Experimental application of a method for hidden parameter tracking in a slowly changing, chaotic system

Results are presented of an experimental application of a method for tracking hidden parameters in slowly changing chaotic systems. The method exploits the time scale separation between fast dynamic variables and a slow drifting parameter. Locally linear tracking models are constructed using data from the reference system sampled on a fast time scale, employing delay coordinate embedding. These reference models are used to track parameter drift. The method is successfully applied to a forced oscillator with a two-well potential. The effect of the choice of prediction time interval is studied. It is also observed that a simple correction for estimated modeling error gives a more sensitive tracking metric. For purposes of comparison with such model-based tracking methods, a heuristic method is also presented for detecting parameter changes using the autocorrelation function of the recorded time series. The relative merits of heuristic versus model-based techniques are discussed. Directions for future work are suggested.