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Linear fitting Kalman filter

机译：线性拟合卡尔曼滤波器

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摘要

Dynamic estimation in signal processing and target tracking often involves non-linear models. These non-linear models are usually linearised through the first-order Taylor approximation in estimation process. However, the error generated by the first-order Taylor approximation is not negligible when the non-linearity of a model is high or the input error is large. This study proposes a new linearisation method through minimising the error between a non-linear function and its linear approximation. A weighted least squares (WLS) algorithm is developed to estimate a linear fitting (LF) function based on the sigma points of the random variable in non-linear transformation. A linear fitting Kalman filter (LKF) is developed based on this principle. The accuracy of the LF transform is analysed using the Kullback–Leibler (KL) distance. The results show that the LF transform has less KL distance to the true distribution compared with the first-order Taylor approximation. To evaluate the estimation performance, simulations are conducted and the results are compared with those of extended Kalman filter (EKF) and unscented Kalman filter (UKF). The results demonstrate that the LKF provides better accuracy than the EKF, and has similar accuracy to the UKF with lower computational cost.
机译：信号处理和目标跟踪中的动态估计通常涉及非线性模型。这些非线性模型通常在估计过程中通过一阶泰勒近似线性化。但是，当模型的非线性较高或输入误差较大时，由一阶泰勒近似法生成的误差不能忽略。这项研究提出了一种通过最小化非线性函数与其线性逼近之间的误差的新线性化方法。开发了加权最小二乘（WLS）算法，以基于非线性变换中随机变量的sigma点估计线性拟合（LF）函数。基于此原理，开发了线性拟合卡尔曼滤波器（LKF）。使用Kullback-Leibler（KL）距离分析LF变换的准确性。结果表明，与一阶泰勒近似相比，LF变换与真实分布的KL距离较小。为了评估估计性能，进行了仿真，并将结果与​​扩展卡尔曼滤波器（EKF）和无味卡尔曼滤波器（UKF）进行了比较。结果表明，LKF比EKF具有更好的精度，并且具有与UKF相似的精度，且计算成本较低。

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