An improved GNSS ambiguity best integer equivariant estimation method with Laplacian distribution for urban low-cost RTK positioning

Abstract The integer least squares (ILS) estimation is commonly used for carrier phase ambiguity resolution (AR). More recently, the best integer equivariant (BIE) estimation has also attracted an attention for complex application scenarios, which exhibits higher reliability by a weighted fusion of integer candidates. However, traditional BIE estimation with Gaussian distribution (GBIE) faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning, mainly due to the presence of outliers and unmodeled errors. To this end, an improved BIE estimation method with Laplacian distribution (LBIE) is proposed, and several key issues are discussed, including the weight function of LBIE, determination of the candidates included based on the OIA test, and derivation of the variance of LBIE solutions for reliability evaluation. The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution (TBIE), and significantly outperforms the ILS-PAR and GBIE methods. In an urban expressway test with a Huawei Mate40 smartphone, the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50% improvements compared to the ILS-PAR and GBIE methods. In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics, the positioning accuracy of LBIE in three directions is 0.112 m, 0.107 m, and 0.252 m, respectively, with improvements of 17.6%, 27.2%, and 26.1% compared to GBIE, and 23.3%, 28.2%, and 30.6% compared to ILS-PAR. Moreover, its computational time increases by 30–40% compared to ILS-PAR and is approximately half of that using TBIE.