Mixed One-way and Two-way Ranging to Support Terrestrial Alternative Position Navigation & Timing

Two-way ranging between the ground station and aircraft can provide true-range measurement allowing for horizontal positioning using only two stations. However, this infrastructure benefit comes at a cost, as the two-way ranging requires interaction between ground station and aircraft, which limits system capacity. In this respect, one-way ranging which provides pseudo-range measurement works well because it has no capacity limitations. Its drawback is that we need one extra measurement to solve for the horizontal position and clock offset. In this paper, we look at positioning using mixed one-way and two-way ranging, which can work in limited geometry situation while having a high system capacity. In mixed positioning, two modes are considered: 1) clock calibration and 2) clock coasting mode. In clock calibration mode, determination of the airborne user clock offset is made as the clock offset may be unknown or exceed some targeted threshold. To achieve the calibration, at least three measurements are needed to estimate the horizontal position and clock offset. Calibration of the clock allows for clock-coasting mode where the horizontal position can be determined with fewer measurements through coasting with the previously determined clock offset. In this mode, only two pseudo-range measurements are required to navigate the aircraft. However, one must take care as the uncertainty of the clock offset will grow as time increases. The error growth speed depends on clock precision of the onboard clock. For the aircraft navigation, integrity must be considered. Generally, under reasonable geometry, at least three measurements are needed to estimate the horizontal position of the aircraft and clock offset. One more measurement is necessary for detecting a faulty measurement source, and if additional measurements are available, it is possible to isolate the faulty measurement source. This paper details how the measurement errors effect on horizontal positioning and clock offset by examining different cases using one-way and possibly two-way ranges. With the knowledge of these initial measurement uncertainties, it is possible to obtain the allowable coasting time within which the system can meet the requirements without clock update. Moreover, this paper utilizes a classical method to detect the faulty measurement source using one redundant range measurement to examine mixed ranging integrity and the effect of clock offset.