Closed-form performance for location estimation based on quantized data in sensor networks

For a large and dense sensor network, the impact of sensor density is investigated on the performance of a maximum likelihood (ML) location estimator using quantized sensor data. The ML estimator fuses quantized data transmitted from local sensors to estimate the location of a source. A Gaussian-like isotropic signal decay model is adopted to make the problem tractable. This model is suitable for situations such as passive sensors monitoring a target emitting acoustic signals. The exact Cramér-Rao lower bound (CRLB) on the estimation error is derived. In addition, an approximate closed-form CRLB by using the Law of Large Numbers is obtained. The closed-form results indicate that the Fisher information is a linearly increasing function of the sensor density. Even though the results are derived assuming a large number of sensors, numerical results show that the closed-form CRLB is very close to the exact CRLB for both high and relatively low sensor densities.