A Beidou navigation deception detection method based on carrier-to-noise ratio hopping

Abstract

This application relates to a BeiDou navigation spoofing detection method based on carrier-to-noise ratio (CNR) jumps. The method includes: performing A / D sampling and signal tracking on the satellite navigation signal; calculating broadband power and narrowband power based on carrier frequency and code phase; calculating the average power ratio of the broadband and narrowband power; using the average power ratio to calculate the CNR of each satellite at each epoch; calculating the CNR difference between consecutive epochs and the inter-satellite CNR difference based on the CNR of each satellite at each epoch; using the CNR difference between consecutive epochs and the inter-satellite CNR difference as test statistics to construct a first hypothesis testing model and a second hypothesis testing model; solving for the unknown first and second test thresholds based on the expanded Gaussian distribution expression and a pre-set false alarm probability; and performing a dual detection decision based on the known first and second test thresholds. This method balances technical effectiveness and low cost.

Description

Technical Field

[0001] This application relates to the field of satellite navigation interference detection technology, and in particular to a method for detecting BeiDou navigation deception based on carrier-to-noise ratio jumps. Background Technology

[0002] With the further widespread application of the BeiDou Navigation Satellite System, various industries have increasingly higher requirements for the accuracy of BeiDou satellite timing. However, due to the openness and replicability of civilian navigation signals, they are easily deceived and interfered with, threatening timing security.

[0003] Current research on satellite navigation spoofing signal detection methods is extensive. Commonly used methods include carrier-to-noise ratio (CNR) detection, angle of arrival (ADR) detection, time of arrival (TOA) detection, consistency checks, and cryptographic methods. Absolute power detection is susceptible to multipath propagation and factors such as antenna type and attitude, leading to false alarms and reduced detection accuracy. ADR detection requires an array antenna on the receiver, which is too costly for civilian receivers. TOA detection detects spoofing signals based on the difference in signal arrival times, but it is not suitable for detecting generative spoofing signals; however, it is more effective for detecting repeater-based spoofing signals. Consistency checks are not ideal for detecting intermediate and advanced spoofing signals. Cryptographic methods require addressing the message structure, detecting spoofing signals by altering the structure. They cannot be used in known and deterministic signal systems and are only applicable to preventing generative spoofing. Existing spoofing signal detection technologies cannot simultaneously achieve both effectiveness and low cost. Therefore, improving the effectiveness of spoofing interference detection under controllable cost conditions is urgently needed, and related research is essential. Summary of the Invention

[0004] Therefore, it is necessary to provide a BeiDou navigation spoofing detection method based on carrier-to-noise ratio jump that can balance technical effectiveness and low cost to address the above-mentioned technical problems.

[0005] A BeiDou navigation spoofing detection method based on carrier-to-noise ratio jump, the method comprising:

[0006] Acquire satellite navigation signals received by the antenna; perform A / D sampling and signal tracking on the satellite navigation signals to obtain the carrier frequency and code phase;

[0007] Calculate the broadband power and narrowband power based on the carrier frequency and code phase; calculate the average power ratio of the broadband power and narrowband power; and use the average power ratio to calculate the carrier-to-noise ratio of each satellite at each epoch.

[0008] The differences in carrier-to-noise ratio (CNR) between different epochs and between satellites are calculated based on the CNR of each satellite at each epoch. The differences in CNR between different epochs and between satellites are used as test statistics to construct a first hypothesis testing model and a second hypothesis testing model. The first hypothesis testing model includes an unknown first test threshold. The second hypothesis testing model includes an unknown second test threshold.

[0009] The differences in carrier-to-noise ratio between consecutive epochs and the differences in inter-satellite carrier-to-noise ratio are expanded into a Gaussian distribution. Based on the expanded Gaussian distribution expression and the pre-set false alarm probability, the unknown first and second test thresholds are solved to obtain the known first and second test thresholds.

[0010] A dual-detection decision is made based on the known first and second detection thresholds.

[0011] In one embodiment, calculating broadband power and narrowband power based on carrier frequency and code phase includes:

[0012] The integral values ​​within the coherent integration time interval of the I and Q paths are calculated based on the carrier frequency and code phase.

[0013] The integral values ​​within the coherent integration time interval of the I and Q paths are used to calculate the result.

[0014]

[0015] Where k represents the time series, M represents the number of samples used to calculate broadband power, and I 2 (k) represents the integral value within each coherent integration time interval of path I, Q 2 (k) represents the integral value of Q path within each coherent integration time interval.

[0016] In one embodiment, the integral values ​​within the coherent integration time interval of the I and Q paths are calculated based on the carrier frequency and code phase.

[0017] The narrowband power is calculated using the integral values ​​within the coherent integration time interval of the I and Q paths.

[0018]

[0019] Therefore, the power ratio at time k can be obtained as follows:

[0020]

[0021] Its average value is

[0022]

[0023] in, K is the number of samples in the carrier-to-noise ratio calculation interval.

[0024] In one embodiment, the carrier-to-noise ratio is calculated using the average power ratio, including:

[0025] The carrier-to-noise ratio is calculated using the average power ratio.

[0026]

[0027] Where μ represents the average power ratio at time k, and T coh C represents the coherent integration interval, and C / N0 represents the carrier-to-noise ratio.

[0028] In one embodiment, a first hypothesis testing model and a second hypothesis testing model are constructed using the difference in carrier-to-noise ratio between preceding and following epochs and the difference in inter-satellite carrier-to-noise ratio as test statistics, including:

[0029] The first hypothesis testing model is constructed using the difference in carrier-to-noise ratio between consecutive epochs as the test statistic.

[0030]

[0031] Where H0 indicates the absence of a deception signal, H1 indicates the presence of a deception signal, and ΔC time γ represents the difference in carrier-to-noise ratio between consecutive epochs, and γ1 represents the unknown first test threshold.

[0032] In one embodiment, a second hypothesis testing model is constructed using the inter-satellite carrier-to-noise ratio difference as the test statistic.

[0033]

[0034] Where, ΔC stars γ represents the difference in inter-satellite carrier-to-noise ratio, and γ2 represents the unknown second test threshold.

[0035] In one embodiment, the differences in carrier-to-noise ratio (CNR) between successive epochs and the differences in inter-satellite CNR are expanded using a Gaussian distribution, including:

[0036] Expanding the carrier-to-noise ratio difference between consecutive epochs using a Gaussian distribution yields the Gaussian distribution expression for the carrier-to-noise ratio difference between consecutive epochs as follows:

[0037]

[0038] in, and These are the mean and variance of the Gaussian distribution of the difference in carrier-to-noise ratio between consecutive epochs, respectively, with C representing the abbreviation for carrier-to-noise ratio.

[0039] In one embodiment, the inter-satellite carrier-to-noise ratio difference is expanded using a Gaussian distribution to obtain the Gaussian distribution expression for the inter-satellite carrier-to-noise ratio difference.

[0040]

[0041] in, and These are the mean and variance of the Gaussian distribution of the inter-satellite carrier-to-noise ratio difference, respectively.

[0042] In one embodiment, the pre-set false alarm probability is:

[0043]

[0044] in, The Gaussian distribution expression for the carrier-to-noise ratio, γ H This indicates the higher of the two thresholds, γ1 and γ2.

[0045] In one embodiment, a dual-detection decision is made based on a known first and second detection thresholds, including:

[0046] If the calculated difference in carrier-to-noise ratio between consecutive epochs is greater than the known first test threshold, it indicates the presence of a spoofing signal, and the inter-satellite carrier-to-noise ratio difference decision is continued; otherwise, there is no spoofing signal.

[0047] If the calculated inter-satellite carrier-to-noise ratio difference is greater than the known second test threshold and the time when the spoofing signal is detected is the same as the time when it is detected using the carrier-to-noise ratio of the preceding and following epochs, then a spoofing signal is considered to exist; otherwise, no spoofing signal exists.

[0048] The aforementioned method for detecting BeiDou navigation deception based on carrier-to-noise ratio (CNR) jumps calculates the CNR of each satellite at each epoch. It then uses the CNR differences between consecutive epochs and inter-satellite CNR differences calculated based on the CNR of each satellite at each epoch to construct a first hypothesis testing model and a second hypothesis testing model. Next, it solves for the unknown first and second detection thresholds using the Gaussian distribution expressions derived from the expanded CNR differences between consecutive epochs and inter-satellite CNR differences, along with a pre-set false alarm probability. Finally, it performs a dual-threshold decision based on the known first and second detection thresholds. This method is simple to implement, has low algorithm complexity, and achieves good deception interference detection results, meeting the requirements for civilian navigation signal deception detection. Furthermore, this method can be directly applied to existing receiver equipment, reducing hardware requirements and enabling widespread application, thus significantly lowering application costs. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating a BeiDou navigation deception detection method based on carrier-to-noise ratio jumps in one embodiment.

[0050] Figure 2This is a flowchart of a method for detecting a jump in carrier-to-noise ratio between consecutive epochs in one embodiment;

[0051] Figure 3 This is a flowchart of a method for detecting inter-satellite carrier-to-noise ratio jumps in one embodiment. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] In one embodiment, such as Figure 1 As shown, a BeiDou navigation spoofing detection method based on carrier-to-noise ratio jumps is provided, including the following steps:

[0054] Step 102: Obtain the satellite navigation signal received by the antenna; perform A / D sampling and signal tracking on the satellite navigation signal to obtain the carrier frequency and code phase.

[0055] After setting up the antenna and receiver, power on the device and receive satellite navigation signals through the antenna. The receiver then analyzes and processes the signals. A / D sampling and signal tracking are performed on the satellite signals to capture their carrier frequency and code phase, which are then used to demodulate the navigation message for positioning calculations.

[0056] Step 104: Calculate the broadband power and narrowband power based on the carrier frequency and code phase; calculate the average power ratio of the broadband power and narrowband power, and use the average power ratio to calculate the carrier-to-noise ratio of each satellite at each epoch.

[0057] The integral values ​​of the I and Q paths within the coherent integration time interval are calculated based on the carrier frequency and code phase. Then, the broadband power and narrowband power of different bandwidths are calculated using the integral values ​​of the I and Q paths within the coherent integration time interval. The carrier-to-noise ratio of each satellite at each epoch is solved using the power ratio method.

[0058] Assuming bandwidth is 1 / T c The broadband power is

[0059]

[0060] Bandwidth is 1 / MT c The narrowband power is

[0061] Therefore, the power ratio at time k can be obtained as follows:

[0062]

[0063] Its average value is

[0064]

[0065] in, K is the number of samples in the carrier-to-noise ratio (CNR) calculation interval. The CNR is calculated using the average power ratio.

[0066]

[0067] Where μ represents the average power ratio at time k, and T coh C represents the coherent integration interval, and C / N0 represents the carrier-to-noise ratio.

[0068] Step 106: Calculate the difference in carrier-to-noise ratio between different epochs and the difference in inter-satellite carrier-to-noise ratio based on the carrier-to-noise ratio of each satellite at each epoch. Use the difference in carrier-to-noise ratio between different epochs and the difference in inter-satellite carrier-to-noise ratio as test statistics to construct a first hypothesis testing model and a second hypothesis testing model. The first hypothesis testing model includes an unknown first test threshold. The second hypothesis testing model includes an unknown second test threshold.

[0069] The first hypothesis testing model is constructed using the difference in carrier-to-noise ratio between the previous and subsequent ephemeris as the test statistic.

[0070]

[0071] The statistical model for the second hypothesis test, constructed using the inter-satellite carrier-to-noise ratio difference as the test statistic, is as follows:

[0072]

[0073] Step 108: Expand the difference in carrier-to-noise ratio between consecutive epochs and the difference in inter-satellite carrier-to-noise ratio using a Gaussian distribution. Solve for the unknown first and second test thresholds based on the expanded Gaussian distribution expression and the pre-set false alarm probability to obtain the known first and second test thresholds.

[0074] Set the false alarm probability P f =α, since the satellite navigation signal follows a Gaussian distribution, the resulting carrier-to-noise ratio difference sequence and inter-satellite carrier-to-noise ratio sequence also satisfy a Gaussian distribution.

[0075] Satellite navigation signals approximate a Gaussian distribution when there are no spoofing signals, i.e.

[0076]

[0077] Among them, μ r and These are the mean and variance of the Gaussian distribution, respectively.

[0078] The jump value after the carrier-to-noise ratio difference between the preceding and following epochs still follows a Gaussian distribution, i.e.

[0079]

[0080] in, and These are the mean and variance of the Gaussian distribution, respectively.

[0081] Similarly, the difference in carrier-to-noise ratio between different satellites can also be considered to follow a Gaussian distribution.

[0082]

[0083] in, and These are the mean and variance of the Gaussian distribution, respectively.

[0084] Based on the pre-set false alarm probability

[0085]

[0086] The thresholds γ1 and γ2 are calculated, and a dual-detection decision is performed. It is worth noting that the false alarm probability is pre-set.

[0087]

[0088] The process of determining the thresholds γ1 and γ2 after establishing the Gaussian distribution expression and the two detection models is existing technology and will not be elaborated upon in this application.

[0089] Step 110: Perform a dual-detection decision based on the known first and second detection thresholds.

[0090] like Figure 2 The specific process of the spoofing detection method based on the jump in carrier-to-noise ratio between consecutive epochs is as follows:

[0091] Based on the obtained carrier-to-noise ratio, the difference in carrier-to-noise ratio between consecutive epochs is calculated to obtain the sequence ΔC. time1 ΔC time2 ΔC time3 ......ΔC timen If the difference in carrier-to-noise ratio between consecutive epochs exceeds a threshold, it indicates the presence of a deception signal, and the inter-satellite carrier-to-noise ratio difference determination continues; otherwise, there is no deception signal.

[0092] like Figure 3 The specific process of the spoofing detection method based on the inter-satellite carrier-to-noise ratio jump is as follows:

[0093] Based on the obtained carrier-to-noise ratio, the inter-satellite carrier-to-noise ratio difference is calculated to obtain the sequence ΔC. stars1 ΔC stars2 ΔC stars3 ...ΔC starsnIf the inter-satellite carrier-to-noise ratio difference exceeds a threshold, and the time when the spoofing signal is detected is the same as the time when it is detected using the carrier-to-noise ratio of the preceding and following epochs, then a spoofing signal is considered to exist; otherwise, no spoofing signal exists.

[0094] In the aforementioned BeiDou navigation spoofing detection method based on carrier-to-noise ratio (CNR) jumps, this application calculates the CNR of each satellite at each epoch. It then uses the CNR difference between consecutive epochs and the inter-satellite CNR difference calculated based on the CNR of each satellite at each epoch to construct a first hypothesis testing model and a second hypothesis testing model. Next, it solves for the unknown first and second test thresholds using the Gaussian distribution expressions derived from the expanded CNR differences between consecutive epochs and the inter-satellite CNR differences, along with a pre-set false alarm probability. Finally, it performs a dual-threshold decision based on the known first and second test thresholds. This application is simple to implement, has low algorithm complexity, and achieves good spoofing interference detection results, meeting the requirements for civilian navigation signal spoofing detection. Furthermore, this method can be directly applied to existing receiver equipment, reducing hardware requirements and enabling widespread application, thus significantly lowering application costs.

[0095] In one embodiment, calculating broadband power and narrowband power based on carrier frequency and code phase includes:

[0096] The integral values ​​within the coherent integration time interval of the I and Q paths are calculated based on the carrier frequency and code phase.

[0097] The integral values ​​within the coherent integration time interval of the I and Q paths are used to calculate the result.

[0098]

[0099] Where k represents the time series, M represents the number of samples used to calculate broadband power, and I 2 (k) represents the integral value within each coherent integration time interval of path I, Q 2 (k) represents the integral value of Q path within each coherent integration time interval.

[0100] In one embodiment, the integral values ​​within the coherent integration time interval of the I and Q paths are calculated based on the carrier frequency and code phase.

[0101] The narrowband power is calculated using the integral values ​​within the coherent integration time interval of the I and Q paths.

[0102]

[0103] Therefore, the power ratio at time k can be obtained as follows:

[0104]

[0105] Its average value is

[0106]

[0107] in, K is the number of samples in the carrier-to-noise ratio calculation interval.

[0108] In one embodiment, the carrier-to-noise ratio is calculated using the average power ratio, including:

[0109] The carrier-to-noise ratio is calculated using the average power ratio.

[0110]

[0111] Where μ represents the average power ratio at time k, and T coh C represents the coherent integration interval, and C / N0 represents the carrier-to-noise ratio.

[0112] In one embodiment, a first hypothesis testing model and a second hypothesis testing model are constructed using the difference in carrier-to-noise ratio between preceding and following epochs and the difference in inter-satellite carrier-to-noise ratio as test statistics, including:

[0113] The first hypothesis testing model is constructed using the difference in carrier-to-noise ratio between consecutive epochs as the test statistic.

[0114]

[0115] Where H0 indicates the absence of a deception signal, H1 indicates the presence of a deception signal, and ΔC time γ represents the difference in carrier-to-noise ratio between consecutive epochs, and γ1 represents the unknown first test threshold.

[0116] In one embodiment, a second hypothesis testing model is constructed using the inter-satellite carrier-to-noise ratio difference as the test statistic.

[0117]

[0118] Where, ΔC stars γ represents the difference in inter-satellite carrier-to-noise ratio, and γ2 represents the unknown second test threshold.

[0119] In one embodiment, the differences in carrier-to-noise ratio (CNR) between successive epochs and the differences in inter-satellite CNR are expanded using a Gaussian distribution, including:

[0120] Expanding the carrier-to-noise ratio difference between consecutive epochs using a Gaussian distribution yields the Gaussian distribution expression for the carrier-to-noise ratio difference between consecutive epochs as follows:

[0121]

[0122] in, and These are the mean and variance of the Gaussian distribution of the difference in carrier-to-noise ratio between consecutive epochs, respectively, with C representing the abbreviation for carrier-to-noise ratio.

[0123] In one embodiment, the inter-satellite carrier-to-noise ratio difference is expanded using a Gaussian distribution to obtain the Gaussian distribution expression for the inter-satellite carrier-to-noise ratio difference.

[0124]

[0125] in, and These are the mean and variance of the Gaussian distribution of the inter-satellite carrier-to-noise ratio difference, respectively.

[0126] In one embodiment, the pre-set false alarm probability is:

[0127]

[0128] in, The Gaussian distribution expression for the carrier-to-noise ratio, γ H This indicates the higher of the two thresholds, γ1 and γ2.

[0129] In one embodiment, a dual-detection decision is made based on a known first and second detection thresholds, including:

[0130] If the calculated difference in carrier-to-noise ratio between consecutive epochs is greater than the known first test threshold, it indicates the presence of a spoofing signal, and the inter-satellite carrier-to-noise ratio difference decision is continued; otherwise, there is no spoofing signal.

[0131] If the calculated inter-satellite carrier-to-noise ratio difference is greater than the known second test threshold and the time when the spoofing signal is detected is the same as the time when it is detected using the carrier-to-noise ratio of the preceding and following epochs, then a spoofing signal is considered to exist; otherwise, no spoofing signal exists.

[0132] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0133] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0134] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A BeiDou navigation spoofing detection method based on carrier-to-noise ratio jump, characterized in that, The method includes: Acquire satellite navigation signals received by the antenna; perform A / D sampling and signal tracking on the satellite navigation signals to obtain the carrier frequency and code phase; The broadband power and narrowband power are calculated based on the carrier frequency and code phase; the average power ratio of the broadband power and narrowband power is calculated, and the carrier-to-noise ratio of each satellite at each epoch is calculated using the average power ratio; The differences in carrier-to-noise ratio (CNR) between successive epochs and between satellites are calculated based on the CNR of each satellite at each epoch. The differences in CNR between successive epochs and between satellites are then used as test statistics to construct a first hypothesis testing model and a second hypothesis testing model. The first hypothesis testing model includes an unknown first test threshold. The second hypothesis testing model includes an unknown second test threshold. The differences in carrier-to-noise ratio between the preceding and following epochs and the differences in carrier-to-noise ratio between satellites are expanded using a Gaussian distribution. Based on the expanded Gaussian distribution expression and the pre-set false alarm probability, the unknown first test threshold and the unknown second test threshold are solved to obtain the known first test threshold and the second test threshold. Perform dual detection decision based on the known first and second detection thresholds; Using the differences in carrier-to-noise ratio (CNR) between preceding and following epochs and the differences in inter-satellite CNR as test statistics, a first hypothesis testing model and a second hypothesis testing model are constructed, including: The first hypothesis testing model is constructed using the difference in carrier-to-noise ratio between the preceding and following epochs as the test statistic. Where H0 indicates the absence of a deception signal, H1 indicates the presence of a deception signal, and ΔC time γ represents the difference in carrier-to-noise ratio between consecutive epochs, and γ1 represents the unknown first test threshold. The second hypothesis testing model is constructed using the inter-satellite carrier-to-noise ratio difference as the test statistic. Where, ΔC stars γ represents the difference in inter-satellite carrier-to-noise ratio, and γ2 represents the unknown second test threshold; The differences in carrier-to-noise ratio (CNR) between preceding and following epochs and the differences in inter-satellite CNR are expanded using a Gaussian distribution, including: Expanding the carrier-to-noise ratio difference between consecutive epochs using a Gaussian distribution yields the Gaussian distribution expression for the carrier-to-noise ratio difference between consecutive epochs as follows: in, and These are the mean and variance of the Gaussian distribution of the difference in carrier-to-noise ratio between consecutive epochs, respectively, where C is an abbreviation for carrier-to-noise ratio; Expanding the inter-satellite carrier-to-noise ratio difference using a Gaussian distribution yields the Gaussian distribution expression for the inter-satellite carrier-to-noise ratio difference as follows: in, and These are the mean and variance of the Gaussian distribution of the inter-satellite carrier-to-noise ratio difference, respectively.

2. The method according to claim 1, characterized in that, Calculating broadband power and narrowband power based on the carrier frequency and code phase includes: The integral values ​​within the coherent integration time interval of the I and Q paths are calculated based on the carrier frequency and code phase. The broadband power is calculated using the integral values ​​within the coherent integration time interval of the I and Q paths. Where k represents the time series, M represents the number of samples used to calculate broadband power, and I 2 (k) represents the integral value within each coherent integration time interval of path I, Q 2 (k) represents the integral value of Q path within each coherent integration time interval.

3. The method according to claim 2, characterized in that, The method further includes: The integral values ​​within the coherent integration time interval of the I and Q paths are calculated based on the carrier frequency and code phase. The narrowband power is calculated using the integral values ​​within the coherent integration time interval of the I and Q paths. Therefore, the power ratio at time k can be obtained as follows: Its average value is in, K is the number of samples in the carrier-to-noise ratio calculation interval.

4. The method according to claim 3, characterized in that, The carrier-to-noise ratio is calculated using the average power ratio, including: The carrier-to-noise ratio is calculated using the average power ratio. Where μ represents the average power ratio at time k, and T coh C represents the coherent integration interval, and C / N0 represents the carrier-to-noise ratio.

5. The method according to claim 1, characterized in that, The pre-set false alarm probability is in, The Gaussian distribution expression for the carrier-to-noise ratio, γ H This indicates the higher of the two thresholds, γ1 and γ2.

6. The method according to claim 1, characterized in that, The dual-detection decision is performed based on the known first and second detection thresholds, including: If the calculated difference in carrier-to-noise ratio between consecutive epochs is greater than the known first test threshold, it indicates the presence of a spoofing signal, and the inter-satellite carrier-to-noise ratio difference decision is continued; otherwise, there is no spoofing signal. If the calculated inter-satellite carrier-to-noise ratio difference is greater than the known second test threshold and the time when the spoofing signal is detected is the same as the time when it is detected using the carrier-to-noise ratio of the preceding and following epochs, then a spoofing signal is considered to exist; otherwise, no spoofing signal exists.

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