Wavelet denoising and cycle slip detection and repair of BDS triple-frequency signal

The traditional triple-frequency code-phase combination method is easily affected by the pseudorange observation noise, and it is difficult to detect the insensitive small cycle slip. The triple-frequency geometry-free (GF) phasemethod has the ability to detect sensitive small cycle slip, but it has the problem of ill-conditioned equations. In view of this, this paper proposes a method of combining code-phase combination and GF model using wavelet denoising. Firstly, the pseudorange observations were denoised by wavelet transform. Then, the optimal combination model is constructed by selecting the optimal combination coefficient. Therefore, the quality of source data is ensured by wavelet denoising, and the accuracy of cycle-slip detection and repair is improved by code-phase combination and GF combination. At the same time, the problem of ill-conditioned equations is solved. Finally, the least square method combined with QR decomposition algorithm is used to fix the optimal integer of the cycle slip and repair the cycle slip by using spatial search and 1-norm minimum principle, and the triple-frequency measurement data of the BeiDou Navigation Satellite System (BDS) is collected for experimental verification. The experimental results show that the optimal combination model of wavelet transform denoising can detect and repair all kinds of cycle slips, especially for insensitive small cycle slips.