Adapt the steady-state Kalman gain using the normalized autocorrelation of innovations

A discrete linear time-varying stochastic system with scalar measurement data is considered for which neither measurement noise variance nor power of process noise is known. A novel adaptive Kalman filter that gradually approaches the optimum steady-state gain is proposed in this letter. Different from previous adaptation schemes, our algorithm adjusts the Kalman gain depending on the normalized autocorrelation of the prediction error sequence of the suboptimal filter. We also present how to choose appropriate latency time and sample window length in the adaptation process. In our experiments, the filter shows advantages over several other methods under the same conditions.