Multipath is the phenomenon that occurs when the signal from GNSS satellites reflects on objects surrounding the survey environment and reaches the receiver's antenna through multiple paths. Usually, the receiver collects the direct and the reflected signal, which is delayed in relation to the direct one. Consequently, the pseudorange and carrier-phase measurements are tracked for a composed signal, and not for the direct signal, causing the multipath error. Multipath effect is the main factor influencing short baselines in GPS relative positioning because the errors related to satellite, receiver and atmosphere can be well reduced by the double difference methods. In static survey, the antenna is commonly located far away from reflectors to reduce multipath effect. In this case, the main remained multipath effect is due to high-frequency, which may be easier mitigated by denoising methods. But for kinematic applications, near reflectors are generally unavoidable and, in this case, the lowfrequency multipath is much more predominant and it still remains as the main challenge for high precision positioning. This effect has great influence on the ambiguity solution and it is very difficult to be removed it from the data, mainly, due to its abrupt variations in kinematic applications. Spectral analysis has a powerful technique to analyze this kind of non-stationary signals: the wavelet transform. But even so, several processes and specific ways of processing are necessary to work together in order to investigate low-frequency multipath. Although low-frequency multipath has a non-stationary behavior for kinematic signals, which requires the evolutionary spectrum estimation, in this paper it is proposed a technique of locally stationary spectrum estimation. The signal is analyzed in small windows of data during the kinematic processing. To process data of each epoch, data from some previous epochs are used together in the multipath detection, but just the current epoch is corrected. Thus, the details and features of the proposed method involving wavelets techniques will be presented in this paper. Some experiments were carried out in a kinematic mode with a controlled and known vehicle movement. The data were collected in the presence of objects placed close to the vehicle to cause, mainly, lowfrequency multipath. The ambiguity solution and the coordinates in each epoch were analyzed and compared. In summary, the possibilities of applying spectral analysis involving wavelets will be discussed, as well as the improvements and the difficulties for low-frequency multipath mitigation in kinematic applications.