Adaptive Kalman filtering algorithm based on maximum-likelihood criterion

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. Our explanation 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/ global positioning system) 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.