Two-error covariance analysis algorithms for suboptimal decentralized Kalman filters

Abstract

In the design of a decentralized Kalman filter, simplified models of both the system dynamics and the measurement dynamics are used within the local filters and frequently a suboptimal combining algorithm is used within the central filter to obtain a computational advantage. In this case, the root-mean-square estimation error based on a central filter covariance matrix will not be representative of the true estimation error incurred. In fact, the suboptimal decentralized Kalman filter may diverge when used in an actual implementation if one does not consider the performance of the filter design as compared with the true model and an associated optimal combining algorithm. At present, the behavior of such a suboptimal decentralized Kalman filter can be evaluated only via a more expensive Monte Carlo simulation. This paper provides the missing error covariance analysis algorithms, which can be used to computationally evaluate the suboptimal decentralized Kalman filter by determining the true root-mean-square estimation error of a global estimate.