Square root parallel Kalman filtering using reduced-order local filters

The basic parallel Kalman filtering algorithms derived by H.R. Hashemipour et al. (IEEE Trans. Autom. Control. vol.33, p.88-94, 1988) are summarized and generalized to the case of reduced-order local filters. Measurement-update and time-update equations are provided for four implementations: the conventional covariance filter, the conventional information filter, the square-foot covariance filter, and the square-foot information filter. A special feature of the suggested architecture is the ability to accommodate parallel local filters that have a smaller state dimension than the global filter. The estimates and covariance or information matrices (or their square roots) from these reduced-order filters are collated at a central filter at each step to generate the full-size, globally optimal estimates and their associated error covariance or information matrices (or their square roots). Aspects of computational complexity and the ensuing tradeoff with communication are discussed