Satellite Navigation Jamming Detection Method Based on Joint Estimation of Energy and Covariance

Abstract

The present invention discloses a satellite navigation suppression interference detection method based on joint estimation of energy and covariance, comprising the following steps: calculating an upper threshold value and a lower threshold value of an energy detection statistic; calculating the energy detection statistic of a received signal and comparing it with the upper and lower threshold values, respectively; if the energy detection statistic is greater than the upper threshold value, determining that an interference signal is present, otherwise, no interference signal is present; if the energy detection statistic is between the upper and lower threshold values, executing the next step; replacing the energy detection statistic with the statistic of a covariance detection method and calculating a new threshold value; if the statistic of the covariance detection method is greater than the new threshold value, determining that an interference signal is present, otherwise, no interference signal is present. The method of the present invention overcomes the deficiency of traditional methods that are limited by the signal-to-noise ratio, and the joint detection of the two methods has better detection performance under low signal-to-noise ratio.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite signal suppression interference, and in particular to a satellite navigation suppression interference detection method based on energy and covariance joint estimation. Background Art

[0002] The Global Navigation Satellite System (GNSS), the core of positioning, navigation, and timing systems, plays a vital role in both military and civilian applications, becoming an essential part of a nation's infrastructure. However, the complex electromagnetic environment surrounding GNSS radios poses a threat to GNSS, exposing it to a variety of both intentional and unintentional interference. Suppressing interference, however, is a low-cost and potentially wide-ranging threat, attracting close attention worldwide.

[0003] Currently, the most widely used suppression interference detection methods are matched filter detection, covariance detection and energy detection. Matched filter detection requires sufficient information about the navigation signal, otherwise it cannot be used; covariance detection has good detection performance under low signal-to-noise ratio conditions and does not require any prior information, but its use of a fixed threshold does not meet actual needs.

[0004] Energy detection methods include single threshold energy detection method and double threshold energy detection method. The principle of single threshold energy detection model is as follows: Figure 1 As shown in the figure, the principle is to input a time domain signal, convert it into A / D data, square the sampled values, accumulate and sum them, and then take the average value. Finally, this value is compared with a preset threshold to determine whether interference is present. The disadvantage of this method is that the detection performance is easily affected by the signal-to-noise ratio.

[0005] The dual-threshold energy detection method is an improvement on the single-threshold energy detection method. It adds a low threshold value and improves the detection performance under low signal-to-noise ratio to a certain extent. The principle of its detection model is as follows: Figure 2 As shown in the figure, H0 indicates the presence of only noise and no interference signal; H1 indicates the presence of an interference signal. The basic principle is to make a decision by comparing the sampled signal energy detection statistics with the decision threshold. If the value is greater than the upper threshold, interference is detected; if the value is less than the lower threshold, no interference is detected. No decision is made if the value falls in the middle threshold. A disadvantage of this method is that not making a decision when the value falls in the middle threshold can result in some missed detections, affecting detection performance. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a satellite navigation suppression interference detection method based on joint estimation of energy and covariance. This method combines the advantages of energy detection and covariance detection methods and proposes a joint detection method, that is, first using the energy detection method. If the energy statistical value is outside the double threshold, the presence or absence of the signal can be directly determined. If the energy statistical value is between the two thresholds, covariance detection can be used again. The joint detection of the two has better detection performance under low signal-to-noise ratio.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] A satellite navigation suppression interference detection method based on energy and covariance joint estimation includes the following steps:

[0009] Step 1: Calculate the upper threshold of the energy detection statistic based on the false alarm probability of the energy detection method. Then calculate the lower threshold of the energy detection statistic based on the upper threshold and the probability that the received signal falls within the middle threshold without making a decision in the absence of interference.

[0010] Step 2: Calculate the energy detection statistic of the received signal and compare it with the upper threshold and the lower threshold respectively. If the energy detection statistic is greater than the upper threshold, it is determined that there is an interference signal. If the energy detection statistic is less than the lower threshold, it is determined that there is no interference signal. If the energy detection statistic is between the upper threshold and the lower threshold, execute step 3.

[0011] Step 3: Use the statistical value of the covariance detection method to replace the energy detection statistical value, and calculate a new threshold value. If the statistical value of the covariance detection method is greater than the new threshold value, there is an interference signal, otherwise there is no interference signal.

[0012] In the above solution, in step 1, the upper threshold and the lower threshold are calculated as follows:

[0013]

[0014]

[0015] Among them, λ2 is the high threshold, λ1 is the low threshold, P f is the false alarm probability of the energy detection method, α0 is the probability that the received signal falls into the middle threshold without making a decision in the absence of interference, is the noise variance, Q -1 (·) is the inverse function of the standard Gaussian complementary cumulative distribution function.

[0016] In the above solution, in step 2, the energy detection statistics are calculated as follows:

[0017]

[0018] Where Y is the energy detection statistic, N is the number of samples, n = 1, 2, ..., N, and x(n) is the received signal.

[0019] In the above scheme, in step 3, the statistical value calculation method of the covariance detection method is as follows:

[0020] Under the binary hypothesis model, assuming that L discrete signals are received, where L is a positive integer, the vectors of the received signal x(n), interference signal j(n), and noise signal w(n) are expressed as follows:

[0021]

[0022] Then the statistical covariance matrices of X(n), J(n) and W(n) are:

[0023] R x =E[x(n)x T (n)]

[0024] R j =E[j(n)j T (n)]

[0025] R w =E[w(n)w T (n)]

[0026] Define the sample autocorrelation function l=0,1,...,L-1; N is the number of samples, and the sample covariance matrix S is used instead of the statistical covariance matrix R of the received signal X , and use the sample autocorrelation function λ(l) to approximate the statistical covariance matrix R X The statistical autocorrelation function of , the sample covariance matrix S is expressed as:

[0027]

[0028] The statistical value of the covariance detection method is defined as T = T1 / T2, where T1 is the average value of the sum of the absolute values of the autocorrelation functions of all samples in S, and T2 is the average value of the autocorrelation functions of the samples on the diagonal of S. The expression is as follows:

[0029]

[0030]

[0031] S nm Represents the element in the nth row and mth column of the sample covariance matrix S;

[0032] Due to the symmetry of S, T1 and T2 are rewritten as follows:

[0033]

[0034] T2=|λ(0)|

[0035] Therefore, the statistical value of the covariance detection method is:

[0036]

[0037] In the above solution, the calculation method of the new threshold value in step 3 is:

[0038] A. When the interference signal does not exist, using the central limit theorem, the expected and variance expressions of the detection statistics T1 and T2 are obtained as follows:

[0039]

[0040]

[0041]

[0042] Where L is the number of discrete signals, is the noise variance, N is the number of sampling samples; T1(N) is the value of the test statistic T1 when the number of sampling samples is N, T2(N) is the value of the test statistic T2 when the number of sampling samples is N; E(T1(N)) is the expectation of the test statistic T1(N), E(T2(N)) is the expectation of the test statistic T2(N), var(T2(N)) is the variance of the test statistic T2(N);

[0043] Then the false alarm probability of the covariance detection method is for:

[0044]

[0045] Where μ is the hypothesized detection threshold, P(·) represents the probability, and Q(·) represents the standard Gaussian complementary cumulative distribution function;

[0046] B. When there is an interference signal, using the central limit theorem, the expected and variance expressions of the detection statistics T1 and T2 are obtained as follows:

[0047]

[0048]

[0049]

[0050] in, is the interference signal power; for simplicity, let

[0051]

[0052] α l is the correlation coefficient of the normalized interference signal, j(n) is the interference signal when the sample number is n, j(nl) is the interference signal when the sample number is nl, and E[·] is the expectation;

[0053] Detection probability of covariance detection method and the probability of missed detection They are:

[0054]

[0055]

[0056] Where SNR is the signal-to-noise ratio;

[0057] C. New threshold value μ * The calculation method is to take the value when the error perception function F(μ) reaches the minimum value. The error perception function F(μ) is the false alarm probability function and the missed detection probability function P m The sum of (μ):

[0058]

[0059]

[0060]

[0061] G=2(AB)

[0062] F=B 2 -A 2

[0063] in,

[0064] Through the above technical solution, the satellite navigation suppression interference detection method based on joint energy and covariance estimation provided by the present invention has the following beneficial effects:

[0065] 1. The present invention solves the problem of not making a judgment on the middle confusion area in the dual-threshold energy detection method. The improved covariance detection method is applied to the middle area, and the two are combined for detection, which greatly improves the detection performance.

[0066] 2. The present invention improves the problem that the fixed threshold of the traditional covariance detection method does not conform to the actual situation. The error perception function is constructed to simultaneously meet the minimum probability of missed detection and the minimum probability of false alarm, and obtain the optimal threshold under the current signal-to-noise ratio. This threshold is independent of the signal-to-noise ratio, so the detection capability is not affected by noise fluctuations, thereby improving the detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the embodiments or the prior art.

[0068] Figure 1 It is the principle diagram of the single threshold energy detection model;

[0069] Figure 2 It is the principle diagram of the dual-threshold energy detection model;

[0070] Figure 3 A schematic flow chart of a method for joint detection of energy and covariance based on GNSS interference suppression provided by an embodiment of the present invention;

[0071] Figure 4 A comparison chart of detection probability simulation results between the method provided by an embodiment of the present invention and other methods under different signal-to-noise ratios. DETAILED DESCRIPTION

[0072] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0073] The present invention provides a satellite navigation suppression interference detection method based on energy and covariance joint estimation, such as Figure 3 As shown, the following steps are included:

[0074] Since the power of GNSS signals is very weak when they reach the ground, generally at -130dBm, the present invention treats GNSS signals as background noise when performing interference detection, that is, silent detection. After oversampling the received signal, the problem of whether it contains interference signals or not can be expressed as:

[0075]

[0076] Where N is the number of samples, j(n) and w(n) are the sampling values of the interference signal and noise, respectively, and are independent of each other. H0 means that only noise exists and no interference signal exists; H1 means that the interference signal exists.

[0077] Step 1: Calculate the upper threshold of the energy detection statistic based on the false alarm probability of the energy detection method. Then calculate the lower threshold of the energy detection statistic based on the upper threshold and the probability that the received signal falls within the middle threshold and no judgment is made in the absence of interference.

[0078] The upper and lower thresholds are calculated as follows:

[0079]

[0080]

[0081] Among them, λ2 is the high threshold, λ1 is the low threshold, P f is the false alarm probability of the energy detection method, α0 is the probability that the received signal falls into the middle threshold without making a decision in the absence of interference, is the noise variance, Q -1 (·) is the inverse function of the standard Gaussian complementary cumulative distribution function.

[0082] Step 2: Calculate the energy detection statistic of the received signal and compare it with the upper and lower thresholds. If the energy detection statistic is greater than or equal to the upper threshold, it is determined that there is an interference signal. If the energy detection statistic is less than the lower threshold, it is determined that there is no interference signal. If the energy detection statistic is between the upper and lower thresholds, proceed to step 3.

[0083] The energy detection statistics are calculated as follows:

[0084]

[0085] Where Y is the energy detection statistic, N is the number of samples, n = 1, 2, ..., N, and x(n) is the received signal.

[0086] Compare the energy detection statistic Y with the preset decision thresholds λ1 and λ2. If Y>λ2, it is determined that an interference signal exists; if Y≤λ1, it is determined that there is no interference; if it falls between the thresholds, execute the next step.

[0087] Step 3: Use the statistical value of the covariance detection method to replace the energy detection statistical value, and calculate a new threshold value. If the statistical value of the covariance detection method is greater than or equal to the new threshold value, there is an interference signal, otherwise there is no interference signal.

[0088] The statistical value calculation method of the covariance detection method is as follows:

[0089] Under the binary hypothesis model, assuming that L discrete signals are received, where L is a positive integer, the vectors of the received signal x(n), interference signal j(n), and noise signal w(n) are expressed as follows:

[0090]

[0091] Then the statistical covariance matrices of X(n), J(n) and W(n) are:

[0092] R x =E[x(n)x T (n)]

[0093] R j =E[j(n)j T (n)]

[0094] R w =E[w(n)w T (n)]

[0095] Define the sample autocorrelation function l=0,1,...,L-1; N is the number of sampling samples. Since it is difficult to obtain the statistical covariance matrix, the sampling idea is used to calculate the sample covariance of the statistic, and the sample covariance matrix S is used instead of the statistical covariance matrix R of the received signal. X , and use the sample autocorrelation function λ(l) to approximate the statistical covariance matrix R X The statistical autocorrelation function of , the sample covariance matrix S is expressed as:

[0096]

[0097] The statistical value of the covariance detection method is defined as T = T1 / T2, where T1 is the average value of the sum of the absolute values of the autocorrelation functions of all samples in S, and T2 is the average value of the autocorrelation functions of the samples on the diagonal of S. The expression is as follows:

[0098]

[0099]

[0100] S nm Represents the element in the nth row and mth column of the sample covariance matrix S;

[0101] Due to the symmetry of S, T1 and T2 are rewritten as follows:

[0102]

[0103] T2=|λ(0)|

[0104] Therefore, the statistical value of the covariance detection method is:

[0105]

[0106] The new threshold value is calculated as follows:

[0107] A. When the interference signal does not exist, using the central limit theorem, the expected and variance expressions of the detection statistics T1 and T2 are obtained as follows:

[0108]

[0109]

[0110]

[0111] Where L is the number of discrete signals, is the noise variance, N is the number of sampling samples; T1(N) is the value of the test statistic T1 when the number of sampling samples is N, T2(N) is the value of the test statistic T2 when the number of sampling samples is N; E(T1(N)) is the expectation of the test statistic T1(N), E(T2(N)) is the expectation of the test statistic T2(N), var(T2(N)) is the variance of the test statistic T2(N);

[0112] Then the false alarm probability of the covariance detection method is for:

[0113]

[0114] Where μ is the hypothesized detection threshold, P(·) represents the probability, and Q(·) represents the standard Gaussian complementary cumulative distribution function;

[0115] B. When there is an interference signal, using the central limit theorem, the expected and variance expressions of the detection statistics T1 and T2 are obtained as follows:

[0116]

[0117]

[0118]

[0119] in, is the interference signal power; for simplicity, let

[0120]

[0121] α l is the correlation coefficient of the normalized interference signal, α l =E[j(n)j(nl)] / σ j 2 ; j(n) is the interference signal when the sample number is n, j(nl) is the interference signal when the sample number is nl, and E[·] is the expectation;

[0122] Detection probability of covariance detection method and the probability of missed detection They are:

[0123]

[0124]

[0125] Where SNR is the signal-to-noise ratio;

[0126] C. New threshold value μ * The calculation method is to take the value when the error perception function F(μ) reaches the minimum value. The error perception function F(μ) is the false alarm probability function and the missed detection probability function P m The sum of (μ):

[0127]

[0128]

[0129]

[0130] G=2(AB)

[0131] F=B 2 -A 2

[0132] in,

[0133] Determine the statistical value T of the covariance detection method and the new threshold value μ * If T>μ * , then there is an interference signal, if T≤μ * , there is no interference signal.

[0134] Figure 4 To compare the simulation performance of various methods under different signal-to-noise ratios on MATLAB, it can be seen that the method of the present invention has a higher detection probability under lower signal-to-noise ratio conditions.

[0135] The method of the present invention combines the advantages of energy detection and covariance detection methods. Specifically, the energy detection method is used first. If the energy detection statistic is outside the double threshold, the presence of the signal can be directly determined. If the energy detection statistic is between the two thresholds, covariance detection can be used. The present invention optimizes the threshold of the covariance detection method to minimize the error perception function and calculate the threshold of the covariance detection. This threshold is independent of the signal-to-noise ratio, so the detection capability is not affected by noise fluctuations. This overcomes the shortcomings of the classic method that are limited by the signal-to-noise ratio. The combined detection of the two methods has better detection performance than a single detection method, especially at low signal-to-noise ratios.

[0136] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A satellite navigation suppression interference detection method based on joint energy and covariance estimation, characterized in that: The steps include: Step 1: Calculate the upper threshold of the energy detection statistic based on the false alarm probability of the energy detection method. Then calculate the lower threshold of the energy detection statistic based on the upper threshold and the probability that the received signal falls within the middle threshold without making a decision in the absence of interference. Step 2: Calculate the energy detection statistic of the received signal and compare it with the upper threshold and the lower threshold respectively. If the energy detection statistic is greater than or equal to the upper threshold, it is determined that there is an interference signal. If the energy detection statistic is less than the lower threshold, it is determined that there is no interference signal. If the energy detection statistic is between the upper threshold and the lower threshold, proceed to step 3. Step 3: Use the statistical value of the covariance detection method to replace the energy detection statistical value and calculate a new threshold value. If the statistical value of the covariance detection method is greater than or equal to the new threshold value, there is an interference signal, otherwise there is no interference signal; The calculation method of the new threshold value in step 3 is: A. When the interference signal does not exist, using the central limit theorem, the expected and variance expressions of the detection statistics T1 and T2 are obtained as follows: Where L is the number of discrete signals, is the noise variance, N is the number of sampling samples; T1(N) is the value of the test statistic T1 when the number of sampling samples is N, T2(N) is the value of the test statistic T2 when the number of sampling samples is N; E(T1(N)) is the expectation of the test statistic T1(N), E(T2(N)) is the expectation of the test statistic T2(N), var(T2(N)) is the variance of the test statistic T2(N); Then the false alarm probability of the covariance detection method is for: Where μ is the hypothesized detection threshold, P() represents the probability, and Q(·) represents the standard Gaussian complementary cumulative distribution function; B. When there is an interference signal, using the central limit theorem, the expected and variance expressions of the detection statistics T1 and T2 are obtained as follows: in, is the interference signal power; for simplicity, let α l is the correlation coefficient of the normalized interference signal, j(n) is the interference signal when the sample number is n, j(nl) is the interference signal when the sample number is nl, and E[·] is the expectation; Detection probability of covariance detection method and missed detection probability They are: Where SNR is the signal-to-noise ratio; C. New threshold value μ * The calculation method is to take the value when the error perception function F(μ) reaches the minimum value. The error perception function F(μ) is the false alarm probability function and the missed detection probability function P m The sum of (μ): G=2(AB) F=B 2 -A 2 in, 2. The satellite navigation suppression interference detection method based on energy and covariance joint estimation according to claim 1 is characterized in that: In step 1, the upper and lower thresholds are calculated as follows: Among them, λ2 is the high threshold, λ1 is the low threshold, P f is the false alarm probability of the energy detection method, α0 is the probability that the received signal falls into the middle threshold without making a decision in the absence of interference, is the noise variance, Q -1 (·) is the inverse function of the standard Gaussian complementary cumulative distribution function.

3. The satellite navigation suppression interference detection method based on energy and covariance joint estimation according to claim 1 is characterized in that: In step 2, the energy detection statistics are calculated as follows: Wherein, Y is the energy detection statistic, N is the number of samples, n represents the sample number, n = 1, 2, ..., N, and x(n) is the received signal.

4. The satellite navigation suppression interference detection method based on energy and covariance joint estimation according to claim 1 is characterized in that: In step 3, the statistical value calculation method of the covariance detection method is as follows: Under the binary hypothesis model, assuming that L discrete signals are received, where L is a positive integer, the vectors of the received signal x(n), interference signal j(n), and noise signal w(n) are expressed as follows: X(n)=[x(n) x(n-1) … x(n-L+1)] T J(n)=[j(n) j(n-1) … j(n-L+1)] T W(n)=[w(n) w(n-1) … w(n-L+1)] T Then the statistical covariance matrices of X(n), J(n) and W(n) are: R x =E[x(n)x T (n)] R j =E[j(n)j T (n)] R w =E[w(n)w T (n)] Define the sample autocorrelation function l=0,1,...,L-1; N is the number of samples, and the sample covariance matrix S is used instead of the statistical covariance matrix R of the received signal X , and use the sample autocorrelation function λ(l) to approximate the statistical covariance matrix R X The statistical autocorrelation function of , the sample covariance matrix S is expressed as: The statistical value of the covariance detection method is defined as T = T1 / T2, where T1 is the average value of the sum of the absolute values of the autocorrelation functions of all samples in S, and T2 is the average value of the autocorrelation functions of the samples on the diagonal of S. The expression is as follows: S nm Represents the element in the nth row and mth column of the sample covariance matrix S; Due to the symmetry of S, T1 and T2 are rewritten as follows: T2=|λ(0)| Therefore, the statistical value of the covariance detection method is:

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