Converted Measurement Filter Algorithm Based on Second-Order Taylor Expansion

‍ ‍Target tracking is a crucial function of radars. Owing to the nonlinear relationship between the radar measurements obtained in a polar or spherical coordinate system and the motion state of the target in a Cartesian coordinate system， the algorithm fails to update the motion state of the target directly according to the measurement information during target tracking. Therefore， this study proposes converting a measurement filtering algorithm based on second-order Taylor expansion to solve this nonlinear problem caused by different coordinates between the measurements and the state of the target. The statistical characteristics of the converted measurement error were analyzed by Taylor series expansion. Nonetheless， since the unbiased converted measurements and the statistical characteristics of the converted measurement error were all related to the true range and angle information of the target， which cannot be obtained in practice， the measurement information obtained by the radar was considered to substitute for the true information in the corresponding expression. However， this substitution method makes the statistical error characteristics of the converted measurements similar to the measurements obtained by the radar at each moment. Therefore， a converted measurement method was proposed to calculate the statistical characteristics of the converted measurement error based on prediction information. When the model in the equation of state matches the target motion pattern and the measurement noise is large， the predicted information is often more accurate than the original measurement information. The errors of the first-order expansion term of the second-order Taylor series expansion were considered to improve the consistency of converted measurements and converted error covariance， and a converted measurement method was proposed to calculate the statistical characteristics of conversion error based on the predicted information. Based on the predicted information， the proposed method converted the original measurements to the Cartesian coordinate system based on second-order Taylor series expansion and calculated the statistical characteristics of the conversion error. The truncation error of the conversion process was reduced by the proposed method via second-order Taylor approximation， which essentially uses the higher-order linear model to improve the performance of the algorithm by fitting the nonlinear model. Combining the proposed converted measurement method with the classic Kalman filtering framework， a Kalman filtering algorithm with predicted information based on second-order Taylor expansion was proposed to track the non-maneuvering targets. In addition， considering the maneuvering characteristics of the target， the proposed algorithm was extended with the improved interactive multiple-model filter framework， and the estimated state of the maneuvering target was obtained by fusing the estimation results of multiple sub-model filters. The simulation results show that the former algorithm has better tracking performance than existing filtering algorithms， and the estimated state of the target is more consistent with the covariance of the estimation error； that is， its credibility is higher， and the complexity of the proposed algorithm is lower. The latter algorithm can also track maneuvering targets effectively and has better tracking performance than the compared methods.