基于滤波过程的卡尔曼滤波发散判定方法

Method of divergence detection for Kalman filter based on filtering process

分析了传统的基于单步量测的新息序列不等式判据等方法进行卡尔曼滤波发散判断的局限性,根据卡尔曼滤波过程的稳定性定义,采用矩阵序列极限形式给出了基于滤波过程的更加严格的滤波发散判据以及判断滤波发散的实际算法。根据4个判定条件,不但可以判断滤波过程是否发散,而且可以在很大程度上克服不等式判据的缺陷。该方法是基于整个滤波过程而不是基于单步量测,避免了原方法对量测野值比较敏感的缺点,提高了判断的抗野值能力,有利于减少误判风险以及提高判断的可靠性和准确性。仿真结果表明,结论是正确和有效的。

Firstly, the disadvantages of the traditional method of remainder inequation used to detect the divergence of Kalman filter based on single measurement are analyzed in detail. Then a new method is first presented by means of a matrix sequence limit, according to the stability of filtering process. The key to the method is four equivalent divergence detecting conditions based on filtering process. Particularly, our method is insensitive to the measurement outlier and mainly characterized by being not based on single measurement but on filtering process. So our method can detect divergence with high reliability, high validity and strong outlier resistance, and reduce the risk of false detection that the traditional method has. Finally, a useful detecting arithmetic is given. Simulation shows that the result is correct and effective.