Convergence analysis of state estimation for UAV formation under GPS‐denied environments

Abstract

In this article, we focus on the state estimation and formation control problem for a multi‐UAV system, where only parts of UAVs have GPS measurements, that is, the anchors, and the other UAVs measure their relative positions with anchors. With a second‐order discrete‐time model of each UAV in the formation, we analyze the convergence of state estimation (including its expectation and covariance) for commonly used consensus‐based formation control protocols, under the effect of control and measurement noise. More specifically, based on the discrete‐time stability analysis, we obtain the sufficient and necessary conditions for the expectation stability of the formation control. Using the fixed point theorem in positive symmetric matrix subspace and observability analysis, we rigorously prove that the covariance of estimation is bounded if and only if the anchor node set is globally reachable. Based on our analysis, the formation control parameters and system topology can be designed to satisfy sufficient conditions, such that the desired formation pattern can be achieved for the multi‐UAV dynamic system under GPS‐denied environments. Simulation results corroborate the effectiveness of our theoretical results.