Nonlinear Estimation Using Optimized Extension Based Multiple Conversion Approach with Generalized Conversion for Target Tracking

For estimation, minimum mean square error is one of the most widely accepted criteria. The optimal MMSE estimate is the posterior mean. For linear Gaussian systems, the posterior mean can be calculated easily. For nonlinear problems, it is hard to be obtained, although the posterior distribution can be solved by the joint distribution of the estimand and its measurement. Aim at this, the multiple conversion approach (MCA) uses several predesigned hypothesized distributions to match the true joint distribution. To match the truth better, the recently proposed optimized conversion extension (OCE) approach introduces one more distribution into the MCA. It has also proven that the MCA using the OCE outperforms the original one. However, practical nonlinear estimation problems are diverse. For a nonlinear problem, obtaining such an estimator which outperforms the existing estimators is hard. In this paper, considering the effectiveness of the recently proposed generalized conversion based filter (GCF) for conversions with high dimensions, we introduce it within the OCE framework. It is proven that the obtained new estimator called OCE-G can outperform the MCA using the original OCE and match the truth more sufficiently. Finally, a filtering algorithm using the OCE-G based on the interacting multiple conversion is proposed for dynamic problems. Compared with several popular nonlinear filters, a bearing-only filtering problem is used and simulated to demonstrate the effectiveness of the proposed approach and algorithm.