Generalized-Conversion-Based Nonlinear Filtering Using Deterministic Sampling for Target Tracking

For nonlinear filtering, the linear minimum mean square error (LMMSE) estimation is popular. An LMMSE-based estimator using a measurement conversion can outperform the LMMSE estimator using the original measurement. However, to optimally obtain both the dimension and the form of such a conversion is difficult because this involves functional optimization. To solve this problem, this article proposes a generalized-conversion-based filter (GCF) using deterministic sampling (DS). Being an LMMSE-based estimator using a general conversion of the measurement, the estimation performance of the GCF depends only on the conversion-related moments, which are calculated using DS. A constraint on the conversion is used to reduce possible evaluation errors of using a DS method to calculate those moments. The GCF optimizes the moments by obtaining both the optimal dimension and the sample points of the conversion rather than the specific form of it. Then, the final form of the GCF is analytically obtained. For tracking of multiple or maneuvering targets, the likelihood based on the proposed GCF is also derived, and it can be calculated using the obtained conversion sample also in an analytical form. Simulation results demonstrate the effectiveness of the GCF compared with some popular and recently proposed nonlinear estimators, including the LMMSE estimator and existing conversion-based filters.

I. Introduction

Practical estimation problems are always nonlinear. An estimator or filter infers a quantity from its measurements corrupted by noise. Nonlinear estimators and filters are widely applied in many fields, e.g., navigation, tracking, and guidance systems. For nonlinear estimation, minimum mean square error (MMSE) is a popular criterion. The posterior mean is the optimal MMSE estimate [4]. For linear Gaussian problems, the Kalman filter (KF) [16] is the MMSE estimator. For nonlinear problems, obtaining the posterior mean is difficult. Approximating the posterior distribution using the sequential Monte Carlo method, a class of estimators was proposed [7], [25]. In this article, we consider only point estimators, which directly estimate the quantity without obtaining its posterior distribution, since they may be simple and adequate for many practical applications [17].