Novel pseudo-linear Kalman filtering for 3D angle-only tracking in the presence of observer’s location errors

Abstract

This paper presents novel pseudo-linear Kalman filtering algorithms for three-dimensional (3D) angle-only tracking (AOT) in the presence of observer’s locations perturbed by random noises. These random observer’s location errors (OLEs) seriously deteriorate the filtering precision, since the additional errors are introduced into the angle measurements when the noisy observer location is directly used to estimate the target state of interest. A new pseudo-linear measurement model is firstly constructed in the presence of OLEs, and the first two-order statistical moments of the pseudo-linear measurement noises are analyzed conditioned on the exact observer location. Then, on the premise of deriving the azimuth and elevation errors caused by OLEs and re-analyzing the first two-order statistical moments of the pseudo-linear measurement noises conditioned on the noisy observer location, a novel pseudo-linear Kalman filter in the presence of OLEs (abbreviated as OPKF) is put forward. A closed-form bias estimate of this proposed OPKF is further derived recursively, and the corresponding bias-compensated and instrumental variable-based pseudo-linear Kalman filters in the presence of OLEs are finally designed to improve filtering precision. The advantages of filtering precision of the proposed method over the existing pseudo-linear Kaman filter and its variants are demonstrated by an example of 3D AOT in the presence of OLEs, in terms of different levels of sensor accuracy and observer’s location errors.