Closed-form performance for location estimation based on fused data in a sensor network

For a large and dense outdoor sensor net-work, the impact of sensor density and signal to noise ratio (SNR) are investigated on the performance of a maximum likelihood (ML) location estimation algorithm. The ML estimator fuses data, in the form of signal amplitudes, 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 and meaningful. 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 has been 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 product of the sensor density and the SNR. 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.