Relative Positional Precision

3.E.i. - Relative Positional Precision We know that every point located on a survey has an uncertainty in its location that can be represented by an error ellipse. ALTA/ACSM Land Title Surveys

Relative Positional Precision ALTA/ACSM Land Title Surveys Target Measured angle and distance Occupied Station

Relative Positional Precision ALTA/ACSM Land Title Surveys Occupied Station Uncertainty in the angle measurement (exaggerated) Target

Relative Positional Precision ALTA/ACSM Land Title Surveys Occupied Station Uncertainty in the distance measurement (exaggerated) Target

Relative Positional Precision ALTA/ACSM Land Title Surveys

Relative Positional Precision ALTA/ACSM Land Title Surveys

Relative Positional Precision ALTA/ACSM Land Title Surveys

3.E.i. - Relative Positional Precision The size (length of the semi-major and semi-minor axes), and orientation of the error ellipse is a function of: (1)the uncertainties in the measurements that were made and, (2)the confidence level we are using (95%). ALTA/ACSM Land Title Surveys

3.E.i. - Relative Positional Precision Think about the “Bell Curve” – If we want a high probability (confidence) in our measurements, our uncertainty will be larger ALTA/ACSM Land Title Surveys

3.E.i. - Relative Positional Precision ALTA/ACSM Land Title Surveys 95% Probability, but large uncertainty

3.E.i. - Relative Positional Precision Think about the “Bell Curve” – If we want a lower amount of uncertainty, we can accomplish that, but with a lower probability (i.e. a lower percentage of the time) ALTA/ACSM Land Title Surveys

3.E.i. - Relative Positional Precision ALTA/ACSM Land Title Surveys Smaller Uncertainty, but only with 5% probability

3.E.i.- R.P.P. defined “ the length of the semi-major axis, expressed in feet or meters, of the error ellipse representing the uncertainty due to random errors in measurements in the location of the monument, or witness, marking any corner of the surveyed property relative to the monument, or witness, marking any other corner of the surveyed property at the 95 percent confidence level (two standard deviations). ALTA/ACSM Land Title Surveys

Relative Positional Precision ALTA/ACSM Land Title Surveys The length of the semi-major axis in this error ellipse

3.E.v.- Relative Positional Precision The maximum allowable Relative Positional Precision [the maximum length of the semi- major axis] for an ALTA/ACSM Land Title Survey is 2 cm (0.07 feet) plus 50 parts per million (based on the direct distance between the two corners being tested) ALTA/ACSM Land Title Surveys

Relative Positional Precision Note that R.P.P. is not expressed at a point, but rather it is related to the relationship betweenthe two points being tested… The size of the error ellipse is a function of the error ellipses at each of the two end points of that line. ALTA/ACSM Land Title Surveys

Relative Positional Precision ALTA/ACSM Land Title Surveys

Relative Positional Precision The RPP for the line is compared to the allowable RPP (0.07 feet (2 cm) plus 50 ppm). The 50 ppm is based on the length of the line connecting the two points being tested. ALTA/ACSM Land Title Surveys

Relative Positional Precision Example: If the line being tested is 1,000 feet long, what is the allowable RPP for that line? ALTA/ACSM Land Title Surveys 0.07 feet+[(50)/1,000,000]*1000= 0.12 feet Can we achieve this?

3.E.iv.- Measurement Procedures To achieve a low level of random error uncertainty, the surveyor must: (1)use appropriately trained personnel (2)compensate for systematic errors, including those associated with instrument calibration ALTA/ACSM Land Title Surveys

3.E.iv.- Measurement Procedures The surveyor shall: (3) use appropriate error propagation and measurement design theory (selecting the proper instruments, geometric layouts, and field and computational procedures) … to control random errors such that the maximum allowable Relative Positional Precision is not exceeded. ALTA/ACSM Land Title Surveys

Relative Positional Precision If the RPA for the line being tested exceeds the allowable 0.07 feet and 50 ppm, we can… make redundant measurements use higher precision equipment develop a different survey design … to decrease the size of the error ellipses at the endpoints of the line ALTA/ACSM Land Title Surveys

3.E.v.- Relative Positional Precision It is recognized that in certain circumstances, the size or configuration of the surveyed property, or the relief, vegetation or improvements on the surveyed property will result in survey measurements for which the maximum allowable Relative Positional Precision may be exceeded. This must be explained (see Section6.B.ix) ALTA/ACSM Land Title Surveys

Relative Positional Precision A simple 3-step process to address R.P.P. on your survey: 1.Understand: What are the primary sources of random errors in your measurements ? ALTA/ACSM Land Title Surveys

Relative Positional Precision 2. Develop reliable estimates of the magnitude of those random errors from each of those sources ALTA/ACSM Land Title Surveys

Relative Positional Precision 3. Use a correctly weighted Least Squares adjustment to process your data ALTA/ACSM Land Title Surveys

Estimating R.P.P. 1.“What are the primary sources of random errors in your measurements ?” ALTA/ACSM Land Title Surveys

Estimating R.P.P. “What are the primary sources of random errors in your measurements ?” In an angle (with electronic total station): Pointing Centering the instrument Centering the target Reading (straight out of the manual) ALTA/ACSM Land Title Surveys

Estimating R.P.P. “What are the primary sources of random errors in your measurements ?” In a distance (with EDM): Centering the instrument Centering the target Reading (straight out of the manual) ALTA/ACSM Land Title Surveys

Estimating R.P.P. “What are the primary sources of random errors in your measurements ?” With GPS: Centering the instrument Centering the target “Reading” (this is a function of the quality of your observation (PDOP, SNR, length of observation, etc.) and the length of your baseline) ALTA/ACSM Land Title Surveys

Estimating R.P.P. 2.“Develop reliable estimates of the magnitude of the random errors from each of those sources.” ALTA/ACSM Land Title Surveys

Estimating R.P.P. Develop reliable estimates of the magnitude of the random errors from each of those sources These cannot be “WAGs” They need be statistically based (Note that random reading errors for angles and distances come directly from the equipment manual; and random ‘reading’ errors for GPS will be generated by the processing software) ALTA/ACSM Land Title Surveys

Estimating R.P.P. 3.These uncertainties are used in the least squares program for a weighted (best fit) solution. ALTA/ACSM Land Title Surveys

Uncertainty in Conventional Measurements Following is an example of the determination of the magnitude of significant random errors in a conventional measurement… ALTA/ACSM Land Title Surveys

Uncertainty in Conventional Measurements ALTA/ACSM Land Title Surveys Analyze the angular measurement at station 2 (BS station 1 and FS station 3). Analyze the distance measurement from 2 to 3

Uncertainty in Conventional Measurements Significant sources of Uncertainty (random error) in Angle Measurements Significant sources of Uncertainty (random error) in Distance Measurements ALTA/ACSM Land Title Surveys

Significant Sources of Uncertainty in Angular Measurements Pointing* Centering the instrument Centering the target Reading * * These two are a function of how many pointings & readings we make.Let’s assume we are turning 1 direct & 1 reverse (or turning the angle and closing the horizon) with an electronic total station (where the standard deviation is 2” DIN from the manual).This is 4 pointings & 4 readings. ALTA/ACSM Land Title Surveys

Pointing Ed Mikhail and Gordon Gracie in their book Analysis and Adjustments of Survey Measurements, estimate the standard deviation of a single pointing(  p ) to be 1 to 4 seconds.We will assume  p = 2 seconds.But we need the standard deviation for 4 pointings (n = 4).  for 4 pointings   p  n        ” ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Centering the instrument Mikhail and Gracie estimate the standard deviation of the instrument centering (  c ) to be 0.5 to 3 mm.We will assume  c = 1 mm ( feet). But we need to know how this impacts the angle. (Where D 1 = length of backsight.D 2 = length of foresight. D 3 = Distance between backsight and foresight)    c D 3 )  D  D      X   rads   ” ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Cont’d    c D 3 )  D  D      X   rads   ”

Centering the target What is the standard deviation of your target centering (  T )? If the target is on a tripod, it should be the same as the standard deviation of your instrument centering. But what if your target is a prism on 8 feet of range pole on a windy day?What is  T then?! We will assume the target is on a tripod (  T = 1 mm). Again, we need to know how this impacts the angle. ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Centering the target (where D 1 = length of backsight.D 2 = length of foresight and  T is 1mm ( feet)(target is on tripod)    T (D 2 + D 2 ) 1/2  D D  12            X   rads   ” ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Centering the target But what if our target was on 8 feet of range pole on a windy day?Estimate  T is 2 cm (0.066 feet)[Is this even a reliable estimate??] (Where D 1 = length of backsight.D 2 = length of foresight and  T is 2 cm (0.066 feet)    T (D 1 + D 2 )  D  D   22 1/2            X   rads   ” ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Reading From manufacturer the Standard Deviation is 2” for one D&R (2” DIN).Remember, we turned a direct and reverse (or turned the angle and closed the horizon) – either way, we had 4 readings, so the DIN out of the manual is the number we need. The equation:   R  n   (where n = number of readings) ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Cont’d   R  n     

Pointing = 1.0” Centering the Instrument = 1.2” Centering the Target (on a tripod) = 1.0” Reading = 1.0” ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

 = (  p 2 +  i 2 +  t 2 +  r 2 ) 1/2 ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Cont’d  = ( ) 1/2 = 2.1 seconds standard deviation in our angle measurement

But what if we used 8 feet of range pole? Pointing = 1.0” Centering the Instrument = 1.2” Centering the Target = ? Reading = 2.0” ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

 = ( ) 1/2 = ??? standard deviation in our angle measurement ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Angular Measurements

Significant Sources of Uncertainty in Distance Measurements Centering the instrument Centering the target Instrument error ALTA/ACSM Land Title Surveys

Centering the instrument If our instrument is on a tripod, remember we already estimated the standard deviation as 1 mm ( feet). There is no equation to use; the impact of the standard deviation of the instrument centering on the distance is simply that number(1 mm or feet) ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

Centering the target If our target is on a tripod, remember we already estimated the standard deviation as 1 mm ( feet). There is no equation to use; the impact of the standard deviation of the instrument centering on the distance is simply that number(1 mm or feet) ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

Centering the target But what if our target was on 8 feet of range pole on a windy day?We estimated (guessed) the standard deviation as 2 cm (0.066 feet). Again, there is no equation to use; the impact of the standard deviation of the instrument centeringon the distance is simply that number(2 cm or feet) ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

Instrument Error From the manufacturer, Standard Deviation is 2 mm and 2 ppm ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

Centering the Instrument = 1 mm Centering the Target (on a tripod) = 1 mm Instrument Error = 2 mm + 2 ppm ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

What is total standard deviation?  = ( ( *2) 2 /1,000,000 2 ) 1/2  =0.008 feet standard deviation in our distance measurement ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

But what if we used 8 feet of range pole? Centering the Instrument = 1 mm Centering the Target = 2 cm Instrument Error = 2 mm + 2 ppm ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

What is total standard deviation?  = ( ( *2) 2 /1,000,000 2 ) 1/2  =0.066 feet standard deviation in our distance measurement ALTA/ACSM Land Title Surveys Develop reliable estimates of the magnitude of the random errors in Distance Measurements

Total Uncertainty in this Conventional Measurement  1  Using the semi-major axis as the defining factor for Relative Positional Precision, we need to check to see which is greater, the angular error or the distance error (target on tripod)… Angular: ’ X sin 2.7” = feet Distance: feet Therefore, angular error is greater ALTA/ACSM Land Title Surveys

Total Uncertainty in this Conventional Measurement  1  But this is for  What about 95%   = feet 95% C.I.  =0.032 feet for course 2-3 (target on tripod) ALTA/ACSM Land Title Surveys

Total Uncertainty in this Conventional Measurement  1  Using the semi-major axis as the defining factor for Relative Positional Precision, we check to see which is greater, the angular error or the distance error (target on 8 feet of range pole)… Angular: ’ X sin 20.2” = feet Distance: feet Therefore, angular error is greater ALTA/ACSM Land Title Surveys

Total Uncertainty in this Conventional Measurement  1  But this is for  What about 95% or   = feet 95% C.I.  =0.032 feet for course 2-3 (target on 8 feet of range pole) ALTA/ACSM Land Title Surveys

Allowable Relative Positional Precision in this Conventional Measurement What is the allowable RPP?  = 0.07’ + 50 ppm (from the Standards) ALTA/ACSM Land Title Surveys