Parameter estimation for 1D PWL chaotic maps using noisy dynamics

Abstract

Many physical situations involve chaotic systems implemented in hardware. Among them onedimensional piecewise linear maps are popular candidates for such applications because of their property of generating robust chaos. In physical implementations, the control parameter of these maps may deviate from its ideal value due to hardware imprecision. Since the dynamics of a chaotic map is completely defined by its control parameter, one needs to know the value of the 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 of the map, by utilising noise that is always present in the system. We present this in the form of an algorithm and demonstrate its efficacy through simulated results. We also determine the bounds on the signal-to-noise ratio required for successful parameter estimation. The proposed approach is expected to be beneficial to the existing noise reduction techniques and time series recovery algorithms that require a reasonably accurate knowledge of the map.

Digital System Performance Enhancement of a Tent Map-Based ADC for Monitoring Photovoltaic Systems

“…An alternative solution, therefore, is to evaluate the effects non-ideal TM gain has on the performance of a TM-based ADC output and compensate for it through post-processing of the data, thus enabling the enhanced estimation of the initial conditions (the analogue input signal) from the digital ADC output. The eventual aim for this research is to employ an algorithm to estimate changes in TM gains from the ADC output (similar to that proposed by Dutta et al [15]) and then estimate the initial conditions, thus producing a self-calibrating ADC.…”