On the application of minimum phase space volume parameter estimation

In this paper, we consider the influence of high dimensional noise process on the accuracy of signal parameter estimation in low dimensional chaotic noise. Because of the inherently deterministic nature of the chaotic signal, instead of conventional probabilistic methods, a complexity measure based on phase space volume (PSV) of the reconstructed attractor is used to identify unknown system parameters. It was shown that through minimization of PSV a very effective system identification procedure could be achieved. This procedure however relies upon the fact that PSV of the chaotic process is negligible for embedding dimensions higher than the true dimension of the chaotic attractor, therefore any additional high dimensional noise degrades the estimation accuracy. Monte Carlo simulations are carried out to illustrate the efficiency of the minimum PSV method for parameter estimation in the presence of high dimensional noise. To reduce the optimization complexity a kd-tree search algorithm was used which takes only order Nlog(N) operations.