Measurement of small signal variations using one-dimensional chaotic maps

A novel electronic signal Measurement System (MS) based on one-dimensional chaotic maps (Logistic Map (LM) and Tent Map (TM)) has been developed, analysed and tested. Firstly, an in-depth theoretical analysis of each map was performed using MATLAB based computation, and the results demonstrated that the high sensitivity, to initial conditions, of each map was suitable for small signal change detection and measurement. A new 3D representation of chaos map output for varying initial input was also developed allowing the suitability of any one-dimensional chaotic map to be determined.
An electronic implementation of the chaotic maps, using low noise and low cost components was developed along with a feedback and a series based MS. The implementations were tested and the experimental results demonstrate a matching within ±1 %, between theory and the electronic implementations, both maps exhibiting behaviour identical to the theoretical maps, ranging from fixed point stability, periodicity and chaos.
Each map implementation was tested separately and as part of a complete MS and the results reveal that the proposed measurement technique can detect and measure input signals changes as low as 5 over a 10 V input range, which yields a greater resolution than a MS using an 20 bit Analogue to Digital Converter (ADC) over the same input range.
The main advantage of the presented MS is that the accuracy of the measurement is independent of the input range which is not the case with classical approach to measurement based on conditioning circuitry followed by an ADC as the minimum detectable change is directly proportional to the input range.