Multichannel multistatic combined TSoA and TDoA positioning system based on precise analytical solution of positioning equations

Exact analytical solutions of elliptic and hyperbolic equations in a multichannel multistatic positioning system are obtained. The results of modeling the Time Sum of Arrival (TSoA) and Time Difference of Arrival (TDoA) methods for estimating the object coordinates by arrival times with fluctuations are presented. Particular attention is paid to the causes of gross errors in case of problematic configurations of base stations (BS) and the position of the object. The study revealed that the advantages of the TSoA method over the TDoA method include a reduction in the area with anomalous errors and better accuracy outside the BS perimeter, and the advantage of TDoA over TSoA should include more accurate work inside the BS perimeter. Based on the identified advantages, optimization of a multichannel multistatic positioning system, which combines the advantages of TSoA and TDoA methods, is proposed. As a result of the simulation, it was found that the combined TSoA/TDoA method, based on the exact analytical solution of equations, has an order of magnitude higher accuracy in determining the object's coordinates than the frequently used method of linearization of hyperbolic equations. Due to these advantages, the proposed algorithm is promising for remote determination of the parameters of unmanned vehicles in “smart city” technologies.