Localization of charged objects using a planar electrostatic sensor array

Localization of charged objects is of great interest in a diverse range of industrial, commercial and military applications. This paper presents a method for locating charged objects in a plane using an electrostatic sensor array. Based on a simplified analytical model of the electrostatic sensor embedded in a grounded surface, a closed-form solution to the localization problem is derived for a linear sensor array, while the Newton-Raphson numerical method is used to approximate the solution for three randomly positioned sensors. Numerical simulations show that the charged object can be accurately located using the linear sensor array in areas far from the electrodes and the grounded surface. Depending on the initial value, the numerical solution for randomly positioned sensors may converge to correct or incorrect results and may diverge as well.