基于区间估计的最小二乘法在卡尔曼滤波中的应用研究

Application of least squares based on interval estimation in Kalman filter

卡尔曼滤波是以最小均方误差为估计的最佳准则来寻求一套递推估计的算法。最小二乘估计是最常用的估计理论,它能保证每个偏差都较小,而区间估计反映误差范围使用起来把握大,但它无法估计单点的误差。针对滤波精确度问题,为使估计值误差达到最小,滤波精确度提高,提出了采用区间估计与最小二乘法估计2种策略结合的新方法,充分利用二者优势,求得观测点与估计点的距离的平方和最小值,对目标函数多次拟合。仿真实验结果表明,区间估计最小二乘卡尔曼算法大大提高滤波精确度,与区间卡尔曼滤波相比,它有较小的误差,滤波性能也得到很好的提升,极大的降低了噪声在滤波过程中干扰,在以后实际工作中将得到很大应用。

Kalman filter is one of algorithms to seek a set of recursive estimation based on minimum mean square error estimation rule. Least squares estimation is the most commonly used estimation theory, it can ensure that every deviation will be small, but the interval estimation reflects the error range. It is well be used. But it can＇t estimate the error of a point. In order to make the estimate error minimum and improve filtering accuracy, this article combines interval estimation and least squares estimate and makes full use of their advantages which can get minimum value of distance square sum between observation points and estimation points. big error, greatly improves the Kalman filtering accuracy and the future, it will be used in more works. The simulation results show that the new method reduces a reduces the noise interference in the process of filtering. In