基于信噪比检验的双参数岭型Kalman滤波及其在BDS星地联合定轨中的应用

将Kalman滤波病态性诊断与处理相结合，提出基于信噪比检验的双参数岭型Kalman滤波。在分析Kalman 滤波的病态性以及岭型 Kalman 滤波的缺陷后，引入信噪比统计量度量每个待估参数受病态性影响的大小，将待估参数区分为涉扰参数和非涉参数，并利用两个岭参数对两类参数进行不同强度的修正，结合广义岭估计思想给出两个岭参数的选取方法。该算法在降低状态参数估计方差的同时尽量减少岭型Kalman滤波引入的偏差。利用STK仿真5颗GEO卫星+24颗MEO卫星+3颗IGSO卫星的北斗卫星星座并进行分布式自主定轨，结果表明提出的新算法能够有效改善病态性对Kalman滤波的不良影响，且相对于岭型Kalman滤波具有更高的定轨精度。

Double-Parameter Ridge-Type Kalman Filter Based on Signal-to-Noise Ratio Test and Its Application in BDS Combined Orbit Determination with Satellite-Ground Observations

In this paper, the ill-conditioning diagnosis and processing of Kalman filter are combined. First, the ill-conditioning of Kalman filter and the disadvantage of ridge-type Kalman filter are analyzed. Then, the signal-to-noise ratio (SNR) statistic is introduced to measure how much each parameter suffers from the ill-conditioning. Accordingly, all parameters are divided into two parts: involved parameters and non-involved parameters. Then, the two parts of parameters are corrected with two ridge parameters of different sizes. This method is named double-parameter ridge-type Kalman filter and can reduce the bias introduced in ridge-type Kalman filter, while reducing the variance of the state parameter estimation. Finally, in the simulation, the new algorithm is discussed in detail with a specific mixed navigation constellation of 5 GEO, 3 IGSO 24 MEO. The results show that the new algorithm has higher orbit accuracy relative to ridge-type Kalman filter and the common Kalman filter.