噪声相关系统中估计误差方差奇异的滤波融合算法

Filtering Fusion Algorithm with Singular Covariances of Filtering Errors in Systems with Cross-correlated Noises

多传感器的线性随机动态估计系统复杂多样,其中,各传感器之间的观测噪声相关系统得到广泛研究。但在实际应用中,噪声相关系统的状态向量还可能受到各种约束,如:等式约束、不等式约束、运动学定律等,使得估计误差方差阵可能是奇异的。理论上这些先验信息有利于更精确的估量,但现有的融合算法存在局限性,无法应用于这类情况。针对此类问题,基于线性最小均方误差(MMSE)准则,提出了最优加权的估计融合算法。通过仿真,将最优加权的估计融合算法与中心式融合算法进行对比分析,比较了两种算法的估计误差,数值结果验证了该算法的有效性。

The multi-sensor linear stochastic dynamic system is complex and diverse.Among them,noise-related systems in which the observation noises of sensors are often correlated to each other have been extensively.But in practical applications,the covariances of filtering errors are singular because the state vector in noise-related systems may also be subject to some constraints,such as equality constraints,inequality constraints,law of kinematics and so on.Theoretically,these prior information can enhance the accuracy of state estimation,but the existing fusion algorithms cannot be applied directly due to their limitations.In this paper,an optimal weighted estimation fusion algorithm is proposed based on the linear least mean square error(MMSE)criterion.Our proposed fusion algorithm is compared with the centralized Kalman filtering algorithm in terms of estimation errors by numerical simulations,which show the efficiency of our proposed algorithm.