Multipath and Atmospheric Propagation Errors in Offshore Aviation DGPS Positioning J. Paul Collins, Peter J. Stewart and Richard B. Langley 2nd Workshop on Offshore Aviation Research Centre for Cold Ocean Resources Engineering Memorial University of Newfoundland St. John s, Nfld. September 23 24, 1998
INTRODUCTION Part 1: Part 2: Impact of tropospheric delay on DGPS pseudoranges. Results of using simple model to account for vertical separation of aircraft and reference antennas. Impact of reference station multipath on computed aircraft position. Possible solutions, software and hardware techniques.
Differential Differential tropospheric tropospheric zenith zenith delay delay upto upto 1000m 1000m above above reference reference station. station. (Represents (Represents zenith zenith DGPS DGPS correction correction error error due due to to altitude altitude separation.) separation.) Differential delay at zenith (m) 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 (1) High Pressure, Vy. Humid (2) Humid Standard Day (3) Standard Day (4) Very Humid Contribution (5) High Pressure, Dry (6) Dry Standard Day (7) Low Pressure, Dry 0.29 0.57 0.44 0.30 0.28 0.26 0.24 0.05 5 degree mapping function = 10.16 (approx.) 0.00 0 100 200 300 400 500 600 700 800 900 1000 Differential height (m)
DGPS DGPS correction correction errors errors at at the the zenith, zenith, when when using using UNB1 UNB1 tropospheric tropospheric delay delay model model at at aircraft aircraft and and reference reference station. station. Differential error at zenith (m) 0.10 0.05 0.00-0.05-0.10-0.15-0.20-0.25-0.30 5 degree mapping function = 10.16 (approx.) (1) High Pressure, Vy. Humid (2) Humid Standard Day (5) High Pressure, Dry (6) Dry Standard Day (7) Low Pressure, Dry 0 100 200 300 400 500 600 700 800 900 1000 Differential height (m) 0.07 0.04 0.03-0.13-0.27
RECEIVER TECHNOLOGY 12 C/A-code range error (meters) 10 8 6 4 2 Standard correlator 1-chip spacing BW = 2.0 MHz (max. error = 80 m) E C, D A Strobe correlator, BW = 10.5 MHz (similar to theoretical MEDLL, BW = 8 MHz) B Narrow correlator 0.1-chip spacing BW = 8.0 MHz Second-derivative correlator BW = 20.46 MHz RMS theoretical error limit for 1 second observation time (MMSE estimator, BW = 20.46 MHz) F 0 0 10 20 30 40 50 60 70 80 Multipath delay (meters) Weill, L.R. (1997). Conquering multipath: The GPS accuracy battle. GPS World, April, pp. 59-66.
2 ( ) ( α 1) MULTIPATH MODELLING Requires pseudorange and dual frequency carrier phase measurements: ( ) C = ρ + c dt dt + I + T + m + n 1 1 C1 C1 ( ) cdt dt N I T m n Φ1 = ρ + + λ1 1 1 + + Φ + 1 Φ1 ( ) cdt dt N I T m n Φ 2 = ρ + + λ 2 2 2 + + Φ + 2 Φ2 Single frequency combination includes ionospheric contribution: C = 2I λ N + m + n m n 1 Φ1 1 1 1 C C1 Φ Φ1 I f1 = I = α ; α f 2 1 ( λ λ ) ( 1) 1 1 2 2 ( ) ( 1) ( ) Φ1 Φ2 N N mφ mφ nφ nφ = 2I1 + 2 + 2 + 2 α α α 1 1 2 2 1 2 1 2 ( 1) 2 2 C1 1 + Φ1 + Φ2 = mc + nc + B+ M N 1 1 Φ + Φ α 1 α 1 Final combination dominated by pseudorange multipath (m C1 ) and noise (n C1 ).
CALIBRATING MULTIPATH C 4. 0915Φ + 3. 0915Φ = m + n + B+ MΦ + NΦ 1 1 2 C C 1 1 Combination of pseudorange (C 1 ) and dual frequency carrier phases (Φ 1, Φ 2 ) is dominated by pseudorange multipath (m C1 ) and noise (n C1 ). However, accuracy is limited by unknown biases, B, primarily the combination of the carrier phase integer ambiguities. This technique calibrates B from repeated multipath measurements at satellite crossover points, where the multipath should be the same for both satellites. Multipath maps can be constructed as a function of azimuth and elevation angle. Kee, C. and B. Parkinson (1994). Calibration of multipath errors on GPS pseudorange measurements. Proceedings of ION GPS-94, Salt Lake City, Utah, September 20-23, pp. 353-363.
RAW AND SMOOTHED C/A C/A CODE MULTIPATH (1) (1)
RAW AND SMOOTHED C/A C/A CODE MULTIPATH (2) (2)
MULTIPATH ELEVATION ANGLE DEPENDENCE
RAW RAW AND AND SMOOTHED DATA, DATA, VERTICAL POSITION 100 Time [hours] 0 2 4 6 8 10 12 14 16 18 20 80 60 Raw C/A code Smoothed C/A code Vertical Position Error [m] 40 20 0-20 -40-60 -80-100 -121.922-119.135-108.007-102.381-173.834-258.048-124.909
RAW DATA, SMOOTHED POSITIONS 100 80 CA-L1 1 min mean 10 min mean 60 Vertical Position Error [m] 40 20 0-20 -40-60 -80-100 0 2 4 6 8 10 12 14 16 18 20 Time [hours]
RESULTS SUMMARY Residual tropospheric effects, after adequate modelling, only contribute sub-decimetre biases in height. Error in height due to multipath could approach 100 metres. Smoothed data susceptible to cycle slips in noisy reference station environment. Filtering aircraft positions using velocity information should reduce large errors.
CONCLUSIONS Residual tropospheric delays should not be a problem for offshore aviation DGPS. Simple model drastically reduces what small error there is. Multipath has potential for severe problems. Combination of techniques: Receiver and antenna technology to limit maximum multipath error. Filtering in either pseudorange domain and/or position domain at aircraft using velocity information.