Filter and piecewise smoother on the matrix Lie group
Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Luo, Yarong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: GPS solutions - Berlin : Springer, 1995, 27(2023), 4 vom: 05. Juli |
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| Übergeordnetes Werk: |
volume:27 ; year:2023 ; number:4 ; day:05 ; month:07 |
| Links: |
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| DOI / URN: |
10.1007/s10291-023-01460-2 |
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| Katalog-ID: |
SPR05215422X |
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| 520 | |a Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. | ||
| 650 | 4 | |a Matrix Lie group of double direct isometries |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -extended Kalman filter |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -extended information filter |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Two-filter smoother |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Piecewise smoother |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Guo, Chi |4 aut | |
| 700 | 1 | |a Chen, Yichao |4 aut | |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s10291-023-01460-2 |z lizenzpflichtig |3 Volltext |
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10.1007/s10291-023-01460-2 doi (DE-627)SPR05215422X (SPR)s10291-023-01460-2-e DE-627 ger DE-627 rakwb eng Luo, Yarong verfasserin aut Filter and piecewise smoother on the matrix Lie group 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. Matrix Lie group of double direct isometries (dpeaa)DE-He213 -extended Kalman filter (dpeaa)DE-He213 -extended information filter (dpeaa)DE-He213 Two-filter smoother (dpeaa)DE-He213 Piecewise smoother (dpeaa)DE-He213 Guo, Chi aut Chen, Yichao aut Enthalten in GPS solutions Berlin : Springer, 1995 27(2023), 4 vom: 05. Juli (DE-627)357170016 (DE-600)2094351-9 1521-1886 nnns volume:27 year:2023 number:4 day:05 month:07 https://dx.doi.org/10.1007/s10291-023-01460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2023 4 05 07 |
| spelling |
10.1007/s10291-023-01460-2 doi (DE-627)SPR05215422X (SPR)s10291-023-01460-2-e DE-627 ger DE-627 rakwb eng Luo, Yarong verfasserin aut Filter and piecewise smoother on the matrix Lie group 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. Matrix Lie group of double direct isometries (dpeaa)DE-He213 -extended Kalman filter (dpeaa)DE-He213 -extended information filter (dpeaa)DE-He213 Two-filter smoother (dpeaa)DE-He213 Piecewise smoother (dpeaa)DE-He213 Guo, Chi aut Chen, Yichao aut Enthalten in GPS solutions Berlin : Springer, 1995 27(2023), 4 vom: 05. Juli (DE-627)357170016 (DE-600)2094351-9 1521-1886 nnns volume:27 year:2023 number:4 day:05 month:07 https://dx.doi.org/10.1007/s10291-023-01460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2023 4 05 07 |
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10.1007/s10291-023-01460-2 doi (DE-627)SPR05215422X (SPR)s10291-023-01460-2-e DE-627 ger DE-627 rakwb eng Luo, Yarong verfasserin aut Filter and piecewise smoother on the matrix Lie group 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. Matrix Lie group of double direct isometries (dpeaa)DE-He213 -extended Kalman filter (dpeaa)DE-He213 -extended information filter (dpeaa)DE-He213 Two-filter smoother (dpeaa)DE-He213 Piecewise smoother (dpeaa)DE-He213 Guo, Chi aut Chen, Yichao aut Enthalten in GPS solutions Berlin : Springer, 1995 27(2023), 4 vom: 05. Juli (DE-627)357170016 (DE-600)2094351-9 1521-1886 nnns volume:27 year:2023 number:4 day:05 month:07 https://dx.doi.org/10.1007/s10291-023-01460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2023 4 05 07 |
| allfieldsGer |
10.1007/s10291-023-01460-2 doi (DE-627)SPR05215422X (SPR)s10291-023-01460-2-e DE-627 ger DE-627 rakwb eng Luo, Yarong verfasserin aut Filter and piecewise smoother on the matrix Lie group 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. Matrix Lie group of double direct isometries (dpeaa)DE-He213 -extended Kalman filter (dpeaa)DE-He213 -extended information filter (dpeaa)DE-He213 Two-filter smoother (dpeaa)DE-He213 Piecewise smoother (dpeaa)DE-He213 Guo, Chi aut Chen, Yichao aut Enthalten in GPS solutions Berlin : Springer, 1995 27(2023), 4 vom: 05. Juli (DE-627)357170016 (DE-600)2094351-9 1521-1886 nnns volume:27 year:2023 number:4 day:05 month:07 https://dx.doi.org/10.1007/s10291-023-01460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2023 4 05 07 |
| allfieldsSound |
10.1007/s10291-023-01460-2 doi (DE-627)SPR05215422X (SPR)s10291-023-01460-2-e DE-627 ger DE-627 rakwb eng Luo, Yarong verfasserin aut Filter and piecewise smoother on the matrix Lie group 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. Matrix Lie group of double direct isometries (dpeaa)DE-He213 -extended Kalman filter (dpeaa)DE-He213 -extended information filter (dpeaa)DE-He213 Two-filter smoother (dpeaa)DE-He213 Piecewise smoother (dpeaa)DE-He213 Guo, Chi aut Chen, Yichao aut Enthalten in GPS solutions Berlin : Springer, 1995 27(2023), 4 vom: 05. Juli (DE-627)357170016 (DE-600)2094351-9 1521-1886 nnns volume:27 year:2023 number:4 day:05 month:07 https://dx.doi.org/10.1007/s10291-023-01460-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2023 4 05 07 |
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Enthalten in GPS solutions 27(2023), 4 vom: 05. Juli volume:27 year:2023 number:4 day:05 month:07 |
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Enthalten in GPS solutions 27(2023), 4 vom: 05. Juli volume:27 year:2023 number:4 day:05 month:07 |
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Matrix Lie group of double direct isometries -extended Kalman filter -extended information filter Two-filter smoother Piecewise smoother |
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Luo, Yarong @@aut@@ Guo, Chi @@aut@@ Chen, Yichao @@aut@@ |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR05215422X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231014064635.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230706s2023 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10291-023-01460-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR05215422X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10291-023-01460-2-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Luo, Yarong</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Filter and piecewise smoother on the matrix Lie group</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix Lie group of double direct isometries</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-extended Kalman filter</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-extended information filter</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Two-filter smoother</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Piecewise smoother</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Guo, Chi</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chen, Yichao</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">GPS solutions</subfield><subfield code="d">Berlin : Springer, 1995</subfield><subfield code="g">27(2023), 4 vom: 05. 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Luo, Yarong |
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Luo, Yarong misc Matrix Lie group of double direct isometries misc -extended Kalman filter misc -extended information filter misc Two-filter smoother misc Piecewise smoother Filter and piecewise smoother on the matrix Lie group |
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Filter and piecewise smoother on the matrix Lie group Matrix Lie group of double direct isometries (dpeaa)DE-He213 -extended Kalman filter (dpeaa)DE-He213 -extended information filter (dpeaa)DE-He213 Two-filter smoother (dpeaa)DE-He213 Piecewise smoother (dpeaa)DE-He213 |
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misc Matrix Lie group of double direct isometries misc -extended Kalman filter misc -extended information filter misc Two-filter smoother misc Piecewise smoother |
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misc Matrix Lie group of double direct isometries misc -extended Kalman filter misc -extended information filter misc Two-filter smoother misc Piecewise smoother |
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misc Matrix Lie group of double direct isometries misc -extended Kalman filter misc -extended information filter misc Two-filter smoother misc Piecewise smoother |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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Filter and piecewise smoother on the matrix Lie group |
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Filter and piecewise smoother on the matrix Lie group |
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10.1007/s10291-023-01460-2 |
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filter and piecewise smoother on the matrix lie group |
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Filter and piecewise smoother on the matrix Lie group |
| abstract |
Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract We propose a filter and a piecewise smoother based on the matrix Lie group of double direct isometries (%${\mathrm{SE}}_{2}(3)%$) to improve the accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) system based on a low-cost inertial measurement unit (IMU). First, we derive the %${\mathrm{SE}}_{2}(3)%$-extended Kalman filter (%${\mathrm{SE}}_{2}\left(3\right)%$-EKF) based on the group of double direct isometries in the earth-centered earth-fixed (ECEF) frame, and we prove that the left %${\mathrm{SE}}_{2}\left(3\right)%$-EKF satisfies the posterior Cramer–Rao lower bound. Next, we develop the extended information filter (EIF) and two-filter smoother (TFS) based on the matrix Lie group of double direct isometries. Finally, we design a piecewise smoother algorithm to improve the real-time performance of the smoother. Experiments show that the plane and 3D positioning accuracy of the proposed filter and smoother based on the Lie group is better than that based on the Euclidean space. Compared to the traditional filter and smoother based on the Euclidean space, the root mean square (RMS) of the plane and 3D positioning errors of our proposed algorithm are reduced by 38.6% and 17.4% before smoothing, and 46.8% and 26.7% after smoothing. Meanwhile, when the piecewise length reaches 1 min on the data of about 27 min, the piecewise smoother we proposed can almost achieve the accuracy of using full data to smooth. Without losing precision, the piecewise smoother can get the smoothing result in a shorter time and thus improve the real-time performance of the smoothing algorithm. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| title_short |
Filter and piecewise smoother on the matrix Lie group |
| url |
https://dx.doi.org/10.1007/s10291-023-01460-2 |
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Guo, Chi Chen, Yichao |
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10.1007/s10291-023-01460-2 |
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2024-07-04T01:32:27.133Z |
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| score |
7.3996277 |