GPS Fundamentals Your location is: 37o 23.323’ N 122o 02.162’ W

Global Positioning System Your location is: 37o 23.323’ N 122o 02.162’ W There are 3 segments to GPS:<B> 1. The Space Segment consists of 24 SVs (21 operational and 3 spares). They orbit the earth every 12 hours at ~20,000 km (12,500 miles). Their orbital planes are at 55 degrees to the equatorial plane. 2. The Control Segment consists of a Master Control Station <B> in Colorado and 4 monitor stations <B> in Hawaii, Ascension Island [South Atlantic], Diego Garcia [Indian Ocean], and Kwajelein [West Pacific]. The Control Segment tracks the SVs<B> and sends their positions to the Master Control Station <B> The Master Control Station compiles all of the orbital data and sends it back to the monitor stations <B> The Control Segment then sends the orbital data back to the SVs as a navigation message <B> 3. The User Segment consists of the GPS equipment (receiver, antenna, radios, etc.) <B> The User Segment receives signals sent by the Space Segment <B> This info is required for the User Segment to determine a position <B>

Satellite Signal Structure Carrier L1 L2 Frequency 1575.42 MHz 1227.60 MHz Wavelength 19cm 24cm Code Modulation C/A-code - P(Y)-code P(Y)-code NAVDATA NAVDATA C/A - Coarse Acquisition Code P - Precise Code (Y-Code when encrypted) NAVDATA - Satellite health, satellite clock corrections, and ephemeris parameters. GPS uses two carrier frequencies, L1 and L2. The CODES are modulated on these frequencies. Just like a radio station. These are RFs so they can be jammed. C/A-code is only on the L1 Freq. NAVDATA consists of satellite health, satellite clock corrections, and satellite ephemerides.

What is Measured? GPS Observables Code Ranges Carrier Phases Autonomous Position Relative Position There are two types of GPS observables: <B> 1. Code ranges (actually pseudoranges) <B> 2. Carrier phases From the code range observables we can obtain autonomous positions. <B> Code range observations are NOT used in post-processing. However, the autonomous position derived from code observations are used as a starting point for processing carrier phase observations. From the carrier phase observables we obtain relative positions between two receivers. <B> Relative positions are derived from determining the vector between two receivers.

Code Range Results Autonomous Position +/- 10 m (30 ft) error (horizontal) +/- 15 m (45 ft) error (vertical)

Inverse from Measurement Carrier Phase Results Inverse from Measurement Reduced Baseline or Vector (cm precision) Azimuth = 212o 42’ 49.8244” Distance = 557.05307 m Delta Elevation= 4 .8751 m With Carrier Phase observables, we are actually collecting raw data to determine a baseline from antenna phase center to antenna phase center <B> What the software does, is compute a baseline reduced to the points over which the antennae are setup.<B> Baselines can be expressed in azimuth, distance, and difference in elevation<B> or dx,dy,dz<B> D X = -408.251 m D Y = -84.830 m D Z = -369.413 m OR

ECEF Coordinate System X = -2691542.5437 m Y = -4301026.4260 m Z = 3851926.3688 m +Z -Y +X X Y Z GPS positions are in reference to an Earth Centered-Earth Fixed coordinate system. <B> This coordinate system is a Cartesian coordinate system with it’s origin of this coordinate system is the center of mass of the earth. The XZ-plane is coincident with mean Greenwich. The XY-plane is coincident with the equatorial plane. This coordinate system moves with the rotation of the earth. Any point we want to define <B> will be in terms of XYZ. Some interesting notes: Points in the US west of 90 W have negative X values All points in the US have negative Y values Z values are not necessarily coincident with antenna hts. However, (in some areas of the US) the Y value can be.

Reference Ellipsoid WGS-84 Ellipsoid H a b b f a = 6378137.000000 m a = semi-major axis b = semi-minor axis H a b b f WGS-84 Ellipsoid a = 6378137.000000 m b = 6356752.314245 m 1/f = 298.2572235630 a There are times when it is necessary to model the shape of the Earth. However, this is not easily accomplished since the Earth’s shape is very complex and uneven. To simplify the modelling, let’s assume the Earth has a rounded, smooth surface. What would you expect then expect this shape to be? The answer is an ellipsoid. The reason it is not a spheroid is because the earth is rotating. Centrifugal forces from the Earth’s rotation causes the Earth to bulge at the equator. This gives the Earth an oblate shape instead of a perfectly round one. An ellipsoid is defined by three parameters: semi-major axis, semi-minor axis, and flattening (actually 1/flattening). For geodetic purposes, ellipsoids are defined with the semi-major axis coinciding with the equatorial plane and the semi-minor axis coinciding with the polar axis. If we wanted to define a point,<B> it would be in ellipsoidal coordinates. That is, latitude, longitude and ellipsoidal height. <B> The reference ellipsoid used for GPS is called WGS-84 (World Geodetic System 1984) <B> This has been the standard datum for GPS since 1987. l

ECEF and WGS-84 ECEF X = -2691542.5437 m Y = -4301026.4260 m Z = 3851926.3688 m +Z -Y +X WGS-84 f = 37o 23’ 26.38035” N l = 122o 02’ 16.62574” W H = -5.4083 m b a X Y Z l f H How do ECEF and WGS-84 relate to each other? Before we referenced a point in the ECEF coordinate system. There is also a reference in WGS-84. a, in WGS-84, coincides with the X-axis and b coincides with the Z-axis.<B> The ab-plane is now coincides with the XZ-plane which contains Greenwich. This is our 0 longitude. Our point now has ellipsoidal coordinates in WGS-84. <B> Some notes of interest: The heights in WGS-84 are ellipsoidal heights are NOT elevations. This is why you can get a [ellipsoidal] height of 30 meters at sea level. Ellipsoidal heights can be negative! This is true of the network here in Sunnyvale. By convention, positive longitudes are the eastern hemisphere and negative longitudes are the western hemisphere. In a similar manner, positive latitudes are the northern hemisphere and negative latitudes are the southern hemisphere.

GPS Heights vs. Elevations Earth’s Surface h h e e e h N N Ellipsoid N Geoid e = Orthometric Height h = Ellipsoid Height N = Geoid Height e = h - N

Errors Sources in GPS Selective Availability (SA) (Turned Off!) Anti-Spoofing (AS) Multipath Ionospheric Noise Human Error

Multipath Mountains, trees, towers, and buildings are just a few examples of possible obstructions. Remeber, the GPS signal is an RF signal that can easily be blocked. <B> If obstructions are present, it’s important that you note the azimuth and elevation above the horizon of these structures<B> You can then account for these in your planning. Also, some structures that are obstructions in one direction can also be sources of multipath in another direction.<B> Beware of other sources of multipath.<B>

Atmospheric Effects Ionosphere Troposphere > 10 km < 10 km Ionosphere is a layer of the atmosphere filled with charged particles that delay the signal from the satellite to the receiver. With short baselines, less than ten kilometers, the effect are almost equal, and will be canceled out of the solution. > 10 km < 10 km

Human Error

Survey Requirements 10:30 10:35 What is required to create a GPS vector between two points? 1. At least 2 receivers are needed.<B> 2. They must be capable of logging carrier phase observables<B> 3. At least 4 common SV’s must be tracked at each station<B> 4. All visible SV’s must maintain good geometry (DOP) <B> 5. Data must be logged at common times (Time of day & epochs) Once these requirements are met a vector can be derived either thru post-processing or in real-time. <B>

Summary There are three segments to GPS. All must be working to use GPS. There are 2 GPS signals, L1 and L2. Code Range measurements result in autonomous positions with several meter precision. Carrier Phase measurements result in relative positions with centimeter precision.

Summary (cont..) GPS results are in reference to an ECEF coordinate system and the WGS-84 ellipsoid. Errors in GPS can be minimized by planning and utilizing proper surveying techniques. At least 4 SVs are required to determine a position or survey with GPS. At least 2 receivers are required to survey with GPS.

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