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Introduction to GPS: The Global Positioning System

# Chapter 6: Ambiguity-Resolution Techniques

## Overview

The previous chapter showed that centimeter-level positioning accuracy could be achieved with the carrier-phase observables in the relative positioning mode. A prerequisite to this, however, is the successful determination of the initial integer ambiguity parameters (in fact, the integer double-difference ambiguity parameters). This process is commonly known as ambiguity resolution. Resolving the ambiguity parameters correctly is equivalent to having very precise ranges to the satellites, which leads to high-accuracy positioning [1].

The ambiguity parameters are initially determined as part of the least-squares, or Kalman filtering, solution [2, 3]. Unfortunately, however, neither method can directly determine the integer numbers of the ambiguity parameters. 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 solution [4]. 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 was carried out using long observational time spans (typically a few hours). This allows for the receiver-satellite geometry to change considerably, which helps in separating the ambiguity parameters from the baseline solution. As such, even though the least-squares solution would contain real-valued numbers for the ambiguity parameters, they were very close to integer values. Consequently, the correct integer values were simply obtained by rounding off the real-valued numbers to the nearest integers [4]. Another least-squares adjustment was then to be carried out, considering the integer-valued ambiguity...