Computation of the factorized error covariance of the difference between correlated estimators

In estimating the states of a discrete linear system, it is not uncommon to have several estimates available, based on different data sets, where each estimate is optimal for the set of data reduced to form it. When the data sets overlap, with individual observations contained in more than one set (so that the same observations are replicated, not just separate observations of the same state), consistency of the estimates must be judged in a way that accounts for the common observations. Two techniques for computing the error covariance of the difference between such estimates are discussed. One algorithm is based upon post-processing of the Kalman gain profiles to sequentially compute the UD factors of the covariance of the relative error. Another method based upon SRIF (square root information filter) algorithms can be applied to relative error analysis of least squares parameter estimation problems. In the absence of process noise, the SRIF method is computationally more efficient and more flexible than the Kalman gain method. The relative error covariance algorithms are applied to a Venus orbiter simulation and their performances are compared.