Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Online Identification of Stochastic Continuous-Time Wiener Models Using Sampled Data

Mohamed Abdalmoaty, Efe C. Balta, John Lygeros, Roy S. Smith

Abstract

It is well known that ignoring the presence of stochastic disturbances in the identification of stochastic Wiener models leads to asymptotically biased estimators. On the other hand, optimal statistical identification, via likelihood-based methods, is sensitive to the assumptions on the data distribution and is usually based on relatively complex sequential Monte Carlo algorithms. We develop a simple recursive online estimation algorithm based on an output-error predictor, for the identification of continuous-time stochastic parametric Wiener models through stochastic approximation. The method is applicable to generic model parameterizations and, as demonstrated in the numerical simulation examples, it is robust with respect to the assumptions on the spectrum of the disturbance process.

Online Identification of Stochastic Continuous-Time Wiener Models Using Sampled Data

Abstract

It is well known that ignoring the presence of stochastic disturbances in the identification of stochastic Wiener models leads to asymptotically biased estimators. On the other hand, optimal statistical identification, via likelihood-based methods, is sensitive to the assumptions on the data distribution and is usually based on relatively complex sequential Monte Carlo algorithms. We develop a simple recursive online estimation algorithm based on an output-error predictor, for the identification of continuous-time stochastic parametric Wiener models through stochastic approximation. The method is applicable to generic model parameterizations and, as demonstrated in the numerical simulation examples, it is robust with respect to the assumptions on the spectrum of the disturbance process.
Paper Structure (13 sections, 37 equations, 5 figures, 1 algorithm)

This paper contains 13 sections, 37 equations, 5 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. Proposed Approach
  4. Offline method: The OE-QPEM estimator
  5. Proposed identification method
  6. Recursive computation of the OE predictor
  7. Recursive computation of the gradient vector
  8. Algorithm Summary
  9. Theoretical Motivation
  10. Numerical Examples
  11. Example 1
  12. Example 2
  13. CONCLUSIONS

Figures (5)

  • Figure 1: Ten MC simulations of Algorithm \ref{['alg']} applied to \ref{['eq:model_ex1']}.
  • Figure 2: Ten MC simulations of Algorithm \ref{['alg']} applied to \ref{['eq:model_ex2']} when the true disturbance model is given by Case 1. The estimates of $b$ and $c$ (not shown) exhibit the same behaviour.
  • Figure 3: Ten MC simulations of an online OE-QPEM algorithm that ignores $w(t)$. The estimates of $b$ and $c$ (not shown) exhibit the same behaviour, and $\sigma$ is not estimated here.
  • Figure 4: Ten MC simulations of Algorithm \ref{['alg']} applied to \ref{['eq:model_ex2']} when the true disturbance model is given by Case 2. The estimates of $b$ and $c$ (not shown) exhibit the same behaviour.
  • Figure 5: Ten MC simulations of Algorithm \ref{['alg']} applied to \ref{['eq:model_ex2']} when the true disturbance model is given by Case 3. The estimates of $b$ and $c$ (not shown) exhibit the same behaviour.