Schmidt Kalman filter in autonomous orbit determination of navigation satellites

doi:10.11947/j.AGCS.2024.20230228

Abstract

Abstract:

To further improve the accuracy of autonomous orbit determination (AOD) of BDS navigation satellites with the equivalent observation Kalman filter, the Schmidt Kalman filter algorithm is applied, considering the cross covariance information between two correlated satellite states of the inter-satellite link observation. The formula for the measurement update and time update of Schmidt Kalman filter according to the observation one by one is deduced, and the square root filtering is also used to ensure the positive definite of the covariance matrix of state variable. The simulation and observed data test result of autonomous orbit determination shows that the Schmidt Kalman filter algorithm can perceptibly improve the AOD accuracy compared with the equivalent observation Kalman filter.

Key words: navigation satellite, inter-satellite link, autonomous orbit determination, BDS, decentralized filtering

CLC Number:

P227

Xiaoyong SONG, Yuanxi YANG, Yue MAO, Rengui RUAN, Long WANG. Schmidt Kalman filter in autonomous orbit determination of navigation satellites[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(5): 879-888.

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参数名称	模型
仿真星座	3 GEO＋3IGSO＋24MEO
星间测量体制	Ka星间双向测距
Ka星间测量噪声及测量误差模型	0.2 m，考虑相对论修正
地球引力场	12阶次EGM96模型
日月位置	JPL DE405
潮汐	IERS2003模型
太阳光压	ECOM模型9参数
先验轨道光压模型仿真误差	光压直射分量随机加5%模型误差
EOP参数	IERS后处理参数
锚固站及坐标	北京、喀什、绥阳，坐标采用ITRF2000
Ka星地测量噪声及测量修正模型	0.2 m，锚固站星地大气修正采用Saastamoinen模型

卫星号	等效观测Kalman滤波结果				Schmidt Kalman滤波结果
卫星号	R	T	N	URE	R	T	N	URE
C1	0.436	1.603	0.593	0.547	0.175	1.112	1.225	0.373
C2	0.398	1.591	0.388	0.509	0.200	1.066	1.255	0.383
C3	0.358	1.416	0.504	0.462	0.241	1.024	0.964	0.368
C4	0.333	0.931	1.078	0.433	0.260	2.010	0.243	0.478
C5	0.383	1.108	1.099	0.488	0.177	0.293	1.259	0.312
C6	0.214	1.487	0.863	0.403	0.132	0.301	1.496	0.331
C7	0.202	0.911	0.287	0.275	0.108	0.155	0.865	0.205
C8	0.191	0.868	0.315	0.263	0.109	0.131	0.942	0.218
C9	0.171	0.820	0.374	0.246	0.121	0.118	0.970	0.228
C10	0.163	0.872	0.419	0.251	0.088	0.110	0.956	0.211
C11	0.168	0.883	0.332	0.250	0.078	0.146	0.973	0.211
C12	0.194	0.902	0.297	0.269	0.099	0.182	0.980	0.222
C13	0.256	0.892	0.337	0.315	0.097	0.197	0.967	0.219
C14	0.230	0.972	0.304	0.304	0.101	0.179	0.892	0.207
C15	0.327	0.558	0.634	0.362	0.110	0.191	0.939	0.220
C16	0.358	0.529	0.574	0.384	0.104	0.197	0.926	0.215
C17	0.368	0.530	0.550	0.392	0.115	0.200	0.997	0.233
C18	0.397	0.580	0.599	0.423	0.127	0.201	0.997	0.238
C19	0.368	0.603	0.607	0.399	0.143	0.196	0.888	0.230
C20	0.358	0.580	0.635	0.390	0.132	0.198	0.889	0.223
C21	0.357	0.602	0.632	0.391	0.127	0.208	0.919	0.226
C22	0.355	0.569	0.616	0.386	0.113	0.184	0.936	0.221
C23	0.368	0.499	0.509	0.388	0.156	1.320	0.176	0.307
C24	0.369	0.548	0.555	0.394	0.115	1.339	0.143	0.292
C25	0.377	0.521	0.584	0.401	0.103	1.342	0.105	0.288
C26	0.308	0.492	0.637	0.342	0.071	1.349	0.076	0.279
C27	0.295	0.496	0.633	0.331	0.071	1.374	0.092	0.284
C28	0.326	0.504	0.680	0.361	0.077	1.367	0.101	0.284
C29	0.363	0.521	0.679	0.394	0.116	1.355	0.137	0.295
C30	0.366	0.517	0.643	0.395	0.147	1.329	0.146	0.304
统计	0.322	0.868	0.600	0.379	0.135	0.876	0.863	0.278

滤波算法	R	T	N	URE
等效观测滤波	0.834	3.460	2.668	1.194
SCHMIDT滤波	0.493	4.584	1.947	1.104
集中式滤波	0.489	4.488	1.963	1.088