Weighted geometric dilution of precision calculations with matrix multiplication

To enhance the performance of location estimation in wireless positioning systems, the geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units. Since GDOP represents the geometric effect on the relationship between measurement error and positioning determination error, the smallest GDOP of the measurement unit subset is usually chosen for positioning. The conventional GDOP calculation using matrix inversion method requires many operations. Because more and more measurement units can be chosen nowadays, an efficient calculation should be designed to decrease the complexity. Since the performance of each measurement unit is different, the weighted GDOP (WGDOP), instead of GDOP, is used to select the measurement units to improve the accuracy of location. To calculate WGDOP effectively and efficiently, the closed-form solution for WGDOP calculation is proposed when more than four measurements are available. In this paper, an efficient WGDOP calculation method applying matrix multiplication that is easy for hardware implementation is proposed. In addition, the proposed method can be used when more than exactly four measurements are available. Even when using all-in-view method for positioning, the proposed method still can reduce the computational overhead. The proposed WGDOP methods with less computation are compatible with global positioning system (GPS), wireless sensor networks (WSN) and cellular communication systems.