A practical method for calculating reliable integer float estimator in GNSS precise positioning

Abstract

To overcome the problem that a fixed estimator is contaminated by a system error for the ambiguity be misjudged in the GNSS precise positioning, a reliable integer float estimator is recommended. Accordingly, the method for determining a finite number of integer vectors based on a given reliability probability is proposed, the formula for calculating the variance matrix of the recommended estimator is derived, and the judgment method of the estimator’s availability is proposed. The detailed process and the effect of the method are also demonstrated using examples to facilitate user application.

Keywords:

• GNSS
• Ambiguity resolution
• Integer fixed estimator
• Reliable integer float estimator
• Variance matrix

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes on contributors

Xianwen Yu is currently an associate professor in the School of Transportation, Southeast University in Nanjing, China. He received his Ph.D. degree in Precision Instrument and Machinery from Southeast University in 2009. His current research interest is in GNSS precise positioning algorithms.

Siqi Xia is a master student in School of Transportation, Southeast University in Nanjing, China. His current research interests include cycle slip detection and high precision GNSS data processing.

Wang Gao is a lecturer at Southeast University in Nanjing, China. He received his Ph.D. degree from School of Transportation, Southeast University in 2018. His current research interest focuses on multi-system and multi-frequency GNSS integer ambiguity resolution and high-precision positioning.

Additional information

Funding

This study is supported by the National Natural Science Foundation of China (grant numbers 41674035 and 41974030).