## 1 Introduction  
Today, navigation is done worldwide, with the aid of the global positioning system (GPS) receivers. More than 400 million people worldwide rely on the satellite navigation to deliver the position, velocity, and time (PVT) information. At least four GPS satellites are required to provide a user position solution, which includes a position in three-dimensional coordinate and time information. The strength of received GPS signal transmitted from a satellite to the ground users is about \(-157\) dBm below the noise floor of \(-138.5\) dBm [1, 2, 3]. GPS is a direct-sequence spread-spectrum (DSSS) code-division-multiple-access (CDMA) system, and it can deal with the wideband noise and narrowband interference with low power contributed by the processing gain of the spreading code [4]. GPS receivers acquire and track the satellite signal using the correlation properties between the received satellite signal and the locally generated carrier and spreading code replicas. A maximum correlation value occurs, when the locally generated replicas align those of the received signal. However, the maximum correlation would be degraded due to the low received power GPS signal or the high power narrowband interference, especially in urban or indoor environments. It is because the received signal power might be blocked or shadowed by buildings or trees around the users. Accordingly, the number of acquired GPS satellites decreases extremely, such that the navigation performance is degraded or interrupted eventually. Researches focusing on the low received power GPS signal processing have attracted a lot of attentions in recent years [5, 6, 7, 8, 9]. [PERSON] and [PERSON] in 2000 [5] compared several acquisition methods on criteria of receiver operation characteristics (ROCs), and suggested an approach, the non-coherent acquisition method, for weak signal acquisition. [PERSON] in 2001 [6] reported a block acquisition method for weak GPS signal. The block acquisition method uses a predetection and integration time of 20 milliseconds, and subsequently formed 20 different accumulation parts, where each corresponds to a possible bit transition. As a result, this approach could acquire a weak signal with carrier-to-noise ratio (\(\rm{C/N_{0}}\)) as low as 21 dB-Hz. [PERSON] and [PERSON] _et al._ in 2006 [7] proposed a differential combining (DFC) method for acquiring the weak GPS signal. The performance of the DFC method is superior to the conventional non-coherent approach [5] on the criteria of ROCs. The DFC could reduce the 3 dB processing loss of the non-coherent approach and improved the sensitivity by about 1.6 dB. The authors in 2009 [8] reported a weighted coherent overlapping (WCO) tracking method for low received power tracking. It could enhance the correlation value by coherent integration time method without reducing the Doppler window. In [9], the authors implemented the empirical mode decomposition (EMD) method to reduce the noise effect of the collected raw GPS signal. The signal-to-noise ratio (SNR) was therefore improved in the GPS signal acquisition process. Most of the methodologies make efforts to enhance the acquisition performance based on the criteria of ROCs, which is a statistical process. For a satellite signal with low received power in the received GPS signal, the maximum correlation peak might be below the predetermined detection threshold, and it subsequently would be declared as signal absent. This paper therefore reports a solution called the signal existence verification (SEV) process to detect and verify whether the signal is absent. The SEV process is developed based on the time-frequency analysis [10], and it can detect the characteristic of the low received satellite signal on the generated spectrogram of the satellite signal. Furthermore, the SEV process could provide an additional stage for signal detection without changing the signal acquisition or tracking algorithms.