Global Navigation Satellite Systems (GNSS) are often the target of malicious attacks and interferences, mainly spoofing, thus posing a significant threat to both civilian and military equipment, and therefore necessitating efective detection and identification of such attacks. In this 'Work-in-Progress' paper, we propose the application of Machine Learning neural networks, a methodology proven highly efective in fields like cyberattack detection, to identify spoofing events across various scenarios. Our approach consists in computing non-time related metrics from a dataset of known spoofed signals, using the observables and signal-level measurements provided by a GNSS software receiver. The training is validated on both spoofed and clean scenarios to ensure a comprehensive approach. Furthermore, we provide a description of the feature's importance in the decision-making process of the model.
To meet the needs of the United States armed forces, the first model of a satellite geolocation system, TRANSIT, was implemented in the early 1960s. Developed by the U.S. Navy, TRANSIT was quickly followed by more sophisticated models, particularly the Global Navigation Satellite System (GNSS), which was the first satellite-based geolocation system open to civilians.s. Since then, the Geolocation and Navigation Satellite System (GNSS) technology has made enormous progress and has become indispensable for a plethora of uses in daily life. It has become a major economic and political issue, hence the development of the Galileo and Beidou-3 systems by European and Chinese respectively. Its architecture and functioning make it an easy target for malicious attacks: in the recent years, successful attempts of spoofing and jamming by rogue states or academic figures have shifted the debate on the urgent need to detect attacks and mitigate the damage. Civil GPS, which are embarked in civil transportation facilities, mainly boats or cars, are particularly vulnerable to this kind of threats but occurrences of jacking of secured military utilities have also been reported, e.g. Iran allegedly stole a US Air Force drone using low-cost spoofing [1].
Spoofing involves transmitting counterfeit GNSS-like signals to generate a false position in the target receiver without disrupting GNSS operations, ultimately gaining control over the receiver. This technique entails mimicking a false signal that shares the same code phase, carrier frequency, and Doppler frequency shift as the authentic navigation satellite signal, thereby enabling interference and signal capture.
Many counter techniques have been developed and published in the recent years, the majority focusing on analyzing signal level characteristics in order to trigger alarms when abnormal behavior is detected. They cover mainly disruption detection, for instance an abrupt change in either amplitude, beat carrier phase, code phase, and primarily power monitoring (RPM). In that sense, signal quality monitoring (SQM) consists in detecting distortions in the correlation peak that results from the correlation of the received signal and the local replica. For instance, among these SQM techniques, the most common metrics are often the delta and ratio tests [2], even though a wide range of similar metrics have also been proposed in the literature. Moreover, authentication of the signal by verifying the origin and integrity of signals is used to identify and prevent unauthorized or counterfeit transmissions [1].
In the past two decades, the integration of machine learning into practical, real-world applications has experienced a remarkable surge, including the improvement of GNSS navigation performance.[3] Despite this massive expansion to very various domains, GNSS spoofing detection through machine learning implementation is fairly restrained [4, 5, 6, 7, 8]. Many of these works involve detection techniques that require PVT observables, and thus they cannot be applied until the GNSS receiver has succeeded in obtaining a position fix, which may take several seconds in cold start.
In this paper, we provide a comparative analysis of many of the existing anti-spoofing techniques when they are tested in a common framework comprising the same GNSS software receiver and the same input datasets of spoofed signals. To do so, a layer of machine learning algorithms is implemented in order to gather all the outputs provided by the considered antispoofing techniques, and then to determine the relevance of such techniques on the model decision process that is followed by the machine learning algorithms. Machine learning’s greatest strength lies in its ability to discover patterns, outliers and hidden relationships in vast and intricate amounts of data, and therefore this feature is expected to help in unveiling which are the most efective anti-spoofing techniques among those being considered. It is important to remark that the input data for the machine learning algorithms (in our case, the output of the anti-spoofing techniques) often requires pre-processing such data through techniques like removal, cross-combination, and scaling, rather than directly converting these data into binary data (i.e. hard-decisions) for triggering alerts. These pre-processed data is then used as input for the machine learning model, which generates binary output predicting the presence of spoofing [9].
Once the introduction and motivation of this paper has been introduced, the remaining of this paper is structured as follows. The problem statement and the specific tasks that are conducted in the present work are briefly presented in Section 2. Next, a high-level explanation of the mathematics and technology used in this work is introduced in Section 3. The fundamentals of the considered Machine Learning architecture and its explicit the features are discussed in Section 4. Finally, the experimental setup is described in Section 5 and conclusions are drawn in Section 6.
This work has two primary objectives. Firstly, we aim at developing a robust and eficient spoofing detection system that leverages machine learning techniques, including both traditional algorithms and neural networks to practically predict a malicious spoofing attempt. In parallel, we collect metrics recently introduced in the literature along with exclusive metrics to retrospectively evaluate their weight in the machine learning process. The ultimate goal is to establish a ranking that reflects the efectiveness of each metric in detecting spoofing attempts. By combining a sophisticated detection system with a comprehensive understanding of the factors influencing its success, we hope to enhance the overall reliability and practicality of our approach.
To achieve this, we will: • Analyze multiple datasets containing both genuine and spoofed GNSS signals. • Investigate, extract and build relevant features and metrics for spoofing detection using a software receiver. • Train and evaluate a machine learning neural network to identify the most efective approach. • Assess the impact of diferent features on the decision-making process of the models. • Validate the performance of the developed system in realistic scenarios.
A typical GNSS signal can be represented in a simplified manner by Eq (
In a spoofing attack, the attacker generates a counterfeit GNSS signal, sp(), that closely
resembles the genuine signal, gn(). The goal is to deceive the GNSS receiver into locking
onto the counterfeit signal instead of the genuine one. The received signal in the presence of a
spoofing attack can be modeled by Eq (
The signal model forms the basis for feature extraction and analysis in the subsequent stages of our spoofing detection system. By exploring the diferences between genuine and counterfeit GNSS signals, we can identify meaningful features and metrics that can be used as input for the machine learning models.
A GNSS software receiver is a GNSS receiver that processes the received signals using software algorithms. It consists of several modules working together to acquire, track, and decode the GNSS signals. These modules operate in a synchronized manner to compute the position, velocity, and time (PVT) information [11]. The main components of a software receiver are summarized in Fig. 1 and briefly described below: • Signal Acquisition: This module searches for and acquires the GNSS signals transmitted by the satellites. It correlates the incoming signals with locally generated replicas of the PRN codes to determine the time delay and Doppler frequency shift. • Signal Tracking: Once a signal is acquired, the tracking module continuously adjusts the local replicas of the PRN code and carrier frequency to keep them aligned with the incoming signal. This process involves adjusting the code delay and carrier frequency using tracking loops, such as the code phase tracking loop and the carrier phase tracking loop. • Demodulation and Decoding: After tracking the signals, the receiver demodulates and decodes the navigation data. This information includes satellite ephemeris, clock corrections, and other auxiliary data. These data are essential for calculating the PVT solution.
• PVT Calculation: The receiver uses the decoded navigation data and the measured pseudoranges to compute the PVT solution. This calculation involves solving a set of nonlinear equations, which can be done using various algorithms, such as the least squares method or the extended Kalman filter.
Neural Networks are a subset of machine learning, mimicking the structure and function of biological neural networks, like the ones found in the human brain. It is typically structured with an input layer, one or multiple hidden layers and an output layer, they are well suited for modeling non-linear relationships. Therefore they have been increasingly used in various fields, from image recognition to language processing [5]. In this work, we choose to focus on one in particular:
The Multi-Layer Perceptron is a type of feedforward artificial neural network that consists of multiple layers of interconnected neurons. These connections have associated weights that are adjusted during the training process. The network learns to optimize these weights using an algorithm such as backpropagation, which minimizes the error between the predicted output and the actual target values. MLP is convenient in our case for multiple reasons. Firstly, it is a complex enough model to be able to handle complex and high-dimensional data to sense the outliers and patterns in non-linear relationships. Secondely, despite being highly eficient in most cases, it remains a fairly straightforward and computationally light algorithm in our particular architecture. This eficiency also facilitates the empirical search for optimal parameters through methods such as grid search[12].
To train and evaluate the performance of our machine learning models, we extract a set of features from the received GNSS signals. The following metrics are used for feature extraction[13] [14]: • Carrier to noise spectral density (/0): It measures the strength of the GNSS signal relative to the noise level. It is an essential metric to assess signal quality and can be afected by spoofing attacks.
The /0 is computed by first calculating the signal power and noise variance 2 from
the tracked signal. Specifically, the signal power is calculated as = 2 + 2 , where
and represent the in-phase and quadrature components of the signal. We plot it in Fig.
2. In that case, the scenario being a 10 dB power advantage, the metric is expected to raise,
suggesting there might be an issue. The dataset involves a 2 ms (milliseconds) time delay
or ’push’, also described as a ’two chip delay’, the signal is delayed by the duration of two
pulses. In our case the software receiver, never being able to locate the newest strongest
peak, is keeping track of the authentic signal instead of tracking the spoofed signal.
The noise variance 2 is obtained from the deviation of the noise level from its mean over
a certain interval. The /0 is then given by the formula:
(
2 ()
In this equation, , () and , () correspond to early and late taps, respectively, which
are seconds ahead and behind the prompt tap () in the in-phase component at time .
Since the delta test exhibits symmetry, [∆ ()] = 0 under conditions free from multipath
and spoofing.
• Quadrature discriminant metric: This metric is similar to the delta metric, but for the
quadrature component. It is represented as and calculated as follows in Eq (
2 ()
ELP = arctan
︂( , ()
, () −
, () )︂
, ()
(
, , () + , ()
2 ()
• Magnitude Diference Metric ( ): This metric evaluates the diference between the
magnitudes of the early and late taps normalized by the prompt tap magnitude. It can
help detect spoofing attacks. It is calculated in Eq (
MD = √︀, ()2 + , ()2 −
√︀, ()2 + , ()2
√︀ ()2 + ()2
• Q-channel Signal Quality Monitoring (SQM) metric: It is also denoted as sqm, is a novel
SQM metric proposed in [15] to address the limitations of traditional SQM metrics, such
as limited spoofing detection accuracy and low robustness due to false alarms caused by
environmental efects like multipath. Traditional SQM metrics are mainly constructed
based on the in-phase correlator outputs in the tracking loop of a GNSS instrument. During
a spoofing attack, the interaction between genuine and fake signals may lead to a transfer
of correlation energy into the quadrature channel. This abnormal quadrature channel
energy serves as the primary indicator for the sqm metric. In the absence of spoofing,
the typical value of Q-channel energy is 0, while the typical value of I-channel energy is
large and nonzero. When spoofing is present, even a weak abnormal energy can quickly
appear in the Q-channel. The metric is given in Eq (
+
()
()
(
The metric is computed using with Eq (
⎡1⎤ y = ⎢⎢⎣23⎥⎦⎥ , 4
⎡1⎤ y = ⎢⎢⎣23⎥⎦
⎥ 4 ︂[ ]︂
AA
context. Using Least Squares Regression on four points of each side of the correlation
function centered on its peak, the sum of the two slopes is the metric used to detect any
spoofing. Starting from the least squares regression, we can use the normal equations
to find the slopes for the left and right sides of the correlation function. Given 4 points
on each side, we can express the problem in matrix form. Let A and A be the 4 × 2
matrices for the left and right sides respectively, where the first column contains the time
shift values and the second column is filled with ones:
(
︂[ ]︂ AA = Ay, = Ay These normal equations can be solved to obtain the slope and intercept (, , , ) for each side. In matrix notation, these solutions would be: ︂[ ]︂ = (AA)− 1Ay,
= (AA)− 1Ay
︂[ ]︂
After obtaining the slopes and , we can calculate the Slope Asymmetry Metric
(SAM) as the sum of the two slopes in Eq (
SAM = +
A significant deviation of the SAM metric from zero would indicate potential spoofing.
In this study, we employ two publicly available datasets to evaluate the performance of our machine learning models, namely the Texas Spoofing Test Battery (TEXBAT) provided by the University of Texas at Austin, and the Oak Ridge Spoofing and Interference Test Battery (OAKBAT) from the US Oak Ridge National Laboratory. These datasets consist of diverse scenarios of spoofed GPS L1 C/A signals, as well as the baseline clean scenarios. • TEXBAT dataset [19]: The Texas Spoofing Test Battery (TEXBAT) is a collection of six highifdelity digital recordings of live static and dynamic GPS L1 C/A spoofing tests, conducted by the Radionavigation Laboratory of the University of Texas at Austin. The purpose of TEXBAT is to serve as the data component of an evolving standard aimed at defining spoof resistance for civil GPS receivers. The recordings capture a wide range of bandwidth and quantization considerations to support the evaluation of various authentication techniques. TEXBAT includes six spoofing attack scenarios and two clean datasets, with parameters such as spoofing type, platform mobility, power advantage, frequency lock, noise padding, and file size. The battery enables researchers to develop and evaluate spoofing detection techniques by studying the response of GPS L1 C/A receivers to the diferent spoofing attack scenarios presented in TEXBAT [20]. • OAKBAT dataset [21]: The OAKBAT dataset is a more recent dataset explicitly designed for GNSS spoofing detection research. It has been developed following the same methodology as the TEXBAT dataset to provide more data for researchers as those specific resources have proven to be scarce. This collection of digitized RF signals serves as both a complementary "sibling" and an advancement to the widely used TEXBAT dataset. It comprises both authentic and spoofed GNSS signals collected in controlled environments, with the latter being generated using a commercially available signal simulator. The OAKBAT dataset consists of 16 unique datasets, with eight sets containing only the GPS L1 C/A signal and another eight sets containing only the Galileo E1 signal. Each group has two spoof-free, clean baseline sets and six sets with various degrees and types of spoofing. The datasets share several common parameters and are designed with reproducibility and accessibility in mind, making it an invaluable resource for researchers in the field of GNSS security and robustness.
Our experimental setup comprises three main components: downloading spoofing or clean scenarios from the TEXBAT and OAKBAT datasets, processing the scenarios through a modified version of our software receiver to extract and build desired metrics, and building a machine learning neural network using these metrics as input.
1. Datasets: We aimed to include a diverse range of scenarios from both TEXBAT and OAKBAT datasets. In our experiments, we specifically used the Scenario 2 dataset from the TEXBAT collection, referred herein as ’ds2’. This scenario, also known as Static Overpowered Time Push (SOTP), features a spoofing attack where the spoofer has a 10 dB power advantage over the authentic signal ensemble. This scenario showcases the efects of a timing attack with a significant power advantage, forcing authentic signals into the noise floor and making the interaction between authentic and counterfeit signals less apparent. We also used the scenario 2 of the OAKBAT dataset, herein referred as ’os2’, which gives similar features. To have a more complete training, we also used the two clean of spoofing static scenarios from both datasets. As a validation feature, scenario 4, herein referred as ’os4’, of the OAKBAT dataset will be utilized.
2. Data Processing: We employed the FGI-GSRx software receiver for signal processing and analysis, which is provided as a companion software to [22]. Developed by the Finnish Geospatial Research Institute (FGI), this versatile GNSS software-defined radio tool is built with MATLAB, allowing users to process and analyze GNSS signals, which is particularly useful for research purposes. In our study, we used the FGI-GSRx software to evaluate the performance of spoofing detection techniques. We input the entire dataset into the software receiver but we focus on a shortened sample, which spans from approximately 10 seconds before the start of spoofing to 10 seconds after, according to the timestamps given by [ 19] for the TEXBAT dataset and [21] for OAKBAT.
For the non-spoofed scenarios, we compute from 100 to 120 seconds for the TEXBAT dataset and 110 to 130 seconds for the OAKBAT dataset. As a result, most metrics comprise 20,000 epochs, given that observations are obtained from the GPS L1 C/A signal every 1 ms. Some other metrics, such as those using the /0, are obtained every 1 s. It is also important to remark that only one satellite is being processed at a time in the results to be shown next, in particular SV3 for TEXBAT and SV8 for OAKBAT.
3. Machine Learning: We implemented a feedforward neural network using python libraries TensorFlow and Keras to classify the presence of spoofing attacks based on the metrics extracted from the GNSS signals, with the goal of predicting the binary label. The choice to use a neural network was motivated by multiple reasons. The main reason is their ability to model complex relationships very well, which is not as eficient in diferent models like Support Vector Machines (SVMs) or the gradient boosting XGBoost. They are able to extract non-linear relationships and intricate interactions between features. Another reason is their flexibility in tuning the parameters and the architecture of the layer; as the training dataset is still to be updated with more various scenarios, the adaptability of Multi-Layer Perceptron (MLP) simplifies the modeling process. On the other hand, it is important to pay attention to overfitting and bias while training, some early setups really struggled to accurately predict the spoofing due to strong overfitting. To compare performances, we also implemented an SVM model in our preliminary stages. While the SVM model delivered results comparable to the MLP, we decided to concentrate on optimizing and detailing results from the neural network due to its aforementioned benefits. We aim in this work at using binary classification to predict whether an epoch, here a 1 ms period, is spoofed or not. The algorithm consists of categorizing data into two classes: True or False. During the preprocessing, we first removed extreme outliers, mainly the first 1,000 points of the implementation, to eliminate any anomalous efects at the beginning of the dataset. Then, we applied a 1-second (1,000 points) rolling mean to smooth the data and reduce the noise. Thus, our input data is reduced from 20,000 epochs to 19,000 for 11 features. We also add the spoofed label that indicates whether a row is spoofed (equals 1) or not (equals 0). The dataset is randomly divided between training and test datasets with a ratio 70%− 30%. To this efect, we utilized the train_test_split function from the Scikit-learn Python library. This function first shufles the dataset randomly, then allocates a specified proportion of data points to the training set and the remainder to the test set As a result, the training and test datasets are composed of 13 300 and 5700 points respectively.
Additionally, we computed the correlation between the diferent features to better understand their relationships and potentially reduce dimensionality as illustrated in Fig. 5: it displays the 11 features used before reducing the dimensionality as well as the label value spoofed. It is important to remark that the importance of the correlation is given by the absolute value: a value close to 1 or -1 means a strong relationship between the variable whereas the closer to 0 the weaker the link. Reducing dimensionality is primordial in making the training more eficient by getting rid of useless noisy features and particularly to avoid overfitting: other methods could be implemented such as Principal Component Analysis (PCA) to reduce the number of features using their variance [23].
To better training performance, the metrics of size 20,000 are scaled using MinMaxScaler following the formula: std =
− min
max − min
scaled = std * (max − min) + min
(
In our model, we employed an L2 regularization technique to prevent any single feature from dominating the learning process. This technique adds a penalty proportional to the square of the magnitude of the weights to the loss function, discouraging the model from assigning too much importance to any particular feature. This helps in reducing overfitting and makes the model more generalizable [24].
The architecture of the implemented neural network is as follows: • Input layer: A dense layer with 32 neurons and a ReLU activation function, which takes the feature vector with a length equal to the number of metrics.
• Dropout layer: A dropout layer with a dropout rate of 0.5 is added to prevent overfitting.
• Hidden layer: A dense layer with 16 neurons and a ReLU activation function. The Rectified Linear Unit layer (ReLU) is an activation function that simply retains positive inputs and sets all negative inputs to zero. Although simple, this function has several interesting properties that make it very useful in neural networks. Firstly, while being a linear function for positive values, ReLU introduces non-linearity due to the threshold at zero, allowing neural networks with ReLU activations to model complex patterns and relationships. Secondly, ReLU leads to sparse activation, meaning that at any layer, some neurons can output a true zero, contrary to tanh and sigmoid functions that only can approach the zero value, making the network more eficient and easier to train. Thirdly, the computation is very straightforward and basic, making the computation very eficient, the function can be represented as () = max(0, )[25]. • Dropout layer: Another dropout layer with a dropout rate of 0.5 is added. • Output layer: A dense layer with a single neuron and a sigmoid activation function, as this is a binary classification problem.The sigmoid activation function, also known as the logistic function, is commonly used in the output layer of binary classification problems due to its ability to map any real-valued number into the range between 0 and 1. This makes it useful for outputting probabilities for the two classes in a binary classification problem. The sigmoid function is represented as () = 1/(1 + − ) where is the input to the function.
The model is compiled using the Adam optimization algorithm and the binary cross-entropy loss function, which is appropriate for a binary classification task. After hypertuning the parameter using a randomSearch, The model is trained on the training dataset for 30 epochs with a batch size of 32 and learning rate = 0.01. The performance of the model is evaluated on the test dataset using validation data during training.
In this section, we present the results obtained from our experiments. The primary objective was to retrospectively identify the most influential metrics in our algorithm’s decision-making process during training, in the idea to mitigate the "black-box" efect of such algorithms. At this point of time we build the ranking for a dataset composed of both TEXBAT and OAKBAT second scenarios and the OAKBAT clean static scenario. (ds2+os2+cleanStatic_os). To compute the metrics importance, we use two diferent methods: • Feature importance using connections weights This method aims at computing the relative importance of input features by calculating the weights of the neural network [26]. In our code, we evaluate the weight in between the input layer and the first hidden layer. The results are shown in the left hand side plot of Fig. 6. • Permutation importance This method involves randomly shufling the values of a single feature, running the model with the shufled data, and measuring the change in performance. The larger the performance drop, the more important the feature. To visualize the results, we plot the importance of each feature with bar style, as well as the standard deviation error to estimate uncertainty in the right hand side plot of Fig. 6. It is worth noting that this does not represent a percentage because it doesn’t involve breaking a whole into parts: it represents the average diference between the model with and without shufling over multiple tries (here ten times for each feature). A feature could even have a negative value if shufling it actually improves the model, for instance if the metrics only add noise to the model [27].
The first method uses directly the inner working of the neural network but treats the metrics independently, which could cause a wrong estimation of features’ correlation and therefore output wrong results. The second method is not relying on the model’s structure, thus can more adequately estimate more complex models despite being computionally heavier. We hope to have a better vision of the model computation by exhibiting those two methods together.
In this section, we discuss the validation for our merged datasets (os2+ds2+oakbatCleanStatic). To ensure a comprehensive evaluation, we validate on two independent datasets: the spoofed OAKBAT scenario ’os4’ and the clean TEXBAT ’cleanStatic’ scenario. This approach allows us to gauge the algorithm’s performance in detecting and diferentiating between the two types of data.
Firstly, being sure that our algorithm does not wrongly overly identify spoofing events in a clean dataset is primordial: hereby the left hand side plot in Fig. 7 shows the /0 over the acquisition stage of the GNSS receiver according to the predictions on the non-spoofed scenario. The results are quite promising: over 80 % of the epochs are predicted correctly.
In terms of the spoofed dataset, we plot the /0 where the color-coded data points represent diferent prediction states in the right hand side plot of Fig. 7 alongside with the confusion matrix in Fig. 8: we observe that the model identifies almost perfectly the non-spoofed period (in blue, 98% precision) whilst it struggles more on the spoofed event (79%). This is confirmed by the confusion matrix Fig. 8: 417 spoofed epochs are being predicted wrongly. For a practical use, we could convene that if the frequency of predicted spoofing exceeds a specified threshold (e.g., 75%) within a certain time frame, it is likely that a spoofing attempt is in progress. Tab. 1 summarizes all the validation results.
We proceeded to test our model using only the top five (CNO, ccafMetric, MetricSAM, ELP, Msqm) and top three (CNO, ccafMetric, MetricSAM, ELP, Msqm) metrics according to their importance given in Fig. 6. The model’s performance degraded slightly: this suggests that even the lowest ranked metrics have valuable information, as illustrated in Tab. 2. Therefore, while our analysis confirms the significant impact of the top-ranked metrics, it also highlights the collective contribution of all metrics in achieving optimal detection accuracy. Regarding the clean Oakbat dataset, the results are sensibly the same.
This work-in-progress article showcases an approach for developing an eficient machine learning-based spoofing detector concomitantly with a importance review of various metrics build in the process. This paper uses the neural network multi-layer perceptron neural network on selected metrics and combined datasets to classify artificially created spoofing scenarios. The procedure involves acquiring primary data through a software receiver, constructing the desired metrics mathematically, and applying classical machine learning pre-processing and scaling techniques.. The results give promising results as the algorithm is able to display spoofing and non spoofing events with correct results (with a minimum of 82% recall). As our range of validated datasets is fairly limited, we aim at improving the work by expanding the dataset with home generated spoofing scenarios using the Skydel GSG-8 GNSS simulator available at the SPCOMNAV research group. Those new datasets will enable a wider range of spoofing attacks, helping reduce the potential bias in our results.
This work was supported in part by the Spanish Agency of Research (AEI) under the Research and Development projects PID2020-118984GB-I00/AEI/10.13039/501100011033 and PDC2021121362-I00/AEI/10.13039/501100011033.
Support for DOI 10.13139/ORNLNCCS/1664429 dataset (OAKBAT) is provided by the U.S. Department of Energy, project LOIS 9445 under Contract DE-AC05-00OR22725. Project LOIS 9445 used resources of the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory, which is supported by the Ofice of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. [19] A. Lemmenes, P. Corbell, S. Gunawardena, Detailed analysis of the TEXBAT datasets using a high fidelity software GPS receiver (2016) 3027–3032. doi: 10.33012/2016.14668. [20] T. Humphreys, J. Bhatti, D. Shepard, K. Wesson, The Texas spoofing test battery: Toward a standard for evaluating GPS signal authentication techniques (2012). [21] A. Albright, S. Powers, J. Bonior, F. Combs, A tool for furthering GNSS security research: The oak ridge spoofing and interference test battery (OAKBAT) (2020) 3697–3712. doi: 10. 33012/2020.17712. [22] K. Borre, I. Fernández-Hernández, J. A. López-Salcedo, M. Z. H. Bhuiyan (Eds.), GNSS Software Receivers, Cambridge University Press, Cambridge, 2022. doi:10.1017/ 9781108934176. [23] L. van der Maaten, E. Postma, H. Herik, Dimensionality reduction: A comparative review,
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