摘要
研究了带衰减观测和随机传感器偏差的多传感器AR信号融合辨识与估计问题.首先,将AR模型转换为状态空间模型,将状态和传感器偏差进行增广得到一个等价的状态空间模型,给出了当系统模型精确已知下的最优滤波算法.然后,当AR信号参数、衰减观测随机变量的数学期望和方差未知时,提出了两段辨识算法.第一段采用递推增广最小二乘法(RELS)得到AR信号参数的局部估值,并利用按矩阵加权线性无偏最小方差最优估计准则得到AR信号参数的融合估值.第二段利用相关函数得到虚拟观测噪声方差、衰减观测随机变量的数学期望和方差的估值.最后,将每时刻辨识的未知参数代入最优滤波算法中,获得分布式加权自校正融合滤波算法.分析了算法的收敛性.仿真验证了算法的有效性.
This paper studies the problem of fusion identification and estimation for multi-sensor autoregressive(AR) signals with fading measurements and stochastic sensor biases.First,the AR model is transformed into an equivalent state space model by extending the state and sensor bias,and the optimal filtering algorithms are given when the system model is accurately known.When parameters of AR model,and mathematical expectations and variances of random variables describing the phenomena of fading measurements are unknown,a two-stage identification algorithm is presented.In the first stage,the recursive extend least squares(RELS) algorithm is applied to get local estimates of AR parameters.Then,fusion estimates of AR model parameters are obtained by using matrix-weighted optimal fusion estimation criteria in the linear unbiased minimum variance sense.In the second stage,correlation functions are applied to obtain estimates of variances of virtual measurement noises and mathematical expectations and variances of fading measurement random variables.Finally,by substituting identified unknown parameters into optimal filtering algorithms at each moment,a distributed weighted self-tuning fusion filtering algorithm is obtained.Convergence of algorithms is analyzed.A simulation example shows the effectiveness of the proposed algorithms.
作者
万涛
孙书利
WAN Tao;SUN Shuli(School of Electronic Engineering,Heilongjiang University,Harbin 150080)
出处
《系统科学与数学》
CSCD
北大核心
2021年第1期1-16,共16页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(61573132)资助课题。
关键词
衰减观测
随机传感器偏差
多传感器系统
AR信号
融合辨识与估计
Fading measurement
stochastic sensor bias
multi-sensor system
AR signal
fusion identification and estimation
