一种基于极大似然准则的自适应卡尔曼滤波算法

An Adaptive Kalman Filtering Algorithm Based on Maximum-Likelihood Criterion

在系统不能确切建模或模型本身会产生改变的应用场合,传统卡尔曼滤波算法的性能受到直接影响,甚至无法正常应用。基于标准卡尔曼滤波假设,利用极大似然估计准则推导了一种新的自适应卡尔曼滤波算法,这种滤波算法的主要思路是利用新息序列对系统和量测噪声方差阵Q和R实时估计和调整,以实时反映系统模型的变化。在相关理论分析的基础上,针对低成本惯性/GPS组合导航系统对这种自适应卡尔曼滤波方法的性能进行了仿真分析,与传统卡尔曼滤波算法进行了比较,探讨了这种算法的实用性。

When it is difficult to establish a model accurately or when the model changes from time to time, the performance of the traditional Kalman filtering algorithm is adversely affected and, in extreme cases, it cannot even be used normally. According to the maximum likelihood estimation criterion, a new adaptive Kalman algorithm is proposed in this paper. In the full paper, we explain and discuss our new algorithm in much detail; here we give only a briefing. Our explaination and discussion center around two matrices： R, the measurement noise covariance matrix and Q, the system noise covariance matrix. Our discussion includes three cases： adjustment of R alone; adjustment of Q alone; simultaneous adjustment of R and Q. The variance matrices of system noise and measurement noise can be estimated and adjusted in real-time using this algorithm. This adaptive algorithm is more efficiently adaptable to the change of system model. We applied our algorithm to studying the performance of low-cost INS/GPS （Inertial Navigation System/ GPS） integrated navigation system, whose model changes from time to time. Simulation results show that our new Kalman filtering algorithm can obtain the performance of this low-cost INS/GPS system but the results obtained with traditional Kalman filtering algorithm are not convergent.