Network Localization Cramér-Rao Bounds for General Measurement Models

A closed-form Cramér-Rao bound (CRB) for general multi-modal measurements is derived for D-dimensional network localization (D ∈ {2,3}). Links are asymmetric and the measurements among neighboring nodes are non-reciprocal depending on an arbitrary differentiable function of their position difference, subject to additive Gaussian noise (with variance that may depend on distance). The provided bound incorporates network connectivity and could be applied for a wide range of typical, unimodal ranging measurement methods (e.g., angleof-arrival or time-of-arrival or signal strength with directional antennas) or multi-modal methods (e.g., simultaneous use of unimodal ranging measurements). It was interesting to see that for specific network connectivity, MSE performance of various different ranging measurement methods coincide, while performance of network localization algorithms is clearly sensitive on network connectivity.