That cycle-slips remain undetected will significantly degrade the accuracy of the navigation solution when using carrier phase measurements in global positioning system （GPS）. In this paper, an algorithm based on length-4 symmetric/anti-symmetric （SA4） orthogonal multi-wavelet is presented to detect and identify cycle-slips in the context of the feature of the GPS zero-differential carrier phase measurements. Associated with the local singularity detection principle, cycle-slips can be detected and located precisely through the modulus maxima of the coefficients achieved by the multi-wavelet transform. Firstly, studies are focused on the feasibility of the algorithm employing the orthogonal multi-wavelet system such as Geronimo-Hardin-Massopust （GHM）, Chui-Lian （CL） and SA4. Moreover, the mathematical characterization of singularities with Lipschitz exponents is explained, the modulus maxima from wavelet to multi-wavelet domain is extended and a localization formula is provided from the modulus maxima of the coefficients to the original observation. Finally, field experiments with real receiver are presented to demonstrate the effectiveness of the proposed algorithm. Because SA4 possesses the specific nature of good multi-filter properties （GMPs）, it is superior to scalar wavelet and other orthogonal multi-wavelet candidates distinctly, and for the half-cycle slip, it also remains better detection, location ability and the equal complexity of wavelet transform.
