On stochastic approximation and an adaptive Kalman filter

The orthogonality between the innovations process and the one-step predicted state of a discrete-time Kalman filter is used to specify a stochastic approximation algorithm for simple, adaptive Kalman filtering. The filter is adaptive in the sense that on-line filter signals are used to train the gain matrix to its correct, steady-state form. The problem considered is one of training the gain matrix when the time-invariant plant dynamics are known, but the plant noise and observation noise covariance matrices are unknown. No direct identification of these covariances is required. Simulation results are presented to illustrate the simplicity and soundness of the proposed adaptive filter structure. The simplicity of the proposed adaptation method indicates that it might easily be implemented in real-time data or signal processing applications.