一种顾及有色噪声的四星座GNSS动态导航滤波算法
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摘要
经典Kalman滤波要求噪声是高斯白噪声,而动态GNSS定位的观测误差和状态预测误差往往是有色噪声。本文提出一种简便的有色噪声函数模型拟合滤波算法,采用前面历元的观测残差和状态残差建立有色噪声模型,削弱有色噪声对动态导航解算的影响。采用四星座GNSS接收机观测数据进行动态导航实验,结果表明,顾及有色噪声的动态导航滤波算法比未顾及有色噪声的经典Kalman滤波算法定位精度更高,三维位置精度提升9%以上。
Classic Kalman filtering requires noise to be Gaussian white noise. However, the observation error and the state prediction error in GNSS kinematic positioning are colored noise. This paper establishes the colored noise model by using past observation residuals and state residuals in order to weaken the effects of colored noise on kinematic navigation solutions. Quad-constellations GNSS receiver measurements are used for a kinematic navigation experiment, and the results show that the algorithm can effectively improve positioning accuracy, as compared with the classic Kalman filtering algorithm with no consideration of the colored noise. The improvement rate of three-dimensional position accuracy is over 9%.
Classic Kalman filtering requires noise to be Gaussian white noise. However, the observation error and the state prediction error in GNSS kinematic positioning are colored noise. This paper establishes the colored noise model by using past observation residuals and state residuals in order to weaken the effects of colored noise on kinematic navigation solutions. Quad-constellations GNSS receiver measurements are used for a kinematic navigation experiment, and the results show that the algorithm can effectively improve positioning accuracy, as compared with the classic Kalman filtering algorithm with no consideration of the colored noise. The improvement rate of three-dimensional position accuracy is over 9%.
引文
[1] 赵长胜,陶本藻.有色噪声作用下的卡尔曼滤波[J].武汉大学学报:信息科学版,2008,33(2):180-182(Zhao Changsheng,Tao Benzao.Kalman Filtering of Linear System with Colored Noises[J].Geomatics and Information Science of Wuhan University,2008,33(2):180-182)
[2] 崔先强,杨元喜,高为广.多种有色噪声自适应滤波算法的比较[J].武汉大学学报:信息科学版,2006,31(8):731-735(Cui Xianqiang,Yang Yuanxi,Gao Weiguang.Comparison of Adaptive Filter Arithmetics in Controlling Influence of Colored Noises[J].Geomatics and Information Science of Wuhan University,2006,31(8):731-735)
[3] Choi H D,Ahn C K,Lim M T.Time-Domain Filtering for Estimation of Linear Systems with Colored Noises Using Recent Finite Measurements[J].Measurement,2013,46(1):2 792-2 797
[4] 杨元喜,任夏,许艳.自适应抗差滤波理论及应用的主要进展[J].导航定位学报,2013,1(1):9-15(Yang Yuanxi,Ren Xia,Xu Yan.Main Progress of Adaptively Robust Filter with Applications in Navigation[J].Journal of Navigation and Positioning,2013,1(1):9-15)
[5] Sui L F,Mou Z K,Gan Y,et al.Unscented Kalman Filter Algorithm with Colored Noise and Its Application in Spacecraft Attitude Estimation[C].The 1st International Workshop on the Quality of Geodetic Observation and Monitoring Systems,2015
[6] 邹韬,赵长胜,丁圳祥.有色观测噪声下的无迹卡尔曼滤波算法[J].测绘通报,2015(6):24-27(Zou Tao,Zhao Changsheng,Ding Zhenxiang.Unscented Kalman Filter of Nonlinear Systems with Colored Measurement Noise[J].Bulletin of Surveying and Mapping,2015(6):24-27)
[7] Cai C S,Gao Y,Pan L,et al.Precise Point Positioning with Quad-Constellations:GPS,Beidou,GLONASS and Galileo[J].Advances in Space Research,2015,56(1):133-143
[8] 杨元喜.自适应动态导航定位[M].北京:测绘出版社,2006(Yang Yuanxi.Adaptive Navigation and Kinematic Positioning[M].Beijing:Surveying and Mapping Press,2006)
[2] 崔先强,杨元喜,高为广.多种有色噪声自适应滤波算法的比较[J].武汉大学学报:信息科学版,2006,31(8):731-735(Cui Xianqiang,Yang Yuanxi,Gao Weiguang.Comparison of Adaptive Filter Arithmetics in Controlling Influence of Colored Noises[J].Geomatics and Information Science of Wuhan University,2006,31(8):731-735)
[3] Choi H D,Ahn C K,Lim M T.Time-Domain Filtering for Estimation of Linear Systems with Colored Noises Using Recent Finite Measurements[J].Measurement,2013,46(1):2 792-2 797
[4] 杨元喜,任夏,许艳.自适应抗差滤波理论及应用的主要进展[J].导航定位学报,2013,1(1):9-15(Yang Yuanxi,Ren Xia,Xu Yan.Main Progress of Adaptively Robust Filter with Applications in Navigation[J].Journal of Navigation and Positioning,2013,1(1):9-15)
[5] Sui L F,Mou Z K,Gan Y,et al.Unscented Kalman Filter Algorithm with Colored Noise and Its Application in Spacecraft Attitude Estimation[C].The 1st International Workshop on the Quality of Geodetic Observation and Monitoring Systems,2015
[6] 邹韬,赵长胜,丁圳祥.有色观测噪声下的无迹卡尔曼滤波算法[J].测绘通报,2015(6):24-27(Zou Tao,Zhao Changsheng,Ding Zhenxiang.Unscented Kalman Filter of Nonlinear Systems with Colored Measurement Noise[J].Bulletin of Surveying and Mapping,2015(6):24-27)
[7] Cai C S,Gao Y,Pan L,et al.Precise Point Positioning with Quad-Constellations:GPS,Beidou,GLONASS and Galileo[J].Advances in Space Research,2015,56(1):133-143
[8] 杨元喜.自适应动态导航定位[M].北京:测绘出版社,2006(Yang Yuanxi.Adaptive Navigation and Kinematic Positioning[M].Beijing:Surveying and Mapping Press,2006)