Parametre Belirsizliği Altında Çoklu Algılayıcılara Ait Bağımlı Ölçümlerle Hipotez Sınaması

Abstract

extensively in modelling of dependent random variables. Joint probability dist-ribution of data using copula theorem has been defined parametrically. Thereare numerous advantages of copula function usage in modelling of joint pro-bability distribution of dependent data. Major one is the separation of marginaldistribution and dependence structure in data from each other. Joint probabi-lity distribution functions (PDF) that is not in closed form, could also be repre-sented using copula functions. In this thesis, Gaussian and Student’s t copulafunctions has been taken into account.The dependence between consecutive measurements are modelled in Marko-vian chains.It has been assumed that, marginal distributions of sensor measurements andcopula functions have unknown deterministic parameters. It has been assumedthat in data obtained from sensor measurements, marginal probability densityfunctions (PDF) is known parametrically but joint probability distribution func-tion is not known. The unknown parameters of copula functions and marginaldistributions have been estimated and state sequence have been detected un-der parameter uncertainty using the joint detection and estimation method.The classical Viterbi algorithm, the optimal recursive solution in estimation ofstate sequence which is formed up of finite state Markovian processes, cannotbe used directly due to unknown parameters. The estimation of unknown pa-rameters using Per-Survivor Processing algorithm, is also embedded into thestructure of the the Viterbi algorithm. Therefore, state sequence and unknownparameters have been estimated simultaneously.To solve the problem taken into account in this thesis, it has been observedthat a method based on "Expectation Maximization (EM)" has been developedin literature [1]. According to present EM algorithm solution [1] in literature,based on detecting probable state sequence with unknown parameters withdependent observations measured of multiple sensors, improvements in com-putational complexity have been accomplished. At the same time, this methodmakes detections offline, using all measurements during observation interval. In this thesis, state of nature detection are made online manner each insant of time. In other solutions, presented in literature, although sometimes not taken into account in models and sometimes taken into account in models, not being used extensively in solutions due to high computational complexity requirement, the dependence in time between sensor measurements has been ignored and an effective solution that takes into account the time dependence together with spatial dependence between sensors has not been presented. In this thesis, for the case where dependence between sensors and dependence in time are teken into account together, a joint detection and estimation method that has minimum computational complexity and asymptotically optimal solution has been developed.