Optimal analysis for sensor-target geometries of linear sensor arrays in UWSN

Considering that the bearing measurement noise is distance-dependent in UWSN, this paper studies the sensortarget geometries optimization of linear sensor arrays and presents the optimal localization via noisy bearing measurements. As for the three constrained scenarios of linear sensor arrays, we analyze the optimal sensor-target geometries in terms of the corresponding Fisher information matrix determinant. We remark the methods for obtaining the optimal sensor-target geometries in fixed uniform linear sensor arrays. Then the optimal sensor-target geometries in the Non-fixed uniform linear sensor arrays for two sensors and the ones in the Non-Uniform linear sensor arrays are proved to be isosceles triangles. The isosceles triangles in the two cases are the same when the bearing measurement noise models are the same. For the length of sides of the isosceles triangle, it depends on the bearing measurement noise models and the positions of the target. Finally the comparisons of the three constrained scenarios show that the optimal sensor-target geometries in the Non-Uniform linear sensor arrays can gain the best localization performance.