Parameter estimation for 1D PWL chaotic maps using noisy dynamics

Abstract

Many physical situations involve chaoticsystems implemented in hardware. Among them one-dimensional piecewise linear maps are popular candi-dates for such applications because of their property ofgenerating robust chaos. In physical implementations,the control parameter of these maps may deviate fromits ideal value due to hardware imprecision. Since thedynamics of a chaotic map is completely defined byits control parameter, one needs to know the value ofthe parameter in a hardware realisation. In this paper,we show that it is possible to determine the parameter,through the realisation of the unstable fixed point ofthe map, by utilising noise that is always present in thesystem. We present this in the form of an algorithm anddemonstrate its efficacy through simulated results. Wealso determine the bounds on the signal-to-noise ratiorequired for successful parameter estimation. The pro-posed approach is expected to be beneficial to the exist-ing noise reduction techniques and time series recoveryalgorithms that require a reasonably accurate knowl-edge of the map.