噪声相关非线性系统加权观测融合估计算法

Weighted measurement fusion estimation algorithm for nonlinear system with correlated noises

为了提高非线性系统的估计精度,基于Gauss-Hermite逼近以及加权最小二乘法,提出了噪声相关非线性系统加权观测融合容积卡尔曼滤波器(WMF-CKF)。利用去相关方法去除相关噪声之间的相关性,将原系统转化为噪声互相独立的非线性系统。进而采用Gauss-Hermite逼近方法对多传感器观测数据进行数据压缩。为了降低计算负担,本文采用离线方式计算加权系数矩阵,并最终实现了多传感器非线性系统加权观测融合。与传统的最优集中式融合(CMF)算法相比,本文所提出的融合算法在精度上略低,但可以明显减少计算负担。所提融合算法为非线性多传感器融合估计问题提供了一种有效解决方法。一个带4传感器噪声相关非线性系统的仿真例子说明了算法的正确性。

In order to improve the estimation precision of nonlinear systems, based on Gauss-Hermite approximation and weighted least square method, a weighted measurement fusion cubature Kalman filter(WMF-CKF) for nonlinear systems with correlated noises is proposed.Decorrelation method is used to remove the correlation between the correlated noises, then transforms the original system into a non-linear system with independent noises.And then the Gauss-Hermite(G-H) approximation method is used to compress the multi-sensor measurement data.In order to reduce the computational burden, the weighting coefficient matrix is calculated in an offline manner, and finally the weighted measurement fusion of multi-sensor nonlinear system is realized.Compared with the traditional optimal centralized fusion(CMF) algorithm, the proposed fusion algorithm is slightly lower in precision, but can significantly reduce the computational burden.The fusion algorithm provides an effective solution to the nonlinear multi-sensor fusion estimation problem.A simulation example of a non-linear system with 4-sensor noise correlation shows the correctness of the algorithm.