Quantized lower bounds on grid-based localization algorithm for wireless sensor networks

In this paper, we introduce a Quantized Cramer Rao Bound (Q-CRB) method, which adapts the use of the CRB to handle grid-based localization algorithms with certain constraints, such as localization boundaries. In addition, we derive a threshold granularity level which identifies where the CRB can be appropriately applied to this type of algorithm. Moreover, the derived threshold value allows the users of grid-based LSE techniques to probably avoid some unnecessary complexities associated with using high grid resolutions. To examine the feasibility of the new proposed bound, the grid-based least square estimation (LSE) technique was implemented. The Q-CRB was used to evaluate the performance of the LSE method under extensive simulation scenarios. The results show that the Q-CRB provided a tight bound in the sense that the Q-CRB can characterize the behaviour of location errors of the LSE technique at various system parameters, e.g. granularity levels, measurement accuracies, and in the presence or absence of localization boundaries.