Land Surveying and Global Navigation Satellite Systems. The Cable TV Dilemma

Transcription

1 Land Surveying and Global Navigation Satellite Systems Presented by : Dr. R. S. Radovanovic, A.L.S., C.L.S., PEng SARPI LTD 2010 ABCLS AGM March 3, 2010 The Cable TV Dilemma Does anyone know how cable TV actually works? Does this stop you from feeling competent using a television? What do you do when something goes wrong? What matters more how the cable signal comes to your house, or what you do with the content? How is GPS (now GNSS) different? 1

2 Overview Required How GPS Works segment The overview you can give your neighbour More important How GPS doesn t work segment What is it we are trying to do? Accuracy, reliability, redundancy and meaning in GPS surveys Neat topics in GNSS positioning Active Control Systems Precise Point Positioning Reference frames, geo-referencing and coordinates Positioning With GPS GPS positioning is based on the concept of trilateration Terrestrial Example : A boat on an ocean measuring distances to control points with known coordinates 2

3 Space-borne Trilateration Situation is slightly more complicated in three dimensions Minimum 3 control points required Ambiguity between solutions a nonissue since candidate points are separated by 1000 s of kilometres Concept assumes that true distances are observed Active (send-receive) system required OR Synchronized clocks between transmitters and receivers Illustration Courtesy T. Herring (2001) How Does This Work? GPS Satellites (control points) broadcast two ranging signals on L1 and L2 frequencies ( MHz and MHz) Signals contain ranging code known code on L1 (CA code), unknown code on L2 (P code) Signals contain satellite ephemeris equations to allow calculation of satellite positions at any time and satellite clock offsets Signals contain ionospheric model All GPS receivers can replicate the CA ranging code produced by the satellites If we all agree that the code starts at a particular time (i.e. time 0), then the difference in the code sequence made at the receiver vs the received code is the length of time it took the signal to get there code range measurement 3

4 Correlation Case 2 : Clocks are not synchronized - satellite and receiver clocks are off of some hypothetical base time system (GPS time) Bit generated by receiver at t rx =9200 t rx is behind t gps by 1ms Bit generated by satellite at t sat =9200 t sat is ahead of t gps by 100μs (1e-4 s) Bit generated at t gps = (1e-4) Arrives at receiver at t gps = (1e-4) Receiver thinks it arrives at t rx = (1e-4) - (1e-3) Receiver must shift generated signal by Δt= 67ms - 1ms - 100μs for correlation of received and generated signals to be 1 (0 otherwise) True Range to Satellite = m Pseudorange to Satellite = m Carrier Phase Problem with code measurement chip length is 300 m so measurement is noisy Instead strip the code of the base signal, resulting in the carrier wave (pure sine wave) For L1, wavelength is 19cm, for L2, wavelength is 21cm Again, receiver can reproduce this wave, so compare the wave received from the wave generated to derive range Problem is that you have an unknown number of wavelengths between receiver and satellite that cannot be measured - Integer ambiguity Ambiguity constant so long as lock maintained 4

5 Decoding the Message GPS receivers are bombarded by a barrage of signals at various frequencies : How does the receiver find the GPS signals? Antenna : passes only signals at acceptable GPS frequencies (L1/L2 plus and Doppler effects) Receiver : knows where satellites should be based on almanac and its last recorded position Can predict approximately what satellites are visible Knows what CA codes should be transmitted by these satellites What their Doppler shifts should be Quick Lock On If no position/almanac data available, receiver performs systematic search through frequency/satellite combinations - slow lock on Standard GPS Error Sources Slide Error Source Magnitude Notes Noise 0.1-1m (code) 1-2 mm (carrier) Uncorrelated between receivers and satellites Magnitude is elevation dependant Multipath m (code) 1-10 mm (carrier) Uncorrelated between receivers and satellites Magnitude is elevation dependant Ionosphere m Correlated over space Delays the pseudorange, advances the carrier Eliminated if L1/L2 observations are available (frequency dependant) Broadcast Ionospheric Model removes 50% of error Troposphere 2.3 m (zenith) - 20 m (horizon) (unmodelled) Correlated over space Strict delay, frequency independent Models reduce effect to cm level (zenith) Sat. Clock Sat. Orbit 5-20 m 5-10 m (broadcast), 10cm (precise) Identical effect on all receivers observing the satellite Correlated over space 5

6 Differential Positioning Example of two receivers collecting data in a given area What are the errors affecting these observations? What is the relationship between the errors affecting these observations? Since certain errors are the same or similar between the two observed ranges, they will be removed if we subtract the two! Differential Positioning (DGPS) Why do we need a reference coordinate? Use differential GPS to reduce errors Subtract the raw measurements made at both receivers and we get a cleaner pseudo-observation Problem Can t see the datum + 5 Geometry weakly dependent on base receiver position (20 m ok) Possible result are really only differential vector between two receivers 6

7 What about GLONASS? GLONASS is being heavily marketed as an augmentation to GPS-only positioning More satellites mean better availability right? Problems GLONASS uses different time base than GPS ( - 1 satellite) GLONASS signals are of somewhat lower quality (noisier) My conclusion : If GPS is going to work, GLONASS will not make it more accurate If GPS is not going to work, it is because you need to get out of the trees, and GLONASS is not going to help you there! What about Galileo? A European initiative to develop a modern, independent navigation system Started in 1999, projected to be operational in 2006, then 2011, then 2013, now 2014, etc. etc. Three individual services Open service free service available to all Commercial service encrypted signal to allow autonomous positioning to 1 m (pay for subscription) Public Regulated / Safety of Life service for emergency services (more robust) So what does Galileo-ready mean? 7

8 What about Modernized GPS? Several initiatives to make GPS better in the future L2C (Civilian L2) C/A code on L2 frequency CA lets you directly read signal, rather than use specialized processing techniques (which add noise and lessen sensitivity) Better ionospheric error removal Currently implemented, needed firmware upgrades L5 new civilian signal at MHz Higher power Added frequency lets better ionospheric removal, multipath detection 2009 first satellite, will need new antenna L1C new civilian code on L1 Allows better correlation/tracking, slightly higher power 2013 start M code new military signal Spot beam to provide high power to areas of interest Wide bandwidth, new signal structure Why GPS? Standard Slate of reasons why GPS is wonderful All-weather Line-of-Sight Independent High Real Time Accuracy (Ionospheric Storms, Poor PDOP) (Canopy Cover) ( centimetre level ) Real Reason to use GPS Easy to Train to Use (Blackbox) Fast data collection GIS/CADD friendly Reasonably accurate over long distance Unified computational system 8

9 What are we trying to do? Fundamental Process of Land Surveying is a) Finding and verifying monuments defining old boundaries b) Planting new monuments to define new boundaries c) Making appropriate measurements between old/new monuments to determine spatial relationships between old/new monuments and thus old/new boundaries d) Produce paper (static digital) product to show the rest of the world what the relationship between the old and new boundaries are e) (Sometimes) Determine meaningful elevations of selected points of interest f) (Most times) Make money doing this and preserve the cadastral fabric Really do we care about the measurements, or the meaning of the measurements? GPS Observations and Pseudo-observables What does GPS really measure? Standalone 3D coordinates of point in WGS-84 based on coordinates of observed satellites (accurate to 10-20m horizontally ) Differential Relative XYZ vector between two receivers in WGS-84 system (accurate to several ppm) Geodesy Mathematics converts this XYZ observable into variety of pseudo-observables we commonly use (and mis-interpret!) Datums / Reference Frames Ellipsoids Map Projections 9

10 What kind of trouble can we get into? What is a sue-able error in land surveying? Incorrect stakeout (for client s needs) Incorrect reporting (i.e.. elevations, setbacks) Just as with regular surveying, need proper checks to ensure work is being done properly What can go wrong? How much can it go wrong? What we can do about it? Step 1 : Record the Info GPS is very handy from an auditing point of view since everything done from when the receivers are turned on can be recorded Log raw data for post-processing Base and Rover Don t necessarily post-process everything, but at least you have it if you need to sleuth later Book Base Station Station Height If this is wrong, all heights later will be wrong check, re-check and check at the end of survey Use fixed height poles for rovers or multiple antenna heights Book Evidence Information Easy to get carried away with measuring rather than surveying 10

11 Step 2 : Make Sure the Data Is Good Boils down to 3 parameters : How far from the Base can we go? How long do we occupy? How do we ensure reliability? Juggle practicality / economics with ensuring point is exactly where we said it No different than in conventional surveying What are redundant ties? How far can we go? RTK surveys are accurate to several ppm, but shots can range up to 10 km 2 ppm on 10 km = 2 cm Survey looks like very long sideshots from central point Points widely separated are as relatively accurate as points close together Good for maintaining control over distance Bad for local ties / intersections Key is to assess accuracy of calculated inverses (relative accuracy) 11

12 How Long Do We Observe? GPS errors are temporally correlated Samples close in time share common errors, and so averaging these samples does NOT provide a significantly better estimate Increasing the sampling frequency does NOT improve the accuracy of the mean ONLY solution is to collect data for longer periods (even at lower sampling rate) For typical RTK survey (few km baseline, 1Hz data collection) difference between collecting for 2s, 30s and 1 min is improvement of 1%, 25% and 36% vs. using a single shot Redundant Ties What is redundancy? Having enough useful information to check your work Problem didn t arise with GPS what are redundant ties for a posting with a total station? Can never guarantee results are errorless can only state a positioning accuracy and how certain you are that the result is within this accuracy band More checks, generally better accuracy and/or more reliable Without check measurements, procedures provide enhanced certainty Electronic recording removes large blunders Regular equipment checks (i.e.. pogo plumbing, tribrachs) remove other errors 12

13 Redundant Ties What is the best RTK procedure? Set up base station, book antenna height in metres and feet with two different measuring tapes Survey each point with 5 minute observation spans using tripods instead of pogos again, measure heights with two tapes Break down base station, set up on another surveyed point Go back and re-survey each point in same manner Break down base, re-setup and resurvey points third time Post-process all data What is the best, reasonable RTK procedure? What is reasonable? Surveying such that the chance you have an error is slim, and any error you do have will not cause a sue-able instance Need to know what the properties of GPS measurements are i.e. how accurate are they and how often do they contain blunders Redundant Ties Three popular flavours 1. Survey all points, break down base, re-set up, resurvey Most rigorous, most time consuming True redundancy of all observations 2. Survey all points, go back and resurvey point (base stays same) Seeks to de-correlate errors via satellite motion improved certainty of ambiguity resolution and better averaging results Good redundancy of observations, but lack of redundancy as to where these observations come from (base station setup, height) Kind of time consuming, depending on job 3. Survey point, dump satellites, re-survey point Seeks to maybe improve certainty of ambiguity resolution Errors in observations are very correlated, so averaging is not doing much, but if single shot accuracy is good enough then we are ok Fast surveying 13

14 How often will we get wrong ambiguities? Wrong ambiguities result in large (decimetre +) biases in the results Receiver thinks it has the correct ambiguity, but really has solved the wrong one Receiver's decision based on quality of data coming in and statistical modeling Problem existed with EDM initially, now totally solved Test : get a long data stream of loss-of-lock events, see how often wrong ambiguities are evident How often will we get wrong ambiguities? Apparently, very rarely, and very, very rarely will we get twice the same wrong ambiguity Generally this occurs when you are pushing the RTK to lock 14

15 Step 3 : Use the Data Properly GPS is a three-dimensional system WGS84 Any ellipsoidal measurements (distance, bearing, etc) are derived quantities Confusion arises since processor interfaces allow users to input ellipsoidal, local, map, etc. coordinates for base/rover stations GPS Range Observations GPS Orbits WGS84 Processor dx dy dz WGS 84 Xb Yb Zb WGS 84 Xr Yr Zr WGS 84 User Input Coordinate for RX B (any sys) Output Coordinate for RX R (any sys) Bearings Remember that azimuths and distances are not observables from GPS but derived quantities pseudo-observations GPS pseudo-observation is like a star/sun-shot with a distance attached Convert azimuths to bearings using meridian convergence Convergence = dλ. sin(φ) with dλ difference in longitude between point and reference meridian φ latitude of point 15

16 Ground Distances Ground Distances - Scaling applied to convert ellipsoidal distance to reference ground surface Typical method is to assume locally spherical Earth and derive factor d ell = d s R R + h h 1 d 1 d 2 10 m elevation difference creates a 2 ppm difference in scale factor h 2 Factor is usually calculated as the mean between end points on the line Ellipsoid to Ground Factor Problem arises when you are scaling a set of ground distances to the ellipsoid factor varies based on component points 750 m m m 3 km 9 cm on 6 kilometers discrepancy! 3 km Indicates problem with a surface based coordinate system not path independent 16

17 Ellipsoid to Ground Conversion Problem can be particularly acute in RTK surveys Always set up the RTK on the highest point Scale factor usually calculated based on project height or height of base Survey points are located lower down Discrepancy will occur if base is moved to lower elevation and previously derived coordinate used for new base station Again, not a problem if everything done on the ellipsoid, or in 3D space Mainly problem for unsurveyed territory due to long distances from baseline and dependence on ground coordinates Not theoretically possible to have homogenous ground-based coordinate system Must assume some reference surface for calculations average project height? How do we calculate Elevations? GPS dxyz vectors can be used to derive ellipsoidal height differences between points Official height datum is CVD28 (MSP) ORTHOMETRIC DATUM Conventionally provided via network, agricultural benchmarks, NRCAN benchmarks, etc. Difference between ellipsoidal and orthometric heights are due to geoidal undulations (gravity field) h a H a h b H b N a Nb Models exist to determine undulations in a specific area 17

18 Effect of Neglecting Geoid Lazy way out : Just Assume Ellipsoidal Height Difference = Orthometric Height Difference Problem : geoid/ellipsoid separation is not constant Max. Difference in undulation for points separated by 10 km 60 o N 58 o N o N 54 o N 52 o N o N o W 118 o W 116 o W 114 o W 112 o W 110 o W 0 Error level is below 20ppm specified by MSP, but above accuracy of the GPS ellipsoidal height (few ppm) How do we calculate Elevations? Increasingly common practice is to use very long baselines (+100 km) from a central control point (i.e. Vancouver, Kelowna, etc) to the project area control point Assume known ellipsoidal elevation of control point (i.e. ITRF ties + geoid model) or assumed orthometric elevation of control point (local ASCM) Derive vector from control point to project area control (ellipsoidal height diff) Use geoid model to calc orthometric height difference to project area control Use short length local ties to determine orthometic heights of points of interest in project Theoretically correct, but what elevations do all the other project players work with? Local ASCM s, Agricultural Benchmarks, Transportation Benchmarks all contain local distortions Again measurement vs meaning! 18

19 What about Active Control? Canadian Active Control / BC Active Control / Private Networks provide data from continuously operating reference stations Some networks provide real-time correction service Very handy not to have a base station (economics / efficiency) Conceptually allows very high coordinate repeatability Major concern from practitioner perspective is stability of reference station Physically is the station moving? Coordinate consistency if the station is moving, are the coordinates updated? Coordinate validity is the RINEX header correct? Antenna information correct / updated? Above are not concerns is active control is used as a random base station for the day, but this defeats the georeferencing potential provided by ACS! PPP Example FTMAC Averaged Movments 15 Movement from Average (mm) y = x North East Elevation Day of Year Analysis of nearby points confirms local movement of FTMAC only If FTMAC is used as a base station what happens when checks are made to data collected a year prior? 30 cm / yr 19

20 Active Control System - Implementation Movements at Ucluelet Movement from Average (mm) y = x North East Elevation Year Implication is that all data points around Ucluelet move in this fashion wrt ITRF aggravating from a GIS perspective, but necessary if this data is to be eventually merged with data around Vancouver! Typical Case Task : Establish points with known elevations to support excavation/paving operations underneath a ash disposal facility Due to increase in truck sizes, clearance is limited Existing pad had subsided in areas, heaved in others Project Engineer wanted final grade to be at original design drawing elevation, rather than simply ensuring clearance Do you know what the original design elevation was referenced to? I heard there was an original plant elevation benchmark somewhere but no one can find it... maybe you can ask the drafting group to find something we keep all the drawings for all the plants in the company in one master system so there has to be something in there.! 20

21 Typical Case One full day on site later, a report is found that schematically shows the location of two benchmarks, one of which has a listed elevation Are these benchmarks related to the design of the ash plant? Where are these benchmarks physically? A second full day later, benchmarks (mislabeled pizeometers ) are found in locked casings - ties are to known water levels to roughly verify published elevations Elevations are transferred to points set at the Ash Plant, additional elevation benchmarks set and a sketch made of rough positions of benchmarks to aid future treasure-seeking Why did this cost so much?! Epilogue Two days later Hi Robert, I have confirmed the location of BM "A" as the following: N m E m Elev m Please update your dwg so that this information is captured and list the coordinates of the other points. Hello, Thanks for the additional information. I can certainly label the BM A point with your assumed coordinates, but I need to know how the plant datum is defined (i.e. how to define North) if I am to calculate coordinates for the other points. Robert, I found the coordinates on a printout in a report in Geoff s office. I think the coordinates are defined with North as usual. Try that and see how it works. We might want to use the points for future layout, so this would be good to have seeing as you were at site already...! 21

22 Conclusion Knowing about how GPS works is important, but it is much more important to know how to use the information GPS provides! Technology is at a point where global coordinate determination is possible at a very high accuracy Coordinate-based cadastres? Public access to survey level accuracies? Surveyor s role will focus on Being the expert at interpreting coordinate information Designing systems to provide coordinates reliably Assessing evidence of boundaries Providing professional positioning advice Land Surveying and Global Navigation Satellite Systems Presented by : Dr. R. S. Radovanovic, A.L.S., C.L.S., PEng SARPI LTD 2010 ABCLS AGM March 3,