An efficient approach for trilateration in 3D positioning

Trilateration is a common operation to find the object location using its distances or range measurements to three other known points or stations. Traditionally, this problem has been solved either by algebraic or numerical methods. These methods involve long and complex geometric computations which are usually implemented in software. An approach that avoids this complexity is proposed here. Simulation results show improvements of the proposed approach in terms of computational cost and implementation simplicity over the conventional methods used. In addition, the proposed approach is based on vector rotations and uses only simple add and shift operations and therefore can be easily implemented in the hardware (or firmware) of the mobile object.