New Algorithms for Discrete-Time Parameter Estimation

TL;DR

This paper introduces two novel algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation and another for constant parameters without PE, demonstrating improved convergence and boundedness guarantees.

Contribution

The paper presents new algorithms tailored for different parameter conditions, with theoretical convergence guarantees and practical advantages over existing methods like RLS.

Findings

Convergence of estimation error to a compact set under PE.

Boundedness guarantees for constant parameters using projection.

Simulation results outperforming RLS in convergence speed.

Abstract

We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in the presence of time-varying unknown parameters, the parameter estimation error converges uniformly to a compact set under conditions of persistent excitation, with the size of the compact set proportional to the time-variation of unknown parameters. Leveraging a projection operator, the second algorithm is shown to result in boundedness guarantees when the plant has constant unknown parameters. Simulations show better convergence results compared to recursive least squares (RLS) and comparable results to RLS with forgetting factor.