Manifold of a planar array and its effects on the accuracy of direction-finding systems

The authors are concerned with the accuracy of azimuth and elevation estimates provided by a planar array of sensors and its relation to the array manifold differential geometry. The paper builds on previously published results regarding the influence of the manifold differential geometry on the detection and resolution capabilities of linear arrays. The manifold of a planar array is introduced in terms of two families of constant-azimuth and constant-elevation curves, and their differential geometry is analysed as a function of the array configuration. Circular approximation is subsequently employed to derive novel expressions for the Cramer-Rao lower bound on azimuth and elevation estimates in terms of the arc lengths and first curvatures of the respective constant-parameter manifold curves. The scenarios considered include the cases of a single emitter as well as that of two closely spaced uncorrelated emitters of arbitrary powers. The results obtained are demonstrated for the cases of two practical array configurations