A New Recursive Filter for Systems with
B. S. Chow, William P. Birkemeier · 1990
In a previous work, an optimal linear recursive MMSE estimator was developed for a zero-mean signal corrupted hy multiplica- tive noise in its measurement model. This recursive filter cannot he obtained by the recursive structure of a conventional Kalman filter where the new estimate is a linear Combination of the previous estimate and the new data. Instead, the recursive structure was achieved by combining the previous estimate with a recursive innovation, a linear combination of the most recent two data samples and the previous estimate. In this correspondence the signal is extended to be nonzero- mean. In the conventional Kalman filter, the superposition principle can be applied to both the signal and the measurement models for this nonzero-mean extension. However, when multiplicative noise exists, the measurement model becomes nonlinear. Therefore, a new recursive structure for the innovation process needs to he developed to achieve a recursive filter.