自适应滤波方法研究

 证明Ｓａｇｅ－Ｈｕｓａ的自适应卡尔曼滤波算法不能同时估计Ｑ和Ｒ，并分析了该法导致滤波发散的原因。介绍了一种新的自适应卡尔曼滤波算法，该法当Ｒ（或Ｑ）已知时可以准确地估计出Ｑ（或Ｒ）。该法的独特之处在于当对Ｑ（或Ｒ）进行修正估计时，只采用矩阵的乘运算和求逆运算，而不进行加减法运算，因此消除了滤波发散现象。数字仿真表明效果良好。

APPROACH TO ADAPTIVE FILTERING ALGORITHM

This paper proves that Sage Husa′s adaptive Kalman filtering algorithm cannot estimate Q and R simultaneously, and analyses the reason why Sage Husa′s algorithm may lead to filtering divergence. A new algorithm of adaptive Kalman filter is introduced which can estimate Q (or R) accurately when R (or Q)is known. The most particular feature of this algorithm is that only matrix multiplication and inversion are performed while no summation or reduction is carried out in the phase of updating and improving the estimation of Q(or R), hence resulting in no filtering divergence. Digital simulation shows that it is remarkable.