Robust Extended Kalman Filtering in Hybrid Positioning Applications

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4th WORKSHOP ON POSITIONING, NAVIGATION AND COMMUNICATION 2007 (WPNC’07), HANNOVER, GERMANY TABLE I RESULTS OF THE TESTBENCH WITH BLUNDER PROB. b =0.00 Case 1 Case 2 Case 3 b =0% MSE 95% incon MSE 95% incon MSE 95% incon EKF 129 490 14.7 40 138 3.8 11 29 0.0 EKF2 123 453 3.8 45 172 2.2 11 29 0.0 BHA 138 534 15.3 47 168 4.8 12 30 0.0 BH 135 510 15.0 43 156 4.5 12 30 0.0 BM 132 518 14.8 44 152 4.3 12 30 0.0 WLSHA 144 532 16.0 43 155 4.1 12 31 0.0 WLSH 132 493 14.9 39 137 3.4 12 30 0.0 WLSM 133 505 15.3 40 141 3.8 12 30 0.1 Case 4 Case 5 Case 6 MSE 95% incon MSE 95% incon MSE 95% incon EKF 13 33 0.1 9 20 0.0 20 68 0.8 EKF2 13 33 0.0 9 20 0.0 19 64 0.3 BHA 13 33 0.1 9 20 0.0 23 76 1.4 BH 13 34 0.1 9 20 0.0 22 75 1.4 BM 13 50 0.4 9 20 0.0 21 70 1.2 WLSHA 13 34 0.1 9 20 0.0 21 71 0.9 WLSH 13 33 0.1 9 20 0.0 21 70 1.0 WLSM 13 56 0.2 9 20 0.0 21 70 1.0 Case 7 Case 8 Case 9 MSE 95% incon MSE 95% incon MSE 95% incon EKF 18 41 0.0 19 43 0.0 17 37 0.0 EKF2 18 41 0.0 19 43 0.0 17 37 0.0 BHA 19 42 0.0 19 44 0.0 17 38 0.0 BH 19 42 0.0 19 44 0.0 17 38 0.0 BM 19 42 0.0 19 44 0.0 17 38 0.0 WLSHA 19 42 0.0 19 43 0.0 17 37 0.0 WLSH 19 42 0.0 19 43 0.0 17 37 0.0 WLSM 19 42 0.0 19 43 0.0 17 38 0.0 TABLE II RESULTS OF THE TESTBENCH WITH BLUNDER PROB. b =0.05 Case 1 Case 2 Case 3 b =5% MSE 95% incons. MSE 95% incons. MSE 95% incons. EKF 351 1466 42.0 168 693 38.6 85 328 35.2 EKF2 329 1317 37.6 163 667 35.3 84 326 35.0 BHA 162 656 15.5 89 416 9.7 14 35 0.6 BH 177 667 18.5 91 433 11.2 15 40 1.1 BM 193 804 21.1 88 403 12.4 16 42 1.5 WLSHA 170 725 16.4 90 437 9.0 12 30 0.0 WLSH 169 667 17.7 83 414 9.3 14 34 0.2 WLSM 171 653 18.6 79 385 9.5 14 36 0.2 Case 4 Case 5 Case 6 MSE 95% incons. MSE 95% incons. MSE 95% incons. EKF 503 1491 86.5 317 1033 79.2 372 1248 71.6 EKF2 502 1491 86.5 317 1033 79.2 370 1242 71.1 BHA 17 42 0.1 12 29 0.5 21 60 0.9 BH 20 51 0.1 14 36 1.6 32 73 2.6 BM 21 53 1.6 15 39 2.4 34 82 3.8 WLSHA 2397 10689 86.0 2150 10283 78.2 4090 19335 72.7 WLSH 855 1413 84.1 548 1996 75.6 737 2877 68.7 WLSM 762 2351 84.2 487 1815 75.2 696 2574 68.2 Case 7 Case 8 Case 9 MSE 95% incons. MSE 95% incons. MSE 95% incons. EKF 1020 3065 92.3 989 2705 93.8 949 2548 95.5 EKF2 1020 3065 92.3 989 2705 93.8 949 2548 95.5 BHA 25 59 0.3 23 49 0.0 21 45 0.0 BH 28 68 0.4 26 56 0.3 26 57 1.0 BM 30 73 0.9 27 60 0.8 28 61 2.1 WLSHA 7090 25138 90.5 6787 26024 92.5 3839 15123 94.2 WLSH 2351 7926 90.7 2013 6255 93.0 1734 5530 94.8 WLSM 2283 7617 90.4 1873 6032 93.1 1615 4936 94.9 62
4th WORKSHOP ON POSITIONING, NAVIGATION AND COMMUNICATION 2007 (WPNC’07), HANNOVER, GERMANY TABLE III BLUNDER DETECTION WITH BLUNDER PROBABILITY b =0.00 Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 b =0% III III III III III III III III III BHA 0.21 0.28 0.37 0.45 0.55 0.33 0.30 0.41 0.59 BH 0.21 0.27 0.37 0.45 0.55 0.33 0.30 0.41 0.59 BM 0.22 0.29 0.39 0.46 0.56 0.34 0.30 0.41 0.59 WLSHA 0.38 0.43 0.52 0.58 0.66 0.47 0.46 0.57 0.70 WLSH 0.37 0.42 0.51 0.58 0.66 0.47 0.46 0.57 0.70 WLSM 0.37 0.42 0.51 0.58 0.66 0.47 0.47 0.57 0.70 TABLE IV BLUNDER DETECTION WITH BLUNDER PROBABILITY b =0.05 Case 1 Case 2 Case 3 b =5% I II III IV I II III IV I II III IV BHA 0.01 0.03 0.02 0.25 0.02 0.04 0.02 0.30 0.03 0.06 0.03 0.41 BH 0.01 0.03 0.01 0.27 0.02 0.04 0.02 0.32 0.03 0.06 0.02 0.44 BM 0.01 0.03 0.01 0.29 0.02 0.04 0.02 0.34 0.03 0.06 0.02 0.45 WLSHA 0.02 0.02 0.01 0.40 0.03 0.03 0.01 0.42 0.03 0.06 0.02 0.50 WLSH 0.02 0.02 0.01 0.42 0.03 0.03 0.01 0.44 0.03 0.06 0.02 0.52 WLSM 0.02 0.02 0.01 0.42 0.03 0.03 0.01 0.44 0.03 0.06 0.02 0.52 Case 4 Case 5 Case 6 I II III IV I II III IV I II III IV BHA 0.07 0.11 0.09 0.45 0.09 0.16 0.09 0.47 0.05 0.08 0.09 0.39 BH 0.08 0.11 0.09 0.46 0.09 0.17 0.08 0.48 0.05 0.08 0.08 0.41 BM 0.08 0.11 0.09 0.47 0.09 0.17 0.08 0.49 0.05 0.08 0.08 0.42 WLSHA 0.22 0.05 0.00 0.70 0.25 0.08 0.01 0.65 0.15 0.04 0.01 0.69 WLSH 0.22 0.05 0.01 0.69 0.24 0.08 0.01 0.64 0.15 0.05 0.01 0.68 WLSM 0.22 0.06 0.00 0.70 0.23 0.09 0.01 0.64 0.15 0.05 0.01 0.67 Case 7 Case 8 Case 9 I II III IV I II III IV I II III IV BHA 0.08 0.14 0.03 0.27 0.10 0.19 0.02 0.31 0.16 0.25 0.01 0.37 BH 0.08 0.14 0.02 0.29 0.11 0.18 0.02 0.33 0.16 0.25 0.01 0.39 BM 0.08 0.14 0.02 0.30 0.10 0.19 0.02 0.34 0.16 0.25 0.01 0.40 WLSHA 0.24 0.01 0.00 0.72 0.30 0.01 0.00 0.67 0.41 0.01 0.00 0.57 WLSH 0.24 0.01 0.00 0.72 0.30 0.01 0.00 0.67 0.41 0.01 0.00 0.57 WLSM 0.24 0.01 0.00 0.71 0.30 0.01 0.00 0.67 0.41 0.01 0.00 0.57 63
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