Research On Kalman Filter Theory And Its Application In Chaotic Communications

Chaos is a random yet deterministic process in nonlinear dynamical system. Because chaotic signals are sensitive to initial conditions, occupy a wide bandwidth in frequency domain and have non-periodic feature. Chaotic signals have potential application prospect in communications.In chaotic communication, many problems can be solved by adaptive filtering. Kalman filter (KF) and Extended Kalman filter (EKF) is the best filter in Gaussian linear and nonlinear condition. Combining the unscented transform we can get a nonlinear filter: unscented Kalman filter (UKF) which has high computation accuracy and is easily realized. They are widely used in chaotic communication.This thesis will focus on chaos-based communication systems, and uses KF theory as theory background. By using KF and UKF, some research on chaotic keying, chaotic parameter estimation, blind equalization and blind separation are provided.1?We overview the existing chaotic synchronization and chaotic communication method, in which we highlight the principle of three non-coherent parameter estimation algorithms, coherent chaos shift keying (CSK) and differential chaos shift keying (DCSK). As the performance of the DCSK in a multipath fading channel is not good, we proposed a rake reception scheme for DCSK communication systems over a multipath fading channel.2?We explain the basis idea and the algorithm frame of KF. By applying KF-based blind multiuser detection algorithm to the chaotic spread spectrum communication, we evaluate the performance of the KF algorithm. It is better than LMS algorithm. Extended Kalman filter (EKF) and UKF are widely used in non-linear filtering. From the simulation results and the principle of the algorithms, we know that the UKF is superior to EKF. Thus, we introduce the UKF-based adaptive demodulation method and show its efficiency in chaotic communication. In addition, we proposed an UKF based noncoherent detection method for CSK communication system, in which the reference signal is estimated from the received signal by using UKF. Simulation results indicate that the BER performance of the method is better than the FM-DCSK communication system. 3?We analyze the existing principles of blind equalization algorithm, and compare the performance of EKF-based blind equalization algorithm and UKF-based blind equalization algorithm. After that, we proposed a blind equalization algorithm based on dual UKF (DUKF) for chaotic multiple input multiple output (MIMO) communication systems. In the algorithm, two separate state-space representation are used for the signals and the coefficients, and then two unscented Kalman filters are used to estimate chaotic signals and channel coefficients simultaneously. The simulation results show that the algorithm can effectively reduce channel noise, fading, and inter-user interference in chaotic communication systems with multiuser.4?In the study of the blind separation and its application in chaotic communication1) We report the results by using the fast independent component analysis (FastICA) algorithm to realize blind extraction of chaotic signals. According to the nonlinear principal component analysis (NPCA) criterion and the proposed LMS-type and RLS-type adaptive algorithms, we propose a blind source separation algorithm based on KF for the real-time separation.2) Assuming that the dynamics of the chaotic signal to be extracted is known, we proposed an algorithm for blind extraction of chaotic signal from convolutive mixture. This algorithm formulates determination of the desired extracting vector as a nonlinear state estimation, and then uses the unscented Kalman filter (UKF) to seek the extracting vectors. For utilizing the map of the chaotic signal, the algorithm can solve the indeterminacies of the scaling and order of the estimated signals.3) Combining the UKF-based blind extraction algorithm and the UKF-based adaptive demodulation method, we formulate two different state space models for MIMO chaotic communication systems: one for extraction vector and one for the augmented vector which contains chaotic signals and parameters. Then we use DUKF to realize multiuser communications in a multi-input multi-output channel.