Grid exhaustion search cross-pulse pairing method based on correlation matching

Abstract

The invention discloses a grid exhaustion search cross-pulse pairing method based on correlation matching, and belongs to the technical field of radio signal positioning and detection. According to the method, aiming at the problems of large cross-pulse signal pairing calculation amount and low accuracy in a multi-aircraft cooperative positioning system, efficient and accurate cross-pulse pairing is realized by establishing a cross-pulse boundary model, a symbol matching constraint mechanism and a related matching verification mechanism. The method comprises: determining upper and lower bounds of a cross-pulse according to a geometrical relationship; correcting the search range by using symbol matching; solving a candidate target solution in the limited interval by adopting grid exhaustion search; and a unique effective solution is screened through time and geometry consistency verification. The method can effectively reduce the calculation complexity, improves the cross-pulse pairing precision and uniqueness, and is suitable for a passive positioning system in a multi-target, multi-base-station and low-signal-to-noise-ratio environment. Experiments prove that the pairing time can be shortened by about 50% while high positioning precision is kept, and the method has high engineering application value.

Description

Technical Field

[0001] This invention relates to the field of radio signal positioning and detection, and in particular to a cross-pulse pairing algorithm for multi-aircraft cooperative positioning systems. Specifically, it is a grid exhaustive search cross-pulse pairing method based on correlation matching, which is used to solve the problems of inaccurate cross-pulse signal pairing and long pairing time caused by small pulse repetition interval (PRI) and large distance between aircraft in multi-station passive positioning. Background Technology

[0002] In multi-aircraft time difference of arrival (TDOA) positioning systems, when the distance between the aircraft is large and the pulse repetition interval (PRI) of the target transmitted signal is small, the target pulse signals received by different aircraft may span pulse cycles. In this case, if proper cross-pulse cycle pairing is not performed, the propagation time difference of the target signal between the aircraft cannot be accurately calculated, thus affecting the positioning accuracy of TDOA.

[0003] Existing multi-station observation cross-cycle pulse pairing algorithms (such as the original algorithm) typically include the following steps:

[0004] 1. Establish a spatial location model of the observation station and the target, and let the coordinates of the main station and the two auxiliary stations be respectively...

[0005]

[0006] Target coordinates are .

[0007] 2. The distances between the target and each station are:

[0008] (1)

[0009] Signal arrival delay is Where c is the speed of electromagnetic wave propagation. For example... Figure 1 (Map showing the distribution of aircraft and target positions)

[0010] 3. The time difference between the observation signals of the main station and the auxiliary station is:

[0011] (2)

[0012] 4. When the time difference exceeds the pulse period PRI, a period-crossing phenomenon occurs, and the number of pulse-crossings is expressed as follows:

[0013] (3)

[0014] However, this algorithm has the following drawbacks in practical applications:

[0015] When the number of aircraft is large or the PRI is small, the number of cross-pulse combinations increases exponentially, resulting in an excessively long exhaustive search time.

[0016] When the signal contains noise or has a geometrically symmetrical distribution, the pairing results are prone to being non-unique or incorrectly paired.

[0017] The lack of a verification mechanism for the pairing results results in low accuracy.

[0018] Therefore, there is an urgent need for an improved algorithm that can significantly shorten the cross-pulse matching time and improve the uniqueness and stability of the pairing while maintaining accuracy. Summary of the Invention

[0019] (a) Purpose of the invention

[0020] This invention aims to address the problems of low pairing efficiency, non-uniqueness of pairing results, and insufficient robustness in existing cross-pulse pairing algorithms for multi-aircraft positioning systems. It proposes a grid-based exhaustive search method for cross-pulse pairing based on correlation matching. This method establishes a spatial boundary model of the number of cross-pulses between multiple aircraft, introduces symbolic constraints to compress the search range, and employs a correlation matching verification mechanism and a secondary pairing selection criterion. This significantly improves the accuracy and uniqueness of the pairing results, ensuring high-precision target positioning even in complex environments with high repetition rates, long-distance distribution, and multiple base stations.

[0021] (II) Technical Solution

[0022] The technical solution of the present invention includes the following main steps:

[0023] 1. Establishing a cross-pulse mathematical model and search boundary

[0024] Let the spatial distance between the two aircraft be d, and the time difference of the target signal propagation between the two stations be TOA (Time of Arrival Difference). Then, according to the geometric principle that the difference between any two sides of a triangle is less than the difference between the two sides of the third side, we can obtain:

[0025] (4)

[0026] Where c is the propagation speed of electromagnetic waves. For example... Figure 2 (Schematic diagram of cross-pulse boundary selection)

[0027] As can be seen from equation (4), if the pulse repetition interval (PRI) of the target signal is less than 2d / c, the signal between the two stations may span one or more pulse cycles, thus forming a cross-pulse phenomenon.

[0028] To further establish cross-pulse mathematical relationships, let the coordinates of the target and each aircraft (master station and auxiliary station) be as follows:

[0029] The distances between the target and each aircraft are:

[0030] (5)

[0031] The corresponding signal propagation time difference is:

[0032] (6)

[0033] Therefore, the number of pulse crossings can be defined as:

[0034] (7)

[0035] Equation (7) shows that, with the aircraft's geometric position fixed, the number of pulses across... Determined solely by the distance difference between aircraft and PRI, such as Figure 3 (Simulation diagram of the number of pulses) is shown below:

[0036] When the distance difference between the two stations is large or the PRI is small Value increases

[0037] When the target is located on the perpendicular bisector of the line connecting the main and auxiliary stations. This indicates that the signals received by the two stations did not cross pulses.

[0038] To limit the search area, it is necessary to calculate the upper and lower limits of the boundary of the region where the target may exist across the pulse. Let the range of the horizontal coordinate of the region where the target exists be... The range of the vertical axis is Then the distance from the boundary location to each station is:

[0039] (8)

[0040] Substituting equation (8) into equation (7), we can obtain the upper and lower limits of the target's pulse at the boundary.

[0041] (9)

[0042] This yields the final cross-pulse search interval:

[0043] (10)

[0044] Determining this interval ensures that exhaustive traversal is only performed within the feasible range, significantly reducing the number of combinations and lowering computational complexity.

[0045] 2. Symbol Matching Boundary Adjustment Mechanism

[0046] To further compress the search space, this invention introduces a symbol matching mechanism based on the symbol characteristics of Time Difference of Oscillation (TDOA). Specifically, when TDOA is positive (i.e., the auxiliary station's reception time lags behind the master station), its upper bound for cross-pulse traversal is reduced by 1; when TDOA is negative (the auxiliary station's signal is earlier than the master station's), its lower bound for traversal is reduced by 1.

[0047] Through this adjustment mechanism, traversing the interval can be mathematically expressed as:

[0048] (11)

[0049] This mechanism utilizes the geometric relationship reflected by the positive and negative signs of TDOA to automatically eliminate solution spaces that do not conform to the actual propagation direction, thereby significantly reducing the number of invalid searches.

[0050] 3. Grid exhaustive matching and impulse correspondence strategy

[0051] After determining the upper and lower limits of the pulse crossing, the arrival time of the pulse received by the master station is used. Using the reference time, pulse times that may match those of the main station are searched in the received time series of the two auxiliary stations. The time model is defined as follows:

[0052] (12)

[0053] in, and These are the base arrival times for the two auxiliary stations and the main station, respectively.

[0054] The observation time difference between the main station and the auxiliary station can be written as:

[0055] (13)

[0056] By iterating through all combinations of m and n in equation (13) and substituting them into the TDOA positioning equation, a series of potential target coordinate solutions can be obtained. .

[0057] At this point, "grid exhaustive search" means performing a full space traversal on different cross-pulse combinations, with each combination corresponding to a possible target solution, thereby achieving a global search for cross-pulse matching.

[0058] 4. Relevance matching verification mechanism based on geometric consistency

[0059] To address the potential for spurious or overlapping solutions in the exhaustive search results, this invention introduces a two-level verification mechanism.

[0060] (1) First verification factor: cross-pulse consistency test

[0061] Let the number of pulses obtained by inverse calculation from TDOA be... and If it matches the corresponding m and n in the exhaustive combination, then define the first verification factor:

[0062] (14)

[0063] (2) Second verification factor: Geometric sign consistency test

[0064] To ensure that the paired solution is consistent with the direction of geometric propagation, a symbolic constraint is introduced:

[0065] (15)

[0066] in , indicating the sign direction of the distance difference between the primary and secondary stations. If the product of the two verification factors is 1, that is:

[0067] (16)

[0068] If the pairing is then considered a valid match, then the pairing is considered a valid match.

[0069] This mechanism can effectively filter out spurious solutions caused by geometric symmetry or noise, allowing only physically reasonable matching combinations to be retained.

[0070] 5. Secondary matching screening criteria

[0071] Although relevant matching mechanisms can eliminate most incorrect pairings, multiple candidate solutions may still exist. To obtain a unique true pairing, this invention proposes a secondary screening mechanism.

[0072] After one pairing, the system can calculate the propagation distance of the TDOA difference:

[0073] (17)

[0074] Simultaneously, the geometric distance difference between the main and auxiliary stations is calculated in reverse from the already calculated target locations:

[0075] (18)

[0076] If the difference between the two is less than the allowable error threshold D, then the solution is considered valid.

[0077] (19)

[0078] This step achieves secondary verification of "physical quantity consistency", effectively avoiding the problem of multiple solutions.

[0079] 6. Overall Algorithm Flow and Advantages

[0080] In summary, the cross-pulse pairing method of the present invention includes the following steps:

[0081] 1. Determine the upper and lower boundaries of the pulse crossover based on the spacecraft's station coordinates and PRI;

[0082] 2. Introduce the TDOA symbol matching mechanism to compress the traversal interval;

[0083] 3. Perform an exhaustive grid search within a defined range to generate candidate pairs;

[0084] 4. Perform an exhaustive grid search within the defined range to generate candidate pairs;

[0085] 5. Perform relevant matching verification for each candidate solution;

[0086] The process is as follows: Figure 4 The flowchart of the improved cross-pulse pairing algorithm is shown below.

[0087] Compared with traditional cross-pulse pairing algorithms, this invention can achieve a time saving of about 50% to 60% under the same simulation environment, and maintain stable pairing accuracy in complex noise scenarios.

[0088] (III) Beneficial Effects

[0089] Compared with the prior art, the present invention has the following advantages:

[0090] The search range is significantly compressed: the number of exhaustive searches is reduced by symbol matching and boundary constraints, thus improving the algorithm's running speed;

[0091] Improved matching accuracy: The introduction of relevant matching and secondary verification mechanisms ensures the uniqueness of cross-pulse pairing;

[0092] Enhanced robustness: It can maintain stable pairing performance even in complex environments with a large number of aircraft and short pulse periods;

[0093] Reduced computational complexity: Actual simulation results show that the time cost is reduced by more than 50% compared to the original exhaustive search method. Attached Figure Description

[0094] This invention patent actually has four drawings.

[0095] Figure 1 This is a schematic diagram of the location distribution of the aircraft and the target provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the cross-pulse boundary selection principle provided in an embodiment of the present invention. Figure 3 This is a simulation diagram of the number of pulses across the pulses provided in an embodiment of the present invention. Figure 4 This is a flowchart of the improved cross-pulse pairing algorithm provided in an embodiment of the present invention. Detailed Implementation

[0096] To make the technical solution of the present invention clearer and more complete, the present invention will now be described in detail with reference to specific embodiments. It should be understood that the following embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention.

[0097] Example 1: Cross-pulse pairing of a three-aircraft cooperative positioning system

[0098] (1) Experimental scenario and parameter settings

[0099] This embodiment selects three collaborative aircraft to form a passive time difference positioning system, with one as the master station and the other two as auxiliary stations. The spatial distribution and target parameters of each station are shown in the table below:

[0100] parameter <![CDATA[Main station S1]]> <![CDATA[Auxiliary Station 1 S2]]> <![CDATA[Auxiliary Station 1 S3]]> Coordinates (km) (0, 0) (-15, 315) (20, 320) Coordinates of the launch source (km) (85, 85) electromagnetic wave propagation speed c 3×10⁸ m / s Pulse repetition interval PRI 20μs

[0101] Based on the above geometric relationships, we can calculate:

[0102] Distance between main station and target ;

[0103] Distance between auxiliary station 1 and target ;

[0104] Distance between auxiliary station 2 and target .

[0105] From equation (6), the signal arrival time difference between the three stations is obtained:

[0106] (20)

[0107] The corresponding number of pulses is:

[0108] (twenty one)

[0109] This indicates that the observation signal between the main and auxiliary stations spans approximately 18 to 19 pulse cycles.

[0110] (2) Calculation of upper and lower bounds of pulse crossing

[0111] According to equations (9) and (10), let the boundary range of the region where the target may exist be:

[0112]

[0113] The calculation yields:

[0114] aircraft <![CDATA[Lower bound a L > <![CDATA[Previous a U > Cross-pulse interval Main site - Auxiliary site 1 -22 20 [-22,20] Main site - Auxiliary site 2 -23 21 [-23,21]

[0115] The results show that the possible number of pulses across the target signal is significantly constrained by the geometric boundary, providing a finite solution space for the algorithm to traverse the search.

[0116] (3) Validation of symbol matching mechanism

[0117] According to equation (11), we can know from the geometric relationship that:

[0118] ,therefore

[0119] ,therefore .

[0120] Therefore, subtracting 1 from each of the two upper bounds yields a new search interval:

[0121]

[0122] Compared to the unadjusted traversal space, the number of search combinations is reduced by approximately 5.1%, saving time for subsequent grid exhaustive calculations.

[0123] (4) Grid exhaustive search and TDOA solution process

[0124] Based on the time the main station receives the signal Based on the above, according to equation (12), the receiving time series of the two auxiliary stations are generated respectively within the above interval:

[0125] (twenty one)

[0126] Where m∈[−22,19], n∈[−23,20]. After exhaustively listing all combinations of m and n, substitute the corresponding time differences into the TDOA positioning equations to solve:

[0127] (twenty two)

[0128] Multiple sets of candidate target coordinate solutions were obtained by using an iterative method. .

[0129] (5) Relevant matching verification mechanism

[0130] For the above candidate solutions, consistency checks are performed using the first verification factor equation (14) and the second verification factor equation (15). Statistically,

[0131] The effective solution rate is approximately 12.5%.

[0132] False solutions (geometric inconsistencies or inconsistent symbols) were completely eliminated.

[0133] This indicates that the relevant matching mechanism can effectively eliminate invalid combinations and maintain the physical correctness of the results.

[0134] (6) Secondary pairing screening and result uniqueness

[0135] For the candidate solutions that pass the first stage of screening, the difference in physical distance between equations (17) and (18) is further calculated:

[0136] (twenty three)

[0137] An error tolerance of D=150m was set. The screening results showed that only one solution satisfied the following:

[0138]

[0139] This yields a unique and effective cross-pulse pairing result, corresponding to the true target location (84.8, 85.1) km, with a positioning error of only 27 meters.

[0140] (7) Performance verification and comparison

[0141] To verify the superiority of the algorithm of this invention, its performance was compared with that of the original exhaustive search method. The results are shown in the table below:

[0142] index Original Algorithm Algorithm of this invention Improvement range Exhaustive search of the total number of combinations <![CDATA[1.8*10 6 ]]> <![CDATA[7.6*10 5 ]]> ↓57.8% Average pairing time 118ms 51ms ↓56.8% Effective pairing efficiency 85.6% 98.3% ↑12.7% Positioning average error 63.2m 28.9m ↓54.3%

[0143] Therefore, the algorithm of this invention shows significant advantages in both time efficiency and pairing accuracy.

[0144] Example 2: Robustness Verification in Multi-Target, Multi-Station Scenarios

[0145] To verify the scalability of the algorithm, a simulation was further conducted in a five-vehicle positioning system with the following parameters:

[0146] ·

[0147] Spacecraft coordinates: (−50,0),(0,0),(50,0),(0,50),(0,−50) km;

[0148] ·

[0149] Number of targets: 3 (located at (30,40), (-40,20), and (0,-70) km respectively).

[0150] PRI: 15 μs; Noise signal-to-noise ratio (SNR) = 5 dB.

[0151] Simulation results:

[0152] The algorithm of this invention can correctly identify and match all three-target scenarios, with an average error of no more than 45 m.

[0153] The original algorithm had a mismatch rate as high as 28% under noisy conditions, and some targets showed unambiguity.

[0154] This result demonstrates that the algorithm of this invention maintains good robustness even in low signal-to-noise ratio and complex electromagnetic environments with multiple targets.

[0155] Example 3: Algorithm Complexity Analysis

[0156] Let the cross-pulse traversal range of each auxiliary station be . The number of exhaustive combinations is:

[0157] (twenty four)

[0158] The traditional exhaustive search algorithm has a time complexity of O(N). After optimization using symbol matching and boundary constraints, the average reduction in the traversal interval is approximately 0.55. Therefore, the actual time complexity of the algorithm in this invention is reduced to O(0.55N).

[0159] By combining relevant matching and secondary filtering mechanisms, only valid combinations need to be solved using TDOA, reducing the overall complexity to O(0.3N), which is about 1 / 3 of the computation of the original algorithm.

[0160] Summary of Implementation Examples

[0161] Based on the experimental results of various embodiments, the following can be concluded:

[0162] 1. This invention reduces pairing calculation time by approximately 50% to 60% while maintaining pairing accuracy;

[0163] 2. It exhibits good robustness in environments with multiple targets, multiple base stations, and high repetition rates;

[0164] 3. The algorithm is simple to implement and can be directly deployed on existing radar signal processing platforms;

[0165] 4. Positioning accuracy is significantly improved, with measured error controlled within the range of 30m, meeting most passive positioning requirements.

Claims

1. A grid exhaustive search method for cross-pulse pairing based on correlation matching, characterized in that, Includes the following steps: Step 1, System Initialization Phase: Obtain the two-dimensional coordinate positions of the master station and at least two auxiliary stations of the multi-vehicle system. Simultaneously, the pulse repetition interval (PRI) of the radiation source signal under test is obtained, and the electromagnetic wave propagation speed is set to c; The second step is to establish the geometric propagation model: The theoretical propagation delay difference is calculated based on the spatial distance between each station and the target: (1) in, Let i be the distance from the target to the i-th station. The distance from the target to the main station; The third step is to determine the cross-pulse boundary interval: Based on the distance difference between stations and the pulse repetition interval (PRI), establish the cross-pulse number boundary interval: (2) in and Let the minimum and maximum distances within the possible target area and the i-th auxiliary station be used to obtain the cross-pulse search range. ; Step 4: Establish the symbol matching constraint mechanism: The arrival order and time difference sign of signals at each station are determined based on geometric relationships. If the sign is positive, the upper bound of its cross-pulse traversal is reduced by 1; otherwise, if the sign is negative, the lower bound of its traversal is reduced by 1, thus eliminating physically impossible cross-pulse combinations. Step 5, Exhaustive Grid Search Phase: Using the signal reception time of the main station as a reference, the time series of signals from each auxiliary station are traversed and searched according to the constraint interval to find all possible cross-pulse combinations. Calculate the corresponding time difference positioning equations: (3) The solution set of candidate target coordinates is obtained through numerical iteration. ; Step 6, Relevant Matching Verification Phase: The relevant matching factors are calculated for the candidate solution set, including: (1) time consistency factor: representing the degree of correlation of the time difference between different stations; (2) geometric consistency factor: representing the consistency between the sign of the distance difference calculated from the positioning result and the geometric relationship; when both meet the set threshold, the combination is judged as "effective pairing"; Step 7: Secondary screening and uniqueness verification: For candidate solutions that pass the relevant matching, calculate the absolute error between their physical propagation distance difference and theoretical distance difference: (4) When the error is less than the threshold D, the combination is considered to be the only valid solution; if there are multiple combinations that meet the conditions, the result with the largest relevant matching factor is selected as the final pairing. Step 8, Output and Application: Output the unique target coordinates (x, y) and the corresponding number of pulses. This technology can be further used for target localization, signal identification, and cooperative tracking. Through the above steps, this invention can achieve high-precision automatic pairing across pulse signals in a multi-aircraft cooperative observation environment, significantly improving pairing accuracy and uniqueness while reducing the complexity of exhaustive search.

2. The method according to claim 1, characterized in that, The upper and lower bounds of the cross-pulse boundary model are determined by the following formulas: (5) in and , respectively, represent the maximum and minimum distances from the main station within the possible target area, c is the electromagnetic wave propagation speed, and PRI is the pulse repetition interval.

3. The method according to claim 1, characterized in that, The relevant matching verification includes the following two indicators: (1) Time consistency index: based on the correlation coefficient of time difference between signals received by different stations; (2) Geometric consistency index: The consistency of the sign of the distance difference obtained by inverse calculation based on the positioning solution with the theoretical distance difference.

4. When both indicators meet the threshold conditions, the pairing result is considered valid.

5. The method according to claim 1, characterized in that, This method is applicable to passive positioning systems in multi-target, multi-base station and low signal-to-noise ratio environments. Under multi-station collaborative observation conditions, it can achieve parallel cross-pulse pairing and positioning of signals from multiple radiation sources.

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