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。

An adaptive cubature Kalman filter algorithm based on singular value decomposition (SVD-ACKF) was proposed for orbit determination by optoelectronic theodolite when unknown or inaccurate noise statistics lead to low precision and divergence of filter. First, Sage-Husa maximum a posteriori and its improved form were used to estimate noise statistics online, and SVD instead of Cholesky decomposition in was used order to improve the stability of numerical calculation. Then, the mathematical model of orbit determination was expound, compared with the Euler method, improved Euler method was used to disperse the orbital dynamics equations with J2 perturbation. Finally, the simulation results show that improved Eular method can achieve a higher discrete precision, and SVD-ACKF algorithm can improve the accuracy and stability.