We propose a novel algorithm for the joint estimation of spoofer location (LS) and GPS time using multireceiver direct time estimation (MRDTE). To achieve this, we utilize the geometry and known positions of multiple static GPS receivers distributed within the power substation. The direct time estimation computes the most likely clock parameters by evaluating a range of multipeak vector correlations, each of which is constructed via different pregenerated clock candidates. Next, we compare the time-delayed similarity in the identified peaks across the receivers to detect and distinguish the spoofing signals. Later, we localize the spoofer and estimate the GPS time using our joint particle and Kalman filter. Furthermore, we characterize the probability of spoofing detection and false alarm using Neyman Pearson decision rule. Later, we formulate the theoretical Cramér Rao lower bound for estimating the localization accuracy of the spoofer. We validate the robustness of our LS-MRDTE by subjecting the authentic open-sky GPS signals to various simulated spoofing attack scenarios. Our experimental results demonstrate precise localization of the spoofer while simultaneously estimating the GPS time to within the accuracy specified by the power community (IEEE C37.118 standard for synchrophasors).

中文翻译：

---

GPS 多接收器联合直接时间估计和欺骗器定位


我们提出了一种使用多接收器直接时间估计 （MRDTE） 联合估计欺骗器位置 （LS） 和 GPS 时间的新算法。为了实现这一目标，我们利用了分布在变电站内的多个静态 GPS 接收器的几何结构和已知位置。直接时间估计通过评估一系列多峰值向量相关性来计算最可能的 clock 参数，每个相关性都是通过不同的预生成 clock candidates 构建的。接下来，我们比较接收器之间识别峰值的时间延迟相似性，以检测和区分欺骗信号。稍后，我们定位欺骗器，并使用我们的联合粒子和卡尔曼滤波器估计 GPS 时间。此外，我们使用 Neyman Pearson 决策规则来描述欺骗检测和误报的概率。后来，我们制定了理论 Cramér Rao 下限来估计欺骗者的定位准确性。我们通过将真实的开阔天空 GPS 信号置于各种模拟欺骗攻击场景中来验证 LS-MRDTE 的稳健性。我们的实验结果表明了欺骗器的精确定位，同时估计 GPS 时间达到电力社区（同步相量的 IEEE C37.118 标准）规定的精度范围内。