2.1 Definitions of relevant variables

In general, a $J/S$ ratio is defined as the ratio of the jamming signal power, devoted as ${J_r}$ , to the authentic GNSS signal power, devoted as ${S_r}$ . The $J/S$ ratio is usually expressed in decibels and is defined by Equation (1). A specific $J/S$ ration value that causes a GNSS receiver to lose track of an already acquired authentic GNSS signal may be called critical jamming to signal ratio, devoted as ${(J/S)_c}$ .

(1) \begin{align}J/S = {J_r} - {S_r}\end{align}

The calculation of the jamming signal power ${J_r}$ in relation to the distance from the jammer, assuming free-space propagation, is given in dBW by Equation (2).

(2) \begin{align}{J_r} = {J_t} + {G_t} + {G_r} - L - {L_{FSPL}} = {J_t} + {G_t} + {G_r} - L - 20\ {\rm{lo}}{{\rm{g}}_{10}}\left( {\frac{{4\pi df}}{c}} \right)\end{align}

Where:

• • ${J_t}$ is transmitted jamming signal power

• • ${G_t}$ and ${G_r}$ are transmitting and receiving antenna gain, respectively

• • $L$ is receiver losses which do not affect propagation

The Free Space Path Loss (FSPL) equation is expressed by Equation (3), where $f$ is the frequency of the radio wave and $d$ is the distance between the receiver and the transmitter (jammer in our case).

(3) \begin{align}{L_{FSPL}} = \left( {\frac{{4\pi df}}{c}} \right)\end{align}

The FSPL method was preferred to models adjusted to ground signal reflection like the two-ray path model because the aircraft GPS antenna is on top of an aircraft; the fuselage of the aircraft serves almost like a ground, meaning the effect of reflected signals from the ground is near zero. Considering negligible losses in the receiver and negligible receiving antenna gain as an isotropic antenna and using the effective isotropic radiated power $EIRP$ , then Equation (2) can be rewritten as Equation (4):

(4) \begin{align}{J_r} = EIRP - 20\ {\rm{lo}}{{\rm{g}}_{10}}\left( {\frac{{4\pi df}}{c}} \right)\end{align}

Throughout the paper, the jamming power values will be described in both EIRP and electric field strength (E) at the aircraft GPS antenna location. The conversion between the two variables is described by Equation (5), where EIRP is effective isotropic radiated power in dBm, $E$ is electric field strength in ${\rm{dB\;}}\mu {\rm{V}}/{\rm{m}}$ , and $d$ is the distance in meters.

(5) \begin{align}EIRP = E + 20\ {\rm{log}}\left( d \right) - 104.8\end{align}

With a known value of ${S_r}$ , the $J/S$ ratio can be determined using Equation (1). In reverse, assuming the knowledge of ${(J/S)_c}$ value, it is possible to calculate from Equation (1) the critical jamming power ${J_c}$ that will prevent the receiver from authentic GNSS signal reception.

The value of ${S_r}$ can be derived from the Convention on International Civil Aviation, Aeronautical Telecommunications, Volume I, Radio Navigation Aids, Annex 10 [21] which states: ‘Each GPS satellite shall broadcast SPS navigation signals with sufficient power such that, at all unobstructed locations near the ground from which the satellite is observed at an elevation angle of five degrees or higher, the level of the received RF signal at the antenna port of a three dBi linearly-polarised antenna is within the range of −158.5 dBW to −153 dBW for all antenna orientations orthogonal to the direction of propagation.’ Similarly, the GPS Interface Specification [22] states: ‘minimum RF signal strength for the GPS L1 C/A signal, is −128.5 dBm’.

It is also possible to compute the maximum distance at which the jamming signal with a given power can jam the GNSS receiver can be obtained, devoted as ${d_{max}}$ . The maximum distance computation is expressed by Equation 6.

(6) \begin{align}{d_{max}} = \frac{c}{{4\pi f}}{10^{\frac{{EIR{P_t} - {J_c}}}{{20}}}}\end{align}

2.2 ADS-B quality indicators

The scope of the paper is limited to the analysis of ADS-B quality indicators broadcasted in ADS-B 1090ES ICAO Version 2 technology, namely NACp, NIC, SIL and SDA, as the main position quality indicators. In April 2024, over 96% of aircraft were equipped with ADS-B version 2 in the European region [23]. The following is the description of the four relevant ADS-B quality indicators and their broadcasting.

NACp provides a graduated indication of position accuracy based on the estimated position uncertainty (EPU) parameter. The EPU is defined as the radius of a circle, centred at the reported position, such that the probability that the actual aircraft position lies outside this circle is 0.05 [24, 25]. When the position information is reported by a GPS or GNSS system, EPU is commonly called horizontal figure of merit (HFOM). The NAC indicator takes values from 0 to 11. If an update has not been received from an onboard data source for NACp within the past 2.6 seconds, then the NACp subfield shall be encoded as zero, indicating unknown accuracy [24, 25].

NIC carries information about the value of the Integrity containment radius ( ${R_c}$ ). This value is derived from the horizontal protection level (HPL), the horizontal integrity limit (HIL) or another means of establishing an appropriate radius of containment. For the airborne position messages, the NIC indicator can take values from 0 to 11, while for the surface position messages, the NIC value can take only values 0, 6, 7, 8, 9, 10, 11 [24, 25].

SIL defines the probability of the reported horizontal position exceeding RC defined by NIC without alerting, assuming no avionics faults. i.e., SIL addresses the integrity of signal-in-space (SIS). The indicator takes values from 0 to 3. For GNSS position sources, the HIL or HPL is provided with a probability of $1 \times {10^{ - 7}}$ per hour, which sets the SIL value to three [24, 25].

SDA indicates the probability of ADS-B system malfunction causing false or misleading information to be transmitted. The ADS-B system in this context includes the ADS-B transmission equipment, ADS-B processing equipment, position source, and any other equipment that processes the position data transmitted by the ADS-B system. The indicator takes values from 0 to 3 [24, 25].

When an aircraft is airborne, the NIC indicator is determined from the airborne position message. When an aircraft is on the ground, the NIC indicator is determined from the surface position message and the aircraft operational status message. The NACp, SIL and SDA indicators are transmitted either within the aircraft operational status message or the target state and status message. The update rate of the quality indicators varies from 2.5 to 0.5 seconds depending on multiple factors. More details can be found in the standards Radio Technical Commision for Aeronautics RTCA [24], The European Organisation for Civil Aviation Equipment (EUROCAE) [25]. The latency between the parameter computations and its transmission is less than 1.5 seconds [24, 25].

If GNSS position information is unavailable in the last 60 seconds, for example, due to GNSS jamming, the transmission of the airborne position message and surface position message should be stopped. However, if barometric altitude is available then ADS-B message transmission is not suppressed. Nevertheless, since the surface position message does not contain barometric altitude the message stops transmitting when the aircraft is jammed because no position information is computed. As stated in RTCA 2009; EUROCAE 2009: ‘ADS-B Surface position Message (as well as Aircraft Operational Status Messages) is no longer broadcast 60 $ \pm $ 1 s after stopping the data input’ [24, 25].

2.3 Jamming equipment used

For the experimental measurements, two different GNSS jammers were used. For Boeing measurements, the STARGAL jammer was used. Whereas for the other three measurements on Airbus, Beechcraft and Tecnam the TG5CA jammer [26] was used. Both jammers allow for adjustment in the output power. Additionally, an external attenuator was used for the Airbus measurement allowing for better control over the output power. Furthermore, the transmission antenna used with the jammers was equipped with a metal base which minimises transmission to negative elevation angles. The stated power and electric field intensity values throughout the paper are measured for a 20 MHz bandwidth centred at the GPS L1 carrier frequency, 1575.42 MHz.

The STARGAL jammer model is a digital multi-sweep (DDS) based system that generates a type of interfering signal referred to as linear chirp. The jamming is transmitted in the frequency range of 1,563 MHz to 1,587 MHz, with a dwell time of 0.1 microseconds per the 30 kHz frequency step. This results in a sweep repetition rate of 12.5 kHz.

The TG5CA jammer transmits a sweeping jamming signal at the GPS L1 centre frequency with a bandwidth of 20 MHz measured for 99% power using the $\beta /2$ method as per ITU’s recommendation [27]. The maximum radiated power is an EIRP of 36.6 dBm or 4.6 W in the configuration with the manufacturer-supplied antenna. The interference signal is generated through frequency modulation using a sawtooth pattern with a frequency of approximately 85.3 kHz which corresponds to a sweep period of about $12\mu s$ .

2.4 Experimental measurement

In total four experimental measurements were carried out testing four aircraft models each from a different manufacturer. Specifically tested aircraft models were:

• • Boeing B737 Max

• • Airbus A319

• • Beechcraft King Air 350

• • Tecnam P2006T

The first two aircraft represent commercial aviation whereas the other two can be categorised as general aviation aircraft. Both ground and flight measurements were carried out. The ground measurements involved Boeing B737 Max and Airbus A319. While Beechcraft King Air 350 (B350) and Tecnam P2006T were in flight measurements.

In all measurements, aircraft were subjected to an increasing jamming signal power while the response in ADS-B quality indicators and cockpit avionics was monitored. To ensure sufficient ADS-B data recording an additional ADS-B receiver was deployed at the testing grounds. The ADS-B quality indicators mentioned in Section 2.2 were decoded from the captured data. The method of decoding and the presence of specific indicators in individual types of messages can be found in in RTCA [24] and The European Organisation for Civil Aviation Equipment (EUROCAE) [25].

2.5 Logistic regression model for GNSS position outage versus jamming signal power

For further analysis, the logistic regression modelling the conditional probability of GNSS position outage in relationship to the power of the jamming signal was created. The logistic regression showcases a more accurate and detailed statistical description of the dependency. Only data from the part of flights where the aircraft is approaching the jammer were used for the analysis. This data filtering was applied since it is not possible to determine when the receiver exactly starts tracking the authentic signal due to an unspecified time delay it takes to start broadcasting the position information in ADS-B data. Data from the ground measurement were also filtered only to include those captured during periods of increasing jamming signal power.

The logistic function described in Equation 7. was fitted to the data of jamming signal power and the GNSS receiver output, represented by two states, 1 and 0. Value one means positional information is unavailable whereas zero means position information is available.

(7) \begin{align}p\left( x \right) = \frac{1}{{1 + {e^{ - \left( {x - \mu } \right)/s}}}} = \frac{1}{{1 + {e^{ - \left( {{\beta _0} + {\beta _1}x} \right)}}}}\end{align}

Where:

• • x – jamming signal power (independent continuous variables)

• • $\mu $ – location parameter (the midpoint of the curve, where $p\left( \mu \right) = 1/2$ , $\mu = - {\beta _0}/{\beta _1}$

• • s – scale parameter, $s = 1/{\beta _1}$

Position information unavailability was derived from the NACp and NIC indicators. The position was considered lost once at least one of those indicators reached zero. Specific parts of a flight further described in Section 3.3, when the aircraft antenna was shielded from the jamming signal by the airframe, were excluded from the logistic regression dataset.

3.1 Boeing B737 Max results

In the zero elevation jammer-aircraft configuration, further referred to as B $737_{zer}$ , the loss of positions on both GNSS receivers as well as in ADS-B occurred at EIRP = 0.832 mW equivalent to −0.36 dBm. This corresponded to E = 78 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −68.3 dBm at the aircraft receiver for an aircraft antenna gain of −5 dB.

In the negative elevation jammer-aircraft configuration, further referred to as B $737_{neg}$ , both GNSS receivers failed at EIRP = 2.63 mW or 4.2 dBm. This corresponded to E = 82.6 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −66.6 dBm at the aircraft receiver for an aircraft antenna gain of −8 dB representing the combined effect of the jammer’s and the aircraft’s antenna characteristics.

The values of NACp, NIC, SIL and SDA during B $737_{zer}$ and B $737_{neg}$ are shown in Figs 1 and 2, respectively. The NACp and NIC indicators remain stable in a normal operation range until jamming power reaches over −69 dBm when a certain fluctuation can be seen which leads to a drop to zero in both indicators. The SIL and SDA parameters remained unchanged throughout the experiment. After a certain time, the ADS-B containing the quality indicators cease transmission completely, resulting in the unavailability of all these parameters.

Figure 1. Values of ADS-B quality indicators during B737 measurement with zero aircraft-jammer elevation.

Figure 2. Values of ADS-B quality indicators during B737 measurement with negative aircraft-jammer elevation.

3.2 Airbus A319 results

In the first measurement with zero elevation jammer-aircraft configuration, further referred to as A $319_{zer1}$ , a loss of GPS position occurred at a transmitted EIRP of 0.845 mW or −0.73 dBm. This corresponded to E = 77.6 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −68.6 dBm. During the subsequent reduction of jamming signal power, the GPS position information was restored at an EIRP of 0.267 mW or −5.73 dBm, which corresponded to E = 72.6 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −73.6 dBm.

In the second measurement with zero elevation jammer-aircraft configuration, further referred to as A $319_{zer2}$ , a loss of GPS position occurred at a transmitted EIRP of 0.424 mW or −3.73 dBm. This corresponded to E = 74.6 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −69.9 dBm. The re-establishment of GPS position occurred at an EIRP of 0.212 mW or −6.74 dBm, which corresponded to E = 71.6 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the interference signal was −74.5 dBm.

In the first measurement with negative elevation jammer-aircraft configuration, further referred to as A $319_{neg1}$ , a loss of GPS position occurred at an EIRP of 1.3 mW or 1.14 dBm. This corresponded to E = 79.7 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −69.5 dBm. The reacquisition of position occurred at an EIRP of 0.27 mW or −5.7 dBm which corresponded to E = 72.66 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the interfering signal was −76.5 dBm.

In the second measurement with negative elevation jammer-aircraft configuration, further referred to as A $319_{neg2}$ , a loss of GPS position occurred at an EIRP of 2.1 mW or −3.3 dBm. This corresponded to E = 81.7 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the jamming signal was −67.5 dBm. The reacquisition of GPS position occurred at an EIRP of 0.054 mW or −12.7 dBm which corresponded to E = 65.66 dB $\mu $ V/m at the aircraft antenna location. The calculated power of the interfering signal was −83.5 dBm.

In all four measurements, a similar trend in all ADS-B quality indicators can be observed. All indicators from the four A319 measurements are displayed in order in Figs. 3–6. In most cases, during the initial phase of interference, when positional information is still available, the decrease in the value of the NIC indicator precedes the decrease in the NACp and SIL indicators. The fall of the SIL indicator to zero completely copies the decrease of the NACp indicator to zero. After the aircraft loses the ability to provide position information, NIC = 0 continues to be transmitted. After approximately 60 seconds of position unavailability, all quality indicators transmission is terminated also in accordance with ADS-B standards [24, 25].

Figure 3. Evolution of quality indicators values for measurement A $319_{{\rm{zer}}1}$ .

Figure 4. Evolution of quality indicators values for measurement A $319_{{\rm{zer}}2}$ .

Figure 5. Evolution of quality indicators values for measurement A $319_{{\rm{zer}}3}$ .

Figure 6. Evolution of quality indicators values for measurement A $319_{{\rm{zer}}4}$ .

3.3 Beechcraft King Air 350 results

In nominal conditions without the presence of GNSS interference, the NACp indicator values ranged between 10 and 11. The NIC indicator remained constant at a value of eight. Parameters SIL and SDA were also constant during the portion of the flight with no jamming with SIL = 3 and SDA = 2.

During the first overflight, further referred to as B $305_1$ , the NIC indicator decreases from eight to zero at 07:47:35.59 which corresponds to a jamming signal power level of −65.75 dBm. At 07:47:36.99 NACp and SIL indicators decreased to zero. The delay in comparison to NIC occurred due to a longer repetition period of the ADS-B message containing the NIC indicator. The ADS-B quality indicators when approaching the jammer during the first overflight are displayed in Fig. 7.

Figure 7. Evolution of ADS-B quality indicators for measurement B $350_1$ .

During the second overflight, further referred to as B $305_2$ , the NACp, NIC, and SIL indicators all decreased to a value of zero at 07:54:21.14 which corresponds to a jamming signal power level of −72.99 dBm. Prior to that, the NACp parameter had already dropped from a level of 10 to 9 at a power level of −73.53 dBm indicating a position error larger than 30 meters, which could be indicative of the interference as such an error should not normally occur when utilising SBAS.

After directly passing over the jammer, a partial regeneration of the NACp parameter to a value of nine was noticed, followed by a drop to zero and subsequent complete regeneration with NACp gradual increase to ten at 7:56:42. The SIL parameter during both overflights returned to a value of three immediately when NACp acquired a value other than zero. The changes in ADS-B quality indicators when approaching the jammer during the second overflight are displayed in Fig. 8.

Figure 8. Evolution of ADS-B quality indicators for measurement B $350_2$ .

Right after passing the jammer in B $350_1$ , still within the jammer impact area, position information was re-obtained for a short period. This was likely due to the aircraft antenna being shielded from the jamming signal fuselage. This is also reflected in the ADS-B quality indicators, showing a temporary increase in NACp to 10. However, within a few seconds, the NACp indicator dropped again to 0. Only after this sequence, the aircraft receiver regenerated and returned to normal operation. The same phenomenon occurred during B $350_2$ as well. The changes in the NACp indicator during both overflights are visualised on a map in Fig. 9.

Figure 9. Flight trajectory with NACp values colour-coding for measurements B $350_1$ and B $350_2$ (scale 1:65,000).

3.4 Tecnam P2006T results

During the first overflight, further referred to as ${\mathrm{P2006T}_1}$ , the calculated power of the jamming signal at the aircraft location, at which the position information was lost, was −75.6 dBm. At this power level, NACp decreased from 10 to 0, NIC decreased from 9 to 0, and SIL decreased from 3 to 0. Values of all quality indicators during ${\textrm{P2006T}_1}$ are displayed in Fig. 10. Shortly after entering the jammer impact area, the aircraft’s GPS antenna was partially obstructed by the aircraft’s airframe, resulting in the increase of NACp to eight and SIL returning to three. However, the NIC value remained at zero during the entire overflight.

Figure 10. ADS-B quality indicators values for measurement ${\textrm{P2006T}_1}$ .

During the second flight through the jammed area, further referred to as ${\textrm{P2006T}_2}$ , the ability to provide position data was lost at a power level of −69.3 dBm. At this moment, the NIC indicator decreased from 8 to 0, SIL decreased from 3 to 0, and NACp decreased from 9 to 0. This most likely indicates that the receiver did not fully regenerate after the previous interference as NACp did not reach ten and NIC did not reach nine which were values preceding the first impact of jamming. Changes in ADS-B quality indicators from ${{P2006T}_2}$ are displayed in Fig. 11.

Figure 11. ADS-B quality indicators values for measurement ${\textrm{P2006T}_2}$ .

3.5 Aircraft resilience comparison

Table 1 summarises and compares the power values at which the tested aircraft GPS receivers lost the GPS L1 signal indicated by the NACp indicator dropping to 0. The mean value of the jamming power is −68.44 dBm, with a standard deviation of 2.61 dBm. Table 1 also includes all the values necessary to compute the jamming signal power at the aircraft antenna.

Table 1. Measured/calculated values at which the GNSS receiver stopped providing position data in ADS-B messages across all conducted measurements

EIRP – jammer effective isotropic radiated power; d – horizontal and ${\rm{\Delta }}$ H – vertical distance between the aircraft antenna and the jammer; E – intensity of the electric field at the aircraft antenna location; G – gain of the aircraft antenna in the direction of the jammer; P – power of the jamming signal

The re-acquisition of the previously lost GPS L1 signal does not occur immediately upon reaching the power at which re-acquisition is possible. There is a time delay involved in the receiver regeneration. Thus, when the aircraft is airborne, it is not possible to exactly determine the interference signal power that prevents the receiver from re-acquiring the GPS L1 signal. Therefore, only the results from stationary measurements are included in Table 2 which displays values at which the GNSS receiver was able to re-acquisition the GPS signal, re-establish position in ADS-B data, and ADS-B quality parameters returned to nominal values. The mean value of the jamming power sufficient to prevent the GPS L1 signal acquisition is −75.48 dBm, with a standard deviation of 4.95 dBm.

Table 2. Measured/calculated values at which the GNSS receiver was able to re-establish the provision of positional data

EIRP – jammer effective isotropic radiated power; d – horizontal and ${\rm{\Delta }}$ H – vertical distance between the aircraft antenna and the jammer; E – intensity of the electric field at the aircraft antenna location; G – gain of the aircraft antenna in the direction of the jammer; P – power of the jamming

3.6 Logistic regression model outcomes

Using the methodology described in Section 2.5, a logistic distribution displayed in Fig. 12 was obtained. The distribution has the following parameters: mean value $\mu $  = −70.10 dBm, standard deviation $\sigma $ = 3.14 dBm, corresponds to the scale parameter s = 1.88. Given this logistic distribution, the jamming signal power level corresponding to the 95% probability that the receiver is jammed is −64.55 dBm. Analogously, the jamming power level at which there will be a 95% probability that the receiver will not be jammed in other words 5% probability the receiver is jammed corresponds to −75.63 dBm.

The classification matrix (sometimes called confusion matrix) was used for the assessment of the goodness-of-fit for the logistic regression model. A 50% cut-off point on the probability scale was used to classify all values. The logistic model with above-specified parameters has accuracy = 0.84, sensitivity = 0.75, and specificity = 0.88.

3.7 Aircraft critical jamming to signal ratio and jamming impact area

Based on the presented experimental measurements, the value of ${(J/S)_c}$ signifying when the loss of an already acquired GPS L1 signal occurs, was calculated to be 55 dB at the aircraft GNSS antenna location. The ${(J/S)_c}$ = 55 dB value was derived from the mean critical value of the jamming signal power level ${J_c}$  = −70.10 dBm in the logistic regression model and based on the assumption that the average power level of the GPS L1 signal at the Earth’s surface is −125 dBm. The −125 dBm value was chosen as the midpoint of the power range according to ICAO Annex 10 document (2018) after subtracting the 3dB aircraft antenna gain. The result of ${(J/S)_c}$ = 55 dB must be understood in the context of the jamming signal type used in the measurements. Both GNSS jammers used in the presented measurements transmit chirp-type jamming signal which is the most common type of jamming signal used in commercial off-the-shelf jammers. The ${(J/S)_c}$ for other types of jamming signals like the white noise of sawtooth may slightly differ.

Table 3 and Fig. 13 illustrate the size of the GNSS interference impact area in relation to the jammer output power. The radiuses ${\textrm{r}_1}$ and ${\textrm{r}_2}$ of the impact areas in Table 3 were calculated for ${J_c}$ values of −64.55 dBm and −75.63 dBm. These ${J_c}$ values were derived from the logistic regression representing the 95% and 5% probability of position information degradation based on ADS-B quality indicators. The values in Table 3 and Fig. 13 do not account for any antenna gains on the transmitting or receiving side, nor do they include losses in the cabling.

Table 3. Jamming impact area radiuses for 95% and 5% position information degradation probabilities in relation to different jammer output

Figure 12. Probability of GNSS position loss as a function of jamming signal power based on logistic distribution.

Figure 13. Dependence of received jamming signal power on distance for 1 W, 5 W, 10 W and 20 W GNSS jammers. The two dashed lines represent the boundaries of 95% and 5% probability of GNSS position information being impacted by jamming.