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

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.