A polynomial approximation algorithm for real-time maximum-likelihood estimation
IEEE Transactions on Signal Processing
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A general linear and quasi-efficient estimator is presented which is an optimal (for a given criterion) approximation of the maximum likelihood estimator (MLE with nonlinear measurement equation) when the measurements are corrupted by a Gaussian noise. This approach consists of choosing a particular state vector which characterizes the signal. The model is defined by special values of the signal at sample times which are the roots of an orthogonal Lagrange polynomial. It is rigorously established that the linear estimator is quasi-unbiased and has a covariance matrix which is close to the Cramer-Rao lower bound. A practical algorithm is derived, and it is shown to be very easy to implement. This method is successfully applied to the problem of target motion analysis (TMA).