Search optimization method based on shortest target average discovery time

Abstract

The invention provides a shortest target average discovery time-based search optimization method, which comprises the following steps of: firstly, determining a preliminary range of a search area and arranging wave positions of a target search area according to known early warning indication information to calculate the occurrence probability of a target in each wave position; on the basis, a search model based on the shortest target average discovery time under the multi-beam condition is established, search resources are reasonably distributed according to the occurrence probability of the target in the beam position, and the effectiveness of the model under the condition that multiple search beams exist at the same time is verified by comparing and simulating a traditional uniform search method and the condition under a single beam.

Description

Technical Field

[0001] This application relates to the technical fields of detection simulation and signal processing, and particularly relates to a search optimization method based on the shortest average target discovery time. Background Art

[0002] The core of a radar system lies in using multiple array antennas to achieve search and scan of the detection airspace. Being able to select an appropriate airspace wave position arrangement method and search strategy according to the real-time mission environment and parameters is one of the key technologies of a phased array radar, which involves how to optimize the pointing and arrangement of the array antenna beams to achieve the best detection performance.

[0003] When the radar system fails to independently detect a target, it needs to disperse resources to search in a vast airspace, which will greatly reduce the detection efficiency of the radar. At this time, the search strategy can be optimized through prior information. Under the guidance of prior information, the radar system can more precisely allocate resources such as its beam pointing, dwell time, and transmit power, concentrate more energy in a specific area for target search, thereby improving the detection efficiency of the radar and reducing the average time for the target to be discovered, and effectively enhancing the overall battlefield situation awareness ability.

[0004] For guided search, in the face of an area where a target may exist, the radar needs to complete the search of the target area with limited search resources and discover the target within the shortest possible time. After setting the wave positions for the target area, for traditional search methods, the radar generally evenly distributes the search resources to each wave position for illumination search, which will result in waste of some search resources in wave positions with a low probability of target appearance, so that the time taken to discover the target is relatively long. Summary of the Invention

[0005] This application provides a search optimization method based on the shortest average target discovery time, which can be used to solve the technical problem of the relatively long time taken to discover a target.

[0006] This application provides a search optimization method based on the shortest average target discovery time, and the method includes:

[0007] Step 1: Use the known early warning indication information to determine the search area and perform search wave position arrangement within this area;

[0008] Step 2: Calculate the target appearance probability of each wave position within the target search area according to the indication information;

[0009] Step 3: Establish a search model based on the shortest average target discovery time, and allocate the radar search resources of each wave position with the criterion of the shortest average target discovery time;

[0010] Step 4: Establish a search model based on the shortest average target discovery time under multi-beams, and process the data within the search area;

[0011] Further, in Step 1, determining the search area according to the indication information and arranging the search beam positions specifically includes the following steps:

[0012] Step 1-1: Establish an error distribution model for the guidance information provided by the early warning system to represent the prior position information of the target. Assume that the positions of the target provided by the early warning system in elevation and azimuth are (E p , A p ), and the true position of the target is denoted as (E0, A0). Then, (E p , A p ) = (E0, A0) + (ε E , ε A ), where (ε E , ε A ) are the errors of the guidance information provided by the early warning system in the elevation direction and azimuth direction respectively. Assume that the guidance error satisfies the two-dimensional joint distribution of f(ε E , ε A ), and it is obtained that the true position of the target follows a two-dimensional normal Gaussian distribution with a mean of (E p , A p ) - (μ E , μ A ) and a variance of (σ E 2 , σ A 2 ). Denote the probability density function as f(E0, A0);

[0013] Step 1-2: Set the search area of the target. Adopt the three-times mean square deviation method based on the characteristics of the normal distribution. Take the target prediction position as the center, and according to the 3σ principle, take the distances of three times the mean square deviation in both the azimuth direction and the elevation direction to form a rectangle, which is used as the search area of the target;

[0014] Step 1-3: Arrange the beam positions according to the determined search area. Adopt the interleaved beam arrangement method to cover the search area with beam positions.

[0015] Further, in Step 2, calculate the target appearance probability of each beam position within the target search area;

[0016] Since there is a beam broadening effect of the radar beam in the spherical coordinate system, the beam position arrangement is generally carried out in the sine space coordinate system. Therefore, it is also necessary to convert the error of the guidance information from the radar station spherical coordinate system to the sine space coordinate system. For the sake of simplicity, the statistical experiment method can be adopted to calculate the probability of the target appearing in each beam position. The specific steps are as follows:

[0017] Step 2-1: In the spherical coordinate system of the radar station, randomly generate M target coordinate data that follow a two-dimensional error distribution f(ε E , ε A ).

[0018] Step 2-2: Transform the M coordinate data in the spherical coordinate system of the radar station to the sine space coordinate system, and record the number of coordinates that appear in each arranged wave position area as M k , where k is the number of the corresponding wave position;

[0019] The probability that the target appears in each wave position is denoted as p k = M k / M.

[0020] Theoretically, the larger the value of the number of targets M, the closer the probability of the target appearing in each wave position obtained is to the theoretical value; thus, the determination of the target-guided search airspace under the early warning information is completed, and the prior information of the probability of the target appearing in each wave position is obtained.

[0021] Furthermore, in Step 3, with the criterion of the shortest average target detection time, establish a search model based on the shortest average target detection time, and reasonably allocate the radar search resources of each wave position; including the following steps:

[0022] Step 3-1: Model establishment:

[0023] Assume that in a specific distance of interest, the airspace to be searched is divided into N wave positions waiting to be searched. For a target with a specific RCS, the detection probability of the radar for this target in the k-th search wave position is p dk ; if the target appears in the k-th wave position, the probability that the radar detects the target in the i-th scan of wave position k is denoted as P ki = p dk (1 - p dk ) i-1 , denote the interval time of the radar scanning wave position k, that is, the search frame period of the k-th wave position, as t fk , assume that the time when the target appears follows a uniform distribution, then the average time when the target appears at the beginning is 0.5t fk , so from the time when the target appears in wave position k, to the time when the radar scans wave position k for the i-th time, that is, the i-th search frame period and detects the target, the total time elapsed is T i = (i - 0.5)t fk ;

[0024] The average time used for the target to be detected by the radar in the k-th wave position satisfies:

[0025]

[0026] Assume that the total time resource of the radar is T, and during the search time, the radar performs n k reilluminations on each beam position, then we have:

[0027]

[0028] Considering the occurrence probability of the target on each beam position, the average detection time of the target in a specific search area is expressed as:

[0029]

[0030] Assume that when the total time resource is T, the radar performs n k scans on beam position k, and the proportion of the time resource occupied by the search task is L s , that is, the total time used by the radar for the search task is LT s , and at this time, the dwell duration of the radar at each beam position is T d ; for the guided search, it is hoped that the average detection time of the radar for the target is as short as possible. Thus, a search performance optimization model considering the radar time resource constraint is obtained, where the number of scans n k for beam position k is the optimization variable;

[0031]

[0032] For the optimization model, using the Lagrange multiplier method, substituting the constraint conditions into the optimization equation, the optimal search illumination times for each beam position are obtained as:

[0033]

[0034] Step 3-2: Characterize the shortest average target detection time model through the radar search data rate;

[0035] Considering that the search data rate is defined as the number of illuminations of the radar beam on the beam position per unit time, therefore, the optimal search data rate for each beam position under the minimum average target detection time criterion of the radar is expressed as:

[0036]

[0037] The optimal search data rate obtained by using the minimum average target detection time criterion consists of two parts. One part is the total allowable search data rate during the search time, and the other part is the weight factor of different beam positions in the airspace. This weight factor is proportional to the square root of the prior probability of the target appearing at the corresponding beam position; the greater the target appearance probability, the higher the corresponding search data rate.

[0038] Further, in step 4, a search model based on the shortest average target discovery time under multi-beams is established, which specifically includes the following steps:

[0039] When the error of the guiding information is large, or the airspace range to be searched is wide, large-area airspace search is carried out. At this time, for the wide search airspace, it is divided into multiple sub-regions, and during the division process, the wave positions with different target appearance probabilities are distributed as evenly as possible in the divided sub-regions. Multiple beams are used to search each sub-region to further reduce the time to discover the target;

[0040] It should be noted that under the same search conditions, simultaneously transmitting multiple beams will cause the transmission power of each beam to decrease. However, due to the division of sub-airspaces, the area that a single beam needs to search becomes smaller, and the dwell time of the beam on the wave positions within the sub-airspace also increases correspondingly, so that the same signal-to-noise ratio can be obtained when there are multiple search beams simultaneously as when a single beam is used for search; at this time, the corresponding average target discovery time should take the maximum value among the search results of multiple beams to ensure that the radar can search for the target under the worst conditions. At this time, through simulation verification, it can be obtained that the average target discovery time in the case of multiple search beams is less than the result obtained by searching with a single beam, which proves the effectiveness of this method under multiple search beams simultaneously.

[0041] Compared with the prior art, the remarkable progress of the present invention lies in: the present invention establishes a search model with the shortest average target discovery time as the criterion in the case of multi-beams of a digital array radar, and obtains a smaller average target discovery time compared with the case of a single beam and the uniform search method. Moreover, as the proportion of search resources increases, the average target discovery time under various methods becomes smaller, which also shows that under the condition of limited radar resources, the effectiveness of searching the target airspace through multiple beams is higher.

[0042] To more clearly illustrate the functional characteristics and structural parameters of the present invention, the following further explains in conjunction with the drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is the flowchart of the wave position arrangement method;

[0044] Figure 2 is the search arrangement of multiple beams within the target area;

[0045] Figure 3 is the comparison of the average discovery time between the single beam, multi-beams and the uniform search method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] To make the purpose, technical solutions and advantages of this application clearer, the following will further describe the embodiments of this application in detail in conjunction with the drawings.

[0047] First, the embodiments of the present application will be introduced below in conjunction with the accompanying drawings.

[0048] For traditional search methods, after setting the wave positions for the target area, the radar generally evenly distributes the search resources to each wave position for irradiation and search. This will result in waste of some search resources in wave positions with a low probability of target appearance, so that the time taken to detect the target is relatively long. For guided search, in the face of an area where a target may exist, the radar needs to complete the search of the target area within limited search resources and detect the target in the shortest possible time. In view of this situation, it is necessary to reasonably allocate the search resources to different wave positions according to the importance of different wave positions in the target airspace. Essentially, it is to allocate more search resources to the areas with a higher probability of target appearance, so as to shorten the time for the target to be detected.

[0049] A search optimization method based on the shortest average target detection time in the case of multiple beams is as follows:

[0050] Determine the search area according to the indication information and arrange the search wave positions. The process is as Figure 1 shown.

[0051] Establish an error distribution model for the guidance information provided by the early warning system to represent the prior position information of the target. Assume that the positions of the target provided by the early warning system in elevation and azimuth are (E p , A p ), and the true position of the target is denoted as (E0, A0). Then, (E p , A p ) = (E0, A0) + (ε E , ε A ), where (ε E , ε A ) are the errors of the guidance information provided by the early warning system in the elevation direction and azimuth direction respectively. Generally, it is assumed that the guidance error satisfies the two-dimensional joint distribution of f(ε E , ε A ). It can be obtained that the true position of the target follows a two-dimensional normal Gaussian distribution with a mean of (E p , A p ) - (μ E , μ A ) and a variance of (σ E 2 , σ A 2 ). Denote its probability density function as f(E0, A0);

[0052] Adopt the three - times mean square deviation method based on the characteristics of the normal distribution. Taking the target prediction position as the center, according to the 3σ principle, distances of three - times mean square deviation are taken in both the azimuth and elevation directions to form a rectangle, which is used as the target search area. Waveform scheduling is carried out according to the determined search area, and an interleaved beam scheduling method is adopted to cover the search area with waveforms.

[0053] Calculate the target appearance probability of each waveform in the target search area;

[0054] Due to the beam broadening effect of the radar beam in the spherical coordinate system, waveform scheduling is generally carried out in the sinusoidal space coordinate system. Therefore, it is also necessary to convert the error of the guidance information from the radar station spherical coordinate system to the sinusoidal space coordinate system. For the sake of simplicity, a statistical experiment method can be adopted to calculate the probability of the target appearing in each waveform. First, in the radar station spherical coordinate system, M target coordinate data obeying the two - dimensional error distribution f(ε E ,ε A ) are randomly generated; Secondly, the M coordinate data in the radar station spherical coordinate system are transformed to the sinusoidal space coordinate system, and the number of coordinates appearing in each scheduled waveform area is denoted as M k , where k is the number of the corresponding waveform; Finally, the probability of the target appearing in each waveform can be denoted as p k =M k / M.

[0055] Theoretically speaking, the larger the value of the number of targets M, the closer the target appearance probability in each waveform calculated by the above formula is to the theoretical value. Thus, the determination of the target - guided search airspace under the early warning information is completed, and the prior information of the target appearance probability of each waveform is obtained.

[0056] Taking the shortest average target detection time as the criterion, establish a search model based on the shortest average target detection time, and reasonably allocate the radar search resources of each waveform.

[0057] Assume that in a specific distance of concern, the airspace to be searched is divided into N waveforms waiting to be searched. For a target with a specific RCS, the detection probability of the radar for this target in the k - th search waveform is pdk. If the target appears in the k - th waveform, the probability that the radar detects the target in the i - th scan of waveform k can be denoted as P ki =p dk (1 - p dk ) i-1 , denote the interval time of the radar's scan of waveform k (the search frame period of the k - th waveform) as t fk , assume that the target appearance time follows a uniform distribution, then the average time of target appearance at the beginning is 0.5t fk, so starting from when the target appears at wave position k until the radar scans wave position k for the i-th time (the i-th search frame period) and detects the target, the total elapsed time is T i =(i - 0.5)t fk .

[0058] Then it can be obtained that the average time taken for the target to be detected by the radar at the k-th wave position satisfies

[0059]

[0060] Assume that the total time resource of the radar is T, and during the search time, the radar re-illuminates each wave position n k times, then there is

[0061]

[0062] Considering the probability of the target appearing at each wave position, the average detection time of the target in a specific search area can be expressed as:

[0063]

[0064] Assume that when the total time resource is T, the radar scans wave position k n k times, and the proportion of the time resource occupied by the search task is L s , that is, the total time used by the radar for the search task is L s T, and at this time, the dwell duration of the radar at each wave position is T d . For guided search, it is hoped that the average detection time of the radar for the target is as short as possible. Thus, a search performance optimization model considering the radar time resource constraint is obtained, where the number of scans n k for wave position k is the optimization variable.

[0065]

[0066] For this optimization model, using the Lagrange multiplier method and substituting the constraint conditions into the optimization equation, the optimal search illumination times for each wave position can be obtained as:

[0067]

[0068] When the error of the guidance information is large, or the airspace range to be searched is wide, large-area airspace search is required. At this time, for a wide search airspace, the divide-and-conquer idea can be adopted. As Figure 2 shown, the entire search airspace is divided into multiple sub-regions, and wave positions with different target appearance probabilities should be evenly distributed in the divided sub-regions. Use multiple beams to search each sub-region to further reduce the time to detect the target;

[0069] It should be noted that under the same search conditions, transmitting multiple beams simultaneously will cause the transmission power of each beam to decrease. However, due to the sub-space division, the area that a single beam needs to search becomes smaller, and the dwell time of the beam on the wave positions within the sub-space also increases accordingly, enabling the same signal-to-noise ratio to be obtained when multiple search beams exist simultaneously as when a single beam is used for searching. The corresponding average target detection time at this time should be taken as the maximum value among the search results of multiple beams to ensure that the radar can detect the target under the worst conditions. At this time, from Figure 3 It can be seen that the average target detection time in the case of multiple search beams is less than the result obtained by searching with a single beam, which proves the effectiveness of the proposed method with multiple search beams. Under different search resource ratios, the optimized search algorithm with multiple beams adopted in this paper has obtained a smaller average target detection time compared with the case of a single beam and the uniform search method. Moreover, as the search resource ratio increases, the average target detection time under various methods becomes smaller, indicating that the search effect of the radar is better. This is because as the search resources increase, the illumination time of the radar beam on each wave position increases, enabling the radar to detect the target faster. At the same time, this also shows that when the radar resources are limited, the effectiveness of searching the target airspace with multiple beams is higher.

[0070] The embodiments of the present application described above do not constitute a limitation on the protection scope of the present application.

Claims

1. A search optimization method based on the shortest average target discovery time, characterized in that The method includes the following steps: Step 1: Using the known warning indication information, determine the search area and arrange the search wave positions within the area; Step 2: Calculate the target appearance probability of each wave position within the target search area according to the indication information; Step 3: Establish a search model based on the shortest average target discovery time, and allocate the radar search resources of each wave position with the criterion of the shortest average target discovery time; Step 4: Establish a search model based on the shortest average target discovery time under multiple beams to process the data within the search area.

2. The method according to claim 1, characterized in that, In Step 1, determining the search area and arranging the search wave positions within the area according to the indication information includes: Step 1-1: Establish an error distribution model for the guidance information provided by the early warning system to represent the prior position information of the target. Assume that the positions provided by the early warning system in elevation and azimuth of the target are (E p , A p ), and the true position of the target is denoted as (E0, A0). Then, (E p , A p ) = (E0, A0) + (ε E , ε A ), where (ε E , ε A ) are the errors of the guidance information provided by the early warning system in the elevation direction and azimuth direction respectively. Assume that the guidance error satisfies the two-dimensional joint distribution of f(ε E , ε A ). It is obtained that the true position of the target follows a two-dimensional normal Gaussian distribution with a mean of (E p , A p ) - (μ E , μ A ) and a variance of (σ E 2 , σ A 2 ). Denote the probability density function as f(E0, A0); Step 1-2: Set the search area of the target. Adopt the three-times mean square deviation method based on the characteristics of the normal distribution. Taking the target prediction position as the center, according to the 3σ principle, take the distances of three times the mean square deviation in both the azimuth and elevation directions to form a rectangle, which is used as the search area of the target; Step 1-3: Arrange the wave positions according to the determined search area. Adopt the interleaved beam arrangement method to cover the wave positions of the search area.

3. The method according to claim 1, wherein In Step 2, calculating the target appearance probability of each wave position within the target search area according to the indication information includes: Step 2-1: Randomly generate M sets of target coordinate data that follow a two-dimensional error distribution f(ε E , ε A ) in the spherical coordinate system of the radar station; Step 2-2: Transform the M coordinate data in the spherical coordinate system of the radar station to the sine space coordinate system, and record the number of coordinates appearing in each wave position area arranged as M k , where k is the number of the corresponding wave position; Step 2-3: Denote the probability of the target appearing within each wave position as p k = M k / M. The larger the value of the number of targets M, the closer the target appearance probability within each wave position obtained is to the theoretical value; thus, the determination of the target-guided search airspace under the warning information is completed, and the prior information of the target appearance probability of each wave position is obtained.

4. The method according to claim 1, wherein In Step 3, establish a search model based on the shortest average target discovery time, and allocate the radar search resources of each wave position with the criterion of the shortest average target discovery time; It includes: Step 3-1: Model establishment: Assume that in the specific distance of concern, the airspace to be searched is divided into N wave positions waiting to be searched. For a target with a specific RCS, the detection probability of the radar for this target at the k-th search wave position is p dk ; If the target appears at the k-th wave position, the probability that the radar detects the target in the i-th scan of wave position k is denoted as P ki = p dk (1 - p dk ) i-1 . Denote the interval time between scans of wave position k by the radar, that is, the search frame period of the k-th wave position, as t fk . Assume that the time when the target appears follows a uniform distribution. Then the average time when the target appears initially is 0.5t fk . Therefore, starting from when the target appears at wave position k, until the radar scans wave position k for the i-th time, that is, the i-th search frame period, and detects the target, the total time elapsed is T i = (i - 0.5)t fk ; The average time used for the radar to detect the target at the kth wave position satisfies: Assume that the total time resource of the radar is T, and within the search time, the radar performs n k reilluminations on each wave position, then we have: Considering the appearance probability of the target at each wave position, the average discovery time of the target within a specific search area is expressed as: Assume that when the total time resource is T, the radar performs n k scans on waveform position k, where the proportion of time resource occupied by the search task is L s , that is, the total time occupied by the radar for the search task is LT s , and at this time, the dwell duration of the radar for each waveform position is T d ; for guided search, it is hoped that the average detection time of the radar for the target is as short as possible. Thus, a search performance optimization model considering the radar time resource constraint is obtained, where the number of scans n k for waveform position k is the optimization variable. For the optimization model, using the Lagrange multiplier method, substituting the constraint conditions into the optimization equation, the optimal search illumination times of each wave position are obtained as: Step 3-2: Characterize the shortest average target discovery time model through the radar search data rate; Considering that the search data rate is defined as the number of times the radar beam irradiates the wave position per unit time, the optimal search data rate of each wave position under the criterion of the radar's shortest average target discovery time is expressed as: The optimal search data rate obtained by adopting the criterion of the shortest average target discovery time consists of two parts. One part is the total allowable search data rate during the search time, and the other part is the weight factor of different wave positions in the airspace. This weight factor is proportional to the square root of the prior probability of the target appearance at the corresponding wave position; the greater the target appearance probability, the higher the corresponding search data rate.

5. The method according to claim 1, characterized in that, In Step 4, establish a search model based on the shortest average target discovery time under multiple beams, including: When the error of the guidance information is large, or the airspace range to be searched is wide, conduct a large-area airspace search. At this time, for the wide search airspace, it is divided into multiple sub-regions, and during the division process, try to make the wave positions with different target appearance probabilities be evenly distributed in the divided sub-regions, and use multiple beams to search each sub-region to further reduce the time to discover the target; It should be noted that under the same search conditions, transmitting multiple beams simultaneously will cause the transmission power of each beam to decrease. However, due to the sub-space division, the area that a single beam needs to search becomes smaller, and the dwell time of the beam on the wave positions within the sub-space also increases accordingly, enabling the same signal-to-noise ratio to be obtained when multiple search beams exist simultaneously as when a single beam is searching; the corresponding average target detection time at this time should take the maximum value among the search results of multiple beams to ensure that the radar can detect the target under the worst conditions.

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