Accurate Parameter Estimation for Risk-aware Autonomous Systems

TL;DR

This paper introduces a spectral lines-based method for accurately estimating parameters of dynamic models in risk-aware autonomous systems, effectively handling unmodeled deterministic dynamics and noise, with proven robustness and improved performance.

Contribution

It proposes a novel spectral lines-based parameter estimation approach that accounts for deterministic unmodeled dynamics and provides non-asymptotic error bounds, outperforming traditional Gaussian noise methods.

Findings

Spectral lines approach yields lower estimation error with unmodeled dynamics.

Method provides tunable bounds through spectrum optimization.

Approach achieves $ ilde{O}( oot{2}{T})$ regret under ideal conditions.

Abstract

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no unmodeled dynamics, the proposed approach can ensure a $\tilde{O}(\sqrt{T})$ regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.