一类具有等式约束的带乘性噪声系统的最优滤波算法

Optimal Filtering Algorithm for a Class of Systems with Equality State Constraints and Multiplicative Noise

针对动态数据处理领域观测方程中存在乘性噪声的情况,提出在乘性噪声系统中状态附等式约束的一套滤波算法。该算法首先通过把观测向量进行扩维,然后基于投影定理进行滤波求解得到基于线性最小方差的最优滤波算法。通过与基于最优化理论的方法求解得到的算法进行对比分析及仿真对比验证了该算法的有效性。

With the swift development of geomatics, we can take advantage of these priori observed in- formation to establish equality constraints and effectively combine with the Kalman filter to improve the accuracy of the data processing. Multiplicative noise do exist in dynamic data processing field. Basing on that, a set of optimal filtering algorithms for systems with equality state constraints and multiplicative noise are proposed in this paper. First, observation vector is augmented. Then based on the projection theorem guidelines the algorithm are solved. In contrast with algorithms are calculated by mathematical optimization theory, the algorithm proposed in this paper are revealed the validation. Computer simula- tion results are presented to illustrate the algorithm.