary methods of conducting differential observations are in either real-time or in post-processed. The real-time differential is used for mapping or navigation and can be conducted using a receiver such as a PLGR. The post-processed observations are typically used for surveying and store collected data in a survey grade receiver to be processed with software at a later point.

DGPS Positioning Local Differential GPS is a concept that corrects for the errors associated with a known reference station and assumes the errors are the same within a local area. These errors are then broadcasted out to roving sites which use the error corrections and the real time pseudo-range measurements to derive positions of .3-10m @95% with a planning factor of degradation at a rate of 1m/100km. The reference site (previously established and known point) makes pseudo-range measurements to all visible GPS satellites. This reference site compares the observed pseudo-ranges with those calculated between the known location of the reference site and the broadcast positions of the satellites. For small localized systems, the reference site compiles a correction message that calculates all the error in the system (atmospheric, satellite position, and satellite clock error) and transmits this data to the users. The location of the reference sites must be known to the highest possible accuracy, and this would normally be achieved by other survey methods. The local differential system covers a localized area that is limited by the strength of the radio transmitter used to send the corrections within the localized area.

Coast Guard Differential GPS System DGPS Navigation Coast Guard Differential GPS System Initial Operational Capability on 30 Jan 96 Provides pseudo-range corrections over existing radio beacons Corrections to NAD-83 (WGS-84) Observed accuracy 1 to 3 meters out to 150 nautical miles from base station Station sites available on the internet (WWW.NAVCEN.USCG.MIL) Intended for navigation of harbors, the U.S. Coast Guard established a series of radio beacons that retransmit Differential GPS corrections from known reference stations such as Lighthouses. This system that is established along coast lines and along interior waterways such as the Mississippi River have been operational since 1996. The corrections are sent using the USCG The corrections are established using the NAD-83 datum which is the U.S. Geological Survey’s version of the World Wide Geodetic System 1984 (WGS84). The achievable accuracies that can be expected from this local system are in the magnitude of 1-3m @ 95%. The available stations that exist throughout the United States can be found on the USCG website.

DGPS Positioning Wide Area Differential GPS Error correction message signals The Wide Area Differential System is an adaptation of the local system covering a larger area of interest. Because there is a direct relationship to the amount of time that a correction can be transmitted and remain current to be used in computing accurate position, the wide area differential uses multiple reference stations. The concept is that multiple reference stations collect data in the same way as in local differential. Each of the reference stations collects data and computes corrections that are sent in real time to a processor. The processor models the error for the wide region and sends an upload to a communications satellite. The error stream is then broadcast to field users via this same communications satellite. The same errors (atmospheric, satellite position, and satellite clock error) are then corrected for by the field user’s receiver and allows for either coordinates in real-time of post-processed depending on the intended use. The wide area differential system can cover an area in the magnitude of 150 nautical miles. This distance is a direct reflection of the latency (lag) of the correction as it is transmitted, calculated and displayed. Tests have shown that the area covering this amount of area are of the same magnitude and allows for the correction of position to 1-3m @95%. Reference receivers Field receiver Real-time Corrections to Remove S/A etc.

Planned Replenishments - Block IIR Future Developments Planned Replenishments - Block IIR Some IIR improvements over Block II/IIA SVs: More power/better batteries (Life EST 7.8 years) More fuel Two Atomic clocks on at all times Re-programmable CPU, more autonomous Cross Link Ranging - 180 day autonomy with no degradation 21 SVs purchased from Lockheed Martin at $30M each Launches began Jan 97 The applications of GPS are endless. Look in recent issues of GPS World to get an idea of the possibilities. The FAA wants to fly airliners almost exclusively on GPS. For approaches to airports, differential GPS will be required; even PPS is not accurate enough to guarantee safety. Take a look at the Geographic Database Collection lesson for info on GPS contributions to GIS. Under Transportation, railroad companies are using GPS to track trains, the AAA is using GPS to eliminate fraud from its tow truck subcontractors, and rental car companies are installing GPS-aided moving map displays in some of their larger cars. Surveying is now dramatically faster, cheaper, and more accurate than it was just 8 years ago. During Somalia operations, the New Zealand military was able to come up with a GPS correction for each of the DMA map sheets; the original source for our products had been old Soviet maps that weren't exactly up to DMA spec. Casio is even selling a watch that sets its own time by tracking GPS SVs. The important thing about all this is that GPS is completely changing the way navigation and position measuring are done for everyone, not just the military folks who have a PLGR.

Planned Sustainment - Block IIF Future Developments Planned Sustainment - Block IIF Boeing awarded contract for production of 33 Block IIF SVs Improvements over IIR Larger Payload (more fuel, power, etc) 10 year life span DoT option to add L??? & L??? Frequencies Unique ground control (more autonomous) The applications of GPS are endless. Look in recent issues of GPS World to get an idea of the possibilities. The FAA wants to fly airliners almost exclusively on GPS. For approaches to airports, differential GPS will be required; even PPS is not accurate enough to guarantee safety. Take a look at the Geographic Database Collection lesson for info on GPS contributions to GIS. Under Transportation, railroad companies are using GPS to track trains, the AAA is using GPS to eliminate fraud from its tow truck subcontractors, and rental car companies are installing GPS-aided moving map displays in some of their larger cars. Surveying is now dramatically faster, cheaper, and more accurate than it was just 8 years ago. During Somalia operations, the New Zealand military was able to come up with a GPS correction for each of the DMA map sheets; the original source for our products had been old Soviet maps that weren't exactly up to DMA spec. Casio is even selling a watch that sets its own time by tracking GPS SVs. The important thing about all this is that GPS is completely changing the way navigation and position measuring are done for everyone, not just the military folks who have a PLGR.

GLONASS 8 SVs in each of 3 inclined circular orbits 11.25 hour period 19,900 km altitude Life time of SVs is 3 years Uses SGS-85 Datum (within 20m of WGS-84) Five Satellites visible at all points on the globe Satellites broadcast 2 signals Standard Precision Navigation Signal (Civil) High Precision Navigation Signal (military) The second segment is the Space Segment, and this refers to the actual satellites (officially, they're called Satellite Vehicles, or SVs) in orbit. The constellation consists of 24 satellites arranged in 6 orbital planes. There are 4 satellites in each plane and the system was designed so that there would always be at least 4 SVs visible from anywhere in the world at all times. Each satellite orbits the earth in 12 hours. Actually, a satellite will pass over the same location every 23 hours and 56 minutes. This also means that the SVs are not geostationary - they are constantly moving overhead, rising and falling from the perspective of someone on the ground. The orbit is fairly high, making it is a little harder to attack the SVs than if they were in a Low Earth Orbit (LEO). The higher altitude gives broader ground coverage than satellites in a LEO, and allows each SV to pass over an Upload Station twice in every 24 hour period. The life time design of the Block II/IIA is 7.5 years and costs about 53.8 million dollars per satellite. All of the SVs broadcast on the same 2 L-band frequencies - we'll talk more about them later.

Summary History GPS Applications Three Segments of GPS 5 Principles of GPS Operations System Accuracy Other Satellite Navigation Systems Future Developments These are the topics that hopefully have given you a general appreciation for the components of the GPS system and how it all works. Understanding its uses and where the system is evolving aids anyone in the military in applying this technology into their everyday mission.

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