Linear estimation with transformed measurement for nonlinear estimation


The linear minimum mean-sq. error (LMMSE) estimation plays an important role in nonlinear estimation. It's the most effective of all estimators that are linear within the measurement. But, it may not perform well for a highly nonlinear drawback. A generalized linear estimation framework, specifically, linear in remodel (LIT) estimation, is proposed during this work. It employs a measurement remodel operate (MTF) and finds the most effective estimator among all estimators that are linear in MTF, rather than within the measurement itself. The performance of LIT estimation with a proper MTF will be superior to LMMSE estimation because of the good thing about a more acceptable or larger candidate set of estimators determined by the MTF (compared to the set of all linear estimators in LMMSE estimation). Since systematic procedures for constructing an MTF that guarantees enhanced performance for the overall case are tough to provide, we have a tendency to provide several style guidelines, that are illustrated by a numerical example. Further, almost like LMMSE estimation, moments involved in LIT estimation are troublesome to compute analytically normally. Fortunately, many numerical approximations for LMMSE estimation also are applicable to LIT estimation. Approximation of LIT estimation primarily based on the Gauss-Hermite quadrature is presented. Our LIT estimation is demonstrated by applications to target tracking. Its performance is compared with LMMSE estimation by Monte Carlo simulations.

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