Method of Principal Informative Components in Problems of Statistical Measurements of Signal Parameters (Systematic Review)

摘要

Abstract The method of Principal Informative Components (PIC) is presented for problems of statistical measurements, where the signal to be measured cannot be directly observed. Such situations include image reconstruction, system identification, communication channel reversal, media tomography, etc. The common feature of such problems, usually, is instability of their solutions to small variations of initial data that generally require the attraction of special methods of regularization. The basic principle of PIC method consists in employing decomposition of signals in special bases that were formed from eigenvectors of Fischer’s information operator. These bases are related to the method of Principal Components Analysis (PCA), which is well known in statistics, however, they have a somewhat different meaning as compared to the PCA method. The review indicates that by using the special procedures for selecting coordinate vectors, it is possible, first, to guarantee the signal estimation stability to unpredictable factors of problem and, second, to ensure a significant reduction of total measurement error as compared to the “direct” signal estimation, i.e., without the use of basis notions. The review presents a substantiation of PIC method application for problems of linear and nonlinear estimation. The composite technique of coordinate basis optimization is also considered that combines advantages of the physical approach (obviousness and effectiveness) with advantages of statistically informative approach (minimization of statistical errors). The specified technique is based on projecting the arbitrary coordinate basis on PIC subspace. As a result, the range of possible fluctuations of signal estimation is reduced and the upper bound of statistical error of signal measurement is lowered. Some numerical estimates of the PIC method efficiency are given using the example of problem of medium acoustic tomography that confirms the general theoretical conclusions. The review includes the analysis of some information technologies, where the ideas of PIC method hold a good promise for practical application. In particular, it is suggested that one of such promising fields can be MIMO systems that play an important part in 5G wireless access systems.