Parallel and Sequential Block Kalman Filtering

Two sets of block Kalman filtering equations are derived that differ in the manner of generating the initial and updated estimates. Parallel and sequential schemes for generating these estimates are adopted. It is shown that the parallel implementation inherently leads to a block Kalman estimator which provides filtered estimates at the vector (block) level and fixed lag smoothed estimates at the sample level. The sequential implementation scheme, on the other hand, generates the estimates of each sample recursively, leading naturally to a scalar (filter) estimator. These scalar estimates are arranged in a vector form, resulting in a block estimator which solely generates filtered estimates both at the vector and sample levels. Simulation results on a speech signal are also presented which indicate the advantages of the sequential block Kalman filter.