How sensor graph topology affects localization accuracy

We characterize the accuracy of a cooperative localization algorithm based on Kalman Filtering, as expressed by the trace of the covariance matrix, in terms of the algebraic graph theoretic properties of the sensing graph. In particular, we discover a weighted Laplacian in the expression that yields the constant, steady state value of the covariance matrix. We show how one can reduce the localization uncertainty by manipulating the eigenvalues of the weighted Laplacian. We thus provide insight to recent optimization results which indicate that increased connectivity implies higher accuracy. We offer an analysis method that could lead to more efficient ways of achieving the desired accuracy by controlling the sensing network.