Network-Based GNSS Jamming Prediction Enabling Wideband Interference Observation

Sandeep Jada; Mark Psiaki,; Mathieu Joerger

doi:10.33012/navi.763

Abstract

In this paper, we develop and evaluate an autonomous, self-calibrating, receiver-independent carrier-to-noise-density ratio (C/N0)-based jamming detection algorithm capable of processing data from large receiver networks. The algorithm uses optimal detectors that target a predefined false alert rate. Using this algorithm, we processed eight months of data from hundreds of receivers and identified patterns in jamming detection consistent with intentional interference, providing an opportunity to validate the C/N0 detector. We designed a portable experimental radio frequency (RF) data collection setup and developed an optimal power-based jamming monitor to independently detect jamming. With this setup, we detected a genuine jamming event while driving on I-25 in Colorado, United States, and validated the C/N0-based detector through time–frequency analysis of wideband RF data from the event.

Keywords

1 INTRODUCTION

In this paper, we develop a method to detect, predict, and observe recurring global navigation satellite system (GNSS) jamming events caused by motorists on daily or weekly schedules. We first design and implement an autonomous, self-calibrating algorithm to detect jamming using carrier-to-noise-density ratio (C/N0) data from networks of hundreds of heterogeneous receivers. The detector is evaluated with respect to both its high sensitivity to low-power jammers and its robustness to false alerts. The detector offers GNSS jamming prediction capability that is validated through time–frequency analysis of wideband radio frequency (RF) data collected during an interference event that we anticipated on a United States (U.S.) highway.

Over the past decade, RF interference (RFI), such as GNSS jamming and spoofing, has been a growing threat to critical infrastructure that depends on positioning, navigation, and timing (PNT) (C4ADS, 2019; The White House, 2020, 2021). Wide-area jamming is observed in conflict areas (Wu, 2024) and has occurred in the U.S., causing major air traffic disruptions (Dacus et al., 2022; Joerger et al., 2023). A more widely spread source of localized GNSS jamming includes easily acquirable and low-cost personal privacy devices (PPDs) (Federal Bureau of Investigation, 2014; Brunker, 2016).

The RFI mitigation methods of Hegarty et al. (2019), Mitch (2014), Mosavi et al. (2017), and Wesson et al. (2017) use sophisticated and data-intensive signal processing techniques that require dedicated hardware, which would be too expensive for wide-scale deployment.

Jamming detection can also be implemented using off-the-shelf GNSS receiver outputs including C/N0 and automatic gain control (AGC) (Kim et al., 2020; Levigne, 2019; Miralles et al., 2018; Scott, 2011; Strizic et al., 2018; Weston et al., 2010). C/N0-based jamming detectors using fixed detection thresholds have been developed by Borio and Gioia (2015) and Fors et al. (2021). However, these C/N0 methods are insufficient when using hundreds of receivers and antennas of different ages, brands, and models, such as those of the National Geodetic Survey’s (NGS) continuously operating reference stations (CORS) and of the International GNSS Service (IGS). Manually setting thresholds on C/N0 measurements with time-varying distributions is not a viable approach.

To address this issue, in this paper, we develop a self-calibrating Global Positioning System (GPS) L1 C/N0-based jamming monitor that is equipment-agnostic. We implement this algorithm using months of data from 900 CORS and IGS receiver locations to identify daily-repeating jamming. We then deploy our own equipment with a power-based detector to capture wideband data during an example predicted RFI event, thereby validating the C/N0 monitor and the jamming prediction concept.

The C/N0 monitoring and validation algorithm is designed to minimize the risk of missed detection while limiting the risk of false alerts. First, we derive locally Neyman–Pearson optimal detection tests, which minimize the probability of missed detection for cases of small jamming signal power density. We implement our algorithm to provide three detectors using C/N0 measurements, time-differenced C/N0, and uncalibrated RF front-end signal power measurements. Second, to limit the risk of false alerts, we develop an automated, high-fidelity nominal C/N0 modeling methodology. Overbounding theory is leveraged to robustly model C/N0 variations, including at small quantiles (Blanch et al., 2017; DeCleene, 2000; Rife et al., 2006). The parametric error models account for individual receiver and satellite equipment and locations.

We implemented the C/N0-based algorithms using data from 900 CORS receivers over eight months in 2022. We identified daily recurring patterns to predict jamming events at specific locations. To further analyze such events, we built a deployable wideband data collection device with a power monitor that triggers recording and storage. We leveraged this equipment to observe a predicted RFI “in the wild” on a highway in Colorado. Time–frequency spectrogram analyses of the RF front-end signal’s show peak power density variations consistent with those of a chirp jammer (Diez et al., 2022; Kraus et al., 2011; Mitch et al., 2011), which validates the network-based C/N0 jamming prediction method.

This article is organized as follows. In Section 2, we derive optimal hypothesis tests for C/N0 and RF front-end power-based jamming detection. In Section 3, we develop the nominal C/N0 measurement modeling methods. In Section 4, we implement and evaluate the C/N0-based jamming monitor using months of data from large receiver networks. Section 5 describes the detector validation through wideband RF data analysis capturing the signal of a PPD jammer. Section 6 provides concluding remarks.

2 DERIVATION OF C/N0-BASED AND POWER-BASED GNSS JAMMING DETECTORS

In this section, we derive three methods for detecting the presence of jamming using C/N0, time-differenced C/N0, and RF front-end power measurements. We also determine the theoretical probability distributions of the three detection test statistics. These distributions will be validated and their parameters evaluated using data in Section 3.

2.1 C/N0 Test for GNSS Jamming Detection

This section shows that the instantaneous, one-sided, Neyman-Pearson optimal test that minimizes missed detection of small increases in jamming power density is the sum over all satellites of the differences between measured and mean C/N0 weighted by the inverse of their C/N0 measurement variance. An offline, a priori, data-based evaluation of the mean and variance of C/N0 measurements is described in Section 3.

Let C_i,k be the received signal power (in watts) from GNSS satellite i at time step k. Let N₀ be the noise power density in watts per hertz (W/Hz). Let c_i,k be the receiver-provided C/N0 estimate in dB-Hz for the i-th satellite at time step k. Under jamming-free conditions (hypothesis H₀), we model c_i,k using a Gaussian overbounding distribution with mean μ_i,k and variance $σ_{i, k}^{2}$ . The modeling procedure in Section 3.1 describes the Gaussian overbounding process. Gaussian overbounding of C/N0 measurements is consistent with (and a possible refinement over) the Gaussian models used by Murrian et al. (2019) and Wesson et al. (2017). Under H₀, c_i,k is expressed as follows:

$c_{i, k} = {(\frac{C_{i, k}}{N_{0}})}_{d B - H z} \sim N (μ_{i, k}, σ_{i, k}^{2})$ 1

where, for a C/N0 X, we define (X)_dB–Hz = 10log₁₀(X). In the presence of jamming (hypothesis H₁), the jamming power density J_k (in W/Hz) adds to N₀ on the denominator, thus degrading the C/N0 for all satellites in view. J_k is the received jamming power at time step k divided by the bandwidth of the RF front-end. Under H₁, the C/N0 is written as follows:

$c_{i, k} = {(\frac{C_{i, k}}{N_{0} + J_{k}})}_{d B - H z} = {(\frac{C_{i, k}}{N_{0}})}_{d B - H z} - γ_{k}$ 2

where we used the notation $γ_{k} ≜ {(1 + J_{k} / N_{0})}_{d B - H z}$ . Parameter γ_k varies with J_k; it is the ratio of the noise power densities with and without jamming ((N₀ + J_k)/N₀) in decibels. Under H₁, c_ik is distributed as follows:

$c_{i, k} \sim N (μ_{i, k} - γ_{k}, σ_{i, k}^{2})$ 3

The parameter γ_k is the decrease in mean C/N0 due to jamming. We aim to derive a test to detect jamming using the estimated C/N0 for all satellites in view at time k. We first define an observation vector of receiver-provided C/N0s at time step k:

$c_{k} = {[c_{1, k}, \dots, c_{r, k}]}^{T}$ 4

where r is the number of satellites in view at time k. C/N0 measurements are assumed to be uncorrelated across satellites. We define two mutually exclusive and exhaustive hypotheses, H₀ and H₁, which impact Equation (2), as follows:

$\begin{matrix} Null hypothesis H_{0} : γ_{k} = 0 (no jamming) \\ Alternate hypothesis H_{1} : γ_{k} > 0 (jamming) \end{matrix}$ 5

The probability density functions of the C/N0 vector c_k under these two hypotheses can respectively be written as follows:

$p (c_{k} ∣ H_{0}) = \frac{1}{\sqrt{{(2 π)}^{r} | S_{k} |}} \exp (- \frac{1}{2} {(c_{k} - μ_{k})}^{T} S_{k}^{- 1} (c_{k} - μ_{k}))$ 6

$p (c_{k} ∣ H_{1}) = \frac{1}{\sqrt{{(2 π)}^{r} | S_{k} |}} \exp (- \frac{1}{2} {(c_{k} - μ_{k} + 1 γ_{k})}^{T} S_{k}^{- 1} (c_{k} - μ_{k} + 1 γ_{k}))$ 7

where $μ_{k} ≜ {[μ_{1, k}, \dots, μ_{r, k}]}^{T} \in ℝ^{r \times 1}$ and $S_{k} ≜ d i a g ([σ_{1, k}^{2}, \dots, σ_{r, k}^{2}]) \in ℝ^{r \times r}$ are the jam-free mean and covariance of the observation vector, c_k, and 1 = [1,…,1]^T is an r × 1 vector of ones. We use the Neyman–Pearson lemma to write the following optimal test statistic, which minimizes the probability of missed detection (P_MD):

$Λ_{k} (c_{k}, γ_{k}) = \ln (\frac{p (c_{k} ∣ H_{1})}{p (c_{k} ∣ H_{0})})$ 8

where ln() is the natural logarithm function. By substituting Equations (6) and (7) into Equation (8) and simplifying, we obtain the following equation for the test statistic:

$Λ_{k} (c_{k}, γ_{k}) = - {(c_{k} - μ_{k})}^{T} S_{k}^{- 1} 1 γ_{k} - \frac{1}{2} 1^{T} S_{k}^{- 1} 1 γ_{k}^{2}$ 9

Parameter γ_k is unknown because the received jamming power is unknown (it depends on the transmitted jamming power, antenna gain patterns, distance to the jamming source, propagation channel path loss, etc.). Still, we can express a locally optimal test statistic for small jamming power (γ_k → 0) as follows:

${α_{k} ≜ \frac{\partial Λ_{k} (c_{k}, γ_{k})}{\partial γ_{k}} |}_{γ_{k} = 0} = {- (c_{k} - μ_{k})}^{T} S_{k}^{- 1} 1$ 10

Under H₀, the test statistic α_k is distributed as follows:

$α_{k} \sim N (0, σ_{α, k}^{2} ≜ 1^{T} S_{k}^{- 1} 1)$ 11

Let T_k be the detection threshold for the test. Detection occurs if the following inequality is satisfied:

$α_{k} > T_{k}$ 12

We set T_k to meet a predefined requirement on the probability of false alert P_FA,REQ. T_k is computed using the following equation:

$P_{F A, R E Q} = P (α_{k} > T_{k} ∣ H_{0}), i . e ., T_{k} = Q (1 - P_{F A, R E Q}) σ_{α, k}$ 13

where Q() is the quantile function, i.e., the inverse cumulative distribution function (CDF) of the standard normal distribution.

This test is optimal for detecting small, simultaneous decreases in C/N0. We designed the test to be one-sided because we focus on degradation in C/N0 due to jamming. The test can easily be modified to be two-sided, e.g., to detect increased C/N0 due to spoofing, by applying an absolute value operator to α_k in Equations (12) and (13) and by dividing P_FA,REQ by two (2) in Equation (13) to account for both tails of the jam-free distribution.

This method could also be extended to account for C/N0 decreases for satellite subsets by considering additional hypotheses that do not fit under nominal conditions H₀ or jammed conditions H₁. As described by Jada et al. (2021), we conducted a side analysis showing that the test was robust to non-nominal C/N0 variations on satellite subsets caused by higher-than-usual ionospheric activity. A detailed treatment of C/N0 decreases for satellite subsets is beyond the scope of this paper and will be addressed in future work.

Computation of the test statistic α_k and its threshold T_k requires a jamming-free model of the mean C/N0 vector, μ_k, and covariance matrix, S_k. We develop an automated data-based approach for modeling the mean and variance of nominal C/N0 for any receiver and satellite in Section 3.

2.2 Time-Differenced C/N0 Test for Jamming Detection

In contrast with the method described in Section 2.1, jamming detection using time-differenced C/N0 only requires a variance model because time-differencing C/N0 over short time intervals (e.g., over 1 s) eliminates the C/N0’s slow-varying-mean value. The time-differenced test is useful when processing data for which the mean C/N0 model has not been identified.

A time-differenced C/N0 measurement, ∆c_i,k, is defined as follows under jamming:

$Δ c_{i, k} ≜ {(\frac{C_{i, k}}{N_{0} + J_{k}})}_{d B - H z} - {(\frac{C_{i, k - 1}}{N_{0} + J_{k - 1}})}_{d B - H z}$ 14

By substituting Equation (2) into Equation (14) and rearranging, we obtain the following expression:

$Δ c_{i, k} = {(\frac{C_{i, k}}{N_{0}})}_{d B - H z} - {(\frac{C_{i, k - 1}}{N_{0}})}_{d B - H z} - Δ γ_{k}$ 15

where ∆γ_k is defined as $Δ γ_{K} ≜ (γ_{k} - γ_{k - 1})$ . ∆γ_k captures the impact of jamming power variations from time k – 1 to k. The distribution of ∆c_i,k can be expressed as follows:

$Δ c_{i, k} \sim N (- Δ γ_{k}, σ_{Δ i, k}^{2})$ 16

We model the variance $σ_{Δ i, k}^{2}$ of the overbounding Gaussian function based on data using the method described in Section 3, and the mean of $Δ c_{i, k}$ is $- Δ γ_{k}$ because $(μ_{i, k} - μ_{i, k - 1} \approx 0)$ . We aim to derive a test to detect jamming signals from time-differenced C/N0s for all r satellites in view at time step k. We define the observation vector as follows:

$Δ c_{k} ≜ c_{k} - c_{k - 1} = {[Δ c_{1, k}, \dots, Δ c_{r, k}]}^{T}$ 17

For any two satellites i and j, $Δ c_{i, k}$ is assumed to be statistically uncorrelated from $Δ c_{j, k}$ . We define two mutually exclusive and exhaustive hypotheses, H₀ and H₁, which impact Equation (15), as follows:

$\begin{matrix} Null hypothesis H_{0} : Δ γ_{k} = 0 (no change in jamming power density) \\ Alternate hypothesis H_{1} : Δ γ_{k} > 0 (increase in jamming power density) \end{matrix}$ 18

Following the same steps as in Section 2.1, we derive a locally optimal test statistic for $Δ γ_{k} \to 0$ , which is expressed as follows:

$β_{k} ≜ - Δ c_{k}^{T} S_{Δ k}^{- 1} 1$ 19

Under H₀, the test statistic β_k is distributed as follows:

$β_{k} \sim N (0, σ_{β, k}^{2} ≜ 1^{T} S_{Δ k}^{- 1} 1)$ 20

This test statistic is optimal for detecting small simultaneous decreases in time-differenced C/N0 across satellites. The computation of β_k requires a model for the jam-free time-differenced C/N0 covariance matrix S_∆k, which can be modeled a priori using C/N0 data as described in Section 3. The detection threshold for this test is the product of the quantile function evaluated at $(1 - P_{F A, R E Q})$ times $σ_{β, k}$ .

2.3 RF Front-End Signal Power Model

Increased temperature and sun exposure can cause C/N0 to decrease for all satellites as the noise density N₀ increases (Kriezis et al., 2024). Nominal daily variations are captured by the model described in Section 3. Other sources of jamming-unrelated decreases in nominal C/N0 at network receivers include ionospheric disturbances, multipath due to moving objects near the antenna, etc. Some reports, such as those by Fors et al. (2021) and S. Lewis personal communication on bird landings causing C/N0 disturbances, even attribute C/N0 decreases to snow accumulation and bird landings on antennas. Although such disturbances are rare and only impact a subset of satellite C/N0 measurements, they can be a source of false alerts. To confirm the presence of jamming, in Sections 4 and 5, we develop a method to identify and predict repeated jamming events, deploy our own equipment, and record RF front-end data when triggered by a power-based detector.

In this section, we design an RF front-end signal power monitor to detect jamming independently of the C/N0-based detectors. The digitized RF front-end signal is a stream of pairs of real (in-phase), y_I,n, and imaginary (quadrature), y_Q,n, parts of complex-numbered samples at each RF front-end time index n defined as follows:

$y_{n} ≜ y_{I, n} + i y_{Q, n} \in ℂ$ 21

where i is the imaginary unit. Let m be a time index for power measurements. We compute the signal power for the m-th non-overlapping window of N samples, ${y_{m N}, \dots, y_{m N + N - 1}}$ as follows:

$S_{m} ≜ \frac{1}{N} \sum_{l = 0}^{N - 1} {| y_{m N + l} |}^{2} \in ℝ$ 22

For an RF front-end sampling at 25 MHz, we can choose a window of N = 4096 to give approximately 6000 power measurements per second. Under jamming-free, nominal conditions, the power measurement can be overbounded by a Gaussian distribution, which is expressed as follows:

$S_{m} \sim N (μ_{s, m}, σ_{s, m}^{2})$ 23

This assumption is justified using data in Section 3.4.

Under jamming, the RF front-end signal at the RF front-end time index n includes additional components defined as follows:

$y_{n, j a m} ≜ (y_{I, n} + i y_{Q, n}) + (ψ_{I, n} + i ψ_{Q, n})$ 24

where $ψ_{I, n}$ and $ψ_{Q, n}$ are the in-phase and quadrature components of the jamming signal. To express the signal power under jamming, we first expand the square of the magnitude of y_n,jam as follows:

${| y_{n, j a m} |}^{2} = (y_{I, n}^{2} + y_{Q, n}^{2}) + (ψ_{I, n}^{2} + ψ_{Q, n}^{2}) + 2 y_{n, I} ψ_{n, I} + 2 y_{n, Q} ψ_{n, Q}$ 25

Assuming that the nominal signal is independent of the jamming signal, we can write the following expectations:

$E [y_{n, I} ψ_{n, I}] = 0 and E [y_{n, Q} ψ_{n, Q}] = 0$ 26

Thus, the RF-front-end signal power under jamming can be written as follows:

$\begin{matrix} S_{m} & = \frac{1}{N} \sum_{l = 0}^{N - 1} {| y_{m N + l, j a m} |}^{2} \\ = \frac{1}{N} \sum_{l = 0}^{N - 1} {| y_{m N + l} |}^{2} + \frac{1}{N} \sum_{l = 0}^{N - 1} (ψ_{I, m N + l}^{2} + ψ_{Q, m N + l}^{2}) \end{matrix}$ 27

The cross-product terms $y_{n, I} ψ_{n, I}$ and $y_{n, Q} ψ_{n, Q}$ are not included because they average out to zero for sufficiently large N, under the assumption in Equation (26). We define the jamming power contribution term as follows:

$Γ_{m} ≜ \frac{1}{N} \sum_{l = 0}^{N - 1} (ψ_{I, m N + l}^{2} + ψ_{Q, m N + l}^{2})$ 28

Under jamming, using Equations (23) and (28), we can write the RF front-end signal power distribution as follows:

$s_{m} \sim N (μ_{s, m} + Γ_{m}, σ_{s, m}^{2})$ 29

where μ_s,m and $σ_{s, m}^{2}$ are the jamming-free mean and variance defined in Equation (23). Jamming causes an offset Γ_m to the mean of s_m. Thus, we can define two mutually exclusive and exhaustive hypotheses as follows:

$\begin{matrix} Null hypothesis H_{0} : Γ_{m} = 0 (no jamming) \\ Alternate hypothesis H_{1} : Γ_{m} > 0 (jamming) \end{matrix}$ 30

Using Equations (23) and (29) and following the process described in Section 2.1, we can derive a locally optimal hypothesis test for small jamming powers $(Γ_{m} \to 0)$ , with a test statistic defined as follows:

${\hat{η}}_{m} ≜ \frac{s_{m} - μ_{s, m}}{σ_{s, m}^{2}}$ 31

Under H₀, this test statistic has the following distribution: ${\hat{η}}_{m} \sim N (0, 1 / σ_{s, m}^{2})$ . We define a normalized test statistic as follows:

$η_{m} ≜ {\hat{η}}_{m} σ_{s, m} = \frac{s_{m} - μ_{s, m}}{σ_{s, m}} and η_{m} \sim N (0, 1)$ 32

The computation of η_m requires a model of mean jamming-free power μ_s,m and a model of standard deviation σ_s,m. The method for modeling these quantities is described in Section 3.4. The detection threshold for the test is the quantile function evaluated at $(1 - P_{F A, R E Q})$ .

3 NOMINAL C/N0 AND POWER MEASUREMENT MODELING FOR JAMMING DETECTION

In this section, we develop methods for determining models of the nominal mean and variance of C/N0, the variance of time-differenced C/N0, and the mean and variance of power measurements. These models are determined under H₀, i.e., using jamming-free C/N0 and power measurements. The modeling methods must be automated for implementation on a network of heterogeneous receivers.

3.1 Elevation-Dependent C/N0 Mean and Overbounding Variance Model

Figure 1 shows one week of raw, unprocessed GPS L1 C/N0 data collected in May 2021 at the NGS CORS station located in Charlotte, NC (CORS site index: NC77) (NGS, n.d.), for one satellite with pseudorandom (PRN) code number PRN8. Figure 1(a) presents an azimuth–elevation sky-plot with color-coded C/N0 values, showing that the satellite trajectory observed at NC77 repeats itself. In Figure 1(b), the seven overlapping curves, color-coded to distinguish seven days, illustrate that the mean and variance of the C/N0 values exhibit repeating patterns with a cycle period of one sidereal day (the x-axis is in sidereal time). Figure 1(c) illustrates the elevation dependence of the C/N0 measurements.

FIGURE 1

GPS L1 C/N0 for PRN8 at Charlotte, NC (CORS site index: NC77), during a week in May 2021; (a) color-coded C/N0 on an azimuth–elevation sky-plot for PRN8 on May 1, 2021; (b) C/N0 as a function of sidereal time and (c) C/N0 as a function of elevation, showing seven color-coded curves corresponding to seven days. In panel (a), a single day is shown because the azimuth–elevation curves overlap over multiple days.

Figure 2(a) shows a sky-plot for all of the satellites over 24 h. The red-to-blue color code represents C/N0 values ranging from 25 to 54 dB-Hz, highlighting again the strong dependence, for all PRNs, on elevation angle and, to a lesser extent, on individual satellites and their azimuth angles. This dependence is driven by the satellite transmission antenna gain pattern, the travel path of the signal through the atmosphere, the multipath environment, and the receiver antenna gain pattern (Fante et al., 2012, Chapter 1) (O’Brien et al., 2020). In addition, Figure 2(b) suggests that, whereas the C/N0 primarily depends on elevation angle, the range of C/N0 variations across satellites can exceed 15 dB-Hz at low elevation angles and 10 dB-Hz at high elevation. Designing a sensitive detector requires that we narrow down the range of nominal, predictable C/N0 variations.

FIGURE 2

(a) Color-coded GPS L1 C/N0 on an azimuth-elevation sky plot at Charlotte, NC; (b) GPS L1 C/N0 for all satellites (color-coded) as a function of elevation over 24 h. This figure shows that elevation is a major cause of C/N0 variations, but C/N0 values also vary with satellite and azimuth angle.

Therefore, for each individual satellite i at time step k, we model the C/N0 mean as a function of elevation angle using the following quartic polynomial:

$μ_{i, k} = a_{0, i} + a_{1, i} θ_{i, k} + a_{2, i} θ_{i, k}^{2} + a_{3, i} θ_{i, k}^{3} + a_{4, i} θ_{i, k}^{4}$ 33

where θ_i,k is the elevation angle of satellite i at time step k and $[a_{0, i} a_{1, i} a_{2, i} a_{3, i} a_{4, i}]$ are the coefficients of the quartic polynomial determined by fitting jamming-free C/N0 data over one day, as illustrated in Figure 3(a).

FIGURE 3

Overview of the elevation-dependent nominal C/N0 modeling method: (a) mean C/N0 model for PRN 8; (b) sample and modeled standard deviations of C/N0 residuals (samples minus mean) over 2.5° elevation bins for all satellite PRNs (color-coded); (c) normalized C/N0 measurement residuals for all PRNs; (d) Gaussian overbounding of the sample distribution of normalized C/N0 residuals for all PRNs

Then, to model the variance, we subtract the mean C/N0 model from the sample data to compute the C/N0 residuals plotted in Figure 3(b). C/N0 residuals also show an elevation dependence. A 20° elevation mask is applied to avoid C/N0 variations largely affected by multipath reflections from the environment surrounding the receiver antenna, where satellite azimuth angle dependence is significant. The 20°–90° elevation range can be segmented into 2.5° bins to compute the sample standard deviation of the C/N0 residuals versus elevation angle for all satellites over a day. We then fit an elevation-dependent two-term exponential model to the sample standard deviations. The C/N0 standard deviation model at time step k for satellite i is expressed as follows:

${\hat{σ}}_{i, k} = b_{1} e^{- c_{1} θ_{i, k}} + b_{2} e^{- c_{2} θ_{i, k}}$ 34

The coefficients b₁, b₂, c₁, and c₂ are the same for all satellites. Figure 3(c) shows that C/N0 residuals normalized by their model standard deviation have zero mean and unit variance.

This elevation-dependent variance model accounts for 68% of the data, corresponding to samples within ±1 standard deviation (1 –σ) of the mean of a normal distribution. However, the sample C/N0 measurement distribution has wide tails, which must be accounted for when seeking a risk of false alert P_FA,REQ of approximately 10^–6. A false alert risk of 10^–6 will be manually verifiable in Section 4 and will help to ensure a much higher ratio of true versus false alerts.

The quantile-to-quantile (QQ) representation in Figure 3(d) helps to visualize the distribution tails. This figure presents the CDF of normalized C/N0 residuals in Figure 3(c) (y-axis) versus the standard normal distribution (x-axis). The color code distinguishes 32 GPS satellites. If the samples were following a standard normal distribution, their QQ plot would describe a straight line passing through the origin with a slope of unity.

We can determine a single-CDF overbounding Gaussian model of the normalized random C/N0 residuals using the methods of Blanch et al. (2017), DeCleene (2000), and Rife et al. (2006). This model is obtained by multiplying the standard deviation ${\hat{σ}}_{i, k}$ by a factor ζ_OB determined such that the Gaussian overbound, represented by a black line in Figure 3(d), lower-bounds the left tail of the sample CDF and upper-bounds its right tail. This model is conservative more than 68% of the time. Although this model may be of lower fidelity than more complex, higher-order, non-Gaussian distributions, it does have some advantages. First, this model provides a means for determnining an overbound on the detection test statistic distribution in Equation (10) (the overbound for α_k is derived as a linear combination of Gaussian overbounds). Second, according to overbounding theory, this model guarantees an upper bound on the risk of false alerts. Third, the process can be automated, which is instrumental for setting systematic thresholds at hundreds of receiver locations. Thus, the overbounding, elevation-dependent standard deviation is expressed as follows:

$σ_{i, k} = ζ_{O B} {\hat{σ}}_{i, k}$ 35

3.2 Azimuth- and Elevation-Dependent C/N0 Model

Equation (33) does not capture the short-time-scale C/N0 fluctuations shown in Figure 1(b), occurring over tens of seconds to tens of minutes, that repeat with sidereal time and arise from azimuth-dependent antenna gain and multipath effects. If we account for such mean variations using a higher-order model, then the C/N0 model variance can be tightened and the jamming detector sensitivity can be increased. For a given satellite (or PRN), we repeatedly observe that the C/N0 residual variations due to changes in azimuth angle, elevation angle, temperature, and other sensitive parameters can be captured as variations over time. We observed that this model holds with high fidelity for multiple weeks (the model is refreshed monthly). This approach also captures C/N0 variations due to the azimuth- and elevation-dependent antenna gain pattern and multipath. Therefore, we derive a refined model that we refer to as the azimuth- and elevation-dependent model for each individual satellite.

Figure 4(b) shows that the GPS L1 C/N0 measurement variations versus azimuth–elevation at the Charlotte, NC, location repeat over eight days, from May 1 to May 8, 2021. We partitioned the data points for these eight jamming-free days into 2880 azimuth–elevation bins. In each bin, we computed the sample mean: the resulting model is represented as a solid black curve in Figure 4(b).

Figure 4(c) shows the residual C/N0 variations (sample minus mean). Similar to the mean model, in each azimuth–elevation bin, we derive an azimuth–elevation-dependent variance model derived from the residual sample variance. Figure 4(d) shows the C/N0 residual normalized by the model standard deviation, which has a zero mean and a unit standard deviation. An inflation factor is applied using the same overbounding method as in Equation (35) to account for the wide tails of the C/N0 residual distribution.

FIGURE 4

Overview of the azimuth- and elevation-dependent C/N0 measurement modeling method: (a) azimuth–elevation (Az-El) sky-plot for PRN2 at Charlotte, NC, for May 1 to May 8, 2021; (b) C/N0 measurements over eight days (blue) and C/N0 mean model (black); (c) C/N0 measurement residuals, determined as the samples minus the mean model; (d) normalized C/N0 residuals, obtained from C/N0 residuals divided by the modeled standard deviation

Compared with the elevation-dependent model, each one of the 2880 variance parameters is computed using a smaller number of data points. Thus, this higher-dimensional azimuth-elevation-dependent model more accurately captures the mean C/N0 variations, but the variance model is derived from a smaller number of data samples.

This shortcoming is mitigated by using more jamming-free data (e.g., eight days of data instead of one). To efficiently sort through C/N0 data and find jamming-free data, we use the following time-differenced C/N0-based detector, whose nominal model is simpler.

3.3 Elevation-Dependent Time-Differenced C/N0 Measurement Variance Model

The mean of the time-differenced C/N0 is zero when the time interval between C/N0 measurements is 1 s or shorter. Figures 5(a) and (b) show the time-differenced C/N0 for all 32 GPS satellites over a day versus time and versus satellite elevation, respectively. In Figure 5(a), the moving averages of two example PRNs (PRNs 30 and 32), computed over a 1-min window, are shown to support the zero-mean assumption. We use a two-term exponential time-differenced C/N0 nominal model for the variance, identified using the approach described in Section 3.1.

FIGURE 5

Time-differenced C/N0 data from all satellites (PRNs are color-coded) at CORS site NC77 on May 31, 2021, (a) as a function of time and (b) as a function of elevation angle

3.4 RF Front-End Nominal Power Model

The power-based jamming detector in Equation (32) requires an RF front-end nominal, jamming-free power model. This detector is implemented on equipment that we deploy and is “manually” calibrated, assuming that jamming-free data are identified at the start-up time. The mean power, μ_s,m, is computed by averaging the power samples from jamming-free time periods, and the standard deviation, σ_s,m, is computed by overbounding the power residuals (samples minus mean).

Figure 6 shows an example of in-phase, quadrature, and signal power samples, with and without interference. These data were collected during a GPS interference event observed in Blacksburg, VA, described by Jada et al. (2023). The amplitude of the real and imaginary components of the RF front-end signal increases compared with the nominal amplitude during the interference; consequently, the mean of the signal power increases. (This increase is captured by the Γ_m term in Equation (29).)

FIGURE 6

Impact of interference on RF front-end data collected at Blacksburg, VA, in August 2022 for the (a) real part and (b) imaginary part of the RF front-end signal and for the (c) power measurement

4 JAMMING EVENTS DETECTED USING C/N0 DATA FROM CORS AND IGS NETWORKS

In this section, we apply the C/N0-based jamming detection methods to GPS L1 C/N0 data from receiver networks and present an overview of the detected interference leading to interference pattern identification and prediction.

4.1 Automated Jamming Monitor

We developed an automated jamming detection process described by the block diagram in Figure 7. First, a web scraping program retrieves C/N0 data from CORS or IGS databases and downloads GPS almanacs from the U.S. Coast Guard’s Navigation Center database (US Coast Guard, n.d.). We use Keplerian elements from GPS satellite almanacs to compute satellite azimuth and elevation corresponding to each GPS L1 C/N0 entry at all receiver locations in the network. The algorithm first uses the time-differenced C/N0 detector to identify event-free data because it is effective even with a coarse variance model and a constant zero-mean C/N0 model. Once event-free data are identified, receiver- and satellite-specific nominal models are identified from one or more days of data, and the models are stored for future use. The algorithm incorporates this model to run the C/N0-based detectors and record events. All of the steps in this process are designed to be executed autonomously. We deployed this method on the website of Nayak et al. (2025); this interference monitor is refreshed approximately monthly and uses 1-Hz-update-rate data from approximately 900 U.S. CORS sites to generate the interference maps and day-of-year versus time-of-day plots presented in this section.

FIGURE 7

Block diagram illustrating the nominal C/N0 measurement modeling process and the jamming detector using CORS data

4.2 Comparison Between the Three C/N0-Based Detectors for an Example Data Set

In this section, we evaluate the following three C/N0-based detector implementations: (1) the detector derived in Section 2.1 using the elevation-dependent model from Section 3.1, (2) the same detector in (1) but using the high-order, azimuth–elevation-dependent model in Section 3.2, and (3) the time-differenced C/N0-based detector derived in Section 2.2 using the elevation-dependent variance model from Section 3.3. We use C/N0 measurements from an example CORS site, indexed as NC77, in Charlotte, NC (latitude: 35° 7’ 21” N, longitude: 80° 54’ 58” W), to characterize the performance of the three detector implementations. NC77 is located within 200 m from the intersection of Interstates I-77 and I-485 and next to a truck stop, as shown in Figure 8(a). NC77 provides data at a 1-Hz sampling rate. This location is suitable for observing jamming caused by illegal PPDs. PPDs are used by commercial vehicle drivers to avoid being tracked by their employers or by criminals to elude authorities (Coffed et al., 2015; Space-Based PNT National Advisory Board, 2018).

FIGURE 8

Testing using the first detector (time-undifferenced C/N0) with the low-order, elevation-dependent nominal model (Sections 2.1 and 3.1): (a) map showing the geometry of interstates around CORS site NC77; (b) time sequence of test-statistic-to-threshold ratios on May 19, 2021; (c) C/N0 from all satellites (color-coded) in view during jamming; (d) one month of C/N0-based jamming monitoring using the elevation-dependent model at NC77 during May 2021

We first evaluate the C/N0-based jamming detector in Section 2.1 with the elevation-dependent nominal model described in Section 3.1. Figure 8(b) shows the ratios of the test statistic to the detection threshold at 1-s intervals on May 19, 2021. Jamming is detected when the ratio exceeds one. The detection threshold is computed for a false alert risk requirement P_FA,REQ of 10^–6. Figure 8(c) shows the C/N0 for all satellites (color-coded) during one of the six detected events on May 19. This simultaneous decrease in C/N0 over all satellites is typical of a jamming event.

Figure 8(d) shows the same sequence of test-statistic-to-threshold ratios as in Figure 8(b), but for the entire month of May 2021. In this monthly plot, the marker sizes are proportional to the ratio; weekends and weekdays are color-coded, and red marker edges indicate ratios exceeding unity.

To verify that the actual false alert rate met the required P_FA,REQ, we individually checked each of the three dozen detected events: we counted cases in which C/N0 was simultaneously decreasing across three or more satellites. This verification is further described in our conference paper (Jada et al., 2021). Out of 2.6 × 10⁶ test samples during this month, we found no false alerts.

The monthly plots can reveal patterns in the detected events (red markers), for example, among events caused by PPDs in vehicles following a weekly schedule. One such weekly pattern seems to occur on Wednesdays at midnight, on May 5, 12, and 19, but not on May 26.

Figure 8(d) also shows repeating, watermark-like variations in marker sizes of the test-statistic-to-threshold ratio. These variations correspond to the sidereal-time-dependent changes in C/N0 caused by multipath. These repeated fluctuations can be seen over seven days for PRN8 in Figure 1(b). Their repeatability is represented in Figure 4(b) for PRN2 over eight days versus azimuth and elevation (for a receiver at a fixed location, GPS satellites appear at the same azimuth and elevation angles every sidereal day). In Figure 8(d), the repeating variations shift from one solar day to the next because a sidereal day is approximately 4 min shorter than a solar day.

In the elevation-dependent model, these variations are accounted for by using a loosened overbound on the C/N0 residual distribution, which increases the probability of missed detection and decreases detection sensitivity. In contrast, the azimuth- and elevation-dependent nominal C/N0 modeling in Section 3.2 captures these high-frequency variations, which are most likely due to multipath, in the C/N0 mean model. Figure 9(a) shows the resulting test-statistic-to-threshold ratios in May 2021. The repeating sidereal day variations disappear, and additional events are detected.

FIGURE 9

Testing using (a) the time-undifferenced detector with the azimuth- and elevation-dependent nominal model (Sections 2.1 and 3.2) and (b) the time-differenced detector (Sections 2.2 and 3.3)

The time-differenced C/N0 test can also increase the detector’s sensitivity, i.e., reduce its probability of missed detection, because it is unaffected by sidereal-time-dependent variations. The ratio of the time-differenced C/N0 test statistic in Equation (19) over its threshold in Equation (20) is used to generate the monthly detection plot in Figure 9(b) at NC77 over May 2021. The sensitivity of the time-differenced C/N0 detector matches that of the C/N0 detector in Figure 9(a).

This data set includes 2.6 × 10⁶ samples. The actual false alert probabilities, as determined through visual inspection of raw (unprocessed) C/N₀ measurements during the inspection of each individual detected event in Figures 9(a) and 9(b), respectively, are 2 × 10^–6 and 1.7 × 10^–6 (Jada et al., 2021). (If C/N₀ measurements for all satellites do not simultaneously decrease, then the detection is classified as a false alert.)

The improved detection performance shown in Figure 9 as compared with Figure 8(d) is achieved at a cost: (i) more data, covering seven days instead of one, are needed for the azimuth–elevation-dependent modeling process, and (ii) the time-differenced C/N0 test is only sensitive to the rate of change in C/N0.

4.3 Temporal Pattern Identification in Detected Jamming Events

Identifying regularly repeating detection patterns can provide evidence of road user jamming as opposed to other natural disturbances that impact C/N0, such as ionospheric activity. Repeating jamming events detected by our C/N0 monitor can be predicted and then validated through independent wideband RF data analysis. We processed eight months of data from CORS site NC77 and from other sites, including from the IGS network, to find repeated detection patterns.

While the CORS network is predominantly a U.S.-based network, the IGS network is a global network of receivers, and the IGS database has provided receiver outputs at a 1-Hz update rate over the past two decades, as described by IGS (n.d.) and Johnston et al. (2017). In the U.S., the IGS network is sparser than the CORS network, with approximately 50 IGS sites versus 910 CORS sites with a 1-Hz sampling rate. We applied the method in Figure 7 to the IGS network of worldwide receivers and found clear patterns of interference from a site indexed as AMC4 in Colorado Springs, CO, U.S. (latitude: 38° 48’ 10.8” N, longitude: 104° 31’30” W). This finding demonstrates that the algorithm can detect events from any receiver network’s C/N0 database with a customized web scraper and a parser, with the other components of the method remaining unchanged.

Figure 10 shows the temporal distribution of jamming events at (a) NC77 and (b) AMC4 from January 2022 through August 2022. The x-axis is the local time of the day, and the y-axis is the day of the year. The marker sizes capture the event intensity, which scales with increases in test-statistic-to-detection-threshold ratios exceeding one (for clarity, we only display detection and do not show cases in which the ratio is lower than unity). The markers are color-coded from blue to red to identify days of the week from Monday to Sunday, respectively. This color code is shown in the histograms in the bottom panels, with the number of events shown as a function of the day of the week.

FIGURE 10

Jamming events over the first eight months of 2022 for (a) CORS site NC77 and (b) IGS site AMC4

The bottom panels show the distribution of events in the top panels versus the day of the week.

The histograms for NC77 in Figure 10(a) show jamming events predominantly occurring on weekdays, with a maximum number of occurrences on Tuesdays and a minimum on Sundays. Figure 10(b) shows the distribution of detections at IGS site AMC4 located in Colorado Springs, CO, U.S. In this remote location, a clear pattern is discernible, with events regularly detected at 6:00 AM and 2:15 PM on weekdays and relatively few detections on weekends. (Data were unavailable for this IGS site during the second half of February 2022.) This pattern indicates actual jamming. This pattern is so predictable that we may be able to observe it using wideband RF data, which would validate the C/N0-based detector.

5 POWER-BASED OBSERVATION OF A PREDICTED PPD JAMMING EVENT

To validate the C/N0-based detectors, we collected wideband RF front-end data during a jamming event for time–frequency analysis. In this section, we perform a time–frequency analysis of a PPD jamming event in Colorado Springs, CO.

5.1 Hardware Description

The wideband RF data collection system consists of transportable and power-efficient hardware components, as shown in Figure 11. We use an Ettus Universal Software Radio Peripheral (USRP) N200 with a DBSRX2 daughterboard to collect RF data. The USRP is connected to an external Connor Winfield OH100 ovenized crystal oscillator (OCXO). The OCXO, mounted on a circuit board, sends a 10-MHz timing signal as a square wave with a frequency stability of ±10 parts per billion. This stability is needed to compute the GPS PNT solution from wideband RF data. We use a Tallysman 33-8829NMAT GPS patch antenna for the USRP. The USRP is controlled by an Intel Next Unit in Computing (NUC) 6 via a gigabit Ethernet connection. The Intel NUC6 has 4 GB of RAM and a quad-core Intel Celeron processor running a Linux Mint 17 operating system.

FIGURE 11

Equipment used for wideband RF data collection: (a) Ettus USRP N200 with DBSRX2 daughterboard, (b) Tallysman 33-8829NMAT GPS antenna, (c) Connor Winfield OCXO-OH100, (d) Intel NUC6, and (e) u-blox EVK-M8F GNSS receiver

In parallel, we use a u-blox EVK-M8F GNSS receiver as an independent source of C/N0 and AGC measurements. The Intel NUC also collects data from the u-blox receiver via a USB port. Our setup is designed to run on 12-V direct-current (DC) power, which allows us to power the entire setup directly using a car’s DC power output. We developed Python software for wideband RF data collection, power monitoring, and C/N0-based jamming monitoring.

5.2 Analysis of PPD Jamming Observed on Interstate I-25 in Colorado

To analyze the pattern in Figure 10, we drove to the location (AMC4) of the repeating interference and collected wideband RF data. Figure 12(a) shows the power-based jamming detector output and spectrogram of the signal from the event. These data were collected at a 25-MHz sampling rate with a center frequency at GPS L1. The power increase lasted approximately 5 s, consistent with the duration of crossing paths with a vehicle using a PPD. At the time of this data collection, we were not attempting to identify a specific vehicle carrying the jammer. We were processing and visualizing the data with a 5-min delay.

FIGURE 12

Time–frequency analysis of a PPD jamming signal: (a) signal power monitor output; (b) spectrogram showing sweeps in the peak power spectral density

The spectrogram in Figure 12(b) was generated from the 50-μs segment of the signal with the highest power during the collection period. We used a 20-sample sliding Hamming window. The spectrogram at the power peak leaves little doubt about the nature of the interference. Repeated sweeps of peak power density are typical of chirp-type PPDs (Kraus et al., 2011; Mitch, 2014).

In parallel, we evaluated the impact of this PPD on a commercial u-blox receiver. The jamming event was detected by feeding the u-blox C/N0 measurements into our jamming detector. Figure 13(a) shows the u-blox receiver C/N0 decreasing during the PPD jamming event. We also analyzed the PPD’s impact on AGC, which can be used as a jamming indicator (Kim et al., 2020; Levigne, 2019; Miralles et al., 2018; Scott, 2011; Strizic et al., 2018). The AGC gain is a factor applied to a GNSS receiver RF front-end signal before digitization to prevent signal saturation in an environment with higher-than-usual in-band power (Bastide et al., 2003). Figure 13(b) shows the u-blox AGC gain suddenly decreasing in reaction to the additional in-band power introduced by the jammer with a 1-s delay relative to the C/N0 decrease.

FIGURE 13

u-blox EVK-M8F receiver signal quality indicators collected during the PPD jamming event observed in Colorado: (a) C/N0 and (b) AGC

Finally, in Figure 12(a), the test-statistic-to-threshold ratio increases by an order of magnitude over its nominal value. The spectrogram in Figure 12(b) shows that the PPS jamming power is concentrated within ±3 MHz, i.e., targeting the RF front-end bandwidth of typical GNSS receivers. Assuming that all of the jamming power is within the RF front-end bandwidth of the u-blox receiver, the jammer impact parameter γ_k defined in Equation (2) is on the order of 10 dB. We observe this 10-dB decrease in C/N0 in Figure 13(a) for all satellites.

6 CONCLUSION

In this paper, we developed, implemented, and evaluated an autonomous GNSS jamming detection algorithm using C/N0 measurements from large receiver networks. The detectors are self-calibrating, achieve a predefined false alert probability, and are locally Neyman–Pearson optimal in the sense that they minimize the risk of missed detection of small jamming power density. We processed data from networks of hundreds of receivers over several months and found jamming patterns suggesting PPD interference by road users on daily or weekly schedules. Regularly occurring interference is predictable. Thus, to validate the C/N0-based jamming detector, we designed a portable hardware setup for wideband RF data collection and developed a power-based jamming monitor. We analyzed wideband data during a jamming event on a U.S. highway in Colorado and confirmed that the GPS L1 interference that we predicted using a receiver network actually originated from a PPD. Wide-scale receiver-network-based interference monitoring and prediction open the door for future local wideband data-based observations of illegal jamming.

HOW TO CITE THIS ARTICLE:

Jada, S., Psiaki, M., & Joerger, M. (2026). Network-based GNSS jamming prediction enabling wideband interference observation. NAVIGATION, 73. https://doi.org/10.33012/navi.763

Acknowledgments

The authors would like to thank the MITRE Corporation and the U.S. Department of Transportation’s University Transportation Center program under the Center for Assured and Resilient Navigation for Advanced Transportation Systems for their support of this research. The opinions expressed in this paper are our own and do not necessarily represent those of any other person or organization.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Network-Based GNSS Jamming Prediction Enabling Wideband Interference Observation

Abstract

1 INTRODUCTION