Nonlinear estimation by linear estimation with augmentation of uncorrelated conversion

For nonlinear estimation, the linear minimum mean square error (LMMSE) estimator using the measurement augmented by a nonlinear conversion of it can achieve better performance than the LMMSE estimator 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 symmetrized reference distribution, respectively. Then a UC based filter (UCF) is proposed based on LMMSE estimation using the measurement augmented by its uncorrelated conversions. In UCF, the process of measurement augmentation can be continued using the proposed nonlinear UC approach, and all augmenting terms are also uncorrelated under the corresponding conditions. Thus, the nonlinear estimation performance of the UCF has the potential to be continually improved. Simulation results demonstrate the effectiveness of the proposed estimator compared with some popular nonlinear estimators.