Kalman filtering for widely linear complex and quaternion valued bearings only tracking

Abstract

Bearings only target tracking is concerned with estimating the trajectory of an object from noise-corrupted bearing (phase) measurements. Traditionally this problem has been formulated as real valued for the Cartesian coordinate system or modified polar coordinate system. In this study, the authors introduce the bearings only tracking problem for the complex and quaternion domains to take advantage of the natural representation offered by these domains, for multivariate real signals, as well as the greater insights provided into the dynamics of tracking. Moreover, the authors introduce the augmented complex and quaternion extended Kalman filters for the modelling of second-order non-circular complex and quaternion valued signals, for which a widely linear model is shown to be more suitable than a strictly linear model.

A Journey From Improper Gaussian Signaling to Asymmetric Signaling

“…2) Estimation: While detection problems merely identify the presence or absence of improper complex signal, estimation problems include estimating the value of a parameter, or vector of parameters, from a sequence of measurements. Several engineering applications require complex-valued estimations, such as training neural networks [31], passive radar tracking [237], target tracking [238], power systems frequency estimation [18] and fault diagnosis [239] etc. From communication theory perspective, extraction of the transmitted information signal x from the received observations y after undergoing a system, namely channel, is sometimes carried out using estimation based on the likelihood p (y/x).…”

A Robust Recursive Filter for Nonlinear Systems with Correlated Noises, Packet Losses, and Multiplicative Noises

“…Meanwhile, the unknown prediction gain L does not exist in the literature [36,37], which will lead to the different estimation results. Subsequently, the packet losses are described by utilizing the diagonal matrix Σ in (2), which indicates that the different sensors have different failure rates. Since multiplicative noises, correlated additive noises, and packet losses are taken into account, the system (1)-(2) is more generalized to describe the realistic situations in engineering.…”

“…In recent years, the state estimation theory has received extensive attention in many fields of application, such as attitude estimation [1], target tracking [2], signal processing [3], and integrated navigation [4]. State estimation refers to a methodology that is used for estimating the state of a time-varying system through noisy measurements, which are different from other methods [5][6][7][8][9].…”

Iterated Modified Gain Extended Kalman Filter with Applications to Bearings Only Tracking

“…Some good principles for generating the observer maneuver are given in [4] and [5]. So far, most articles in the bearings only tracking field assumed the target moved with a constant velocity [6], [7], [8]. As for tracking a maneuvering target, very limited research has been published in the open literature.…”