A challenging and outstanding problem in applications that involve or rely on GPS signals is to mitigate jamming. We develop a machine learning-based antijamming framework for GPS signals. Three types of jamming signals are considered: continuous wave interference, chirp and pulse jamming. In addition, white Gaussian noise is assumed to be present. From the point of view of communication, information is encoded in the coarse/acquisition (C/A) code. Multiplying the jammed signal by a sinusoidal wave and integrating over one C/A code period leads to a jammed C/A code signal. To mitigate jamming, we study three types of machine learning methods: reservoir computing (echo state network), multi-layer perceptron, and long short-term memory networks (RNNs). A machine can be trained to learn and predict the signal directly or learn and predict jamming where the real signal can be obtained by removing the jammed component from the total received signal. For a high-frequency carrier (e.g., the standard 1575.42 MHz L1 carrier), learning and prediction can be made computationally efficiently on the C/A code signal. The main result is that machine learning can be effective for predicting and extracting weak GPS signals even in a strongly jammed/noisy environment where the jamming amplitude is three orders of magnitude stronger than the GPS signal. We find that the reservoir computing scheme is stable and performs well for all three types of jamming. The multi-layer perceptron is better for predicting the jamming signal than the GPS signal itself, and the long short-term memory networks work well but only for certain jamming types. In particular, with the direct signal prediction method, the bit error rate (BER) associated with reservoir computing (RC) remains at near-zero values (less than 1%) even for jamming signal ratio (JSR) up to 60 dB for the three types of jamming. The multi-layer perceptron (MLP) method breaks down when the JSR is larger than 20 dB for continuous wave interference (CWI) and pulse jamming, 45 dB for chirp jamming. The long short-term memory (LSTM) can perform very well for the chirp jamming with a near zero error rate and give BER larger than 10% when the JSR is around 40 dB for the CWI and pulse jamming. For the jamming prediction method (indirect method), these three machine learning methods perform well, with near-zero BER (less than 1%). Overall, the RC scheme is stable and performs well for three types of jamming. Besides, RC is fast compared to LSTM method, with much less running time.

在涉及或依赖 GPS 信号的应用中，一个具有挑战性和突出的问题是减轻干扰。我们为 GPS 信号开发了一个基于机器学习的抗干扰框架。考虑了三种类型的干扰信号：连续波干扰、啁啾和脉冲干扰。此外，假设存在高斯白噪声。从通信的角度来看，信息被编码在粗/获取（C/A）码中。将干扰信号乘以正弦波并在一个 C/A 码周期内积分会导致干扰 C/A 码信号。为了减轻干扰，我们研究了三种机器学习方法：水库计算（回声状态网络）、多层感知器和长短期记忆网络 (RNN)。可以训练机器直接学习和预测信号，或者学习和预测干扰，其中可以通过从总接收信号中去除干扰分量来获得真实信号。对于高频载波（例如，标准的 1575.42 MHz L1 载波），可以在 C/A 码信号上高效地进行学习和预测。主要结果是，即使在干扰幅度比 GPS 信号强三个数量级的强干扰/嘈杂环境中，机器学习也可以有效地预测和提取微弱的 GPS 信号。我们发现储层计算方案是稳定的，并且对于所有三种类型的干扰都表现良好。多层感知器比GPS信号本身更能预测干扰信号，长短期记忆网络运行良好，但仅适用于某些干扰类型。特别是，对于直接信号预测方法，即使对于高达 60 dB 的干扰信号比 (JSR)，与存储库计算 (RC) 相关的误码率 (BER) 仍保持在接近零的值（小于 1%）。三种类型的干扰。当连续波干扰 (CWI) 和脉冲干扰的 JSR 大于 20 dB，啁啾干扰大于 45 dB 时，多层感知器 (MLP) 方法就会失效。长短期记忆（LSTM）可以很好地处理线性调频干扰，错误率接近于零，并且当 CWI 和脉冲干扰的 JSR 约为 40 dB 时，BER 大于 10%。对于干扰预测方法（间接方法），这三种机器学习方法都表现良好，BER接近于零（小于1%）。全面的，RC 方案稳定，对于三种类型的干扰都表现良好。此外，与 LSTM 方法相比，RC 速度快，运行时间少得多。