Statistical modelling of chaos-based non-coherent Double-Dither code tracking

In this paper, a recently proposed statistical method for examining the correlation function of the chaos-based signals, known as the Chaos Correlation Statistics (CCS), is used to analyse the exact performance of a chaos-based non-coherent Double-Dither tracking loop in presence of noise. The motivations for this work are the sub-par performance of Delayed Lock Loop (DLL) and Tau-Dither Loop (TDL) because of their inherent vulnerability to correlator imbalance and noise. Moreover, the CCS has not been applied to the Double-Dither Loop (DDL) and the control law has not been examined for this type of loop when the signal being tracked is a discrete chaotic signal derived from Chebyshev polynomials. The performance of the DDL in terms of instantaneous and cumulative timing estimation is examined and compared for both the balanced and unbalanced cases. It is found that the performance of chaos-based DDL is superior to that of the DLL and TDL as it is not susceptible to correlator imbalance and noise respectively.