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This thesis presents the prediction algorithm for the price of the share of risky asset. The price of the share is presented by dynamic model and observation is presented by the measurement model. Dynamic model is derived by using Stochastic Calculus. The algorithm is simulated by using Matlab.

Chaotically modulated signals are used in various engineering areas such as communication systems, signal processing applications, automatic control systems. Because chaotically modulated signal sequences are broadband and noise-like signals, they are used to carry binary signals especially in secure communication systems. In this thesis, a target tracking problem under interference at chaotic communication systems is investigated. Simulating the chaotic communication system, noise-like signal sequences are generated to carry binary signals. These signal sequences are affected by Gaussian channel noise and interference while passing through the communication channel. At the receiver side, target tracking is performed using Optimum Decoding Based Smoothing Algorithm. The estimation performances of optimum decoding based smoothing algorithm at one dimensional chaotic systems and nonlinear chaotic algorithm map are presented and compared with the performance of the Extended Kalman Filter application.

This thesis considers a communication system with chaotic modulation. Noise-like signals are generated by chaotic systems with different parameters to modulate binary digital signals. Demodulation is performed by both the Extended Kalman Filter (EKF) and Optimum Decoding Based Smoothing Algorithm (ODSA). Simulations are performed using both of these algorithms for different parameters affecting the performance of the communication system. Simulation results of these algorithms are compared.

A white Gaussian noise measurement model is widely used in target tracking problem formulation. In practice, the measurement noise may not be white. This phenomenon is due to the scintillation of the target. In many radar systems, the measurement frequency is high enough so that the correlation cannot be ignored without degrading tracking performance. In this thesis, target tracking problem with correlated measurement noise is considered. The correlated measurement noise is modeled by a first-order Markov model. The effect of correlation is thought as interference, and Optimum Decoding Based Smoothing Algorithm is applied. For linear models, the estimation performances of Optimum Decoding Based Smoothing Algorithm are compared with the performances of Alpha-Beta Filter Algorithm. For nonlinear models, the estimation performances of Optimum Decoding Based Smoothing Algorithm are compared with the performances of Extended Kalman Filter by performing various simulations.

This thesis analyzes the process of deblurring of degraded images generated by space-variant nonlinear image systems with Gaussian observation noise. The restoration of blurred images is performed by using two methods / a modified version of the Optimum Decoding Based Smoothing Algorithm and the Bootstrap Filter Algorithm which is a version of Particle Filtering methods. A computer software called MATLAB is used for performing the simulations of image estimation. The results of some simulations for various observation and image models are presented.