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对光电经纬仪量测噪声统计特性未知或不精确导致实时定轨精度降低甚至发散的问题,设计了基于奇异值分解的自适应容积卡尔曼滤波(SVD-ACKF)算法。首先,利用Sage-Husa极大后验估计器及其改进形式对噪声统计特性进行在线估计,使得CKF算法具有应对噪声变化的自适应能力,并使用SVD代替传统Cholesky分解以提高数值计算的稳定性。然后,阐述了实时定轨数学模型,提出使用欧拉预测校正法对带J2项摄动的轨道动力学方程进行离散。仿真实验表明:欧拉预测校正法将轨道动力学方程的离散精度提高了1 970.411 m。在量测噪声协方差矩阵取值恶劣时,SVD-ACKF算法将实时定轨精度维持在43 m左右,并且具有更好的数值稳定性。
The SVD-ACKF algorithm based on Singular Value Decomposition (SVD-ACKF) is designed for the problem that the theodolite theodolite has unknown or inaccurate statistical characteristics, which leads to the decrease or even divergence of the real-time orbit determination accuracy. First of all, using the Sage-Husa maximum a posteriori estimator and its improved form to make an on-line estimation of the noise statistical properties, the CKF algorithm has adaptive ability to cope with noise variation and SVD instead of the traditional Cholesky decomposition to improve the stability of numerical calculation . Then, the mathematical model of real-time orbit determination is elaborated, and Euclidean prediction and correction method is proposed to discretize the orbital dynamics equation with the perturbation of J2. Simulation results show that the Euler prediction method improves the discrete accuracy of the orbital dynamics equation by 1,970 m. When the measured noise covariance matrix is bad, SVD-ACKF algorithm keeps the accuracy of real-time orbit determination about 43 m and has better numerical stability.