### Abstract

Precise GPS positioning relies on tracking the carrier-phase. The fractional part of carrier-phase can be measured directly using a standard phase-locked loop, but the integer part is ambiguous and the ambiguity must be resolved based on sequential carrier-phase measurements to ensure the required positioning precision. In the presence of large phase-measurement noise, as can be expected in a jamming environment for example, the amount of data required to resolve the integer ambiguity can be large, which requires a long time for any generic integer parameter estimation algorithm to converge. A key question of interest in significant applications of GPS where fast and accurate positioning is desired is then how the convergence time depends on the noise amplitude. Here we address this question by investigating integer least-sqaures estimation algorithms. Our theoretical derivation and numerical experiments indicate that the convergence time increases linearly with the noise variance, suggesting a less stringent requirement for the convergence time than intuitively expected, even in a jamming environment where the phase noise amplitude is large. This finding can be useful for practical design of GPS-based systems in a jamming environment, for which the ambiguity resolution time for precise positioning may be critical.

Original language | English |
---|---|

Pages (from-to) | 149-156 |

Number of pages | 8 |

Journal | Journal of geodesy |

Volume | 81 |

Issue number | 2 |

Early online date | 24 Oct 2006 |

DOIs | |

Publication status | Published - Feb 2007 |

### Keywords

- integer ambiguity resolution
- integer least squares
- precise GPS positioning
- noise
- jamming
- linear-models
- decorrelation

### Cite this

*Journal of geodesy*,

*81*(2), 149-156. https://doi.org/10.1007/s00190-006-0096-y

**Efficiency of carrier-phase integer ambiguity resolution for precise GPS positioning in noisy environments.** / Zhu, Liqiang; Lai, Ying-Cheng; Shah, Mayur; Mahmood, Sultan.

Research output: Contribution to journal › Article

*Journal of geodesy*, vol. 81, no. 2, pp. 149-156. https://doi.org/10.1007/s00190-006-0096-y

}

TY - JOUR

T1 - Efficiency of carrier-phase integer ambiguity resolution for precise GPS positioning in noisy environments

AU - Zhu, Liqiang

AU - Lai, Ying-Cheng

AU - Shah, Mayur

AU - Mahmood, Sultan

PY - 2007/2

Y1 - 2007/2

N2 - Precise GPS positioning relies on tracking the carrier-phase. The fractional part of carrier-phase can be measured directly using a standard phase-locked loop, but the integer part is ambiguous and the ambiguity must be resolved based on sequential carrier-phase measurements to ensure the required positioning precision. In the presence of large phase-measurement noise, as can be expected in a jamming environment for example, the amount of data required to resolve the integer ambiguity can be large, which requires a long time for any generic integer parameter estimation algorithm to converge. A key question of interest in significant applications of GPS where fast and accurate positioning is desired is then how the convergence time depends on the noise amplitude. Here we address this question by investigating integer least-sqaures estimation algorithms. Our theoretical derivation and numerical experiments indicate that the convergence time increases linearly with the noise variance, suggesting a less stringent requirement for the convergence time than intuitively expected, even in a jamming environment where the phase noise amplitude is large. This finding can be useful for practical design of GPS-based systems in a jamming environment, for which the ambiguity resolution time for precise positioning may be critical.

AB - Precise GPS positioning relies on tracking the carrier-phase. The fractional part of carrier-phase can be measured directly using a standard phase-locked loop, but the integer part is ambiguous and the ambiguity must be resolved based on sequential carrier-phase measurements to ensure the required positioning precision. In the presence of large phase-measurement noise, as can be expected in a jamming environment for example, the amount of data required to resolve the integer ambiguity can be large, which requires a long time for any generic integer parameter estimation algorithm to converge. A key question of interest in significant applications of GPS where fast and accurate positioning is desired is then how the convergence time depends on the noise amplitude. Here we address this question by investigating integer least-sqaures estimation algorithms. Our theoretical derivation and numerical experiments indicate that the convergence time increases linearly with the noise variance, suggesting a less stringent requirement for the convergence time than intuitively expected, even in a jamming environment where the phase noise amplitude is large. This finding can be useful for practical design of GPS-based systems in a jamming environment, for which the ambiguity resolution time for precise positioning may be critical.

KW - integer ambiguity resolution

KW - integer least squares

KW - precise GPS positioning

KW - noise

KW - jamming

KW - linear-models

KW - decorrelation

U2 - 10.1007/s00190-006-0096-y

DO - 10.1007/s00190-006-0096-y

M3 - Article

VL - 81

SP - 149

EP - 156

JO - Journal of geodesy

JF - Journal of geodesy

SN - 0949-7714

IS - 2

ER -