Satellite-based ADS-B overlapping signal time of arrival estimation method and system

Abstract

The application discloses a kind of star-based ADS-B overlap signal time of arrival estimation method and system, signal is received by uniform array antenna, based on FastICA algorithm decomposition obtains two ADS-B signals;Since there is uncertainty in signal decomposition by FastICA algorithm, therefore, two kinds of mixed signals are designed for each time delay, that is, any signal may be ahead of another signal;By cross-correlation coefficient signal processing method, the designed mixed signal is calculated with the original mixed signal;Compare two cross-correlation coefficients, find the larger value, which corresponds to the correct order of each signal in the mixed signal, the maximum cross-correlation coefficient corresponds to the relative time delay of two signals;Based on the relative time delay and the order of the mixed signal before separation obtained, the signal is effectively separated, the signal error rate is low, and the arrival time of ADS-B signal is accurately estimated.

Description

Technical Field

[0001] This invention relates to the field of satellite-based communication technology, specifically to a method and system for estimating the arrival time of satellite-based ADS-B overlapping signals. Background Technology

[0002] Automatic Dependent Surveillance-Broadcast (ADS-B) and Multilateration (MLAT) systems are key new technologies in air traffic management, enabling real-time and accurate all-weather monitoring of space traffic conditions.

[0003] MLAT technology is based on the principle of time difference of arrival. It uses the response information between the aircraft and the ground equipment to calculate the time difference of the signal arriving at each ground station to achieve positioning. It is compatible with ADS-B technology. Integrating MLAT technology and ADS-B technology can save costs and expand the monitoring range. Reference [1] proposes a positioning scheme that integrates ADS-B system and MLAT system. On the one hand, the TOA information in the ADS-B signal is demodulated. On the other hand, the time difference (TDOA) of the ADS-B signal received by each receiving station of the MLAT system is obtained. The two information are compared and referenced to achieve aircraft positioning. Reference [2] proposes that multiple ground receivers based on the ADS-B standard are combined into a multi-point positioning system through data fusion. Accurate TOA data is required for target positioning. Therefore, MLAT technology based on ADS-B needs to utilize the time of arrival (TOA) of the ADS-B signal.

[0004] Ground-based ADS-B systems are geographically limited, making it difficult to monitor areas such as oceans and polar regions. In contrast, satellite-based ADS-B systems can cover vast areas of airspace, oceans, and polar regions, meeting the requirements for global, comprehensive, and seamless surveillance coverage. ADS-B aircraft automatically broadcast their information to ground surveillance equipment and neighboring aircraft via omnidirectional broadcasting. Low-Earth orbit (LEO) satellites receive and process this information before transmitting it to ground base stations. However, the coverage area of ​​LEO satellites contains numerous aircraft, leading to signal overlap when receivers simultaneously receive multiple signals. This overlap can result in the loss of crucial information, such as arrival time and location. Therefore, resolving the signal overlap problem in satellite-based ADS-B systems and accurately estimating the TOA (Time of Arrival) information of separated ADS-B signals is essential for achieving multi-point positioning.

[0005] Existing technologies employ Fast Independent Component Analysis (FastICA) to address signal overlap issues in satellite-based ADS-B systems. When decomposing aliased signals, FastICA is insensitive to the relative time delay between signals and avoids intentionally discarding useful signals, thus achieving blind source separation. However, the FastICA algorithm has uncertainties; the separated signals may differ from the original signals in terms of signal order, waveform amplitude, and energy, affecting the measurement of the Time of Arrival (TOA) of the ADS-B signals. Summary of the Invention

[0006] The technical problem this invention aims to solve is that the signals separated by traditional satellite-based ADS-B system signal overlap analysis methods do not have the same order, waveform amplitude, and energy as the original signals, affecting the measurement of ADS-B signal arrival time. This invention aims to provide a method and system for estimating the arrival time of satellite-based ADS-B overlapping signals. It improves upon existing analysis methods by superimposing multiple aliased signals from the two decomposed ADS-B signal sequences. Furthermore, it uses cross-correlation coefficient signal processing to calculate the cross-correlation coefficient between the aliased signals and the original aliased ADS-B signals, thereby accurately estimating the arrival time of the ADS-B signals.

[0007] This invention is achieved through the following technical solution:

[0008] This scheme provides a method for estimating the arrival time of satellite-based ADS-B overlapping signals, including:

[0009] S1: Receive two aliased ADS-B signals based on a uniform array antenna;

[0010] S2: First, preprocess the aliased ADS-B signal, and then extract the ADS-B decomposition signal from the preprocessed aliased ADS-B signal based on the fast independent component analysis method.

[0011] S3: After performing frame header detection and data bit parsing on the ADS-B decomposed signal, two ADS-B signal sequences are obtained;

[0012] S4: Multiple aliased signals are generated by superimposing two ADS-B signal sequences; the frequency of the aliased signals is the same as the frequency of the aliased ADS-B signals, and the aliased signals include two types, each type having one ADS-B signal sequence in front, and each type of aliased signal having a different relative time delay.

[0013] S5: Calculate the cross-correlation coefficient between each aliased signal and the aliased ADS-B signal, and find the aliased signal with the largest cross-correlation coefficient;

[0014] S6: The order of the aliased signals with the highest cross-correlation coefficients is used as the order of the aliased ADS-B signals, and the arrival time of the aliased ADS-B signals is calculated based on the relative time of the aliased signals with the highest cross-correlation coefficients.

[0015] The working principle of this scheme is as follows: The satellite-based ADS-B overlapping signal time estimation method provided in this scheme receives the signal through a uniform array antenna and decomposes it into two ADS-B signals based on the FastICA algorithm. Due to the uncertainty of the signal decomposition by the FastICA algorithm, it is designed that each time delay corresponds to two aliased signals, that is, either signal may lead the other signal. The cross-correlation coefficient signal processing method is used to calculate the cross-correlation coefficient between the designed aliased signal and the original aliased signal. The two cross-correlation coefficients are compared, and the larger value is found, which corresponds to the correct sequence of each signal in the aliased signal. The time delay time corresponding to the largest cross-correlation coefficient is the relative time delay of the two signals. Based on the obtained relative time delay of the aliased signal and the separation sequence, the signal is effectively separated, the obtained signal has a low bit error rate, and the arrival time (TOA) of the ADS-B signal is accurately estimated.

[0016] A further optimization scheme is that the preprocessing includes: first, performing digital-to-analog conversion on the ADS-B signal to obtain a baseband signal, and then filtering the baseband signal through a low-pass filter before performing centering and whitening processing.

[0017] A further optimized solution is to centrally process the output signal as follows: ;in Represents the original signal. This represents the mean;

[0018] Whitening refers to the process of converting a multidimensional signal into a white signal using linear transformation methods, typically achieved through matrix transformations. The output signal after whitening is: ,in Representing the original signal, the whitening matrix is: And satisfy ; Represents the identity matrix.

[0019] The further optimized solution is that S2 includes the following sub-steps:

[0020] S21: with Using the cost function as the criterion, the mixture matrix is ​​iteratively optimized to find the maximum negative entropy. This makes negative entropy To obtain the maximum value, Indicates the first The next iteration; where... , This indicates the preprocessed ADS-B signal. Represents the original signal; Represents a non-quadratic nonlinear function;

[0021] Negative entropy The maximum value is achieved through optimization. Get:

[0022] Solve by differentiation according to the Kuhn-Tucker criterion. The optimal solution is obtained as follows:

[0023]

[0024] In the formula, It is a constant. , It is the optimized mixing matrix ; Represents non-quadratic nonlinear functions The derivative of .

[0025] A further optimization scheme is to obtain the iterative formula for the mixing matrix using Newton's method:

[0026] ;

[0027] in The derivative of a non-quadratic nonlinear function is given. Let represent the mixture matrix for the (k+1)th iteration; Let represent the mixing matrix of the k-th iteration.

[0028] The difference in Gaussianity of the signal The following three forms are usually chosen:

[0029] (1)

[0030] (2)

[0031] (3)

[0032] in and All are fixed parameters of the function; for ADS-B signals, the following is adopted: It represents negative entropy.

[0033] The further optimized solution is that step three includes the following sub-steps:

[0034] S31: Obtain the fixed frame header and length of the sampled ADS-B signal, calculate the maximum cross-correlation energy between the fixed frame header and a separated signal of the same length, and determine the position of the ADS-B separated signal frame header based on the maximum cross-correlation energy. Analysis of the ADS-B signal data format shows that the ADS-B signal frame header is fixed, located in the first 8 μs, and consists of four 0.5 μs pulses, located at positions 0 μs, 1 μs, 3.5 μs, and 4.5 μs respectively. In this scheme, the frame header detection adopts the principle of matched filtering, determining the frame header position by calculating the maximum cross-correlation energy between the fixed frame header and a separated signal of the same length.

[0035] S32: Digital demodulation of the ADS-B separated signal yields two ADS-B signal sequences. The data bits of the ADS-B signal are encoded using Pulse Position Modulation (PPM). The separated signal obtained using the FastICA algorithm suffers from amplitude inversion. In this scheme, the data bit parsing part uses the method of comparing the absolute values ​​of the sum of the first and second half-chips to determine "0" and "1" for signal demodulation. The absolute value calculation solves the signal inversion problem. If the absolute value of the first half-chip is greater than the absolute value of the second half-chip, then this half-chip is identified as the symbol "0"; otherwise, it is identified as the symbol "1".

[0036] Since the order of the two decomposed ADS-B signals may not be consistent with the order of the signals in the aliased signal, this is because the FastICA algorithm has inherent uncertainties. Specifically, the separated signals may differ from the original signals in terms of signal order, waveform amplitude, and energy. Therefore, for each time delay in the aliased signal, there are two possibilities: one signal may appear before the other.

[0037] A further optimization scheme is that, in order to perform cross-correlation coefficient calculation, the frequency of the aliased signal is the same as the frequency of the aliased ADS-B signal; the aliased signal includes two types, each type is preceded by one ADS-B signal sequence, and the aliased signals of each type have different relative time delays.

[0038] The further optimized scheme is that the relative delay is in μs, and the longest delay time is 120μs.

[0039] A further optimized solution is to express the cross-correlation coefficient as follows:

[0040]

[0041] Indicates the aliasing signal in the design, and This indicates the original aliased signal.

[0042] if ,but and Irrelevant; if ,but and Related; if ,but and Completely relevant.

[0043] For each type of delay, the two aliased signals are compared with the original aliased ADS-B signal to calculate the cross-correlation coefficient. The two cross-correlation coefficients are compared, and the larger value is found. This value corresponds to the correct order of the signals in the aliased signal. The delay time corresponding to the largest cross-correlation coefficient is the relative delay of the two signals.

[0044] This solution also provides a time-of-arrival estimation system for satellite-based ADS-B overlapping signals, used to implement the aforementioned time-of-arrival estimation method for satellite-based ADS-B overlapping signals, including:

[0045] The receiving module is used to receive two aliased ADS-B signals based on a uniform array antenna;

[0046] The preprocessing module is used to preprocess the aliased ADS-B signal and then extract the ADS-B decomposition signal from the preprocessed aliased ADS-B signal based on the fast independent component analysis method.

[0047] The parsing and detection module is used to perform frame header detection and data bit parsing processing on the ADS-B decomposed signal to obtain two ADS-B signal sequences.

[0048] The overlay module is used to overlay multiple aliased signals based on two ADS-B signal sequences;

[0049] The first calculation module is used to calculate the cross-correlation coefficient between each aliased signal and the aliased ADS-B signal, and to find the aliased signal with the largest cross-correlation coefficient.

[0050] The second calculation module is used to use the sequential relationship of the aliased signals with the maximum cross-correlation coefficient as the sequential relationship of the aliased ADS-B signals, and to calculate the arrival time of the aliased ADS-B signals with the relative time of the aliased signals with the maximum cross-correlation coefficient.

[0051] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0052] This invention provides a method and system for estimating the arrival time of satellite-based ADS-B overlapping signals. It improves upon existing analysis methods by superimposing multiple aliased signals based on the decomposed two ADS-B signal sequences. The cross-correlation coefficient signal processing method is used to calculate the cross-correlation coefficient between the aliased signals and the original aliased ADS-B signals to accurately estimate the arrival time of the ADS-B signals. Attached Figure Description

[0053] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0054] Figure 1 A schematic diagram of the arrival time estimation method for satellite-based ADS-B overlapping signals;

[0055] Figure 2 This is a schematic diagram illustrating the signal aliasing that occurs when two ADS-B messages arrive at the receiver in Example 3.

[0056] Figure 3 This is the cross-correlation coefficient between the aliased signal A and the original aliased ADS-B signal in Example 3;

[0057] Figure 4 This is the cross-correlation coefficient between the aliased signal B and the original aliased ADS-B signal in Example 3. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0059] Example 1

[0060] This embodiment provides a method for estimating the arrival time of satellite-based ADS-B overlapping signals, such as... Figure 1 As shown, it includes:

[0061] S1: Receive two aliased ADS-B signals based on a uniform array antenna;

[0062] S2: First, the aliased ADS-B signal is preprocessed, and then the ADS-B decomposition signal is extracted from the preprocessed aliased ADS-B signal based on the fast independent component analysis method. The preprocessing includes: first, the ADS-B signal is downsampled by digital-to-analog conversion to obtain the baseband signal, and then the baseband signal is filtered by a low-pass filter and then centered and whitened.

[0063] The signal output by centralized processing is: ;in Represents the original signal. This represents the mean;

[0064] The signal output by the whitening process is: ,in Representing the original signal, the whitening matrix is: And satisfy ; I represents the identity matrix.

[0065] S2 includes the following sub-steps:

[0066] S21: with Using the cost function as the criterion, the mixture matrix is ​​iteratively optimized to find the maximum negative entropy. This makes negative entropy The maximum value is obtained, where k represents the k-th iteration; where, , This indicates the preprocessed ADS-B signal. Represents the original signal; Represents a non-quadratic nonlinear function;

[0067] Negative entropy The maximum value is achieved through optimization. Get:

[0068] Solve by differentiation according to the Kuhn-Tucker criterion. The optimal solution is obtained as follows:

[0069]

[0070] In the formula, It is a constant. , It is the optimized version value; Represents non-quadratic nonlinear functions The derivative of .

[0071] The iterative formula for the mixture matrix is ​​obtained by solving Newton's method:

[0072] ;

[0073] in The derivative of a non-quadratic nonlinear function is given. Let represent the mixture matrix for the (k+1)th iteration; Let represent the mixing matrix of the k-th iteration.

[0074] S3: After performing frame header detection and data bit parsing on the ADS-B decomposed signal, two ADS-B signal sequences are obtained; Step three includes the following sub-steps:

[0075] S31: Obtain the fixed frame header and length of the sampled ADS-B signal, calculate the maximum cross-correlation energy between the fixed frame header and the separated signal of the same length, and determine the position of the ADS-B separated signal frame header based on the maximum cross-correlation energy;

[0076] S32: Digitally demodulate the ADS-B discrete signal to obtain two ADS-B signal sequences.

[0077] S4: Multiple aliased signals are generated by superimposing two ADS-B signal sequences; the aliased signals include two types, each type preceded by one ADS-B signal sequence, and each type of aliased signal has a different relative delay. The relative delay is in μs, with the longest delay being 120 μs. To enable cross-correlation coefficient calculation, the frequency of the aliased signals is the same as the frequency of the aliased ADS-B signals;

[0078] S5: Calculate the cross-correlation coefficient between each aliased signal and the aliased ADS-B signal, and find the aliased signal with the largest cross-correlation coefficient; the cross-correlation coefficient is expressed as:

[0079]

[0080] Indicates the aliasing signal in the design, and This indicates the original aliased signal.

[0081] if ,but and Irrelevant; if ,but and Related; if ,but and Completely relevant.

[0082] S6: The order of the aliased signals with the highest cross-correlation coefficient is used as the order of the aliased ADS-B signals, and the arrival time of the aliased ADS-B signals is calculated based on the relative time of the aliased signals with the highest cross-correlation coefficient.

[0083] Example 2

[0084] This embodiment provides a time-of-arrival estimation system for satellite-based ADS-B overlapping signals, used to implement the time-of-arrival estimation method for satellite-based ADS-B overlapping signals described in the previous embodiment, including:

[0085] The receiving module is used to receive two aliased ADS-B signals based on a uniform array antenna;

[0086] The preprocessing module is used to preprocess the aliased ADS-B signal and then extract the ADS-B decomposition signal from the preprocessed aliased ADS-B signal based on the fast independent component analysis method.

[0087] The parsing and detection module is used to perform frame header detection and data bit parsing processing on the ADS-B decomposed signal to obtain two ADS-B signal sequences.

[0088] The overlay module is used to overlay multiple aliased signals based on two ADS-B signal sequences;

[0089] The first calculation module is used to calculate the cross-correlation coefficient between each aliased signal and the aliased ADS-B signal, and to find the aliased signal with the largest cross-correlation coefficient.

[0090] The second calculation module is used to use the sequential relationship of the aliased signals with the maximum cross-correlation coefficient as the sequential relationship of the aliased ADS-B signals, and to calculate the arrival time of the aliased ADS-B signals with the relative time of the aliased signals with the maximum cross-correlation coefficient.

[0091] Example 3

[0092] like Figure 2 The diagram illustrates how two ADS-B messages arrive at the receiver and cause signal aliasing in this embodiment. It can be seen that the two signals overlap when... , and .

[0093] The array antenna receives the ADS-B signal, decomposes it into two separate ADS-B signals using the FastICA algorithm, and then obtains the order and relative time delay of the mixed signal based on the cross-correlation coefficient, accurately estimating the TOA of the ADS-B signal.

[0094] The cross-correlation coefficients between the two aliased signals (aliased signal A and aliased signal B) with different time delays obtained from the experiment and the original aliased ADS-B signal are as follows: Figure 3 and Figure 4 As shown. Among them, Figure 3 The corresponding aliasing signal in the design is the sum of ADS-B signal sequence decomposition signal 1 and ADS-B signal sequence decomposition signal 2 with time delay. Figure 4The corresponding aliasing signal in the design is ADS-B signal sequence decomposition signal 2 plus ADS-B signal sequence decomposition signal 1 with time delay. As can be seen from the figure, the maximum value of the cross-correlation coefficient is... Figure 4 The position with a time delay of 6μs indicates that the order of the decomposed signals is that signal 2 leads signal 1 with a relative time delay of 6μs.

[0095] This invention, based on the FastICA algorithm, separates aliased signals insensitive to time delay, and can separate aliased signals with relatively small time delays, thus improving the robustness of the separation algorithm. It can effectively separate ADS-B aliased signals and has good overlapping signal separation capabilities. After processing the separated signal using a frame header detection method based on maximum cross-correlation energy entropy and a data bit parsing method based on the absolute value of the sum of half a chip, the bit error rate of the decomposed signal is low under a certain signal-to-noise ratio. Based on the cross-correlation coefficient signal processing method, the relative time delay and sequence of the mixed signal are estimated from the separated ADS-B signal, thus improving the uncertainty of the FastICA algorithm.

[0096] This invention utilizes a uniform array antenna to receive two ADS-B signals. These two ADS-B signals exhibit signal aliasing. The signals are separated using a Fast Independent Component Analysis (FastICA) algorithm, which extracts the source signal by iteratively finding the maximum negative entropy based on the principle of maximizing negative entropy. The decomposed signals are then subjected to frame header detection and data bit parsing to obtain two ADS-B signal sequences. Frame header detection employs matched filtering, using the maximum cross-correlation energy to detect synchronization pulse data. The data bit parsing process compares the absolute values ​​of half-chips to determine the signal. The design uses "0" and "1" to represent the superposition of two signals with relative time delays. Since the order of the two decomposed ADS-B signals may not be consistent with the order of the signals in the aliased signal, there are two possibilities for the aliased signal corresponding to each time delay: one signal may be in front and the other signal may be behind. The cross-correlation coefficients of the two aliased signals corresponding to each time delay are calculated with the original ADS-B aliased signal. The two cross-correlation coefficients are compared, and the larger value is found. This value corresponds to the correct order of the signals in the aliased signal. The time delay corresponding to the largest cross-correlation coefficient is the relative time delay of the two signals.

[0097] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for estimating the time of arrival of ADS-B overlapping signals based on a satellite, characterized in that, The method comprises the following steps: S1: receiving two mixed ADS-B signals based on a uniform array antenna; S2: pre-processing the mixed ADS-B signals, and extracting ADS-B decomposed signals from the pre-processed mixed ADS-B signals based on a fast independent component analysis method; S3: obtaining two ADS-B signal sequences after frame header detection and data bit analysis of the ADS-B decomposed signals; S4: superimposing a plurality of mixed signals based on the two ADS-B signal sequences; the mixed signals have the same frequency as the mixed ADS-B signals, and the mixed signals include two types, each type has one ADS-B signal sequence in front, and the mixed signals of each type have different relative time delays; S5: calculating the cross-correlation coefficients of each mixed signal and the mixed ADS-B signals, and finding the mixed signal with the maximum cross-correlation coefficient; S6: taking the front-back order relationship of the mixed signal with the maximum cross-correlation coefficient as the front-back order relationship of the mixed ADS-B signals, and calculating the arrival time of the mixed ADS-B signals based on the relative time of the mixed signal with the maximum cross-correlation coefficient. 2.The method of claim 1, wherein, The pre-processing comprises the following steps: firstly, performing digital-to-analog conversion and downsampling on the ADS-B signals to obtain baseband signals; and then, performing centering processing and whitening processing on the baseband signals after filtering processing by a low-pass filter.

3. The method of claim 2, wherein, The signal output by the centralized processing is: ; wherein denotes the original signal, denotes the mean value; The signal output by the whitening process is: wherein denotes the original signal, the whitening matrix is and satisfies ; denotes the identity matrix.

4. The method of claim 2, wherein, S2 comprises the following sub-steps: S21: taking as the cost function, the mixing matrix is iteratively optimized according to the maximum negative entropy criterion so that the negative entropy reaches the maximum, k represents the kth iteration; wherein, , represents the pre-processed ADS-B signal, represents the original signal; represents a non-quadratic nonlinear function; negative entropy maximized by optimizing acquisition: According to the Kuhn-Tucker criterion, the optimal solution is obtained by solving the derivative of the optimal solution is obtained: ； wherein is a constant, , is the optimized value; denotes the derivative of the non-quadratic non-linear function .

5. The method of claim 4, wherein, The iteration formula of the mixing matrix is obtained according to the Newton iteration method: ； wherein denotes the derivative of a non-quadratic non-linear function, denotes the mixing matrix of the (k+1)th iteration; denotes the mixing matrix of the kth iteration.

6. The method of claim 1, wherein, Step three comprises the following sub-steps: S31: obtaining a fixed frame header and length of the sampled ADS-B signals, calculating the maximum cross-correlation energy between the fixed frame header and the separated signals with the same length, and determining the position of the ADS-B separated signal frame header based on the maximum cross-correlation energy; S32: obtaining two ADS-B signal sequences by performing digital bit demodulation on the ADS-B separated signals.

7. The method of claim 1, wherein, The relative time delay is in units of μs, and the longest time delay is 120 μs.

8. The method of claim 1, wherein, The cross-correlation coefficient is expressed as: ； represents a designed aliasing signal, and represents an original aliasing signal; If , then and are not related; if , then and are related; if , then and are perfectly related. 9.A system for estimating time of arrival of ADS-B overlapping signals from space-based sources, comprising: The method for estimating the arrival time of the satellite-based ADS-B mixed signals according to any one of claims 1-8 comprises: a receiving module configured to receive two mixed ADS-B signals based on a uniform array antenna; a pre-processing module configured to pre-process the mixed ADS-B signals, and extract ADS-B decomposed signals from the pre-processed mixed ADS-B signals based on a fast independent component analysis method; an analysis and detection module configured to obtain two ADS-B signal sequences after frame header detection and data bit analysis of the ADS-B decomposed signals; a superimposing module configured to superimpose a plurality of mixed signals based on the two ADS-B signal sequences; a first calculating module configured to calculate the cross-correlation coefficients of each mixed signal and the mixed ADS-B signals, and find the mixed signal with the maximum cross-correlation coefficient; a second calculating module configured to take the front-back order relationship of the mixed signal with the maximum cross-correlation coefficient as the front-back order relationship of the mixed ADS-B signals, and calculate the arrival time of the mixed ADS-B signals based on the relative time of the mixed signal with the maximum cross-correlation coefficient.

Images