Outlier robust system identification: a Bayesian kernel-based approach
This work addresses outlier robustness in system identification, which is crucial for applications like control systems, but it appears incremental as it builds on existing kernel-based methods with a specific noise model.
The paper tackles the problem of robust linear system identification in the presence of outliers by proposing a Bayesian kernel-based method with Laplacian noise modeling, resulting in a substantial improvement in estimation accuracy over state-of-the-art kernel-based methods.
In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.