Performance Comparison and Analysis of ILS and BIE Algorithms for PPP with Phase Ambiguity Resolution

CAO Chao; LIU Zhiqiang; WANG Hu; SONG Jiaming

doi:10.13203/j.whugis20230117

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Performance Comparison and Analysis of ILS and BIE Algorithms for PPP with Phase Ambiguity Resolution

Geodesy and Survey Engineering | 更新时间：2026-11-05

- Performance Comparison and Analysis of ILS and BIE Algorithms for PPP with Phase Ambiguity Resolution
- Geomatics and Information Science of Wuhan University Vol. 50, Issue 10, Pages: 2025-2034(2025)
- 作者机构：
  
  1.河海大学地球科学与工程学院，江苏南京，210098
  2.河海大学智能感知技术创新研究院，山东潍坊,261105
  3.中国测绘科学研究院，北京，100830
- 作者简介：
- 基金信息：
- DOI：10.13203/j.whugis20230117
  CLC： P228
- Received：08 July 2023，
  
  Published：05 October 2025
- 稿件说明：
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曹超,刘志强,王虎，等.PPP相位模糊度ILS与BIE估计算法性能比较与分析[J].武汉大学学报（信息科学版）,2025,50(10):2025-2034.

CAO Chao,LIU Zhiqiang,WANG Hu,et al.Performance Comparison and Analysis of ILS and BIE Algorithms for PPP with Phase Ambiguity Resolution[J].Geomatics and Information Science of Wuhan University,2025,50(10):2025-2034.
曹超,刘志强,王虎，等.PPP相位模糊度ILS与BIE估计算法性能比较与分析[J].武汉大学学报（信息科学版）,2025,50(10):2025-2034. DOI：10.13203/j.whugis20230117

CAO Chao,LIU Zhiqiang,WANG Hu,et al.Performance Comparison and Analysis of ILS and BIE Algorithms for PPP with Phase Ambiguity Resolution[J].Geomatics and Information Science of Wuhan University,2025,50(10):2025-2034. DOI：10.13203/j.whugis20230117

摘要

基于整数最小二乘（integer least squares

ILS）估计的精密单点定位（precise point positioning

PPP）模糊度解算需要进行整数检验，任何漏检和误报均可能导致模糊度固定错误。采用最优整数等变（best integer equivariant

BIE）估计无须进行检验，且其解在所有整数估计类中具有最小均方误差性质。选取全球分布的100个国际全球导航卫星系统服务测站实测数据，分别采取BIE估计、ILS全模糊度固定及部分模糊度固定（partial ambiguity resolution

PAR）解算策略，对不同解算模式下仿动态PPP模糊度固定（PPP with ambiguity resolution

PPP-AR）定位性能进行了对比分析。结果表明，在PPP模糊度估计模型强度相对较弱、收敛精度受限阶段，采用传统ILS算法存在较高AR错误风险，而基于模糊度整数候选解加权融合的BIE最小均方误差解更为稳定，能有效抑制定位解的跳跃。与ILS-PAR解算策略相比，BIE能显著提升PPP-AR收敛速度；在70%与90%分位数下，BIE相较ILS-PAR解算的平面和高程分量收敛时间分别缩短18.8%、13.8%与24.3%、15.9%。在定位精度方面，BIE较ILS-FAR解算结果有明显改善，平面和高程分量精度分别提升43.3%、15.3%（90%分位数），仅略优于ILS-PAR。

Abstract

Objectives

Precise point positioining (PPP) based on integer least squares (ILS) requires the integer testing procedure during which any missed or false test result may lead to incorrect ambiguity fixing. While adopting the best integer equivariant (BIE) estimation scheme

it does not require integer testing anymore and can obtain ambiguity solutions with the property of minimum mean square error in all integer estimation classes.

Methods

Using the observation data of 100 international global navigation satellite system service stations distributed globally

the simulated kinematic PPP with ambiguity resolution (PPP-AR) performance is evaluated and compared under different processing strategies

namely BIE estimation

full ambiguity resolution

and partial ambiguity resolution (PAR).

Results

The results show that in the stage where the strength of the PPP ambiguity estimation model is relatively weak and the convergence precision of estimated ambiguities is limited

traditional ILS algorithm will bring a higher risk of false ambiguity fixing

while the minimum mean square error solution of BIE based on the weighted fusion of ambiguity integer candidate solutions is more stable and can effectively suppress the PPP solution jump caused by abnormal estimation result.

Conclusions

Compared with the ILS-PAR solution strategy

BIE can significantly improve the convergence speed of PPP-AR. Under the 70% and 90% percentiles

the convergence time of horizontal and vertical components is further reduced by 18.8%

13.8%

and 24.3%

15.9% respectively. Moreover

BIE clearly outperforms ILS-FAR improving the positioning accuracy by 43.3% and 15.3% in the horizontal and vertical components respectively (under 90% quantile)

which is only slightly better than ILS-PAR.

关键词

Keywords

references

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