Joint Parameter and State Estimation of Noisy Discrete-Time Nonlinear Systems: A Supervisory Multi-Observer Approach

TL;DR

This paper introduces two supervisory multi-observer schemes for jointly estimating parameters and states of noisy discrete-time nonlinear systems, ensuring finite-time convergence within a user-defined margin.

Contribution

It proposes novel sampling-based observer schemes that guarantee finite-time convergence and adaptive zoom-ins for parameter estimation in nonlinear systems.

Findings

Finite-time convergence within a specified margin

Adaptive zoom-in improves estimation accuracy

Numerical example validates effectiveness

Abstract

This paper presents two schemes to jointly estimate parameters and states of discrete-time nonlinear systems in the presence of bounded disturbances and noise and where the parameters belong to a known compact set. The schemes are based on sampling the parameter space and designing a state observer for each sample. A supervisor selects one of these observers at each time instant to produce the parameter and state estimates. In the first scheme, the parameter and state estimates are guaranteed to converge within a certain margin of their true values in finite time, assuming that a sufficiently large number of observers is used and a persistence of excitation condition is satisfied in addition to other observer design conditions. This convergence margin is constituted by a part that can be chosen arbitrarily small by the user and a part determined by the noise levels. The second scheme exploits the convergence properties of the parameter estimate to perform subsequent zoom-ins on the parameter subspace to achieve stricter margins for a given number of observers. The strengths of both schemes are demonstrated using a numerical example.