Some problems in statistics of random processes arising in signal and image processes.

摘要

First, problem of sequential detection of targets in distributed systems is investigated. A multisensor system is considered in which each sensor performs sequential detection of a target. Binary decisions are transmitted to a center, which fuses them to improve performance of the system. Sensors represent multichannel systems with each one having possibly different number of channels. Sequential detection of a target in each sensor is done by implementing a generalized Wald's sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows to fix the false alarm rate and the rate of missed detection at specified levels. Asymptotic performance of this sequential detection procedure is presented and it is shown that this procedure is asymptotically optimal for general statistical models in the sense of minimizing the expected sample size when the probabilities of erroneous decisions are small. The optimal non-sequential fusion rule is constructed. This rule waits until local decisions from all sensors are received and fuses them. It is optimal in the sense of maximizing the probability of target detection for a fixed probability of false alarm. Performance of the system is illustrated by an example of detecting a deterministic signal in correlated (colored) Gaussian noise. Results of theoretical analysis and Monte Carlo experiment are provided. Results allow us to conclude that the use of the sequential detection algorithm substantially reduces required resources of the system compared to the best non-sequential algorithm.; Second problem is nonlinear filtering problem in pharmacokinetics. System is assumed to be nonlinear in dynamics and observations. General form of dynamics and observations are known with parameters driving them located on known discreet support points in parameter space. Parameters are allowed switching from one support point to another at any time. Both, dynamics and observations contain noise. Problem is complicated by rare availability of observations. Theoretically optimal approach (in the sense of utilizing available information) is proposed. Examples representing both, simulated and real data problems are given. Results show performance superior to both Kalman filter and IMM.