Quasi-Optimal Determination of a Mobile Object Trajectory Using a System of Electrostatic Sensors

The paper considers the problem of determining the trajectory of a mobile object based on information obtained using a system of passive stationary electric field sensors. A theoretical model of a moving material point carrying a priori unknown electric charge is used, expressions are compiled for the field created by it, taking into account the radiation caused by the motion of the charge, and it is shown that in practice it is quite admissible to restrict to the quasi-static approximation. A method is described for determining the instantaneous position of an object based on the measurements of electrostatic sensors taken in an amount sufficient to form an overdetermined system of equations. The method of least squares is chosen as the main calculation algorithm. The possibility of obtaining an optimal estimation of the a priori unknown charge of the moving object in real time is shown. The efficiency of the proposed methodology is confirmed by analyzing an example.