Hyperbolic-SVD-Based Square-Root Unscented Kalman Filters in Continuous-Discrete Target Tracking Scenarios

This article aims at presenting novel square-root unscented Kalman filters (UKFs) for treating various continuous-discrete nonlinear stochastic systems, including target tracking scenarios. These new methods are grounded in the commonly used singular value decomposition (SVD), that is, they propagate not the covariance matrix itself but its SVD factors instead. The SVD based on orthogonal transforms is applicable to any UKF with only nonnegative weights, whereas the remaining ones, which can enjoy negative weights as well, are treated by means of the hyperbolic SVD based on J-orthogonal transforms. The filters constructed are presented in a concise algorithmic form, which is convenient for practical utilization. Their two particular versions grounded in the classical and cubature UKF parameterizations and derived with use of the It\hat{\rm o}-Taylor discretization are examined in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in the presence of ill-conditioned measurements.