基于概率统计方法的微弱GPS信号捕获算法

微弱GPS信号的信噪比较低,需采用更长的相干和非相干积分时间增强信噪比,提出一种从概率统计角度分析相干和非相干积分运算过程的方法。首先给出了复数下变频信号输入的相关运算表达式;然后推导了相干积分的相关输出数学期望和方差,计算出单元捕获失败的概率密度和概率表达式;最后,用Matlab对GPS信号的相干和非相干积分进行仿真。仿真结果验证了捕获失败概率表达式的结论,即由于高斯近似和非相干平均产生的性能损失,非相干积分的捕获性能比相干积分弱3.5 dB。

Acquisition algorithm for weak GPS signal based on probability statistics method

The SNR(signal noise ratio) of weak GPS signal is relatively low,and the coherent integral and incoherent integral are need to take longer time in order to increase the SNR,so this paper puts forward a method to analyze the calculating process of coherent integral and incoherent integral from the aspect of probability statistics.First it gives the calculating expression of the integral of complex down-converter input signal.Then it deduces the mathematical expectation and variance of the correlation output of coherent integral,and calculates the probability density and expression of acquiring failure of a unit.Moreover it uses Matlab to simulate the signal’s coherent integral and incoherent integral.The simulation results verify the probability expression of acquiring failure,that is,the incoherent integral’s acquiring ability is weaker than that of coherent integral by 3.5 dB,due to the performance loss caused by Gaussian approximation and incoherent integral.