Enhanced State Estimation using Multiscale Kalman Filtering

Multiscale wavelet-based representation of data has shown great noise removal abilities when used in data filtering. In this paper, a multiscale Kalman filtering (MSKF) algorithm is developed, in which the filtering advantages of multiscale representation are combined with those of the Kalman filter to further enhance its estimation performance. The MSKF algorithm relies on representing the data at multiple scales using stationary wavelet transform (SWT), applying Kalman filtering on the scaling coefficients at each scales, and then selecting the optimum scale at which the Kalman filter minimizes a cross validation mean square error criterion. The multiscale state space models used in MSKF are also derived using the SWT representation. The MSKF algorithm is shown to outperform the conventional Kalman filter through a simulated example, and the reason behind this improvement is the additional filtering advantage gained by the low pass filters used in SWT