Efficient Least-Squares State Estimation Using Uniform Sampling

Formulating state estimation for a large-scale, discrete-time, linear time-invariant system as a least-squares problem can be computationally challenging as the problem dimensions increase with time. Recently, randomized sampling has demonstrated promising results in approximating this problem by using fewer rows, resulting in a polynomial-sized approximate problem. However, these algorithms necessitate calculating the statistical leverage scores of the rows, which can be challenging. In this paper, we propose an alternative approach to approximate leverage scores by uniformly sampling rows. We demonstrate that this method provides a sufficiently weak form of approximation for obtaining an estimate of each leverage score. Our approach delivers a reasonable approximation of the leverage scores, which is suitable for approximating and solving the least-squares estimation problem with proven theoretical guarantees.