Global navigation satellite systems are widely used across the world because of their continuous/all-weather, global coverage, and high precision positioning. But, three-dimensional positioning accuracy, especially in the vertical direction, remains insufficient because of the geometric distribution of satellites. This is especially true for air-borne objects such as unmanned aerial vehicles, civil aviation devices, and missiles. To solve this problem, we adopt a satellite-ground joint positioning system based on a pseudo-satellite (pseudolite). The introduction of ground pseudolites can significantly reduce the vertical dilution of precision and improve positioning accuracy. This method has been proposed in the 1980s. However, we have to ask a question, as long as we add a pseudolite, can the positioning accuracy be improved? The answer is no. Pseudolites can cause time synchronization problems with satellites, and the resulting timing errors of the pseudolite are converted into pseudorange errors, reducing accuracy. Here, we seek to evaluate the impact of the reduced vertical dilution of precision and the increased range errors associated with the introduction of a pseudolite on the ground. We derive a mathematical formula to explain this relationship. We conclude that when the satellite range error and the change in the position dilution of precision associated with a pseudolite are known, we can calculate an approximate limit for the pseudolite timing accuracy to ensure that the use of the pseudolite improves the positioning accuracy. This work should be of great value in guiding engineering practice.
