优选小波神经网络在周跳探测与修复中的应用

北斗导航定位过程中，传统的周跳探测与修复方法缺乏检验环节，无法保证修复结果的可靠性。为此，提出了一种级联式小波变换结合NARX神经网络多步循环预测修复的方法处理周跳问题。该方法通过构造载波相位双差模型检验量，探测周跳发生历元，采用NARX神经网络预测方法修复周跳，利用优选小波基函数进行周跳修复效果检验。实验证明，相较于经验模态分解和变分模态分解等模态分解法，优选小波神经网络周跳探测与修复方法可用于小周跳探测并判断出周跳正负性；构造的NARX神经网络周跳修复模型，解决了普通神经网络模型和传统多项式拟合法容易造成的二次奇异值问题。相较于长短期记忆(LSTM)和门控循环单元(GRU)深度学习神经网络模型，周跳预测精度分别提高了45.2%和55.9%。

Application of optimal wavelet neural network in cycle slip detection and repair

In the process of BeiDou navigation satellite system (BDS) positioning, the cycle slip phenomenon significantly impacts the accuracy of BDS positioning. Traditional methods for detecting and repairing cycle slips lack effective verification steps, making it difficult to ensure the reliability of the repair results. To address this issue, a new method involving cascading wavelet transforms 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 accuracy of the method has been improved by 45.2% and 55.9%, respectively.