Sparse Initial State Estimation Algorithms

In this chapter, we estimate the sparse initial state of a linear dynamical system from its observations when the inputs are known. We formulate this as a sparse vector recovery problem, a topic well-studied in the signal processing field of compressed sensing. We present several sparsity-aware algorithms from the compressed sensing literature to address this problem, including popular methods such as convex relaxation-based basis pursuit, greedy algorithms like orthogonal matching pursuit and compressive sampling matching pursuit, as well as thresholding techniques, such as iterative hard thresholding, hard thresholding pursuit, and sparse Bayesian learning.