Linear Covariance Analysis and Epoch State Estimators

Abstract

This paper extends in two directions the results of prior work on generalized linear covariance analysis of both batch least-squares and sequential estimators. The first is an improved treatment of process noise in the batch, or epoch state, estimator with an epoch time that may be later than some or all of the measurements in the batch. The second is to account for process noise in specifying the gains in the epoch state estimator.We establish the conditions under which the latter estimator is equivalent to the Kalman filter.

Erratum to: Generalized Linear Covariance Analysis

“…If t * is later than some or all of the measurements, however, it might be more reasonable to assume that e + a * includes the process noise accumulated between the beginning of the observation span and t * , in which case it has nontrivial correlations with e + w * . This modifies the manner in which process noise appears in the covariance analysis of the batch estimator [1].…”