Dilution of Precision in Positioning Systems Using Both Angle-of-Arrival and Time-of-Arrival Measurements

Dilution of precision (DOP) is a value that can describe the effect on the relationship between measurement error and position determination error. The DOP of a positioning system using time of arrival (TOA) measurement such as GPS has been well researched. Some researchers have also investigated the DOP of the angle of arrival (AOA) system. However, the DOP of the AOA and TOA combined system has been rarely studied. As more AOA based systems appear in the market, the AOA/TOA combined system is likely to be used widely in the future. This article investigates the DOP of a positioning system combining AOA and TOA. The concept of DOP is briefly introduced, and the DOP of AOA and of TOA is discussed separately. A unified formula to calculate DOP is derived for a positioning system using AOA and/or TOA measurements. The simulation shows that the DOP value is associated with the size of the deployment of the base stations and the ratio between the standard deviations of TOA and AOA measurements. If the ratio is fixed, when the size approaches infinity, the DOP approaches that of a positioning system using only TOA measurement. On the contrary, when the size approaches infinitely small, the DOP approaches that of a positioning system using only AOA measurement. An Ultra-Wide band positioning system was used to conduct experiments. The results verify that the unified formula can be used to guide the deployment of base stations of the AOA and/or TOA based positioning system.