In the process of BeiDou navigation satellite system(BDS)positioning,the cycle slip phenomenon significantly impacts the accuracy of BDS positioning.Traditional methods for detec-ting and repairing cycle slips lack effective verification steps,making it difficult to ensure the relia-bility of the repair results.To address this issue,a new method involving cascading wavelet trans-forms combined with nonlinear auto-regressive model with exogenous inputs(NARX)neural network multi-step cyclic prediction repair is proposed.The method firstly constructs a test quantity based on the carrier phase double-difference model to detect the specific epochs of cycle slips.Then,the NARX neural network prediction method is employed to repair the cycle slips,using optimally selected wavelet basis functions.Finally,the chosen wavelet basis functions are used to verify the effectiveness of the cycle slip repair.The experiment results show that compared to modal decomposition methods like empirical model decomposition and variational mode decomposition,the proposed method using optimally selected wavelet neural network for cycle slip detection and repair is effective for detecting small cycle slips and determining their polarity.The constructed NARX neural network model for cycle slip repair addresses the issue of quadratic singular values that can arise with ordinary neural network models and traditional polynomial fitting methods.Compared to deep learning neural network models like long short-term memory(LSTM)and gated recurrent unit(GRU),the cycle slip prediction accu-racy of the method has been improved by 45.2%and 55.9%,respectively.
BeiDou navigation satellite systemCarrier phaseCycle slip detection and correctionWavelet transform