推广的Pei-Radman特殊矩阵求逆及其应用

当矩阵的维数比较高的时候，该矩阵求逆就相当麻烦，且计算量很大。为了克服这个缺点，对于非对角元素相同，而对角元素是非对角阵元素加上一个常数的推广Pei-Radman矩阵，本文提出了求其逆的公式。将该求逆结果应用到带公共干扰噪声的多传感器的观测系统中，得到了基于加权最小二乘准则的融合观测即为所有传感器的观测的平均值，而融合观测的噪声为公共干扰噪声的方差加上所有传感器噪声方差的平均值。该算法能明显减少计算负担，提高融合效率，具有重要的物理意义和很大的实际应用价值。一个温度观测的仿真例子证明了推广的Pei-Radman特殊矩阵求逆算法的正确性，也说明了融合观测及其噪声的有效性。

The Inverse of Extended Pei-Radman Matrix and its Application

When the matrix has high dimension, the computational burden of the inversion is very large. In order to overcome this drawback, a new extended algorithm is presented for the inversion of the extended Pei-Radman matrix, which has same non-diagonal element and those diagonal element equals the non-diagonal element plus a constant. Based on the weighted least squares(WLS) method, this inversion result can be applied to the multi-sensor measurement fusion system with common disturbance noise, and obtain that the fused measurement is the average of all sensor measurement and the fused noise variance equals the common noise variance plus the average variance of every sensor measurement noise. This algorithm can obviously reduce the computational burden, and has important physical meaning and application value. An example for the temperature measurement is given, which proves the correctness of the inversion of the extended Pei-Radman matrix and verifies the validity of the fused measurement and the fused measurement noise.