A novel maximum likelihood and moving weighted average based adaptive Kalman filter

For the state estimation with inaccurate noise statistics, the existing adaptive Kalman filters (AKFs) usually have substantial computational complexity or are not easy to estimate online. Inspired by the fact, a new computationally efficient AKF based on maximum likelihood and moving weighted average (MMAKF) is proposed. Firstly, to reduce computational complexity, instead of estimating the noise covariance matrixes, the maximum likelihood principle is introduced to directly estimate the prediction error covariance matrix and innovation covariance matrix. Subsequently, a new moving weighted average algorithm is designed to optimize the estimated results. Then, a computationally efficient AKF is derived, and its convergence performance and application are discussed. Simulation results for the target tracking example illustrate that the proposed AKF can effectively reduce error caused by inaccurate noise statistics and basically keep simplicity and elegance of the classical KF.