Overview

The previous chapter showed that centimeter-level positioning accuracy could be achieved with the carrier-phase observables. A prerequisite to this, however, is the successful determination of the initial integer cycle ambiguity parameters (integer double-difference ambiguity parameters in the relative positioning mode). This process is commonly known as ambiguity resolution or ambiguity fixing. As discussed in Section 2.6, resolving the ambiguity parameters correctly is equivalent to having very precise ranges to the satellites, which leads to high-accuracy positioning. This chapter focuses on the ambiguity resolution for GPS relative positioning.

The ambiguity parameters are initially determined as part of a least-squares, or Kalman filtering, solution [1, 2]. Unfortunately, neither method can directly determine the integer numbers of the ambiguity parameters. This is mainly because the ambiguity parameters are determined from noisy data. What can be obtained are the real-valued numbers along with their uncertainty parameters (so-called covariance matrix) only. These real-valued numbers are in fact difficult to separate from the baseline (i.e., reference-rover separation) solution [3]. As such, since we know in advance that the ambiguity parameters are integer numbers, it becomes clear that further analysis is required.

Traditionally, high-precision GPS relative positioning with carrier-phase observables is carried out using long observational time spans (typically a few hours). This allows for the receiver-satellite geometry to change sufficiently to facilitate the separation of the ambiguity parameters from the baseline solution. As such, even though the least-squares solution contains real-valued numbers for the ambiguity parameters (sometimes called float solution), they are very close to...