Multiple Conversions of Measurements for Nonlinear Estimation

A multiple conversion approach (MCA) to nonlinear estimation is proposed in this paper. It jointly considers multiple hypotheses on the joint distribution of the quantity to be estimated and its measurement. The overall MCA estimate is a probabilistically weighted sum of the hypothesis conditional estimates. To describe the hypothesized joint distributions used to match the truth, a general distribution form characterized by a (linear or nonlinear) measurement conversion is found. This form is more general than Gaussian and includes Gaussian as a special case. Moreover, the minimum mean square error (MMSE) optimal estimate, given a hypothesized distribution in this form, is simply the linear MMSE (LMMSE) estimate using the converted measurement. LMMSE-based estimators, including the original LMMSE estimator and its generalization—the recently proposed uncorrelated conversion based filter—can all be incorporated into the MCA framework. Given a nonlinear problem, a specific form of the hypothesized distribution can be optimally obtained by quadratic programming using the information in the nonlinear measurement function and the measurement conversion. Then, the MCA estimate can be obtained easily. For dynamic problems, an interacting multiple conversion algorithm is proposed for recursive estimation. The MCA approach has a simple and flexible structure and takes advantage of multiple LMMSE-based nonlinear estimators. The overall estimates are obtained adaptively depending on the performance of the candidate estimators. Simulation results demonstrate the effectiveness of the proposed approach compared with other nonlinear filters.

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