A direction-finding and frequency-measuring single-satellite passive positioning method based on ADS-B signals

Abstract

The application discloses a kind of direction-finding-frequency measurement single satellite passive positioning methods based on ADS-B signal, belong to satellite-based ADS-B passive positioning technical field, comprising the following steps: S1: parameter setting, determine search range;S2: calculate the direction-finding, frequency measurement cost function of each search point;S3: calculate the direction-finding, frequency measurement theoretical error of each search point;S4: according to theoretical error, calculate the joint cost function of each search point;S5: in the range of nadir point, the coordinate point that joint cost function is minimum is positioning result in search.This application combines two methods of direction-finding positioning and frequency measurement positioning, determines joint cost function coefficient by calculating the positioning theoretical error of two methods, realizes the reduction of positioning error.

Description

Technical Field

[0001] This invention belongs to the field of satellite-based ADS-B passive positioning technology, specifically relating to a single-satellite passive positioning method based on ADS-B signals for direction finding and frequency measurement. Background Technology

[0002] ADS-B (Automatic Dependent Surveillance-Broadcast) is a broadcast-based air surveillance system. Aircraft obtain their own status information through satellite positioning and various sensors, and periodically encode and broadcast information such as latitude, longitude, speed, and flight status. The surveillance station receives and decodes the messages to determine the aircraft's current location.

[0003] The space-based ADS-B passive positioning system can compare positioning results with received messages, overcoming the deceptive interference problem inherent in ADS-B systems, eliminating false messages, and even locating the source of interference. Furthermore, the system can conduct reconnaissance over distant seas and areas, locating enemy aircraft within a certain range while remaining concealed, which is beneficial for subsequent surveillance and identification.

[0004] For existing satellite-based ADS-B passive positioning systems, Aireon Corporation offers its customers an additional service: ADS-B position message verification. This involves calculating the aircraft's position from the radiated message using passive positioning without demodulating the message, thus verifying the message. This prevents aircraft electronics from transmitting erroneous messages due to malfunction or malicious spoofing. While this technology achieves passive positioning of aircraft targets based on ADS-B signals, its key technology is dual-satellite and multi-satellite TDOA positioning. Although multi-satellite positioning offers higher accuracy, its networking is complex and costly. Furthermore, according to the basic principles of multi-satellite positioning, strict time synchronization between multiple satellites is required to obtain positioning results, which poses difficulties for further research and implementation. In comparison, single-satellite positioning is less expensive and easier to implement in engineering. Additionally, Aireon's technology requires decoding of ADS-B velocity messages and cannot locate the source of encrypted or spoofed messages, presenting significant limitations.

[0005] Traditional passive positioning methods primarily rely on three observations—time difference of arrival (TDOA), azimuth angle of arrival (AOA), and Doppler frequency—to locate targets. For the basic scenario of passively locating a target aircraft using a single satellite receiving ADS-B signals, each of the three traditional methods has its advantages and disadvantages. For time difference-of-arrival (TDOA) positioning, the message signal transmitted by the airborne ADS-B satellite lacks a precise broadcast period, making it impossible to accurately measure distance using the TDOA of a single satellite. Single-satellite passive positioning commonly employs Doppler frequency-based methods; however, because the ADS-B signal length is fixed at 120 microseconds, it results in significant frequency measurement errors and positioning ambiguity. Furthermore, the frequency positioning equation is nonlinear, and the commonly used grid search method has low search efficiency. For azimuth positioning, the positioning accuracy is high when the antenna direction finding accuracy is high, but the positioning error increases with the distance to the target, and the angle measurement error is greatly affected by the satellite attitude. Existing Chinese patent CN110057372 B discloses a single-satellite passive positioning method suitable for spaceborne ADS-B, which realizes the positioning of a high-speed moving aircraft by a single satellite based on the arrival direction of the message wave and the time difference positioning. However, the positioning accuracy is not high because the precise distance measurement is completed by the arrival time difference of a single satellite and the positioning error is affected by the target distance.

[0006] Therefore, it is necessary to propose a single-satellite passive positioning method based on ADS-B signals for direction finding and frequency measurement to solve the above problems. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a single-satellite passive positioning method based on ADS-B signal direction finding and frequency measurement, which solves the problem of low positioning accuracy in the existing technology for single-satellite passive positioning of spaceborne ADS-B.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] This invention provides a single-satellite passive positioning method based on ADS-B signals, comprising the following steps:

[0010] S1: Parameter settings, determining the search range, and obtaining the signal direction angle measurement value α measured by the on-board antenna and receiver in the i-th measurement using a preset algorithm. i β i and frequency measurement value f i And based on the initial position of the satellite, a certain range of empty space below the satellite is divided into grids for subsequent search and positioning points;

[0011] S2: Calculate the direction finding and frequency measurement cost functions for each search point;

[0012] S3: Calculate the theoretical errors of direction finding and frequency measurement for each search point;

[0013] S4: Calculate the joint cost function for each search point based on the theoretical error;

[0014] S5: The coordinate point with the minimum joint cost function within the range of the nadir points is the localization result.

[0015] Furthermore, the preset algorithm is as follows:

[0016]

[0017] In the formula, i=1,2,...,N,ε i ξ i The measurement errors for the two direction angles are ζ. i The measurement error of the instantaneous frequency of the signal, (x T ,y T ,z T (x) represents the target's coordinates in the current measurement coordinate system. i ,y i ,z i ) represents satellite coordinates, v i =[v xi ,v yi ,v zi ] T f0 is the satellite's velocity; f0 is the center frequency; r i The radial velocity v is obtained by differentiating the distance between the satellite and the target. ri .

[0018] Furthermore, step S2 includes:

[0019] A1: Azimuth Measurement: Combining the search algorithm, calculate the cost function for each search point (x, y, z) based on the azimuth measurements at N time points:

[0020]

[0021]

[0022] In the formula, and These are the estimated values ​​of the two azimuth angles at the search point;

[0023] A2: Frequency measurement: The measured frequencies at N times are represented in matrix form as ψ = f0·F + ζ.

[0024] Where ψ=[f1,f2,...,f N ] T F = [F1(x) T ,y T ,z T ),F2(x T,y T ,z T ),...,F N (x T ,y T ,z T )] T ζ=[ζ1,ζ2,...,ζ N ] T If we consider the center frequency f0 in the formula as the quantity to be estimated, then its least squares estimate at the search point (x,y,z) is expressed as:

[0025]

[0026] Among them, F x,y,z =[F1(x,y,z),F2(x,y,z),...,F N (x,y,z)] T ;

[0027] A3: Obtain an estimated signal transmission frequency at each search point, and use the following formula to obtain the optimal solution at the target location for that search point:

[0028]

[0029] A4: Select the coordinates of the location point with the smallest mean square error of the least squares estimate of f0 among all search points. J3 in step A3 is the cost function of the search point in frequency measurement and positioning.

[0030] Furthermore, step S3 specifically includes:

[0031] Assuming the radiation source location and all measurement parameters are independent and follow a zero-mean Gaussian white noise distribution, the mean square value of the direction finding and positioning error can be expressed as:

[0032]

[0033] In the formula, E[] represents the expected value of the expression, and P dS The mean square error matrix of the satellite position. Let be the mean square error matrix for angle measurement, Q1 be the direction finding and positioning error coefficient matrix, U1 be the satellite position error coefficient matrix, and V1 be the angle measurement error coefficient matrix.

[0034] The mean square value of the frequency measurement positioning error can be expressed as:

[0035]

[0036] In the formula, P dS The mean square error matrix of the satellite position. This is the mean square error matrix for Doppler frequency measurements. 1 is the mean square error matrix of satellite velocity, Q2 is the frequency measurement and positioning error coefficient matrix, U2 is the satellite position error coefficient matrix, V2 is the Doppler frequency measurement error coefficient matrix, and W2 is the satellite velocity measurement error coefficient matrix.

[0037] Then the theoretical errors of direction finding and positioning, dr1 and frequency measurement and positioning, at each search point can be calculated:

[0038]

[0039]

[0040] In the formula, trace() means to find the trace of the matrix.

[0041] Furthermore, the joint cost function is obtained by normalizing the three cost functions:

[0042] J = c1J1 + c2J2 + c3J3

[0043] In the formula, c1, c2, and c3 are the coefficients of the three cost functions, respectively;

[0044] in,

[0045] Furthermore, the coefficients c1, c2, and c3 of the three cost functions need to be determined based on the theoretical errors of the two positioning amplifications at different points. The specific calculation steps include:

[0046] B1: Taking the total differential of the direction finding and positioning equations, we obtain the following in the i-th direction finding:

[0047]

[0048] It is written in matrix form as: Q1dX=U1dS+V1dK1

[0049] In the formula, dX=[dx T ,dy T ,dz T ] T dS=[dx i ,dy i ,dz i ] T dK1=[dα,dβ] T

[0050] in,

[0051]

[0052] U1 = Q1

[0053]

[0054] B2: Taking the total differential of the frequency-measuring positioning equation, we obtain the following in the i-th direction finding:

[0055]

[0056] In the formula, c is the speed of light, and the distance between the satellite and the target is...

[0057] It can be written in matrix form as: Q2dX2=U2dS+V2dK2+W2dK3

[0058] Where dK2=[df0,df i ] T dK3 = [dv x ,dv y ,dv z ] T ,

[0059] in,

[0060]

[0061] U2=Q2

[0062]

[0063]

[0064] In the formula, (x T ,y T ,z T (x) represents the target's coordinates in the current measurement coordinate system. i ,y i ,z i ) represents satellite coordinates, v i =[v xi ,v yi ,v zi ] T f is the satellite's velocity; f0 is the center frequency; f i The received signal frequency; r i The radial velocity v is obtained by differentiating the distance between the satellite and the target. ri , i = 1, 2, ..., N.

[0065] The beneficial effects of this invention are as follows:

[0066] This invention combines direction-finding and frequency-measuring positioning methods. By calculating the theoretical positioning errors of the two methods, the joint cost function coefficients are determined, thereby reducing positioning errors. Computer Monte Carlo simulations were performed on the direction-finding-frequency-measuring single-satellite passive positioning algorithm. While keeping other variables constant, the positioning errors of the proposed method and single-observation passive positioning methods (direction-finding only and frequency-measuring only) were tested under different direction-finding and frequency-measuring errors. Simulation results show that the positioning accuracy of this proposed method is superior to that of direction-finding only or frequency-measuring only.

[0067] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0068] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0069] Figure 1 This is a single-satellite positioning scenario diagram according to an embodiment of the present invention;

[0070] Figure 2 This is a flowchart of an embodiment of the present invention;

[0071] Figure 3 This is a schematic diagram comparing the positioning errors of the method of the present invention and the direction-finding-only positioning method under computer Monte Carlo simulation according to an embodiment of the present invention;

[0072] Figure 4 This is a schematic diagram comparing the positioning errors of the method of the present invention and the frequency-only positioning method under computer Monte Carlo simulation according to an embodiment of the present invention. Detailed Implementation

[0073] like Figures 1-4 As shown, this invention provides a single-satellite passive positioning method based on ADS-B signals for direction finding and frequency measurement, comprising the following steps:

[0074] S1: Parameter settings, determining the search range. Specifically, for the i-th measurement, let the target's coordinates in the current measurement coordinate system be (x...). T ,y T ,z T ), satellite coordinates are (x i ,y i ,z i Let the satellite's velocity be v in the current measurement coordinate system. i =[x xi ,y yi ,zzi ] T The distance between the satellite and the target is r. i Differentiating it along the distance direction yields the radial velocity v. ri Considering measurement errors, the signal direction angle α measured by the on-board antenna and receiver in the i-th measurement can be obtained. i and β i and frequency measurement value f i as follows:

[0075]

[0076] Among them, i=1,2,...,N,ε i ξ i The signal direction angle α measured by the on-board antenna and receiver during the i-th measurement are respectively... i and β i Measurement error, ζ i This represents the measurement error of the instantaneous frequency of the signal.

[0077] Since the direction-finding-frequency-measuring positioning equations are nonlinear equations, it is difficult to obtain closed-form solutions. Therefore, a grid search algorithm is used as the positioning solution method. The airspace under the satellite is divided into grids according to the initial position of the satellite for subsequent search of positioning points.

[0078] S2: Calculate the direction finding and frequency finding cost functions for each search point.

[0079] For azimuth measurement, combined with the search algorithm, a cost function is calculated for each search point (x, y, z) based on the azimuth measurement data at N time points:

[0080]

[0081]

[0082] in, and J1 represents the estimated values ​​of the two azimuth angles at the search point, i.e., J1 is the measured signal direction angle α obtained by the on-board antenna and receiver during the i-th measurement. i The cost function, J2, is the signal direction angle measurement value β obtained by the on-board antenna and receiver during the i-th measurement. i The cost function,

[0083]

[0084]

[0085] For frequency measurement, the measured frequencies at N times are represented in matrix form as follows:

[0086] ψ=f0·F+ζ

[0087] Where ψ=[f1,f2,...,f N ] T F = [F1(x) T ,y T ,z T ),F2(x T ,y T ,z T ),...,F N (x T ,y T ,z T )] T ζ=[ζ1,ζ2,...,ζ N ] T .

[0088] If we consider the center frequency f0 in the formula as the quantity to be estimated, then its least squares estimate at the search point (x,y,z) can be expressed as:

[0089]

[0090] Among them, F x,y,z =[F1(x,y,z),F2(x,y,z),...,F N (x,y,z)] T ;

[0091] At each search point, an estimated signal transmission frequency can be obtained using the above formula. However, a search point is considered the optimal solution for the target location only if it meets the following condition:

[0092]

[0093] Select the coordinates of the point with the smallest mean square error of the least squares estimate of f0 among all search points, where J3 is the cost function of the search point in frequency measurement and positioning.

[0094] S3 calculates the theoretical errors of direction finding and frequency measurement for each search point.

[0095] Since the cost functions for azimuth and frequency represent different physical quantities, and the magnitude of measurement error directly affects the mean of each cost function, it is necessary to normalize the three cost functions to obtain the joint cost function of the single-satellite direction finding and frequency measurement joint positioning method:

[0096] J = c1J1 + c2J2 + c3J3

[0097] c1, c2, and c3 are the coefficients of the three cost functions, which need to be determined based on the theoretical errors of the two positioning methods at different points. The specific calculation method is as follows.

[0098] First, by taking the total differential of the direction finding and positioning equations, we obtain the following in the i-th direction finding:

[0099]

[0100] Its matrix form is as follows:

[0101] Q1dX=U1dS+V1dK1

[0102] Where dX=[dx T ,dy T ,dz T ] T dS=[dx i ,dy i ,dz i ] T dK1=[dα,dβ] T And there are

[0103]

[0104] U1 = Q1

[0105]

[0106] Then, by taking the total differential of the frequency measurement and positioning equation, we obtain the result in the i-th measurement.

[0107]

[0108] Where c is the speed of light and the distance between the satellite and the target. Its matrix form is as follows:

[0109] Q²dX² = U²dS + V²dK² + W²dK³

[0110] Where dK2=[df0,df i ] T dK3 = [dv x ,dv y ,dv z ] T And there are

[0111]

[0112] U2=Q2

[0113]

[0114]

[0115] Assuming the radiation source location and all measurement parameters are uncorrelated, and all parameters follow a zero-mean Gaussian white noise distribution, the mean square value of the direction finding and positioning error can be expressed as:

[0116]

[0117] The mean square value of the frequency measurement positioning error can be expressed as:

[0118]

[0119] Therefore, the theoretical errors of direction finding and positioning, dr1 and frequency measurement and positioning, at each search point can be calculated:

[0120]

[0121] S4, calculate the joint cost function for each search point based on the theoretical error;

[0122] Based on the theoretical error calculation formula in step S3, the coefficients of the joint cost function are selected as follows:

[0123]

[0124] The joint cost function of the single-satellite direction finding and frequency finding combined positioning method is:

[0125] J = c1J1 + c2J2 + c3J3

[0126] S5. The coordinate point with the minimum joint cost function within the range of the nadir points is the localization result.

[0127] The working principle of the above technical solution is as follows: This method utilizes an ADS-B receiver mounted on a satellite to continuously receive signals from the target aircraft over a period of time, and measures information such as the angle and frequency of the signals to locate it. For example... Figure 1 A scenario diagram for single-satellite positioning is given. A low-Earth orbit satellite orbits the Earth according to a predetermined trajectory. When it passes over a certain range above the target, the ADS-B signal emitted by the satellite can be received. N times t1, t2, ..., t are selected. N The signal is subjected to direction and frequency measurement, and the target's location is obtained by combining the satellite's position, velocity, attitude angle, and orbit information at various times. Since the satellite's velocity is much greater than the aircraft's flight speed, the positioning time is set to be within 10 seconds. Therefore, the basic assumption of the model is that the aircraft's position remains approximately fixed during the positioning time.

[0128] The beneficial effects of the above technical solution are as follows: This invention combines direction-finding positioning and frequency-measuring positioning methods, and determines the joint cost function coefficients by calculating the positioning theoretical errors of the two methods, thereby reducing positioning errors. Computer Monte Carlo simulations are performed on the direction-finding-frequency-measuring single-satellite passive positioning algorithm, such as... Figure 3 and Figure 4 While keeping other variables constant, the positioning errors of the method of this invention and the passive positioning methods with a single observation (positioning only and positioning only) were tested under different direction finding errors and frequency measurement errors. The simulation results show that the positioning accuracy of the method is better than that of positioning only or positioning only.

[0129] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A single-satellite passive positioning method based on direction finding and frequency measurement using ADS-B signals, characterized in that, Includes the following steps: S1: Parameter settings, determine the search range, and obtain the first [value] through a preset algorithm. In this measurement, the signal direction angle measurements obtained by the on-board antenna and receiver were... and frequency measurement value And based on the initial position of the satellite, a certain range of empty space below the satellite is divided into grids for subsequent search and positioning points; S2: Calculate the direction finding and frequency measurement cost functions for each search point; S3: Calculate the theoretical errors of direction finding and frequency measurement for each search point; S4: Calculate the joint cost function for each search point based on the theoretical error; The joint cost function is obtained by normalizing the three cost functions: In the formula, , , These are the coefficients of the three cost functions; For the first The measurement of the signal direction angle obtained from the on-board antenna and receiver was measured. The cost function, For the first The measurement of the signal direction angle obtained from the on-board antenna and receiver was measured. The cost function, The cost function for searching points in frequency measurement and positioning; in, , ; The theoretical error of orientation finding and positioning at each search point, The theoretical error of frequency measurement and positioning at each search point; S5: The coordinate point with the minimum joint cost function within the range of the nadir points is the localization result.

2. The single-satellite passive positioning method based on ADS-B signal direction finding and frequency measurement according to claim 1, characterized in that, The preset algorithm is as follows: In the formula, , , These represent the measurement errors of the two direction angles, The measurement error is the instantaneous frequency of the signal. These are the coordinates of the target in the current measurement coordinate system. For satellite coordinates, The satellite's velocity; The center frequency; The radial velocity is obtained by differentiating the distance between the satellite and the target. .

3. The single-satellite passive positioning method based on ADS-B signal direction finding and frequency measurement according to claim 2, characterized in that, Step S2 includes: A1: Azimuth measurement: Combining the search algorithm, for each search point Calculate the cost function based on the azimuth measurements at N times: In the formula, and These are the estimated values ​​of the two azimuth angles at the search point; For satellite coordinates, To measure the total number; A2: Frequency Measurement: Represent the measured frequencies at N times in matrix form. , in, , , The center frequency in the formula If it is considered as a quantity to be estimated, then it is at the search point. The least squares estimate at point is expressed as: in, ; A3: Obtain an estimated signal transmission frequency at each search point, and use the following formula to obtain the optimal solution at the target location for that search point: A4: Select all search points The coordinates of the point where the mean square error of the least squares estimate is minimized, in step A3. This is the cost function for searching points in frequency measurement and positioning.

4. The single-satellite passive positioning method based on ADS-B signal direction finding and frequency measurement according to claim 1, characterized in that: Step S3 specifically includes: Assuming the radiation source location and all measurement parameters are independent and follow a zero-mean Gaussian white noise distribution, the mean square value of the direction finding and positioning error is expressed as: In the formula, This indicates the mathematical expectation of the expression. The mean square error matrix of the satellite position. This is the mean square error matrix for angle measurement. This is the direction finding and positioning error coefficient matrix. This is the satellite position error coefficient matrix. This is the angle measurement error coefficient matrix; The mean square value of the frequency measurement positioning error is expressed as: In the formula, The mean square error matrix of the satellite position. This is the mean square error matrix for Doppler frequency measurements. The mean square error matrix of the satellite velocity. This is the frequency measurement and positioning error coefficient matrix. This is the satellite position error coefficient matrix. This is the Doppler frequency measurement error coefficient matrix. This is the error coefficient matrix for satellite velocity measurement; The theoretical error of orientation finding and positioning at each search point is then calculated. and frequency measurement and positioning theoretical error : In the formula, This indicates finding the trace of a matrix.

5. The single-satellite passive positioning method based on ADS-B signal direction finding and frequency measurement according to claim 1, characterized in that: Three cost function coefficients , , The calculation needs to be determined based on the theoretical errors of the two positioning magnification methods at different points. The specific calculation steps include: B1: Taking the total differential of the direction finding and positioning equations, in the first... The following was obtained from the second direction finding: And write it in matrix form: In the formula, , in, B2: Taking the total differential of the frequency measurement and positioning equation, in the first... The following was obtained from the second direction finding: In the formula, c is the speed of light, and the distance between the satellite and the target is... ; Its matrix form is as follows: in, , , in, In the formula, These are the coordinates of the target in the current measurement coordinate system. For satellite coordinates, The satellite's velocity; The center frequency; The frequency of the received signal; The radial velocity is obtained by differentiating the distance between the satellite and the target. , .

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