基于加权最小二乘的卡尔曼滤波算法

Weighted Minimum Mean Square Kalman Filter

为了将卡尔曼滤波(KF)应用于非线性系统中,利用了离散采样点将非线性模型线性化。通过加权最小二乘原理,得到近似的线性化模型,再将KF算法应用于这个线性模型中。结果表明,加权最小二乘与KF结合的方法在非线性模型中的计算结果同扩展卡尔曼滤波(EKF)算法接近,且不需要EKF那样求偏导就能很容易地应用到非线性系统中。这种方法实现容易,预测可靠,具有实际应用的价值。

In order to use Kalman Filter （KF） in nonlinear systems,a new method was proposed. Using the principle that a set of discretely sampled points can be used to form a linear system,the estimator yields performance equivalent to the Extended Kalman Filter （EKF） for nonlinear systems and can be elegantly used to nonlinear systems without the differential steps required by the EKF. We argue that the ease of implementation and more accurate estimation features of the new filter recommend its use in applications.