Constrained modeling and state estimation have attracted much attention in recent years. This paper focuses on target motion modeling and tracking in road coordinates. An improved initialization method,which uses the optimal fusion of the position measurements in different directions,is presented for the constraint coordinate Kalman filter(CCKF). The CCKF is evaluated with a comprehensive comparison to the state-of-art linear equality constraint estimation methods. Numerical simulation results demonstrate the better performance of the CCKF. Then the interacting multiple model CCKF(IMM-CCKF) is proposed to manifest the advantages of the CCKF in complex motion modeling and state estimations. The effectiveness of the IMM-CCKF in maneuvering target tracking with spatial equality constraints is demonstrated by numerical experiments.
Tracking problem in spherical coordinates with range rate （Doppler） measurements, which would have errors correlated to the range measurement errors, is investigated in this paper. The converted Doppler measurements, constructed by the product of the Doppler measurements and range measurements, are used to replace the original Doppler measurements. A de-noising method based on an unbiased Kalman filter （KF） is proposed to reduce the converted Doppler measurement errors before updating the target states for the constant velocity （CV） model. The states from the de-noising filter are then combined with the Cartesian states from the converted measurement Kalman filter （CMKF） to produce final state estimates. The nonlinearity of the de-noising filter states are handled by expanding them around the Cartesian states from the CMKF in a Taylor series up to the second order term. In the mean time, the correlation between the two filters caused by the common range measurements is handled by a mini- mum mean squared error （MMSE） estimation-based method. These result in a new tracking filter, CMDN-EKF2. Monte Carlo simulations demonstrate that the proposed tracking filter can provide efficient and robust performance with a modest computa- tional cost.
