Angle-only filtering in 3D using modified spherical and log spherical coordinates

This paper considers the angle-only filtering problem in 3D using bearing and elevation angle measurements from a single maneuvering sensor. We develop continuous-discrete extended Kalman filter (EKF) based algorithms using modified spherical coordinates (MSC) and log spherical coordinates (LSC), where the dynamic and measurement models are described in continuous and discrete times, respectively. The predicted state estimate and covariance are calculated numerically by integrating a joint vector differential equation. Numerical results show that, while the discrete-time Cartesian EKF outperforms the proposed algorithms for highly accurate measurements, the new algorithms show superior performance as the measurement accuracy decreases. EKF-MSC and EKF-LSC have comparable performance for the examples examined.