Identification of Piecewise Affine State-Space Models via Expectation Maximization

TL;DR

This paper introduces a novel EM-based method for identifying piecewise affine state-space models that avoids jump Markov approximations by using CDF-based probabilities, demonstrated on aircraft simulation data.

Contribution

It proposes a new EM algorithm utilizing CDFs for model transition probabilities, improving identification of piecewise affine models without jump Markov assumptions.

Findings

Effective identification of aircraft model parameters

Avoids jump Markov approximation in model transitions

Demonstrated on simulated JAS 39 Gripen aircraft data

Abstract

This paper deals with the identification of piecewise affine state-space models. These models are obtained by partitioning the state or input domain into a finite number of regions and by considering affine submodels in each region. The proposed framework uses the Expectation Maximization (EM) algorithm to identify the parameters of the model. In most of the current literature, a discrete random variable with a discrete transition density is introduced to describe the transition between each submodel, leading to a further approximation of the dynamical system by a jump Markov model. On the contrary, we use the cumulative distribution function (CDF) to compute the probability of each submodel given the measurement at that time step. Then, given the submodel at each time step the latent state is estimated using the Kalman smoother. Subsequently, the parameters are estimated by maximizing a surrogate function for the likelihood. The performance of the proposed method is illustrated using the simulated model of the JAS 39 Gripen aircraft.