RFI localization using C/N0 measurements from low cost GNSS sensors for robust positioning

Naveed Ahmed; Ardeshir Mohamadi; Hossein Nahadavanchi

doi:10.1515/jogs-2025-0185

Artikel Open Access

RFI localization using C/N₀ measurements from low cost GNSS sensors for robust positioning

Naveed Ahmed , Ardeshir Mohamadi und Hossein Nahadavanchi

Veröffentlicht/Copyright: 6. Oktober 2025

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Abstract

This article studies the radio frequency interference (RFI) source localization in a dynamic collaborative navigation scenario using carrier-to-noise density ratio (C/N₀) measurements available from most of the low-cost commercial-off-the-shelf global navigation satellite system receivers. The work is a part of a robust SmartNav positioning engine that aims to provide highly accurate positioning using low cost sensors. Cases of jamming source localization using both a single node and multiple cooperating nodes have been considered. For the jammer localization using a single node, a synthetic array-based approach has been applied whose principle suggests that a receiver’s output at different positions can be assumed as an output of sensor array elements. In the case of multiple cooperating nodes, the centralized approaches based on combining the measurements from all the nodes are presented. The performance of both approaches has been evaluated though a series of simulations, where dynamic wideband interference signal source has been considered. The article presents the implementation details and results achieved by each approach and discusses the impact of different factors influencing the efficacy of the considered techniques. While results indicate that these techniques are mainly useful for coarse localization of the source, this can still be sufficient for improving the situational awareness of the cooperating nodes enabling them to adopt for safer trajectories.

Keywords: carrier-to-noise density ratio; power difference of arrival; radio frequency interference localization; robust positioning; synthetic array

MSC 2010: 94A12; 94C15; 62P30; 93E10

1 Introduction

The growing threat of Global Navigation Satellite System (GNSS) RFI has been posing various challenges for the operation of systems and infrastructure depending on the unobstructed availability of GNSS signals. Introduction of new applications and services utilizing low-cost communications systems and satellite navigation such as asset tracking, fleet management, road-tolling, etc., encourages the attacks directed at GNSS using the low-cost illegal jamming devices. The GNSS signals’ vulnerabilities have been widely reported and investigated by the researchers globally (Rodningsby et al. 2020, Isoz et al. 2011, Pattinson et al. 2017, Pullen et al. 2012, Balaei et al. 2007), where it has also been shown how easily a low-cost jamming device can affect the operation of systems it is not targeting. The unmanned aerial vehicles (UAVs) often operate in close proximity to high traffic roads and dense urban areas, which increases the chances of them being affected by RFI. It is therefore necessary to develop cost effective methods for detection and localization of interference so that the system can take appropriate counter measures.

1.1 Research background and motivation

The primary objective of this project is to develop the SmartNav Positioning Engine, a state-of-the-art high-precision GNSS solution designed specifically for precise positioning of autonomous vehicles. Unlike conventional GNSS, which struggles in challenging urban and industrial environments due to signal obstructions, multipath effects, and interference, SmartNav is engineered to overcome these limitations. By integrating advanced algorithms, it enhances the performance of low-cost GNSS receivers, enabling them to achieve decimeter-level positioning accuracy – a critical requirement for autonomous navigation.

However, achieving high accuracy alone is not sufficient for the reliable operation of autonomous systems. Another fundamental aspect of the SmartNav Positioning Engine is integrity that is defined as the ability to ensure trustworthiness in positioning data, particularly in the challenging environments that are prone to GNSS interference. Interference detection and localization play a pivotal role in maintaining the system’s robustness, as external disruptions can significantly degrade positioning accuracy, leading to navigation errors or even system failures.

This article specifically focuses on the localization of such interferences, presuming the interference has been detected, paving the path to exploring methods to mitigate their impact on the SmartNav Positioning Engine. By effectively addressing these challenges, the project aims to provide a highly reliable and precise navigation solution that meets the stringent demands of autonomous mobility in complex real-world environments. The discussion of the development of SmartNav Engine is out of the scope of this article, yet it suffices to consider the integrity in relation to the research work.

1.2 State-of-the-art techniques

The jammer localization techniques can be categorized both based on whether the localization task is being performed centrally or distributively and on which measurements/parameters have been considered to perform localization. In the latter case, the techniques are further classified into range based and range free. The range-based methods estimate the distances between the reference nodes, also sometimes called anchor nodes, with known states and the source to be localized. Different metrics can be used to estimate these ranges, for example, received signal strength (RSS), time of arrival, time difference of arrival. Dempster and Cetin (2016) provide an overview of existing localization methods and systems based on the aforementioned measurements, and present a comparison of the discussed localization techniques. The UAV’s control and different antenna rotation techniques have been exploited for the localization and tracking of an RF source in the studies by Isaacs et al. (2014) and Venkateswaran et al. (2013). The localization is performed leveraging the UAV’s ability to track a characteristic behavior of variation in yaw angle and estimate RF bearing using RSS measurements. Different problems with this technique have been identified by the authors, as detection and localization could be challenging in the case of multipath and when the vehicle and RF source are not at same altitude. An antenna array-based solution has been presented by Cetin et al. (2014), which exploits the RFI signal’s AOA parameter to localize it. In this work, the system is tested with the ubiquitous WiFi signals without compromising the infrastructure in the vicinity of the receivers that is relying on the standard navigation systems. The monopole antenna-based array antenna design and the electronics processing the signal do a good job in localizing the source. However, this accuracy and efficiency come at a cost and design complexity. A case study based on fast jammer detection of localization using multiple Android smartphones is presented by Scott (2011). Using the desired measurements that are obtained from several collaborating smartphones, the jammer’s location can be estimated by relating the measured jamming power as a function of observer positions. In the study by Ahmed and Sokolova (2020), a static jammer is localized using the synthetic array approach and least squares method-based centralized approach. The synthetic array (SA) approach, first presented by Borio et al. (2016), suggests that measurements obtained from a set of sensors in different positions can be considered equivalent to those collected by the element or nodes of the physical antenna array.

The techniques discussed in this article target localization of jamming signal sources only and are not applicable to other known threats such as GNSS signal spoofing/meaconing. The aim of the article is to present cost-effective and simple to implement RFI localization techniques suitable for use with commercial-off-the-shelf (COTS) GNSS receivers based on commonly available observables. The current objective is localization of a single jammer. While scenarios of multiple RFI sources present at the same time are possible, this will require additional complex hardware not available within COTS GNSS receivers. Therefore, exploration of these domains is currently outside the scope of the article.

The open sourcing of Android’s capability to analyze raw GNSS measurements available from Android smartphones has accelerated the research related to RFI Interference and localization using C/N₀ measurements. So, juxtapositionally speaking, we consider our work as an evaluation of potentially suitable approaches in a dynamic scenario. In this article, we cover the topic in detail and from many different aspects. The main intention of this article is to evaluate the performance of jamming source localization algorithms considering single node and centralized solutions utilizing the behavior of the C/N₀ measurements in the presence of interference to estimate the location of a jammer in a dynamic collaborative navigation scenario. We have considered wideband noise interference type to study its impact on C/N₀ measurements. The measurement models are applied to convert the observables to the distances from the jammer. The jammer localization performance has been studied based on two different scenarios containing four and six UAVs. The localization approaches presented in this article places the localization methods into two fundamental classes utilizing the C/N₀ output of the receivers. The techniques are studied for the test cases when localization is performed considering the fact whether the jamming source is localized either using the range from a single node or in a collaborative manner where all the participating nodes exchange with each other their navigation states. Finally, the impact of number of nodes ( N ) in the network on the performance of certain class of localization technique is studied for the collaborative cases. The power difference of arrival (PDOA) is implemented as a best-performing centralized localization technique and used for comparison with the results obtained from other centralized approaches. The relatively better performance is achieved with C/N₀ measurement, since we do not need to calibrate the receiver, estimate the unknown transmitted power, and the effects of other unconsidered errors are nullified.

The performance evaluation tasks involve realization of different scenarios based on a network of UAVs that are simulated with UAVs assumingly being physically identical in design. It means the UAVs have the same identical sensor suite onboard allowing us to use the same calibration parameters. The UAVs are maneuvering with dissimilar platform dynamics. A series of simulation scenarios involving multiple UAVs, and a wideband jamming source has been conducted using a hardware GNSS simulator and interference signal generator combination.

While considerable research has been done in terms of RFI detection and localization, such techniques often require expensive equipment and complex infrastructure to be deployed. Our approach is innovative in terms of localizing a quasi/static jammer by utilizing C/N₀ measurements, which are publicly available and do not require complex hardware modifications or infrastructure deployment. In addition, the presented techniques are easily scalable in terms of accommodating more UAVs in the system. This scalability makes the techniques more robust and more accurate in terms of performance.

The remainder of the article is organized as follows. Section 2 describes the C/N₀-based measurement models. Section 3 presents the implementation details of single node and centralized localization techniques. Section 4 describes the simulation scenario that was considered and the equipment setup for the conducted experiments. Section 5 compares simulation results based on the single node and centralized techniques and discusses the impact of different factors on the performance of the presented approaches. Section 6 concludes the article.

2 Measurement models

In this section, we present the C/N₀ measurement models used in this study. The GNSS signals typically follow the log-normal propagation model, suggesting that signal loss can be characterized logarithmically by the distance between transmitter and receiver and nature of the signal propagation environment (Rappaport 2024). Mathematically speaking, (1) represents the signal strength observed at the receiver located at the distance d from the transmitter.

(1) P ( d ) = P ( d 0 ) + 10 α log 10 d d 0 + ε ,

where P ( d 0 ) is the signal strength at a reference distance d 0 and α is a constant called path loss exponent the value of which depends on the propagation environment. It generally varies between 2 and 4, where 2 represents vacuum or nearly free space, whereas the latter value corresponds to a high-density environment such as urban canyon (Rappaport 2024). The last term ε accounts for the miscellaneous factors causing uncertainty in the measurement including shadowing, reflection, multipath, and others. In our study, we are not considering these effects; hence, this factor would be neglected in further analysis. In the case of RFI, the transmit power is an unknown nuisance parameter and has therefore to be either estimated together with the jammer coordinates or accounted for in the measurement model as a factor to be determined through receiver calibration.

2.1 Carrier to noise density ratio (C/N₀)

In the context of a GNSS receiver, C/N₀ is defined as the ratio of signal power that is measured as carrier power to the thermal or white noise power in a unit bandwidth. A GNSS receiver provides C/N₀ estimates for all the tracked satellites that are directly affected by the jammer and its motion relative to the receiver. In the presence of strong interference, the C/N₀ could go below the tracking threshold hampering the receiver to output a valid position, velocity, and time. In the case of interference, the interference signal’s power is also added in the white noise power. Therefore, the effective C/N₀ value decreases in the presence of interference. Unlike signal to noise ratio (SNR) that is a dimensionless quantity, it is generally expressed in dB-Hz units.

2.1.1 C/N₀-based range measurement model

The C/N₀ follows a log normal path loss model relating RSS and the range between the node and possible jammer. Considering a GNSS receiver tracking the i th visible satellite in the constellation, its effective C/N₀ is related to the jamming power as follows (Betz 2001, Borio et al. 2016):

(2) C i N 0 eff = C i N 0 1 + k α J N 0 − 1 ,

where C i represents the power of the signal received from the i th satellite, J is the jamming power at the receiver, and k α is a factor known as spectral separation coefficient (SSC) that quantifies the overlapping between the spectra of original GNSS signal and the interference signal (Betz 2001). The higher value of SSC accounts for greater overlapping between two spectra and would result in higher degradation of the C/N₀. The GPS L1 signals are modulated on the L1 carrier ( f L1 = 1575.42 MHz) using the binary phase shift keying modulation technique. For the jamming signal fully overcoming the L1 signal, this value has been obtained as − 61.9 dB (Dovis 2015). For any RF and interference signal case, this factor can be computed for an entire bandwidth using the expression given below:

(3) k α = ∫ ∞ − ∞ ∣ H r ( f ) ∣ 2 G s ( f ) G i ( f ) d f ,

where H r ( f ) is the receiver’s transfer function, and G s ( f ) and G i ( f ) are the normalized power spectral density functions of the GNSS and interference signals, respectively.

Since the characteristics of the jammer are unknown, the effective C/N₀ model given in Eqs. (2) and (3) is not directly applicable. It also does not account environmental effects on the signal propagation. By using the commonly observed phenomenon of path loss that is commonly experienced by the radio signals in space, we can characterize the jammer’s behavior in the environment. The jamming signal strength degrades because of log-based path loss model given in (1). Considering the jammer signal’s attenuation and the parameter accounting for the mutual interaction of RF and interference signals’ spectra, the model in Eq. (2) is revisited as follows:

(4) C i N 0 eff = β i + 10 α log 10 ( d ) ,

where β i is theoretically defined as follows:

(5) β i = C i N 0 d B − H z − 10 log 10 k α J 0 N 0 − 10 α log 10 ( d 0 ) ,

and J 0 is the jamming signals strength at the reference distance d 0 . Usually, β parameter is unknown and varies from one receiver type to another, and hence is often obtained through careful receiver calibration. The discussion of obtaining this parameter is given in later sections of the article.

A typical GNSS receiver attempts to acquire and tracks each satellite individually, and therefore outputs the C/N₀ for every visible satellite it is tracking. It has been suggested that model presented thus far stays equally valid if we take the average of C/N₀ values of all the visible satellites. Hence, Eq. (4) can be modified as follows:

(6) C a N 0 eff = β ¯ + 10 α log 10 ( d ) .

Considering a network comprising of multiple nodes, the distance of the i th node from the jammer can be estimated from the average C/N₀.

(7) d i = antilog 10 1 10 α C a N 0 eff i − β ¯ .

In summary, the effective average C/N₀ any given instant, n, can be expressed as a function of the instantaneous positions of jammer and the receiver.

(8) C a [ n ] N 0 eff i = β ¯ + 5 α log 10 ( ( x i [ n ] − x j ) 2 + ( y i [ n ] − y j ) 2 + ( z i [ n ] − z j ) 2 ) ,

where ( x i , y i , z i ) and ( x j , y j , z j ) are three-dimensional coordinates of the i th receiver and the jammer, respectively.

3 Jamming source localization techniques

On the basis of the node’s dependency on other nodes to obtain the range information used for localization, we classify the techniques as single-node source localization and the centralized approach where all the nodes in the network contribute to determine the location of the source. The single node-based approaches localize the jammer solely by itself and then exchange the information with other nodes in the network. The centralized approaches work by first getting the distance measurements independently taken by other nodes. This section covers different approaches belonging to each of the class that utilize different receiver observables for range measurement.

3.1 Single-node localization

In this section, single node-based techniques are presented aiming to estimate the jammer location using the measurements available from one node. Such techniques are simple to implement as there is no stringent requirement to deploy a complex infrastructure. The synthetic array approach is mainly discussed to perform localization that suggests that a set of sensors located at different positions can be replaced by a single node moving along the trajectory. Hence, the observables recorded at different positions can be considered as an output from a physical array of sensors (Borio et al. 2016).

3.1.1 Synthetic array approach

The synthetic array approach can be applied to localize both static and quasistatic jammers. A synthetic array can be virtually formed by combining the measurements at N consecutive epochs when jamming is detected. For a particular node i in the network, an objective function can be constructed by combining these measurements. By using the measurement model given in Eq. (8), we can define the objective function as follows:

(9) J i ( x j , y j , z j ) = ∑ n = 0 N − 1 C a [ n ] N 0 eff i − β ¯ − 5 α log 10 ( ( x i [ n ] − x j ) 2 + ( y i [ n ] − y j ) 2 + ( z i [ n ] − z j ) 2 ) ] 2

The solution to Eq. (9) can then be obtained by minimizing the objective function using the unconstrained minimization techniques, and one such method used selected in current work is the gradient descent method (Lemarechal 2012).

3.1.2 Synthetic array with bias estimation

Revisiting the SA principle presented earlier, in the presence of jammer with unknown transmit power P j , the variation in signal strength can be related to the instantaneous jammer position using the log-based path loss model.

(10) P i [ n ] = P j [ n ] − 5 α log 10 ( ( x i [ n ] − x j ) 2 + ( y i [ n ] − y j ) 2 + ( z i [ n ] − z j ) 2 ) .

The unknown transmit power is often termed as reference power, P 0 , at distance, d 0 , from the source. Without losing the generality, the d 0 is assumed to be 1 m, reducing the number of parameters to be estimated. Here, P 0 is interchangeably used with P j . Equation (10) is valid only for the cases when the constant power for the jammer is considered. Variable jammer power would complicate the situation by making it difficult to quantify the log normal relationship. Considering a SA of N elements, the model should accumulate N consecutive measurements. Hence, the model can be updated as follows:

(11) P i [ n ] = ∑ n = 0 N − 1 ( P j [ n ] − 5 α log 10 ( ( x i [ n ] − x j ) 2 + ( y i [ n ] − y j ) 2 + ( z i [ n ] − z j ) 2 ) ) .

By using the C/N₀ model given Eq. (9), we can adapt the objective function formulation, whose minimum would give us an estimate of the jammer position.

(12) J i ( x j , y j , z j ) = ∑ n = 0 N − 1 [ P i [ n ] − 5 α log 10 ( ( x i [ n ] − x j ) 2 + ( y i [ n ] − y j ) 2 + ( z i [ n ] − z j ) 2 ) ] 2 .

The true values refer to the values that are obtained either in absence of RFI or when the receivers’ outputs are not influenced by the interference.

3.2 Centralized approach

Even though the single node-based approaches are simple to implement, they are not very well suited when the node is outside the jammer’s operating range even though it can still get the jammer coordinates from other nodes affected by the jammer. The real benefit of using the centralized approaches is that they exploit the better geometry formed by the nodes and, hence, ensuring better observability of the source. The scenario can be formulated as a convex optimization problem for which the solution can be determined by minimizing the squares of errors between true and estimated jammer location. Weighted least squares (WLS) is one of the most widely used estimation techniques for the convex optimization problems. To localize the jammer in three dimensions, we need measurements from four or more nodes. The presented analysis can be conveniently extended to virtually any number of nodes in the system.

3.2.1 Weighted least squares method

The unknown jammer coordinates can be represented as an input state vector x .

(13) x = x j y j z j .

From the C/N₀ logs recorded by n receivers, a measurement vector y can be obtained using the relationship derived in (7).

(14) y = d 1 d 2 ⋯ ⋯ d n − 1 d n .

Using an initial guess of the jammer’s position, the predicted jammer to nodes distances can be obtained. Different analytical and probabilistic approaches are used to determine the initial estimate for the algorithm (Fontanella et al. 2012). We apply an analytical method of estimating the initial guess by computing the average of nodes’ position at the start of algorithm that maps roughly to the center of the field. A difference of the estimated range and measured range y gives Δ y that can be related to change in the jammer’s position Δ x .

(15) Δ y = H Δ x ,

where H is the measurement matrix also known as geometry matrix. It is normally an N × M dimension matrix, where N is the number of nodes in the system and M is the number of measurements from each node. Its elements comprise of the rate of change of position with respect to distance to the jammer. For a network of n nodes with each node outputting three-dimensional position, the geometry matrix can be estimated as follows:

(16) H = x 1 − x ˆ j d 1 y 1 − y ˆ j d 1 z 1 − z ˆ j d 1 x 2 − x ˆ j d 2 y 2 − y ˆ j d 2 z 2 − z ˆ j d 2 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ x n − 1 − x ˆ j d n − 1 y n − 1 − y ˆ j d n − 1 z n − 1 − z ˆ j d n − 1 x n − x ˆ j d n y n − y ˆ j d n z n − z ˆ j d n ,

where x n , y n , and z n are the n th receiver coordinates, d n is the range estimated using C/N₀ from the n th receiver, and x ˆ j , y ˆ j , and z ˆ j are the estimated jammer coordinates after each iteration. Since the geometry matrix is not square, obtaining inverse is not straightforward. Hence, the change in unknown state and Δ x ˆ can be estimated can be obtained using (17). Note that the parameters with hat are the estimates.

(17) Δ x ˆ = ( H T H ) − 1 H T Δ y .

During the aforementioned analysis, it is natural to trust the short-range measurements more than the long-range measurements (Tomic et al. 2016). Therefore, to quantify this, it is important to give more weights to the short range measurements. The method of determining the estimates in Eq. (18) can be updated by incorporating the weight matrix also called covariance matrix, W .

(18) Δ x ˆ = ( H T W − 1 H ) − 1 H T W − 1 Δ y .

The final solution to the problem can be obtained by nonlinear least squares method that aims to minimize the square of errors that are calculated as the difference between the observed and estimated states. This can be formulated with an objective function given as follows:

(19) J i = min ‖ H Δ x ˆ − Δ y ‖ 2 .

The weight matrix, W in Eq. (18), is a diagonal matrix of dimension N , whose diagonal elements are obtained using range error variance. The matrix deweights the measurements that are expected to be noisier due to poor measurement model, large distance between the node and jammer, inadequate instantaneous geometry, or for any other reason (Kaplan and Hegarty 2017).

In our case, we are considering a distance-based weighting approach that trusts the short distance measurements more by applying more weight to the such measurements as the measurement error tends to grow with the distance. With σ e representing a uniform measurement error uncertainty, the weight corresponding to the measurement from the node i can be given as follows:

(20) w i = σ e 2 1 − d i ˆ ∑ i = 1 N d i ˆ ,

where d i ˆ is the distance estimated using the available measurements, as given in Eq. (7), and N is the number of the nodes in the system. It is emphasized by Nystrom (2017) and Patwari et al. (2003) that the standard deviation of the RSS measurement error remains relatively constant with the distance, suggesting that the observations of the same type have the same measurement error uncertainty that is unbiased and independent. Assuming the errors to remain Gaussian so that e ≈ N ( 0 , σ e 2 ) , the typical values of the standard deviation varies from 4 to 12 dB (Rappaport 2024). In our work, we have considered the value to be 4 dB since we do not model any other external error source and, moreover, the value of the parameter remains same for all the nodes.

3.2.2 Dilution of precision (DOP)

As illustrated previously, the accuracy of the centralized approaches heavily depends on the instantaneous geometry formed by the UAVs. The DOP parameters quantify the effect of geometry on the accuracy of the jammer position estimates, e.g., the horizontal DOP (HDOP) and vertical DOP (VDOP) parameters would represent the effect of geometry on horizontal and vertical position accuracy respectively. Using the geometry matrix definition given in Eq. (16),

(21) ( H T H ) − 1 = D 11 D 12 D 13 D 21 D 22 D 23 D 31 D 32 D 33 .

The expressions for HDOP and VDOP can be obtained using different components obtained from the aforementioned matrix.

(22) HDOP = D 11 2 + D 22 2 ,

(23) V DOP = D 33 2 .

3.2.3 Power difference of arrival

The performance of the localization methods described in the previous sections depends on various parameters, such as unknown bias constant and transmit power that requires either estimation of additional parameters or precise calibration of receivers. The differential approaches have been widely used to alleviate such dependencies, resulting in relatively more accurate position estimates. In our case, we are considering another implementation of centralized approach utilizing the measurements based on the power difference of arrival (PDOA), which are immune to receiver calibration and unknown bias estimation. The nullification of such effects during differencing step guarantees the best possible localization results among the candidate approaches considered in this article. The PDOA-based localization techniques can be implemented in different ways (Nystrom 2017), e.g., a parametric approach is presented by Cheung et al. (2003), which aims to linearize the system by introducing a radius factor in the state matrix to be determined. Robertson et al. (2015) implements PDOA combined with a grid search that searches for the grid or cell with the maximum number of intersection points and concludes that it contains the jammer.

In our case, the PDOA method uses the same path loss model given in Eq. (1). We start the analysis by relating the signal strengths observed by the nodes i and j at the distances d i and d j , respectively, from the source using the path loss model defined for the node-pair i and j in the network.

(24) P ( d i ) = P ( d 0 ) + 10 α log 10 d i d 0 + ε ,

(25) P ( d j ) = P ( d 0 ) + 10 α log 10 d j d 0 + ε .

The difference of received power can be obtained by subtracting power observed at each node as given in Eq. (26) after simplification. This results in cancellation of common terms such as reference power, distance, and other noises that should otherwise be estimated or modeled. The difference can finally be expressed as a ratio of nodes distances from the source.

(26) P i j = P ( d i ) − P ( d j ) = 10 α log 10 d i d j .

Assuming the true difference of received powers can be obtained, the node pair can estimate the position by minimizing the objective function, J , obtained using the nodes’ instantaneous positions and the difference of received powers.

(27) J ( x 0 , y 0 , z 0 ) = ∑ min [ P i j − 5 log 10 × ( x 0 − x j ) 2 + ( y 0 − y j ) 2 ( z 0 − z j ) 2 ( x 0 − x i ) 2 + ( y 0 − y i ) 2 ( z 0 − z i ) 2 2

The final jammer’s position can be computed by averaging the estimated positions obtained after minimizing the aforementioned objective function defined for all possible node pairs in the network. In the context of our work, we compare the PDOA localization results with the centralized approaches introduced in previous sections.

4 Scenario design and implementation

For the evaluation of techniques presented in the preceding sections, we performed the experiments in a controlled lab environment using Spirent Hardware simulators, as the strict regulations in Norway made it difficult to perform tests outdoors. In this section, we present details regarding the scenarios that are designed to simulate and evaluate the performance of different localization algorithms presented in the previous section. The section also covers the discussion about the characteristics of the simulated jammer, receiver calibration procedure, and the experimental setup. Two separate scenarios will be presented that have been used to evaluate the performance of localization methods that study the effect of having more nodes in the system on the position estimates.

4.1 Simulation scenario description

A network of identical UAVs is simulated to move along trajectories shown in Figure 1 over an open field of dimensions 2 km × 2 km. Four and six nodes have been considered for the first and second scenario, respectively. In the current context, an open field guarantees an open sky with clear reception of GNSS signals and offering no atmospheric effects, signal attenuation and blocking (multipath reflection due to urban canyon, foliage, and so on) except due to interference. To ensure better observability during the scenario, the UAVs are programmed to fly at different altitudes following the predefined trajectory. For the sake of simplicity, no wind, jerk, and other effects experienced by the UAVs have been considered in the article. The jammer trajectory is initialized at the center of the field from where the source is simulated to be slowly moving on a simple linear trajectory. Figure 1 shows UAVs and jammer trajectories in the scenarios with a color bar representing the UAVs’ ground speeds at various instants in the scenario, which are also shown separately in Figure 2.

$Figure 1 UAVs and jammer trajectories in the scenario in the local frame for the cases when N = 4 N=4 (top) and N = 6 N=6 (bottom), the ground dimensions are roughly 2 km × \times 2 km (Color bar represents the speed over ground in m/s).$

Figure 1

UAVs and jammer trajectories in the scenario in the local frame for the cases when N = 4 (top) and N = 6 (bottom), the ground dimensions are roughly 2 km × 2 km (Color bar represents the speed over ground in m/s).

Figure 2

Dynamics of the UAVs whose trajectories for the cases when N = 4 (top) and N = 6 (bottom).

4.2 Jammer signals’ characteristics

We have considered the wideband signal as a jammer to study the impact of it on the C/N₀ measurements generated by the receiver. Table 1 presents the details about the simulated platform dynamics and characteristics of the generated wideband interference signals.

Table 1

Simulated wideband signal characteristics and platform dynamics

Property	Wideband signal
Frequency (MHz)	1575.42
Signal power (dBm)	− 60
Signal bandwidth (MHz)	24
Source speed (m/s)	2.5
Course over ground (deg)	0
ON time	(T0 + 3 min) - (T0 + 7 min)

4.3 Experimental setup

The UAV motion trajectories have been generated using Adrupilot, which is an open source and industry standard autopilot simulation software system (Oborne 2019). It is a very comprehensive suite with many integrated tools customizable for a variety of terrestrial, aerial and underwater autonomous vehicles. In our work, we are using the software in the loop (SITL) and mission planner tools to realize and visualize the scenario and generate the ground truth measurements for the GNSS simulator.

The Ardupilot files are reformatted according to the user command file (.ucf) format acceptable by the Spirent GSS8000 Series Hardware GNSS simulator. The simulator generates the GNSS signals based on the simulated UAV platform dynamics. For jamming event simulation, the generated GNSS signals are combined with the jamming signals generated by the Spirent MS3055 Interference Signal Generator (ISG) (Ahmed et al. 2021). In this work, a low-cost NEO-M8T uBlox receiver was used for signal capture and measurement generation. For the tests presented herein, the receiver was configured to log the relevant measurements/data at 2 Hz. It is noted that in this study, only the GPS L1 signals are considered; therefore, the simulator and receiver are configured accordingly to operate at desired frequency.

The simulation scenario is designed to avoid any secondary effects, except jamming, on the UAV-borne receivers performance. Therefore, all the atmospheric effects (i.e., ionospheric and tropospheric delays) as well as phenomena such as multipath, and other possible factors have been excluded. To apply the theoretical model defined in Eq. (8), the NEO-M8T uBlox receiver had to be calibrated to determine the β ¯ parameter value. This has been carried out by performing a static jammer simulation. The test resulted in β ¯ value equal to 8 dB-Hz. This is the receiver’s calibration constant β ¯ as defined in Eq. (8). Since, we have considered the identical receiver models for all the UAVs in the network, the same value can be reused in each case. However, for a different receiver model, this factor needs to be determined through experiments.

A scenario is defined based on the description given in Section 4.1. An interference (.itf) file for the ISG needs to be defined that is generated using an interference Simulation File editor in the simulator’s software environment. The editor lets us set the interference characteristics associated with an antenna of certain node. It contains the interference signals type, signal strength visible at the receiver’ antenna at defined times, signal bandwidth, and other relevant parameters pertaining to specific type of interference signals. Even though the jammer is static, yet the dynamic nodes will not observe the constant jamming signal due to varying distance between the nodes and characteristic of radio signals.

The simulator used in the experiments currently does not provide any provision to connect or simulate multiple receivers simultaneously; therefore, the simulation had to be run N times with different node settings to obtain the raw measurements representing all the nodes. To estimate β ¯ , similar setup is used but with a static receiver. In this case, the jamming signal strength is varied to study a static receiver’s behavior and identify the level where the tracking loop begins losing their lock.

4.4 C/N₀ measurements

The interference is included in the scenario using a step function based on the time instants given in Table 1. Figures 3 and 4 show the effects of interference on the receivers’ average C/N₀ measurements in the presence of wideband jamming for both scenarios (when N = 4 and N = 6 ). There are several observations to be made from these figures that are relevant in regard to the performance of the algorithms presented in this article. First, the jammer’s presence is clearly observable from the deviation of average C/N₀ of up to 25–30 dB-Hz from its nominal value. Second, from the trends observed in the figures, we can have information of both jammers coarse motion relative to the UAV in the scenario and the times when the jammer is ON.

Figure 3

C/N₀ Measurements from the receivers in presence of wideband noise, when N = 4 .

Figure 4

C/N₀ Measurements from the receivers in presence of wideband noise, when N = 6 .

4.5 Selection and application of thresholds on the measurements

For the receiver model considered in the simulations, the static characterization tests form the basis of selection of an apposite threshold to be considered for single node and centralized localization schemes. As a principle, we study the sensitivity of the receiver for wideband interference and determine the region where the response is close to linear so that C/N₀-based range measurement models could be applicable. The static calibration test indicates the C/N₀-based model tends to behave linearly below 42 dB-Hz. Owing to the fact that the hardware design varies from one manufacturer to another, the range over the C/N₀ measurements appear to be linear will also change. This means that for a different receiver, the range should be specifically determined through proper experimentation.

5 Localization results and discussion

Typical systems aim to first detect the interference in an environment by observing the behavior of C/N₀ measurements. In the study by Tani and Fantacci (2008), various statistical approaches have been applied on the incoming GNSS signals to study the quality of the signal. Borio and Gioia (2015) assess a real-time jamming detection using the sum of squares of C/N₀ variations. Regardless of the detection technique, significant variations in average C/N₀, in an otherwise open environment, can be clearly observed. In our work, the supposition that the interference has been detected is only made to focus on the discussion of the performance of the localization approaches.

5.1 Performance of single node source localization techniques

In our simulations, we are considering node 1 for which the length of synthetic array ( N in Eq. (9)) is considered as 4. An objective function, as defined in Eq. (7), has been minimized to estimate the position of the jammer. In the C/N₀ measurement model Eq. (8), the calibration constant β ¯ is considered to be 8, which is obtained after calibrating the receiver using static test. A minimization technique based on gradient descent is used to determine solution of the objective function.

The localization results, obtained after applying single node localization techniques using the two measurement types, have been summarized in Table 2. The trajectory of the jammer is shown in Figure 1, indicating a linear motion in the simulation. From the results shown in the table, it can be seen that the error in x-component of the position varies between 300 and 870 m. Since, a ground-borne jammer has been considered, the z-component results are not very significant.

Table 2

Jammer localization results using single node localization approaches

Meas.	x (m)				y (m)				z (m)				Horizontal (m)
Type	Abs.Err		RMSE		Abs.Err		RMSE		Abs.Err		RMSE		Abs.Err		RMSE
	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max
C/N₀	31.7	972.6	296.3	870.2	3.7	979.4	162.3	349.8	4.1	46.7	17.1	31.9	31.9	1.3 × 10³	337.8	937.8

The initial guess value to start the gradient descent algorithm plays an important role in determining the quality of localization results, which is a common problem in many optimization-based problems. As emphasized in Fontanella et al. (2012), if the initialization value is not correctly chosen, the optimization algorithm could converge to a local minimum. The results would also deviate from the correct solution if the measurements used do not follow assumed theoretical model optimally. An overfitting could result in trapping in local minima, whereas an underfitting could cause a large deviation from an optimal solution. These observations and other assumptions made in our model collectively explain the results given in Table 2.

5.2 Performance of centralized localization techniques

The results given in this section are divided based on the localization techniques implemented for different number of nodes in the scenario. For each case, the localization results using different measurement types (C/N₀ and Difference of Power) have been compared. In addition, the results obtained using PDOA-based centralized localization approach are also presented that seemingly provide the best jammer position estimates.

The centralized techniques combine the measurements from all the nodes in the scenario and estimate the jammer location using WLS. The WLS results using the C/N₀ measurements, when N is considered as 4, are given in Table 3. Comparing the results with single-node localization, the root mean square error (RMSE) of x-component is reduced a half in the worst case. The RMSE in position errors is also reduced from around 900 to 550 m. A big deviation in the z -axis results is momentarily caused due to poor geometry but it has been observed that it remains for a very short duration in the experiment. The PDOA results, as expected due to aforementioned reasons, are the best among all of the candidate techniques. In the worst case, the RMSE in position turns out to be around 420 m.

Table 3

Jammer localization results using centralized approach ( N = 4 )

Meas.	x (m)				y (m)				z (m)				Horizontal (m)
Type	Abs.Err		RMSE		Abs.Err		RMSE		Abs.Err		RMSE		Abs.Err		RMSE
	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max
C/N₀	3.0	681.9	277.8	377.1	1.3	653.9	270.5	421.3	10.1	1.9e4	4.3e3	8.2 × 10³	204.8	910.9	410.3	554.2
PDOA	0.6	961.5	75.6	236.8	24.3	461.2	230.3	401.8	0.1	63.5	47.5	62.7	117.2	981.5	248.8	428.9

The results are definitely not well suited for precise jammer localization - something which is not the goal of this research. As discussed later in this section, the accuracy is determined by the factors such as measurement model selection, measurement errors, and the geometry formed by the UAVs relative to the jammer. However, they are good enough for the intended use case as we aim for situational awareness and environment sensing to detect the presence of jamming source.

Figure 5 shows the variation of estimated jammer positions results as a function of the UAVs’ instantaneous geometry that is represented as an HDOP parameter. The geometries tend to get worse roughly at times t 1 ( t = 130 s) and t 2 ( t = 220 s). The second higher peak at t 2 indicates the comparative geometries that the UAVs form and explains that the geometry is not worse than the previously observed one at t 1 . In the plots, the higher HDOP represents poor geometry that results in poor estimation accuracy. This observation can be verified in the plots that the horizontal range errors tend to rise with rising HDOP trend and vice versa. The HDOP curve shown in the plots applies only on WLS results since the geometry formed by the nodes would be different due to the measurement differencing. The x -axis in the plot represents the 4-min duration when the jammer remains ON in the scenario (see Table 1). The discontinued parts of the error curve represent the instants when the C/N₀ values are above the threshold value that is actually happening at the start and end of the maneuvers when the UAVs are outside the range of the jamming source.

Figure 5

Centralized localization results for N = 4 plotted alongside the HDOP, the PDOA results are shown in dotted green values.

Figure 6 shows the localization results for the same localization techniques for the scenario when two additional nodes are added in the systems to compose a hexagonal formation as seen from a bird’s eye view. The jammer localization results for such case are given in Table 4. Adding more nodes seems to be advantageous as an improvement in the estimated jammer positions is evident from the results given in the table. In the case of C/N₀, the improvement of around 100 m is observed in x-component results and minimum RMSE in position estimation. Improvements in other case of PDOA also observed in the table. Such improvement might not be of statistical significance as the experiments were not performed multiple times. The simulations have been performed a few times, and the repeatability is observed in the results.

Figure 6

Centralized localization results for N = 6 plotted alongside the HDOP, the PDOA results are shown in dotted green values.

Table 4

Jammer localization results using centralized approach ( N = 6 )

Meas.	x (m)				y (m)				z (m)				Horizontal (m)
Type	Abs.Err		RMSE		Abs.Err		RMSE		Abs.Err		RMSE		Abs.Err		RMSE
	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min	Max
C/N₀	1.7	666.8	97.4	237.1	1.0	434.0	253.1	545.0	2.2	1.2 × 10⁴	552.8	2.5 × 10³	63.1	670.2	304.8	559.5
PDOA	0.3	561.3	78.2	180.2	8.8	236.4	129.3	233.8	12.3	65.7	52.6	65.3	92.6	567.0	158.1	273.9

It should be noted that the HDOP curves shown in Figures 5 and 6 are calculated for the value of N to be 4 and 6, respectively. Unlike for the case when N is 4, the careful observation of the right y -axis shows that the HDOP appears to be relatively uniform throughout the duration of the experiment. Therefore, the jammer position estimates do not vary a lot accordingly and hence are more representative of the jammer’s coarse location in the field.

The results presented earlier are potentially reasonable for the situational awareness, so that the nodes could take contingency measure by following another safer trajectory in case of any jamming event. In this section, a comparative analysis of different techniques is presented to study the performance in terms of the results presented in previous section.

The single node approach is usually dependent on the geometric diversity of the C/N₀-based distance measurements taken by a single node. The results presented in Table 2 show that there are significant variations in certain components of the estimated jammer position, which in some cases exceed even more than what observed in the centralized results. This is explained by standalone nature of the algorithms, the unaccounted/unmodeled errors in the node’s position estimates and not very accurate measurement models used for distance measurements.

Figure 7 shows the comparison of difference centralized localization approaches, where the estimated jammer position results in the xy-domain are plotted along with the true jammer coordinates. The C/N₀ results are more contained and compact in the whole 4 km² field that presents a roughly correct picture of the jammer’s trajectory. Disregarding the outliers, in the worst case, the C/N₀ results remain within around 600 m and the PDOA outperforms where the position estimates remain within around 400 m. As expected, the PDOA results remain the most desirable whereas the degree of variation in C/N₀ errors also appears to be concentrated.

Figure 7

2D jammer positions estimated using different centralized localization techniques using N = 4 (above), and N = 6 (below), along with the true trajectory of the jammer shown with green line.

5.3 Factors affecting the localization accuracy

The localization accuracy of the results presented in the previous section depends on various factors. In this section, we highlight some of the factors that often play significant role in determining the efficiency of the approaches.

5.3.1 Measurement model limitations

The measurement models presented in the article consider a near-ideal scenario and do not consider any environmental or platform-related disturbances. The single node and centralized approaches, in their current states, are expected to perform worse in presence of such factors. Studying the performance of said models under varied conditions is beyond the scope of the article.

5.3.2 Measurement uncertainty

To benefit from the considered techniques, it is important to have continuous and accurate node/UAV position estimates. The errors in the UAV position measurements could result in large jammer localization errors.

5.3.3 UAVs’ geometry

The instantaneous geometry formed by the UAVs plays an important role in determining the accuracy of the estimation results. As discussed earlier, the DOP values explain the estimation accuracy that is indirectly dependent on the placement of UAVs in the space. The lower DOP value indicates better accuracy and widespread placement of the UAVs covering most of the available area (in 2D) or volume (in 3D). Figure 8 shows a bird’s eye view pinpointing the best and worst placement of UAVs during the complete duration of two scenarios based on their corresponding best and worst DOP values. It can be observed from the figure that for the best geometries, the UAVs are well spread around the jammer (shown with small red circle) covering the maximum possible volume. In the worst case, however, the UAVs not only cover minimum volume (area in 2D) but also form a corresponding polygon even without including the jammer.

Figure 8

Best and worst geometries formed by the UAVs in the scenario with jammer shown with red circle.

5.4 Expected performance for the cases not considered

As described earlier, the work presented in the article made some assumptions. The scenario has been considered a specific civilian situation where a search and rescue mission to localize only one source is being conducted in a small region. This justifies that the similar GNSS receivers would be used as all the members are equipped with an identical backpack with similar sensor suite. The consideration of atmospheric effects and multipath are going to impact the range measurement model given in Eq. (1), where a different value of path loss exponent α and a factor ε accounting for miscellaneous effects would be used.

For the special scenarios, when the GNSS receivers from different manufacturers are used, they need to individually calibrated first. This would reflect as the calibration constant, β ¯ , to be incorporated in the model given in Eq. (6) used for effective C/N₀ computation. Unavailability of such receivers constrained us to show the results in the article. The receivers could be calibrated irrespective of the type of noise in the environment since the effect of the RFI characteristics is only visible on the observables.

Despite the fact that the estimators give the best case results of 100 s of meters, they are generally considered good enough for situational awareness and coarse localization. A future grid search is necessitated for relatively more accurate and fine localization that is currently beyond the scope of this work.

Even though the UAV-based scenario is simulated, actual receiver measurements have been used to demonstrate the localization techniques. The techniques such as Monte Carlo simulations are quite powerful tools to repeatedly simulate the receiver performance and perform localization considering different aforementioned factors.

6 Conclusion

In this article, we investigated single-node and collaborative localization techniques using the C/N₀ available from the low cost navigation sensors. The contributions of the article include gradient descent-based synthetic array for the 3D localization, and the formulation of test cases for localization purposes highlighting the potential pros and cons. The performance of the average effective C/N₀ has been studied in the presence of a quasistatic wideband jamming source. The case of collaborative localization has been investigated for two different scenarios comprising of four and six identical UAVs. The performance of localization schemes for different scenarios has been assessed studying the impacts of different number of nodes, and different node geometries and their dynamics. The results have been compared with the results obtained using PDOA-based centralized approach that ensures the most accurate results. The main objective of the investigation was not accurate tracking of the jamming source but rather a coarse jammer localization for both the situational awareness and for the navigating entities (static and dynamics) to adopt relevant contingency plans. Given a coarse estimate of the jammer location, critical zones can be identified, and alternate routes can be assigned to escape the effects posed by the source. The performance of different localization techniques has been evaluated and compared against each other, given various assumptions, through a series of experiments in a controlled environment.

Acknowledgments

The author would like to acknowledge Adrian Winter for helping in generating scenarios in ArduPilot environment, and processing them and finally providing me the files to be used by the GNSS Simulator.

Funding information: Authors state no funding involved.
Author contributions: All authors are involved in the research. Naveed Ahmed is involved in the main data collection, simulation, and analysis along with the manuscript preparation. Ardeshir Mohamadi participated in the manuscript preparation with initial review and feedback. Hossein Nahadavanchi supervised, reviewed, and helped in refining the overall quality of the manuscript.
Conflict of interest: The authors declare there is no conflict of interest.
Informed consent: This study did not require or involve any human participation; therefore, no informed consent was required.

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Received: 2025-03-06

Revised: 2025-06-23

Accepted: 2025-06-27

Published Online: 2025-10-06

This work is licensed under the Creative Commons Attribution 4.0 International License.

Artikel in diesem Heft

https://doi.org/10.1515/jogs-2025-0185

Schlagwörter für diesen Artikel

carrier-to-noise density ratio; power difference of arrival; radio frequency interference localization; robust positioning; synthetic array

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RFI localization using C/N0 measurements from low cost GNSS sensors for robust positioning

Artikel

Abstract

1 Introduction

1.1 Research background and motivation

1.2 State-of-the-art techniques

2 Measurement models

2.1 Carrier to noise density ratio (C/N0)

2.1.1 C/N0-based range measurement model

3 Jamming source localization techniques

3.1 Single-node localization

3.1.1 Synthetic array approach

3.1.2 Synthetic array with bias estimation

3.2 Centralized approach

3.2.1 Weighted least squares method

3.2.2 Dilution of precision (DOP)

3.2.3 Power difference of arrival

4 Scenario design and implementation

4.1 Simulation scenario description

4.2 Jammer signals’ characteristics

4.3 Experimental setup

4.4 C/N0 measurements

4.5 Selection and application of thresholds on the measurements

5 Localization results and discussion

5.1 Performance of single node source localization techniques

5.2 Performance of centralized localization techniques

5.3 Factors affecting the localization accuracy

5.3.1 Measurement model limitations

5.3.2 Measurement uncertainty

5.3.3 UAVs’ geometry

5.4 Expected performance for the cases not considered

6 Conclusion

Acknowledgments

References

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RFI localization using C/N₀ measurements from low cost GNSS sensors for robust positioning

2.1 Carrier to noise density ratio (C/N₀)

2.1.1 C/N₀-based range measurement model

4.4 C/N₀ measurements