针对一类非高斯噪声环境下固定点平滑估计问题,设计一种使用最大相关熵准则作为最优估计标准的平滑估计算法,称之为固定点最大相关熵平滑估计(fixed-point maximum correntropy smoother,FP-MCS).首先基于矩阵变换给出最大相关熵Kalman滤波的新表达形式;然后以此为基础,引入新的状态来扩展系统,并推导出固定点最大相关熵平滑估计的在线迭代方程;进一步比较平滑前后状态估计误差协方差,从理论上分析算法的性能改进,同时比较其计算复杂度;最后通过算例验证所设计的算法在非高斯混合噪声干扰下的有效性和优越性.
Fixed-point smoothing estimation algorithm based on information entropy criterion in non-Gaussian environment
For fixed-point smoothing estimation problems in the non-Gaussian environment,this paper proposes a smoothing estimation algorithm based on maximum correntropy as the optimal criterion,which is called fixed-point maximum correntropy smoother(FP-MCS).First,an alternate form of maximum correntropy Kalman filter(MCKF)is given based on matrix transformation.Then,new states are introduced to augment the system,and online iterative equations of the proposed FP-MCS are derived through the new MCKF form.Furthermore,state estimation error covariances are compared before and after smoothing,and performance improvement of the proposed FP-MCS is analyzed theoretically.Meanwhile,its computational complexity is also compared with other algorithms.Finally,an illustrative example is presented to verify the effectiveness and superiority of the proposed FP-MCS in the non-Gaussian mixture noise environment.
state estimationfixed-point smoothingKalman filtermaximum correntropy criterionnon-Gaussian noise
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