Extra-Wide Lane Ambiguity Resolution and Validation for a Single Epoch Based on the Triple-Frequency BeiDou Navigation Satellite System

Abstract

The ambiguity resolution (AR) and validation of the global navigation satellite system (GNSS) have been challenging tasks for some decades. Considering the reliability problem of extra-wide-lane (EWL) ambiguity in the triple-carrier ambiguity resolution (TCAR), a method for validating the reliability of the EWL ambiguity using a single epoch was proposed for the BeiDou Navigation Satellite System (BDS). For the initial EWL ambiguity, obtained using a rounding estimator with a geometry-free (GF) model, the double-difference ionospheric delay was first estimated to construct a relative positioning model with an initial fixed ambiguity. Second, based on the theory of gross error detection and the AR characteristics of EWL, the second-best ambiguity candidate was constructed. Finally, among the two sets of ambiguities, the one with the smaller posterior variance was taken as the reliable ambiguity. The study showed that, for a single epoch, when only one or two satellites had incorrect ambiguities, the AR success rate after ambiguity validation and correction could reach 100% for medium baselines. For long baselines, due to the increase of atmospheric error, the validation was affected to some extent. However, the AR success rates for two long baselines increased from 96.82% and 98.44% to 98.80% and 99.67%, respectively.

Application of Variational Bayesian Filtering Based on T-Distribution in BDS Dynamic Ambiguity Resolution

“…, the combination coefficients are optimal [12]. For medium-length baselines (length ≤ 100 km), according to references [6], the values of the error terms in the overall noise level are: 0.005 m, 0.01 m, 0.1 m, and 0.005 m. According to references [13][14], the optimal combination coefficients for different wavelengths are categorized as wide-lane, medium-lane, and narrow-lane combinations, as shown in Table 1. The table presented in Table 1 provides the combination coefficients (k, l, m, and n) for the carrier phase of four frequencies.…”

“…( ) ( ;0, , ) ( ;0, ) ( ; , ) 22 (14) In the equation, ( ;0, , ) To adaptively estimate the time-varying measurement noise, it is necessary to select a prior distribution for the time-varying parameters and then update the posterior information using variational Bayesian estimation. According to Equation ( 14), the auxiliary random variable and the degree of freedom parameter are treated as a continuous parameter in the Bayesian estimation.…”