We analyze a specific practical problem of bearing-only localization of a stationary target using noisy measurements from three sensors. It is well understood that the performance of any target position estimator is considerably influenced by the sensor-target geometry. The performance achievable can be measured in terms of the Cramer-Rao lower bound (CRLB) on the algorithm covariance. However, the CRLB is calculated assuming exact knowledge of sensors location, which in practice is not true. In this paper, the effect of unavoidable uncertainty in network sensor positions is numerically evaluated in terms of Mean Square Error (MSE), offering detailed comparison with the ideal case of exact sensors location often assumed in the literature. The problem is cast into a probabilistic framework based on Monte Carlo simulations with a static target whose position is estimated through an Extended Kalman Filter (EKF). The positions of the sensors for each simulation are sampled from a Gaussian distribution with a mean equal to the nominal position while the standard deviation takes into account both the placement error during the deployment and the sensor position measurement uncertainty. The presented results confirm the need of our preliminary analysis for the following design of a test range for Autonomous Underwater Vehicles (AUVs).

Keywords: {Gaussian distribution;Kalman filters;Monte Carlo methods;autonomous underwater vehicles;covariance matrices;mean square error methods;nonlinear filters;object tracking;sensor placement;CRLB;Cramer-Rao lower bound;EKF;Gaussian distribution;MSE;Monte Carlo simulations;algorithm covariance;autonomous underwater vehicles;bearing-only AUV tracking performance;extended Kalman Filter;mean square error;noisy measurements;probabilistic framework;sensor deployment;sensor position measurement uncertainty;stationary target;underwater node position;Geometry;Monte Carlo methods;Position measurement;Sensor phenomena and characterization;Uncertainty;Vehicles;Acoustic sensors;bearing-only localization;localization geometry;optimal sensor placement;sensor position uncertainty},

File: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7761134&isnumber=7760990