ABSTRACT
The problem of target position and velocity estimation in active and passive MSRSs is a typical problem of multidimensional parameter estimation. It is accepted to characterize the accuracy of multidimensional estimators with the help of a vector of biases and an Error Covariance Matrix (ECM) 1 . Explicit analytical expressions for direct ECM calculation for specific estimation algorithms are usually difficult to derive. In those cases where ECM calculations are necessary (see, for instance, Section 13.2) computer simulation is to be used. At the same time it is known that maximum likelihood estimates are asymptotically unbiased and efficient under certain, usually satisfied, regularity conditions (e.g., [27]). Therefore, analysis of the ECM for efficient estimates is widely used for the accuracy analysis of maximum likelihood estimates of the same parameters, especially when requirements for estimation accuracy are sufficiently high so that the conditions of asymptotic efficiency are approximately satisfied. An ECM of efficient estimates presents the Cramér–Rao lower bound for estimate errors. It is a reliable approximation of attainable errors when the observation time is long enough (or, more correctly, when the product of the observation time by the signal bandwidth is large enough). The advantage of such an approach is that the ECM of efficient estimates is the inverse of the Fisher information matrix (FIM), so that it determines the maximum attainable accuracy inherent in Likelihood Functions or Functionals (LF) of estimated parameters regardless of specific estimation algorithms.
