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The time it takes to acquire a satellite signal is one of the most important parameters for a Global Navigation Satellite System (GNSS) receiver. The Parallel Frequency space search acquisition Algorithm (PFA) runs faster than the Parallel Code phase search acquisition Algorithm (PCA) when the approximate phase of Pseudo-Random Noise (PRN) code and the approximate value of a Doppler shift are known. However, a large amount of data is needed to be dealt with by the Fast Fourier Transform (FFT) in a traditional PFA algorithm because it processes a narrow-band signal with the initial sampling frequency after the PRN code is stripped. In order to reduce the computational complexity of the traditional PFA algorithm, a down-conversion module and a downsampling module were added to the traditional PFA in the work reported here. Experiments demonstrated that this method not only succeeded in acquiring BeiDou B1I signals, but also the time for acquirement was reduced by at least 80% with the modified PFA algorithm compared with the traditional PFA algorithm. The loss in Signal-to-Noise Ratio (SNR) did not exceed 0·5 dB when the number of coherent points was less than 500.

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In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.

The BeiDou software receiver uses the fast Fourier transform (FFT) to perform the acquisition. The Doppler shift estimation accuracy should be less than 500 Hz to ensure satellite signals to enter a locked state in the tracking loop. Since the frequency step is usually 500 Hz or larger, the Doppler shift estimation accuracy cannot guarantee that satellite signals are brought into a stable tracking state. The straightforward solutions consist in increasing the sampling time and using zero-padding to improve the frequency resolution of the FFT. However, these solutions intensify the complexity and amount of computation. The contradiction between the acquisition accuracy and the computational load leads us to research for a more simple and effective algorithm, which achieves fine acquisition by a look-up table. After coarse acquisition using the parallel frequency acquisition (PFA) algorithm, the proposed algorithm optimizes the Doppler shift estimation through the look-up table method based on the FFT results to improve the acquisition accuracy of the Doppler shift with a minimal additional computing load. When the Doppler shift is within the queryable range of the table, the proposed algorithm can improve the Doppler shift estimation accuracy to 50 Hz for the BeiDou B1I signal.