Fractional order chaotic cryptography in colored noise environment by using fractional order interpolatory cubature Kalman filter

Abstract

In this paper, a novel estimation algorithm based on fractional order interpolatory cubature Kalman filter is introduced to achieve the state estimation in nonlinear discrete-time fractional order systems with colored noise. In the proposed approach, the system with colored noise is transformed to a system with correlated process and measurement noises by presenting a new auxiliary output based on the extension of the measurements differencing method. Then, the novel fractional order interpolatory cubature Kalman filter algorithm is introduced based on these new outputs. The proposed algorithm is applied for the synchronization of fractional order hyperchaotic Lorenz system targeting the cryptography in a communication system where the transmitter and the transmission channel possess colored noise. Simulation results demonstrate the effectiveness of the proposed scheme.