Linear TDOA-based Measurements for Distributed Estimation and Localized Tracking

The paper correctly sets up the error dynamics, motivates distributed observability via Kronecker-structured analysis, and claims that strong connectivity (irreducibility of W) suffices for observability and (hence) existence of stabilizing gains. However, it glosses over two key points: (i) the observer error update has the form A − K C A (with C = DH), so the standard Luenberger result should be invoked for the pair (A, C A) (or else one must assume A invertible to pass from (A, C) to (A, C A)); and (ii) the block-diagonal structure of K is not justified by the Kalman/Luenberger theorem and needs an explicit structured-feedback argument. The candidate solution fills gap (i) by making the “A invertible generically” step explicit and by arguing structural observability via output reachability and perfect matching, but it, too, is incomplete on (ii): it appeals to structural fixed-modes results to conclude that block-diagonal static output injection can stabilize generically, which is stronger than what those results ensure without further hypotheses. Net: both arguments trend in the right direction but omit necessary caveats and assumptions for the structured-gain step.