Practical multivariate statistical multipath detection methods

Results of the cocktail multiple outlier detection (CMOD) algorithm for multipath error detection

Summaries of the positioning errors after rejection of measurements with detected ultipath by CMOD in the test scenarios 3 to 5 for LCPC-10, LCPC-20, LBCH-7 and K-HK7-300 datasets are shown in Tables 4, 6, 8, and 10 respectively. The percentage improvements (or deteriorations) when compared with single-frequency GPS and the same scenarios using MOD are also shown in the table. The results of scenarios 1 to 5 without using MOD and CMOD (i.e., standard least squares) are also shown in the table for comparison. Tables 5, 7 and 9 show the successful rates for detection of multipath errors in scenarios 3, 4 and 5 for LCPC-10, LCPC-20, and LBCH-7 datasets respectively. In the results of K-HK7-300 dataset, CMOD shows deteriorations in 3D position accuracy in scenarios 3 to 5 (see the right-most column in Table 10) when compared with the current singlefrequency GPS system or the multiplefrequency least squares only solutions. This is because the multipath errors on GPS L2 and L5 and/or Galileo E5a and E5b frequencies are highly correlated (their frequencies are very similar) when reflections occur at the very close carrying platform. The introduction of another highly correlated multipath error clearly further drags the estimated position away from the true position. Table 11 shows the coherence of phase multipath errors against the differential path delays and Table 12 shows the correlation functions between frequencies and differential path delays. The orange highlighted values in Table 12 show that the high correlations (correlation functions are greater than 0.95) of some frequency pairs occur when the differential path delays (also antenna-reflector distance) are very short (about less than or equal to one metre). The performance of CMOD is worse than that of MOD in this dataset. There are two potential reasons. Firstly, the relatively small multipath errors may not be detected by MOD but they may be detected by CMOD, which should have a positive impact. However, since there are many multipath contaminated measurements at each epoch in this dataset as shown in Table 3, many measurements are rejected, which then weakens the satellite geometry. Secondly, the highly correlated low-frequency multipath errors from the very close reflector (the carrying platform) may lead to false detection of measurements without multipath error. In addition to the problem of correlation of multipath errors, the number of multipath contaminated measurements in this dataset is much more than the number of good measurements. This in itself leads to difficulty in the detection of multipath errors.

Conclusion

A practical cocktail multiple outlier detection algorithm, called CMOD, is proposed to tackle the undetected outlier problem in classical multiple outlier detection method (MOD) when phase multipath errors in two or more frequencies of a satellite are in-phase. Tests with static test datasets showed that using CMOD with GPS or Galileo three-frequency data may not improve positioning accuracy when compared with MOD results. The author believes that this is due to the fact that there is insufficient redundancy to take advantage of the multiple outlier detection process used in CMOD. The result is the rejection of too many measurements/ satellites, which then weakens the satellite geometry. However, using CMOD with combined GPS and Galileo multiplefrequency data (scenario 5) shows a substantial increase in correct detection of multipath errors and significant reduction in false detection. Only one false detection occurred in only one of the static test datasets that were tested.

Table 4 RMS positioning errors in millimetres and percentage improvement of using CMOD for the test scenarios in LCPC-10 dataset

Table 5 Approximate percentages of correct and wrong detections of using CMOD for scenarios 3 to 5 in the LCPC-10 dataset

Table 6 RMS positioning errors in millimetres and percentage improvement of using CMOD for the test scenarios in LCPC-20 dataset

Table 7 Approx. percentages of correct and wrong detections of using CMOD for scenarios 3 to 5 in the LCPC-20 dataset

Table 8 RMS positioning errors in millimetres and percentage improvement of using CMOD for the test scenarios in LBCH-7

Table 9 Approx. percentages of correct and wrong detections of using CMOD for scenarios 3 to 5 in the LBCH-7 dataset

Table 10 RMS positioning errors in millimetres and percentage improvement of the test scenarios in K-HK7-300 dataset

However CMOD shows a significant deterioration when compared with MOD and the current single-frequency GPS system when dealing with our kinematic data set. The reason has been identified as being due to a very close reflector, which led to a large number of highly correlated multipath contaminated observations (almost all signals are affected by multipath). Actually the author believe that any very close reflector (less than one metre) has the potential to lessen the advantage of using multiple-frequency GNSS data, this is because the frequencies of GPS L2 and L5, and Galileo E5a and E5b are extremely close and hence the magnitude and phase of carrier-phase multipath errors are extremely close. Note that the results of this paper are not affected by the movement (static/kinematic) of the roving receiver because single-epoch data processing is used.

Table 11 Phase multipath errors of the GPS and Galileo frequencies for various differential path delay (DPD)

Table 12 Correlation functions of phase multipath errors among different GPS and Galileo frequencies in Table 11 against the differential path delay (DPD)

Finally the author remarks that, when combining GPS and Galileo, if the number of measurements contaminated by multipath is small compared to the total number of measurements at any epoch, and if there are no very close reflectors (or at least no reflectors that lead to small additional path lengths), then the author believes that the performance of CMOD will be better than that of MOD. Moreover in this case CMOD will be an extremely effective way to reduce the impact of multipath by 3-12% when comparing with MOD and by 65-73% when comparing with the standard least squares solution using the current reliable GPS L1 data. This in turns leads to the recommendation to avoid, as far as possible, locating GNSS antennas close to reflecting surfaces even for the future multiple-frequency GNSS.

References

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