A multi-pulse repetition frequency selection method based on clear area evaluation function

Abstract

This invention discloses a multi-pulse repetition frequency selection method based on a clear zone area evaluation function. The core of this method is to construct a distance-velocity clear zone evaluation function. This method first constructs a distance-velocity clear zone function for each PRI under an initial PRI group within a region of interest. Then, from a probabilistic perspective, a distance-velocity clear zone evaluation function for this PRI group is constructed. Based on the clear zone evaluation function, a clear zone area evaluation function for the current region of interest is calculated. The clear zone area is used as the objective function, and then a gradient descent method is used for optimization. Each iteration involves two steps: first, updating the values ​​of the PRI group based on the gradient, and then updating the parameters controlling the slope of the clear zone area function. This gradient descent update process is repeated until a stopping condition is met or the maximum number of iterations is reached.

Description

Technical Field

[0001] The present invention relates to the technical field of radar waveform design, and in particular to a multi-pulse repetition frequency selection method based on a clear zone area evaluation function. Background Art

[0002] Medium-repetition-rate pulse Doppler radar has been widely used over the past fifty years (Philip G. Davies, Evan J. Hughes. Medium PRF Set Selection Using Evolutionary Algorithms). However, medium repetition rates can lead to dual ambiguity in both range and velocity. For example, if a target's range falls into a range blind spot, or its velocity falls into a velocity blind spot, the target will be obscured. Therefore, a multi-pulse repetition frequency (PRF) approach is needed to resolve this dual range and velocity ambiguity. In this multi-PRF approach, the selection of PRF elements within a PRF set is crucial.

[0003] Most existing PRF group selection methods grid the range-velocity region of interest, determine whether each grid is in a blind zone under each PRF, and then use the M / N detection criterion to integrate the blind zone conditions under each PRF within the PRF group. This integration results in a binary blind zone map corresponding to the PRF group (i.e., each grid has only two values, 0 or 1, with one value indicating that the grid is in a clear zone and the other indicating that it is in a blind zone). The values ​​within all grids in the region of interest are then summed to obtain the area of ​​the clear zone (or blind zone). This area is used as the objective function for PRF optimization, and the PRF values ​​are optimized through exhaustive methods or genetic algorithms to minimize the final blind zone area or maximize the clear zone area. Regarding the optional range of PRF values ​​during the optimization process, one literature (Philip G. Davies, Evan J. Hughes. Medium PRF Set Selection Using Evolutionary Algorithms) sets all pulse repetition intervals (PRI) to integer multiples of the pulse width and stipulates the maximum and minimum boundaries of the optional PRI during the optimization process; another literature (Wei Liu, Zhennan Liang, et al. A Novel Multi-pulse Repetition Frequency Set Selection Method Based on The Clear Area Evaluation Matrix) sets the optional range of PRI during the optimization process to a set of equally spaced numbers, further converting the PRF optimization problem into an integer set optimization problem.

[0004] There are two problems with the existing PRF optimization problem. First, during the optimization process, the optional values ​​of PRI are discrete data points with fixed intervals, which limits the accuracy and flexibility of the optimization. Second, the objective function in the optimization (i.e., the area of ​​the clear zone or the area of ​​the blind zone) is obtained by summing all elements in the binary matrix after gridding the region of interest, which is difficult to express in a specific functional form.

[0005] In view of this, the present invention provides a multi-pulse repetition frequency selection method based on the clear area evaluation function, in which the clear area is represented by a continuously differentiable sigmoid function. This method can break through the limitations of traditional PRF optimization, such as the fixed interval of the optional PRI range and the inability to represent the clear area in functional form, and provide support for the selection of multiple PRFs in the area of ​​interest in a clutter environment. Summary of the Invention

[0006] The present invention provides a multi-pulse repetition frequency selection method based on a clear zone area evaluation function. The core of this method is to construct a distance-velocity clear zone evaluation function. This method first constructs a distance-velocity clear zone function for each PRI under an initial PRI group within a region of interest. Then, from a probabilistic perspective, a distance-velocity clear zone evaluation function for this PRI group is constructed. Based on the clear zone evaluation function, a clear zone area evaluation function for the current region of interest is calculated. The clear zone area is used as the objective function, and then a gradient descent method is used for optimization. Each iteration includes two steps: first, updating the values ​​of the PRI group based on the gradient, and then updating the slope control parameter in the clear zone area function. This gradient descent update process is repeated until a stopping condition is met or the maximum number of iterations is reached.

[0007] To achieve the above object, the technical solution of the present invention is: a multi-pulse repetition frequency selection method based on a clear area evaluation function, comprising the following steps:

[0008] Step S1, initialize the PRI group and the inclination control parameters, and set the learning rate and the maximum number of iterations in the optimization process;

[0009] Step S2, obtaining the corresponding distance-speed clear zone function and clear zone area expression under the initial PRI group and initial inclination control parameters, and calculating the clear zone area under the initial PRI accordingly;

[0010] Step S3, updating the PRI group using the gradient descent method;

[0011] Step S4, updating the inclination control parameters;

[0012] Step S5, updating the clear area after the current iteration of the PRI group and the tilt control parameters;

[0013] In step S6, the stopping condition is determined based on the clear area. If the stopping condition is not met and the maximum number of iterations has not been reached, steps S3, S4, and S5 are repeated. If the stopping condition is met or the maximum number of iterations is reached, the iteration is stopped and the final PRI group is output as the optimization result. The corresponding clear area is the optimal clear area.

[0014] The step S2 comprises the following steps:

[0015] Step S21, calculate the initial PRI group and the corresponding distance-speed clear area evaluation function F under the initial tilt control parameter α RV (r,v);

[0016] Step S22: Based on the clear area evaluation function F RV (r, v), and get the clear area evaluation function expression SRV (T r ,α);

[0017] Step S23, calculate the initial PRI group and α (0) The clear area under

[0018] The step S3 comprises the following steps:

[0019] Step S31, clear area expression S RV (T r ,α) Calculate the partial derivative of each PRI in the PRI group and form the gradient vector

[0020] Step S32, update the PRI group to

[0021] The step S4 comprises the following steps:

[0022] Step S41, calculate

[0023] Step S42, update calculate

[0024] Step S43, compare and like Update Otherwise α (i) =α (i-1) .

[0025] Beneficial effects:

[0026] The present invention proposes a multi-pulse repetition frequency selection method based on a clear zone area evaluation function. By using a continuously differentiable sigmoid function to approximate the distance and speed blind zone conditions, a distance-speed clear zone evaluation function is generated. By adjusting the slope control parameter, the continuously differentiable clear zone evaluation function is made to infinitely approximate the actual non-differentiable blind zone condition. The PRI group is then optimized using the gradient descent method to obtain a PRI group that maximizes the clear zone area within the distance-speed region of interest. Compared with traditional PRI optimization methods, the method based on the clear zone area evaluation function breaks through the limitations of discrete and equally spaced values ​​of alternative PRIs in the optimization process, making the optimization process more directional. It uses a clear and continuously differentiable function expression to represent the objective function in the optimization process, so that the PRI optimization problem is no longer limited to genetic algorithms. Optimization methods such as the gradient descent method for having a clear objective function can be used, breaking through the limitations on the selection of optimization methods. Optimization using this method can obtain a PRF group with a higher clear zone ratio. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 , sigmoid function images under different α;

[0028] Figure 2 , a flowchart of the implementation of the multi-pulse repetition frequency selection method based on the clear area evaluation function;

[0029] Figure 3 ,The distance clear area diagram corresponding to the four PRIs when the PRI group is [333.5,314,414.5,292.5]μs within the range of [30,175]km;

[0030] Figure 4 ,The speed clear area diagram corresponding to the four PRIs when the PRI group is [333.5,314,414.5,292.5]μs in the range of [10,220]m / s;

[0031] Figure 5 ,The range of interest is [30,175]km, and the PRI group is [10,220]m / s when the four PRIs are [333.5,314,414.5,292.5]μs. The distance-speed joint clear area diagram corresponding to the four PRIs is shown in Figure 1 (white is the clear area, black is the blind area);

[0032] Figure 6 , the range of interest is [30,175] km, and the PRI group is [333.5,314,414.5,292.5] μs when the PRI group is [10,220] m / s. The distance-speed clear area diagram after 3 / 4 criterion integration (white is the clear area, black is the blind area);

[0033] Figure 7 ,The range of interest is [30,175]km, and the distance-speed clear area corresponding to the optimal PRI of [10,220]m / s (white is the clear area and black is the blind area). DETAILED DESCRIPTION

[0034] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. A method for selecting a multi-pulse repetition frequency based on a clear area evaluation function has the following specific steps:

[0035] Step S1, initialize the PRI group and the slope control parameters, and set the learning rate and the maximum number of iterations in the optimization process.

[0036] Each PRI group includes 4 repetition frequencies, namely Use F r Indicates the group PRI, that is For the mth repetition frequency, the corresponding distance blind zone width Speed ​​blind zone width Maximum unambiguous distance and maximum unambiguous velocity Expressed as

[0037]

[0038]

[0039]

[0040]

[0041] Where c is the speed of light, is the pulse width corresponding to the mth repetition frequency, t0 is the time for transmitting and receiving, λ is the wavelength, CPI m is the coherent integration time corresponding to the mth repetition frequency, N m is the number of pulses corresponding to the mth repetition rate.

[0042] The range of distance blind zone and speed blind zone is specified as follows:

[0043]

[0044]

[0045] Step S2, obtaining the corresponding distance-speed clear zone function and clear zone area expression under the initial PRI group and initial inclination control parameters, and calculating the clear zone area under the initial PRI based on the obtained function, includes the following steps:

[0046] Step S21, calculate the initial PRI group and the corresponding distance-speed clear area function F under the initial tilt control parameter α RV (r,v).

[0047] The sigmoid function is used to approximate the distance-speed clear zone function. The sigmoid function is an activation function with a function value range of (0,1). It achieves a monotonic change from 0 to 1 near x = 0 and can approximate a step function. The expression of the sigmoid function is

[0048]

[0049] Among them, α controls the inclination of the sigmoid function near x=0. The images of the sigmoid function under different α are as follows: Figure 1 shown.

[0050] The derivative of the sigmoid function is expressed as

[0051]

[0052] The distance region of interest is defined as [R min ,R max ], and to facilitate the subsequent calculation of the clear area, the distance-speed clear area function within the range of the distance blind area should be approximately 0, and the value within the clear area should be approximately 1. Then the distance clear area function corresponding to the mth repetition frequency in the range of interest is Expressed as

[0053]

[0054] in, and Represents the left boundary of the region of interest R min and the right boundary R max The corresponding ambiguity is

[0055]

[0056]

[0057] in, Indicates rounding down.

[0058] The velocity region of interest is defined as [V min ,V max ], and to facilitate the subsequent calculation of the clear area, the value of the clear area function within the speed blind area should be approximately 0, and the value of the clear area function within the clear area should be approximately 1. Then the speed clear area function corresponding to the mth repetition frequency in the speed area of ​​interest is Expressed as

[0059]

[0060] in, and Represents the left boundary of the region of interest V min and right boundary V max The corresponding ambiguity is

[0061]

[0062]

[0063] in, Indicates rounding down.

[0064] When both the distance and velocity are in the clear zone, the point (r, v) is considered to be in the clear zone of the mth repetition frequency. Therefore, the distance-velocity joint clear zone function corresponding to the mth repetition frequency in the range-velocity region of interest is expressed as

[0065]

[0066] Because each repetition The value range of is (0,1), so we can It can be regarded as "the probability that the point (r, v) is in the clear area in the mth repetition frequency".

[0067] In order to improve the reliability of detection, the M / N criterion is used when evaluating the clear area of ​​the PRI group. The M / N criterion means that among N different PRIs, the target falls into the clear area in at least M PRIs, and then it is considered that the target also falls into the clear area of ​​the PRI group. In the present invention, N is taken as 4 and M is taken as 3. The clear area evaluation function F of the entire PRI group is: RV (r, v) can be regarded as the "probability that point (r, v) is in the clear zone under the M / N principle", so the clear zone evaluation function F is constructed from the probability perspective in combination with the M / N criterion. RV (r,v) is

[0068]

[0069] Step S22: according to the clear area function F RV (r, v), and get the clear area evaluation function expression S RV (T r ,α).

[0070] Since the clear area function F RV (r,v) is defined as the probability of being in the clear area. RV (r,v) is approximately 1, and F RV (r,v) is approximately 0, so the area ratio of the clear area can be obtained from F RV (r, v) is integrated in the region of interest, that is,

[0071]

[0072] Among them S all is the total area of ​​the range-velocity region of interest.

[0073] In order to facilitate S RV Perform calculations and divide the grid into the area of ​​interest for distance-velocity. When the grid is small enough, S RV Rewritten in summation form,

[0074]

[0075] Among them, N r and N v The number of grid divisions for distance and velocity within the region of interest, respectively.

[0076] Step S23, calculate the initial PRI group and α (0) The clear area under

[0077] The initial clear area is the area of and α (0) Bring it into S RV Calculate the expression and get

[0078] Step S3, using the gradient descent method to update the PRI group, includes the following steps:

[0079] Step S31, clear area expression S RV (T r ,α) Calculate the partial derivative of each PRI in the PRI group and form the gradient vector

[0080] Since the four PRI variables of the PRI group are symmetrical in function expression and have the same importance to the clear area, the clear area S RV (T r ,α) for T r The representation of partial derivatives for each PRI variable is the same.

[0081] Make the clear area S RV (T r ,α) for the mth repetition frequency Find the partial derivative, that is

[0082]

[0083] For convenience, let Then in the above formula Expressed as

[0084]

[0085] where, according to the definition of the derivative of the product, Expressed as

[0086]

[0087] According to the expressions of distance blind zone function and speed blind zone function, we can derive

[0088]

[0089]

[0090] Substituting the above formula into the equation, we can get the result of partial derivative of the clear area expression with respect to the mth PRI. Calculate the partial derivative of the clear area with respect to the four PRIs to form the gradient vector Right now

[0091]

[0092] Step S32, update the PRI group to

[0093] Define the learning rate in the gradient descent method as ∈, then the updated PRI group for

[0094]

[0095] Step S4, updating the inclination control parameters, includes the following steps:

[0096] Step S41, calculate

[0097] After updating step S3 and α (i-1) Substitute this into the clear area expression to calculate the clear area after updating the PRI group.

[0098] Step S42, update calculate

[0099] As the inclination control parameter α increases, the distance-speed clear zone evaluation function F RV The value of (r, v) near the edge of the blind area will become steeper, making the edge of the blind area sharper, and thus making the clear area S RV At the same time, considering that a large value of α will affect the gradient during the optimization process, it may make the optimization process unable to reach the optimal value, so the value of α is gradually increased during the optimization process, that is,

[0100]

[0101] Among them, k α is the update coefficient of the inclination control parameter, k α >1.

[0102] Will and Substitute into the clear area calculation formula, and we get

[0103] Step S43, compare and like Update Otherwise α (i) =α (i-1) .

[0104] During the update process of α, the updated α may not have a significant effect on the area of ​​the clear area, but greatly increase the gradient. This will cause the updated PRI group in the next iteration to deviate from the optimal PRI group. Therefore, it is necessary to The effect of increasing the clear area determines whether to update α. In view of the above problem, a threshold value Th is set S To measure the updated The effect of increasing the clear area is when updating The increase in the area of ​​the rear clear area exceeds the threshold value Th S , then the updated To effectively increase the clear area, the updated The value is updated for the next iteration. Otherwise, the updated The clear area cannot be effectively increased, and it may even cause the PRI of the next iteration to deviate further from the optimal PRI group. Therefore, the value before the update is retained for the next iteration, that is, α (i) =α (i-1) .

[0105] Step S5: updating the clear area after the current iteration of the PRI group and the tilt control parameters.

[0106] The clear area obtained after this iteration should be

[0107] In step S6, the stopping condition is determined based on the clear area. If the stopping condition is not met and the maximum number of iterations has not been reached, steps S3, S4, and S5 are repeated. If the stopping condition is met or the maximum number of iterations has been reached, the iteration is stopped and the final PRI group is output as the optimization result. The corresponding clear area is the optimal clear area.

[0108] Compare the clear area after this iteration The clear area after the last iteration If the difference between the two clear area areas is less than the set threshold ε0, that is,

[0109]

[0110] Or when the maximum number of iterations is reached, the iteration is stopped; otherwise, and α (i) Substitute into steps S3, S4, and S5 to perform the next iteration. Figure 2A flowchart for the implementation of this method is given.

[0111] The present invention provides the following examples to illustrate the inventive method:

[0112] The verification conditions of the embodiment provided by the present invention are shown in Table 1

[0113] Table 1 Implementation example verification conditions

[0114]

[0115] When the multi-pulse repetition frequency selection method based on the clear area evaluation function proposed in the present invention is used to select the optimal PRI group, the distance region of interest is set to [30, 175] km, the speed region of interest is set to [10, 220] m / s, and the initial PRI group is [333.5, 314, 414.5, 292.5] μs. Figure 3 、 Figure 4 and Figure 5 The distance clear area map, speed clear area map and distance-speed combined clear area map corresponding to the four PRIs in the initial PRI group in the region of interest are given respectively. The distance-speed clear area map of the initial PRI group after 3 / 4 criterion integration is shown as follows: Figure 6 As shown. In the initial PRI group and the initial tilt control parameter α (0) It can be seen that the initial smaller α (0) This leads to the blurring of the blind area edge, and in the subsequent optimization process, the blind area edge will be sharpened by updating α. Figure 7 The obtained distance-velocity clear zone map corresponding to the optimal PRI is [380.9720, 341.9046, 443.7465, 305.9888] μs, and the optimal clear zone area ratio is 95.43%. Under the same constraints, it is superior to the PRF optimization method based on the clear zone area evaluation matrix (the optimal clear zone ratio is 94.34%). The final results show that the method proposed by the present invention can break through the limitations of discrete and equal intervals of PRI group values ​​and the difficulty of expressing the objective function in functional form, and can achieve a more optimal clear zone area, which can effectively provide support for the selection of multiple PRFs for pulse Doppler radar.

[0116] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-pulse repetition frequency selection method based on a clear area evaluation function, characterized in that The steps of the method include: Step S1, initialize the PRI group and the inclination control parameters, and set the learning rate and the maximum number of iterations in the optimization process; Step S2, obtaining the corresponding distance-speed clear zone function and clear zone area expression under the initial PRI group and initial inclination control parameters, and calculating the clear zone area under the initial PRI accordingly; Step S3, updating the PRI group using the gradient descent method; Step S4, updating the inclination control parameters; Step S5, updating the clear area after the current iteration of the PRI group and the tilt control parameters; Step S6: Determine whether the stopping condition is met based on the clear area. If the stopping condition is not met and the maximum number of iterations has not been reached, repeat steps S3, S4, and S5. If the stopping condition is met or the maximum number of iterations is reached, the iteration stops and the final PRI group is output as the optimization result. The corresponding clear area is the optimal clear area. The step S2 comprises the following steps: Step S21, calculate the initial PRI group and initial tilt control parameters The corresponding distance-speed clear zone evaluation function under ; Step S22, based on the clear area evaluation function , we get the clear area evaluation function expression: ; Step S23, calculate the initial PRI group and The clear area under ; The step S3 comprises the following steps: Step S31, clear area expression Calculate the partial derivative of each PRI in the PRI group and form the gradient vector ; Step S32, update the PRI group to ; The step S4 comprises the following steps: Step S41, calculate ; Step S42, update ,calculate ; Step S43, compare and ,like , then update ,otherwise .

2. The method for selecting a multiple pulse repetition frequency based on a clear area evaluation function according to claim 1, wherein: In step S1, the range of the distance blind zone and the speed blind zone is specified as follows: 。 3. The method for selecting multiple pulse repetition frequencies based on a clear area evaluation function according to claim 2, wherein: In the step S21, The distance clearing function corresponding to the repetition frequency in the distance region of interest Expressed as ； in, and Represents the left boundary of the region of interest and right border The corresponding ambiguity is ； in, Indicates rounding down.

4. The method for selecting a multiple pulse repetition frequency based on a clear area evaluation function according to claim 3, wherein: In the step S21, The velocity clear area function corresponding to the repetition frequency in the velocity region of interest Expressed as ； in, and Represents the left boundary of the region of interest and right border The corresponding ambiguity is ； in, Indicates rounding down.

5. The method for selecting multiple pulse repetition frequencies based on a clear area evaluation function according to claim 4, wherein: In step S21, a clear area evaluation function is constructed from a probability perspective. for 。 6. The method for selecting multiple pulse repetition frequencies based on a clear area evaluation function according to claim 5, wherein: In step S22, due to the clear area function Defined as the probability of being in the clear zone, in the clear zone Approximately 1, within the blind area is approximately 0, so the area ratio of the clear area is given by Integrating over the region of interest yields ； in is the total area of ​​the range-velocity region of interest; Perform calculations and divide the distance-velocity region into grids; when the grid is small enough, Rewritten in summation form, ； in, and The number of grid divisions for distance and velocity within the region of interest, respectively.

7. The method for selecting multiple pulse repetition frequencies based on a clear area evaluation function according to claim 6, wherein: In step S31, the result constitutes the gradient vector The method is: make the clear area For the first repetition frequency Find the partial derivative, that is ； For convenience, let , then in the above formula Expressed as ； where, according to the definition of the derivative of the product, Expressed as ； According to the expressions of distance blind zone function and speed blind zone function, we can get ； ； Substituting the above formula into the equation, we can get the expression of the clear area for the first The result of partial derivative of PRI; calculate the result of partial derivative of the clear area with respect to the four PRIs respectively to form the gradient vector ,Right now 。 8. The method for selecting multiple pulse repetition frequencies based on a clear area evaluation function according to claim 7, wherein: In step S43, according to The effect of increasing the clear area determines whether to update The method is: set a threshold value To measure the updated The effect of increasing the clear area is when updating The increase in the area of ​​the rear clear area exceeds the threshold , then the updated To effectively increase the clear area, the updated The value is updated for the next iteration. Otherwise, the updated The clear area cannot be effectively increased, and it may even cause the PRI of the next iteration to deviate further from the optimal PRI group. Therefore, the value before the update is retained for the next iteration, that is, .

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