Motion Modeling and State Estimation in Range-Squared Coordinate

In some target tracking applications, angle measurements are absent due to sensor characteristics, which makes Cartesian states unobservable for a single stationary sensor. When multi-sensor target tracking techniques with only range or Doppler measurements are applied to produce Cartesian state estimates, their performance and efficiency can be benefited from accurate range and Doppler estimates obtained from single sensors. This paper investigates the range and Doppler estimation problem based on motion modeling in range-squared coordinate considering range-squared as a generic coordinate. A pseudostate vector consisting of range squared and its derivatives is defined to completely summarize the dynamic of the Cartesian nearly constant velocity (NCV) motion and it is found time evolution of the pseudostate is linear based on the methodology of state space representation. To estimate the pseudostate from range-Doppler or range-only measurements, a recursive filter is developed using the decorrelated unbiased converted measurement (DUCM) method. Finally, the pseudostate estimates in the range-squared coordinate are converted into the range coordinate using the scaled unscented transformation (SUT) method to produce range and Doppler estimates. Although the conversion is nonlinear, it is performed outside the filtering recursions without propagating nonlinearity approximation errors in the filtering recursions. Numerical experiments with various conditions of measurements demonstrate the superior performance benefits from the proposed accurate linear state equation and estimation method.