Abstract
An improved cycle-slip repair model is proposed for BDS triple-frequency undifferenced observations. Two extra-wide-lane code-phase combinations and one additional geometry-free (GF) carrier-phase combination are employed. To ensure the GF phase combination follows a normal distribution, the residual ionospheric variation of the GF phase combination is corrected in real-time using the previous observation sequence without cycle slip. The integer least squares principle, based on the least-squares ambiguity decorrelation adjustment, is used to solve the fixed value of cycle slip. The corresponding covariance matrix of floating cycle-slip estimations used for construction is updated in real time to improve the fixed efficiency of cycle slip. Moreover, for reliable repair of cycle slip for triple-frequency observations, the critical ratio value between the second-best and best cycle-slip candidates for different residual ionosphere accuracies and different repair success rates are given based on large amounts of simulated data. Lastly, a set of active ionosphere and low-sampling-rate real data was used for evaluation and analysis of the algorithm. Results showed the success rate of cycle-slip repair is 99.997%, even under active ionosphere conditions, with low satellite elevation and low sampling rate. Unfortunately, one cycle-slip group (1, 1, 1) of the C14 satellite was not detected successfully and repaired correctly because of insensitivity to the GF phase combination under bad observation conditions.
Highlights
Cycle-slip detection and repair is an area of active research in precise positioning of global navigation satellite systems (GNSS)
The triple-frequency signals in theory can improve the performance of cycle-slip detection and precise positioning compared with the traditional dual-frequency [1], [2]
Considering the nonnegligible influence of the residual ionospheric variation on the accuracy of the GF phase combinations and the floating cycle-slip estimation, the simple highly efficient sliding window mean (SWM) method was adopted to correct the ionospheric variation at the current epoch using the predicted ionospheric variations, which can ensure the corrected GF combination observations followed a normal distribution
Summary
Cycle-slip detection and repair is an area of active research in precise positioning of global navigation satellite systems (GNSS). The detectable cycle-slip value Nαβγ based on epoch difference can be expressed as follows: Nαβγ = − Lαβγ − ηαβγ I1 + εαβγ (5) It can be seen from Equation (5) that the cycle-slip value of the GF phase combination is affected mainly by the residual ionospheric variation. Because of the adopted different combination of observation values, the estimated parameters are usually only cycle-slip values of three frequencies, and the correlation of the estimated parameters is weaker than that of the ambiguity resolution To solve this problem, integer bootstrapping and ILS are usually employed to obtain the optimal parameter estimation. The structure of the covariance matrix of the three combinational observations in Equation (12) has to consider the influence of stochastic noise after correcting the ionospheric variation as follows:. (7) Repair cycle slip: if the ratio test is passed (Equation (18)), repair original observations using the best cycle-slip candidates; otherwise, mark this epoch for initialization of the ambiguity solution
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