标题： 一种广义的转换测量卡尔曼滤波器 显示英文标题

标题： A Generalized Converted Measurement Kalman Filter

摘要： 本报告推导了一个广义的转换测量卡尔曼滤波器，适用于具有线性状态方程和非线性测量方程的滤波问题，其中状态和测量坐标系统之间存在双射映射。 对于这些问题，开发了一种将观测测量及其协方差矩阵从测量坐标映射到状态坐标的程序，使得转换后的测量无偏，并且转换后的测量协方差矩阵与状态和观测测量无关。 在未观测到所有测量坐标的情况下，引入这些坐标的预测测量作为替代，并通过在转换测量逆协方差矩阵的相应行和列上进行信息置零操作来减轻这些测量对滤波器的影响。 滤波器性能在两个著名的目标跟踪问题上进行了演示，并与标准扩展卡尔曼滤波器和无迹卡尔曼滤波器在这些问题上的性能进行了比较。 这些例子表明，所提出的滤波器在均方误差、一致性以及轨迹丢失方面优于扩展卡尔曼滤波器或无迹卡尔曼滤波器。 显示英文摘要

摘要： This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and measurement coordinate systems. For these problems, a procedure is developed for mapping the observed measurements and their covariance matrices from measurement coordinates to state coordinates, such that the converted measurements are unbiased and the converted measurement covariance matrices are independent of the states and observed measurements. In cases where not all measurement coordinates are observed, predicted measurements of these coordinates are introduced as substitutes, and the impact of these measurements on the filter is mitigated by an information zeroing operation on the corresponding rows and columns of the converted measurement inverse-covariance matrix. Filter performance is demonstrated on two well-known target-tracking problems and is compared with the performance of the standard extended and unscented Kalman filters for these problems. These examples show the proposed filter obtains lower mean squared error, better consistency, and less track loss than either the extended Kalman filter or the unscented Kalman filter.