多源观测逆问题的多尺度分布式分层求解算法

针对多源观测逆问题求解时所需的计算量过大这问题，该文给出了多源观测逆问题的一种多尺度分布式分层求解算法。其基本思想是：首先，对各传感器上采集到的观测数据分别进行多尺度分解；其次，基于每个传感器的观测信息，得到目标信号的小波变换系数的局部最优估计值；然后，基于相对误差协方差矩阵提供的信息，在每个尺度上将目标信号的小波系数或最粗尺度系数的局部估计值进行融合；最后，做小波逆变换，得到目标信号基于全局信息的融合估计值。采用该算法求解多源观测逆问题既能得到与采用集中式求解算法相当的估计效果，又能有效地降低求解所需的计算量，进一步增强算法的可实施性。

The Multi-scale Distributed Algorithm for Solving Inverse Problem with Multiple Observation Sources

In this paper, a multiscale distributed hierarchical algorithm is developed to solve the computational complexity in inverse problem with multiple observation sources.Firstly, algorithm implements wavelet transform respectively on the object signal data obtained from multiple observation processes. Secondty, the wavelet transform coefficients are estimated about object signal using the data from each sensor. Thirdty, all local estimates are efficiently fused based on the information provided by relative error covariance matrix, in order to get a global-information-based estimate of the wavelet transform coefficients with the object signal. Fourthty, the inverse wavelet transform is performed on the scaling coefficients at the coarsest scale and the wavelet coefficients at all scales to obtain the global-information-based estimator. Finally, the performance of the algorithm is evaluated with respect to the RECM-based criterion. It is comcluded that the distributed hierarchical fusion algorithm can not only result in an estimator comparable to that of the method of using central fusion algorithm with relatively light computational load, but also enhance the practicability of new algorithm.