Nonlinear Estimation by LMMSE-Based Estimation With Optimized Uncorrelated Augmentation

For nonlinear estimation, the linear minimum mean square error (LMMSE) estimator using the measurement augmented by its nonlinear conversion can achieve better performance than using the original measurement. The main reason is that the original measurement cannot be fully utilized by the LMMSE estimator in a linear way. To effectively extract additional measurement information which can be further utilized by a linear estimator, a nonlinear approach named uncorrelated conversion (UC) is proposed. The uncorrelated conversions of the measurement are uncorrelated with the measurement itself. Two specific approaches to generating UCs are proposed based on a Gaussian assumption and a reference distribution, respectively. Then a UC based filter (UCF) is proposed based on LMMSE estimation using the measurement augmented by its uncorrelated conversions. To minimize the mean square error of the overall estimate, an optimized UCF (OUCF) with an analytical form is proposed by optimizing the reference distribution based UCs. In the UCF, measurement augmentation can be continued using the proposed nonlinear UC approach, and all augmenting terms are uncorrelated under certain conditions. Thus, the performance of the UCF and the OUCF may be continually improved. Simulation results demonstrate the effectiveness of the proposed estimator compared with some popular nonlinear estimators.