Ultra-low altitude trajectory optimization method, device, and medium based on proportional guidance rate correction

Abstract

The present application provides an ultra-low altitude trajectory optimization method, device, and medium based on proportional guidance rate correction. The method includes: determining the optimal interception angle in the environment; carrying out proportional guidance head law correction; optimizing and solving the proportional guidance correction coefficient; and calculating the adaptive correction proportional guidance coefficient through typical sample points. Compared with the traditional proportional guidance method, the present application improves the guidance law and adds constraints on the ultra-low altitude optimal interception angle. The optimization scheme does not add new variables and has high engineering feasibility. It is suitable for optimizing the guidance section of the trajectory of medium and long-range air defense missiles. The present application provides a new theoretical method and technical approach to solving the problems of ultra-low altitude trajectory design and improving the interception success rate.

Description

Technical Field

[0001] The present application relates to the field of trajectory optimization guidance control, and in particular to an ultra-low altitude trajectory optimization method, device, and medium based on proportional guidance rate correction. Background Art

[0002] Ultra-low-altitude penetration is one of the preferred means of air strikes in modern warfare. Ultra-low-altitude penetration targets fly close to the ground or skimming the sea, characterized by being "low, slow, and small," and they pose a primary threat to China's air defense system. The terminal guidance phase is crucial for determining the success rate of missile interception. The radar seeker activates after the mid- to terminal phase of an air defense missile's rotation. During this phase, the missile relies primarily on the radar seeker to guide its target. The seeker's detection performance is a crucial factor influencing the interception performance of ultra-low-altitude ballistic missiles. When the radar seeker is activated, strong coupled scattering occurs between the ultra-low-altitude target and the environment, generating image interference. This severely disrupts the seeker's detection and tracking performance, causing problems such as mid- to terminal phase anomalies, tracking errors, and target loss, leading to missile interception failures.

[0003] Traditional ballistics are designed to achieve rapid and effective target interception, with energy optimization as the design criterion. During ultra-low-altitude interception, numerous factors influence the missile's flight trajectory. These factors, in addition to ballistic capability, also relate to the guidance and control process, target motion patterns, and target characteristics. Therefore, multivariable and constraint-based trajectory optimization has become a crucial component of modern missile design, possessing significant significance and practical engineering value for improving missile flight quality to meet mission requirements. Trajectory optimization, in essence, involves solving the optimal control problem while satisfying various constraints, and is also a dynamic optimization problem. This invention proposes a technical approach for trajectory constraint and optimization design based on the optimal ultra-low-altitude detection and interception ground-grazing angle. By modifying the proportional guidance law coefficients during the mid- and terminal guidance phases of the missile, the air defense missile is loaded with the optimal intercept angle during ultra-low-altitude interception. This allows the radar seeker to actively suppress image signals at the optimal angle, improving the missile's detection and tracking performance and thus enhancing the missile's interception capability against ultra-low-altitude targets. Summary of the Invention

[0004] The purpose of this application is to provide a method, device, and medium for ultra-low altitude trajectory optimization based on proportional guidance rate correction, suitable for ultra-low altitude interception of medium- and long-range ballistic missiles. The method proposes a technical route for trajectory constraint and optimization design based on the optimal ultra-low altitude detection and interception ground-grazing angle as a criterion. The method corrects the proportional guidance law coefficients during the mid- to terminal guidance phase of the missile guidance, so that the optimal interception angle is loaded during the ultra-low altitude interception of the air defense missile. This allows the radar seeker to actively suppress the image at the optimal angle, improving the detection and tracking performance of the missile's radar seeker, thereby enhancing the missile's ability to intercept ultra-low altitude targets. Compared with traditional proportional guidance methods, when improving the guidance law, the guidance system needs to measure parameters such as target range, speed, and direction. The addition of these parameters also introduces interference signals, placing higher demands on the guidance system. However, the correction scheme does not add new variables and is highly feasible in engineering.

[0005] The technical solutions adopted in this application are as follows:

[0006] According to the first aspect of the present application, a method for optimizing ultra-low altitude trajectory based on proportional guidance rate correction is provided, the method comprising: determining the optimal interception angle in the environment; carrying out proportional guidance head law correction; optimizing and solving the proportional guidance correction coefficient; and calculating the adaptive correction proportional guidance coefficient through typical sample points.

[0007] According to the second aspect of the present application, an ultra-low altitude trajectory optimization device based on proportional guidance rate correction is provided, the device comprising: a determination module configured to determine the optimal interception angle of the environment; a correction module configured to carry out proportional guidance head law correction; an optimization module configured to optimize and solve the proportional guidance correction coefficient; and a calculation module configured to calculate the adaptively corrected proportional guidance coefficient through typical sample points.

[0008] According to the third aspect of the present application, a computer-readable storage medium is provided, on which computer-readable instructions are stored. When the computer-readable instructions are executed by a processor of a computer, the computer executes the ultra-low altitude trajectory optimization method based on proportional guidance rate correction described in each embodiment of the present application.

[0009] This application has at least the following technical effects:

[0010] The ultra-low-altitude trajectory optimization method, device, and medium based on proportional guidance rate correction provided in the embodiments of this application improve upon the traditional proportional guidance method by adding constraints on the optimal ultra-low-altitude interception angle. The optimization scheme does not introduce new variables, resulting in high engineering feasibility and suitability for optimizing the mid-range guidance phase of medium- and long-range air defense missile trajectories. This application provides a new theoretical method and technical approach for solving the problems of ultra-low-altitude trajectory design and improving interception success rates. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and it is clear that a person of ordinary skill in the art can derive other drawings based on these drawings without inventive effort.

[0012] Figure 1 This is a technical roadmap for an ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to an embodiment of the present application;

[0013] Figure 2 This is an overall flow chart of the ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to an embodiment of the present application;

[0014] Figure 3a is the effect of environment type on the mirror scattering characteristics;

[0015] Figure 3b is the effect of roughness on the mirror scattering properties;

[0016] Figure 4a is the trajectory change diagram of working condition 1;

[0017] Figure 4b This is the interception and rubbing angle variation diagram of working condition 1;

[0018] Figure 5a This is the trajectory change diagram of working condition 2;

[0019] Figure 5b This is the interception and rubbing angle variation diagram for working condition 2;

[0020] Figure 6 It is a structural diagram of the ultra-low altitude trajectory optimization device based on proportional guidance rate correction in an embodiment of the present application. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application. That is, the embodiments described herein are only some embodiments of this application, not all embodiments. Generally, the components of the embodiments of this application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0022] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making any creative efforts shall fall within the scope of protection of the present application.

[0023] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0024] like Figure 1 and Figure 2 As shown, Figure 1 It is a technical roadmap of the ultra-low altitude trajectory optimization method based on proportional guidance rate correction in an embodiment of the present application. Figure 1 Where K is the proportional coefficient, x1 is the target height, x2 is the target speed, x3 is the optimal interception angle, x4 is the initial distance between the projectile and the target, and q is the projectile-target line of sight angle. Figure 2 This is an overall flow chart of an ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to an embodiment of the present application. This embodiment of the present application provides an ultra-low altitude trajectory optimization method based on proportional guidance rate correction, the method comprising:

[0025] Step S100, determining the optimal interception angle of the environment;

[0026] Step S200, performing proportional guidance head law correction;

[0027] Step S300, optimizing and solving the proportional guidance correction coefficient;

[0028] Step S400: Calculate the adaptive modified proportional steering coefficient using typical sample points.

[0029] The following will expand on the above four steps to explain in detail the principles of the method provided in the embodiments of the present application.

[0030] The first step is to determine the optimal interception angle of the environment.

[0031] The optimal interception angle is mainly based on the Brewster effect of the mirror, that is, the radar illumination angle with the minimum mirror. Electromagnetic calculation is used to obtain the Brewster angle under different environmental types and environmental parameters. The results of Brewster angle changes with environmental type and roughness parameters are as follows: Figure 3a and Figure 3b As shown, Figure 3a shows the effect of environment type on the mirror scattering characteristics, Figure 3b The effect of roughness on the mirror scattering properties is shown.

[0032] During specific implementation, the corresponding Brewster angle is selected according to the corresponding environmental conditions and determined as the optimal interception angle.

[0033] The second step is to correct the proportional guidance law.

[0034] Based on the traditional proportional guidance law, a compensation is introduced to make corrections so that the sight angle of the guided missile is adjusted and maintained near the optimal interception angle. The corrected guidance relationship can be written as:

[0035]

[0036] Among them, θ is the target grazing angle, q is the sight angle of the missile, K is the proportional coefficient, f is the guidance rate compensation, K f is the corrected proportional guidance coefficient, and x is the correction value. The key lies in determining the form of the correction value x. The above-mentioned method of correcting the guidance law is achieved by introducing a correction term, so the correction value x must include the expected value of the optimal intercept angle.

[0037] In order to satisfy the requirement of smooth transition and take into account the overload constraint, the correction value x is designed in sections. The empirical formula is:

[0038]

[0039] Where, is the first-order derivative of the sight angle between the missile and the target, R n is the missile-target distance when the seeker is turned on, R is the missile-target distance, and the constant R Mid It is the distance between the characteristic point where the target intercept angle is expected to be reached after the turn is completed.

[0040] Combining (1) and (2), we have

[0041]

[0042]

[0043]

[0044]

[0045] in is an intermediate derivation variable, and the parameter Kx is the correction proportional coefficient, which is a dimensionless number. It is related to the state and target characteristics at the time of launch and can be expressed as the following relationship:

[0046] K x =f(q B ,R0,MaT ,H T ) (7)

[0047] The third step is to optimize and solve the proportional guidance correction coefficient.

[0048] By establishing the response surface model, according to R0, Ma T 、H T ,q B The four parameters are expanded as power functions, and the expansion coefficients to be determined are determined by optimization calculation. The response surface model is an optimization method that combines experimental design with mathematical statistics. When the functional relationship between the test results and the known parameters is implicit, the response surface method can be used to design the relationship between the test results and the parameter variables, and conduct continuous experiments on the specified set of design points based on experimental measurements or numerical analysis to obtain the coefficients of the parameter variables. Finally, a functional relationship between the response and the parameter variables is established, and then optimization is performed on this basis. Let q B =x1, R0=x2, M aT =x3、H T =x4,

[0049] Then formula (7) can be written as:

[0050] K x =f(x1,x2,x3,x4) (8)

[0051] A set of simple elementary functions is selected to construct a regression response model to simulate the true function Kx, which is convenient for further operation. Let the generalized model expression be:

[0052] K x =c1X1(x1,x2,x3,x4)+c2X2(x1,x2,x3,x4)+....+c m X m (x1,x2,x3,x4)+ε (9)

[0053] Where ε is the statistical error, which is generally assumed to satisfy the normal distribution with mean zero, that is, E(ε) = 0, so it has no relationship with the free variable; X = (X1, X2, ...., X m ) is the basis function, m is the number of expansion terms. ; c=(c1,c2,...,c m ) are m undetermined coefficients. Using a second-order polynomial as the response surface model (n = 2), the basis function and equation (10) become:

[0054]

[0055]

[0056] Keeping the constant term, first-order term, and second-order square term, and discarding the second-order cross term, the above formula becomes:

[0057]

[0058] The least squares method is used to solve the parameters and the second-order model is transformed into a first-order linear model. Let:

[0059]

[0060] And readjust the coefficient numbers, then transform Equation (11) into a linear model, namely:

[0061] K x =c0+c1x1+c2x2+c3x3+c4x4

[0062] +c5x5+c6x6+c7x7+c8x8

[0063] +c9x9+c 10 x 10 +c 11 x 11 +c 12 x 12 +c 13 x 13 +c 14 x 14 +ε(14)

[0064] Select n s A set of sample points to conduct the experiment (n s ≥15), and then determine the size of the value.

[0065] The fourth step is to calculate the adaptive correction proportional guidance coefficient through typical sample points.

[0066] According to the missile's operating envelope, analyze the sensitive parameters that affect it, determine the optimization conditions and sample points, and use them as the data basis for optimization. For the determined sample points, conduct trajectory simulation, analyze the flight trajectory under different parameter changes, conduct comparisons and analyses, and extract the best design parameters. Assume that the total number of tests is n s , for convenience, the response surface model can be expressed in the following matrix form:

[0067] K x =Xc+ε(15)Usually K x ,ε is (n s ×1)-dimensional vector, X is n s ×15-dimensional matrix, c is a 15-dimensional vector, that is:

[0068]

[0069]

[0070] c=(c0,c1,...,c 14 ) T (18)

[0071] ε=(ε0,ε1,...,ε 14 ) T (19)

[0072] The least squares estimate c obtained by solving the problem satisfies the following minimum:

[0073]

[0074] Expand the above formula:

[0075] L=K x T K x -c T X T K x -K x T Xc+c T X T Xc (21)

[0076] Analyzing the above formula, cTXTKx is a (lxl) matrix or a scalar, so its transpose also has the same properties, then formula (21) is simplified to:

[0077] L=K x T K x -2c T X T K x +c T K x T Xc (22)

[0078] Choose a suitable vector c to minimize L, then take the derivative of L with respect to c, and the vector c that makes the derivative zero is the desired vector.

[0079] Simplified to:

[0080]

[0081] X T Xc * =X T K x (twenty four)

[0082] Then the required parameter c * for:

[0083] c * =(XT X) -1 X T K x (25)

[0084] The covariance matrix of the coefficients obtained by the least squares method is:

[0085] cov(c i ,c j )=σ 2 (X T X) -1 (26)

[0086] It is necessary to select appropriate samples based on the trajectory design indicators and adopt certain criteria to reduce the covariance of the coefficients. The response surface model is obtained and response surface analysis is performed based on the covariance. If the response model does not meet the accuracy requirements, it needs to be redesigned.

[0087] Based on the requirements for intercepting ultra-low-altitude targets, the parameter ranges for optimizing the mid-range guidance phase ultra-low-altitude trajectory are: initial missile-target distance 7–20 km; target velocity range 5–300 m / s; and target altitude range 5–100 m. Within this flight envelope, a design and optimization scheme was conducted with the goal of meeting the optimal interception angle constraint at a missile-target distance of 5.5 km. The optimal interception angle ranged from 7 to 40 degrees. A segmented modeling approach was employed to achieve higher model accuracy within a smaller parameter range and reduce error. Through multiple rounds of iterative calculations, the optimal interception angle range was divided into three segments: 7–15 degrees, 15–25 degrees, and 25–40 degrees. A second-order coupled response surface model was constructed. Based on mathematical calculations of the sample points, the coefficients of the three-segment model are shown in Table 1.

[0088] Table 1 Response surface parameters

[0089]

[0090] The embodiments of the present application provide new theoretical methods and technical approaches for solving the problems of scattering calculation and echo modeling of sea-skimming targets in actual electromagnetic multi-scale ocean environments. Specifically, based on the electromagnetic scattering mechanism of sea-skimming targets in the radar seeker's field of view, an electromagnetic scattering modeling and calculation method is used to perform electromagnetic scattering calculations and simulate the generation of seeker echoes at each moment of ballistic propulsion during high-dynamic seeker motion. After seeker signal processing, target detection, and information resolution, the target's real-time range, velocity, and angular deviation information are obtained and transmitted to the guidance control to drive ballistic propulsion, and the above simulation process is repeated. This achieves real-time closed-loop simulation of the echo characteristics of sea-skimming targets detected and tracked after the terminal guidance phase of an air defense missile is powered on during high-dynamic ballistic flight.

[0091] The following examples of the present application will implement this method under different working conditions to further illustrate the feasibility and progress of the present application.

[0092] Condition 1: The target's flight speed is Ma0.2, the flight altitude is 30 meters, and the initial distance between the projectile and the target is 12 km. The target's ground contact angle is required to reach 14 degrees when the target is 5.5 km away. Based on the response surface model and the model coefficients given in Table 1, and their applicable angle range, the correction parameter Kx = 4.5905 is calculated. The trajectory simulation is performed based on the above calculation parameters, as shown in the following example: Figure 4a and Figure 4b shown. Figure 4a The trajectory changes of working condition 1 are shown. Figure 4b The figure shows the variation of interception ground-grazing angle for working condition 1. The results show that the calculated ground-grazing angle at a missile-target distance of 5.5 km is 14.18 degrees, which is close to the expected angle value.

[0093] Condition 2: The target's flight speed is Ma0.1, the flight altitude is 30 meters, and the initial distance between the projectile and the target is 14 km. The target's ground contact angle is required to reach 25 degrees when the target is 5.5 km away. Based on the response surface model and the model coefficients given in Table 1, and their applicable angle range, the correction parameter Kx = 0.1025 is calculated. The trajectory simulation is performed based on the parameters calculated for Condition 2. Figure 5a and Figure 5b shown. Figure 5a The trajectory changes of working condition 2 are shown. Figure 5b The figure shows the variation of interception ground-grazing angle for working condition 2. The results show that the calculated ground-grazing angle at a distance of 5.5 km is 24.83 degrees, which is close to the expected angle value with an error of only 0.17 degrees.

[0094] Based on the established trajectory design method and optimization design criteria, this example conducts modeling and parameter optimization to meet the optimal interception angle constraint. A response surface model for guidance law modification is developed for different trajectory characteristics, and trajectory simulation and verification under typical operating conditions are conducted. The results demonstrate that the proposed method can achieve the optimal interception angle constraint through parameter modification, demonstrating the feasibility of the design method.

[0095] like Figure 6 , is a structural diagram of an ultra-low altitude trajectory optimization device based on proportional guidance rate correction according to an embodiment of the present application. The present application also provides an ultra-low altitude trajectory optimization device based on proportional guidance rate correction, the device 600 comprising:

[0096] A determination module 601 is configured to determine an optimal interception angle for an environment;

[0097] A correction module 602 is configured to perform proportional seeker law correction;

[0098] An optimization module 603 is configured to optimize and solve a proportional guidance correction coefficient;

[0099] The calculation module 604 is configured to calculate the adaptive modified proportional steering coefficient through typical sample points.

[0100] In some embodiments, the correction module is further configured to:

[0101] Based on the traditional proportional guidance law, a compensation amount is introduced for correction. The corrected guidance relationship is:

[0102]

[0103] Where x is the correction value, θ is the target rubbing angle, q is the sight angle between the missile and the target, K is the proportional coefficient, f is the guidance rate compensation, K f is the corrected proportional guidance coefficient;

[0104] The correction value x is designed in sections, and the empirical formula is:

[0105]

[0106] in is the first-order derivative of the sight angle between the missile and the target, R n is the missile-target distance when the seeker is turned on, R is the missile-target distance, and R Mid is a constant, which represents the distance between the characteristic point at which the target intercept angle is expected to be reached after the turn is completed;

[0107] Combining equations (1) and (2), we get:

[0108]

[0109]

[0110]

[0111]

[0112] in is the intermediate derivation variable, K x is the correction coefficient, which is a dimensionless number. It is related to the state and target characteristics at the time of launch and is expressed as the following relationship:

[0113] K x =f(q B ,R0,M aT ,H T ) (7)

[0114] Where R0 is the distance between the missile and the target at the time of launch; Ma Tis the target flight Mach number; H T is the target's flight altitude; q B At a specific distance R n The optimal interception angle required to be achieved.

[0115] In some embodiments, the optimization module is further configured to

[0116] Establish response surface model, according to R0, Ma T 、H T ,q B The four parameters are expanded by power functions, and the expansion coefficients to be determined are determined by optimization calculation;

[0117] Let q B =x1, R0=x2, M aT =x3、H T =x4, then formula (7) is written as:

[0118] K x =f(x1,x2,x3,x4) (8)

[0119] Select a set of simple elementary functions to construct a regression response model to simulate the true function Kx. Let the generalized model expression be:

[0120] K x =c1X1(x1,x2,x3,x4)+c2X2(x1,x2,x3,x4)+....+c m X m (x1,x2,x3,x4)+ε (9)

[0121] Where ε is the statistical error, assuming it satisfies the normal distribution with mean zero, that is, E(ε) = 0, so that it has no relationship with the free variable; X = (X1, X2, ...., X m ) is the basis function, m is the number of expansion terms, c=(c1,c2,...,c m ) are m undetermined coefficients, and a second-order polynomial is used as the response surface model (n=2). The basis function and formula (9) become:

[0122]

[0123]

[0124] Retaining the constant term, first-order term, and second-order square term in formula (11), and discarding the second-order cross term, formula (11) becomes:

[0125]

[0126] make:

[0127]

[0128] And readjust the coefficient numbers, then transform Equation (11) into a linear model, namely:

[0129] K x =c0+c1x1+c2x2+c3x3+c4x4

[0130] +c5x5+c6x6+c7x7+c8x8

[0131] +c9x9+c 10 x 10 +c 11 x 11 +c 12 x 12 +c 13 x 13 +c 14 x 14 +ε (14)

[0132] Select at least 15 groups of sample points for testing to determine the value.

[0133] In some embodiments, the computing module is further configured to:

[0134] The response surface model is expressed in matrix form as:

[0135] K x =Xc+ε(15)where K x ,ε is (n s ×1)-dimensional vector, X is n s ×15-dimensional matrix, c is a 15-dimensional vector, that is:

[0136]

[0137]

[0138] c=(c0,c1,...,c 14 ) T (18)

[0139] ε=(ε0,ε1,...,ε 14 ) T (19)

[0140] The least squares estimate c obtained by solving the problem satisfies the following minimum:

[0141]

[0142] Expanding formula (20) yields:

[0143] L=K x T K x -c T X T K x -K x T Xc+c T X T Xc (21)

[0144] Analyze formula (21), c T X T K x is an lxl matrix or a scalar, so its transpose also has the same properties, then Equation (21) is simplified to:

[0145] L=K x T K x -2c T X T K x +c T K x T Xc (22)

[0146] Take the derivative of L with respect to c, and the vector c that makes the derivative zero is the desired vector:

[0147]

[0148] Simplify formula (23) to:

[0149] X T Xc * =X T K x (twenty four)

[0150] Then the required parameter c * for:

[0151] c * =(X T X) -1 X T K x (25)

[0152] The covariance matrix of the coefficients obtained by the least squares method is:

[0153] cov(c i ,c j )=σ 2 (X T X) -1 (26)

[0154] According to the preset criteria, appropriate samples are selected to reduce the covariance of the coefficients, the response surface model is obtained and response surface analysis is performed based on the covariance until the response model meets the accuracy requirements.

[0155] It should be noted that the modules described in the embodiments of the present application may be implemented in software or hardware, and the modules described may also be provided in a processor. In some cases, the names of these modules do not constitute limitations on the modules themselves.

[0156] The present application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the ultra-low-altitude trajectory optimization method based on proportional guidance rate correction as described in the preceding embodiments. The computer-readable storage medium may be included in the electronic device described in the preceding embodiments, or may exist independently and not be incorporated into the electronic device.

[0157] It should be noted that the computer-readable medium shown in the embodiments of the present application can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium can be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, which carries a computer-readable computer program. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. A computer program embodied on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, or any suitable combination thereof.

[0158] The above content is only a preferred exemplary embodiment of the present application and is not intended to limit the implementation scheme of the present application. Ordinary technicians in this field can easily make corresponding changes or modifications based on the main ideas and spirit of the present application. Therefore, the scope of protection of the present application shall be based on the scope of protection required by the claims.

Claims

1. An ultra-low altitude trajectory optimization method based on proportional guidance rate correction, characterized by: The method comprises: Determine the optimal interception angle for the environment; Carry out proportional guidance seeker law correction; Optimize and solve the proportional guidance correction coefficient; Calculate the adaptive correction proportional guidance coefficient through typical sample points; The performing of proportional guidance head law correction specifically includes: Based on the traditional proportional guidance law, a compensation amount is introduced for correction. The corrected guidance relationship is: Where x is the correction value, θ is the target rubbing angle, q is the sight angle between the missile and the target, K is the proportional coefficient, f is the guidance rate compensation, K f is the corrected proportional guidance coefficient; The correction value x is designed in sections, and the empirical formula is: in is the first-order derivative of the sight angle between the missile and the target, R n is the missile-target distance when the seeker is turned on, R is the missile-target distance, and R Mid is a constant, which represents the distance between the characteristic point at which the target intercept angle is expected to be reached after the turn is completed; Combining equations (1) and (2), we get: in is the intermediate derivation variable, K x is the correction coefficient, which is a dimensionless number. It is related to the state and target characteristics at the time of launch and is expressed as the following relationship: K x =f(q B ,R0,M aT ,H T ) (7) Where R0 is the distance between the missile and the target at the time of launch; Ma T is the target flight Mach number; H T is the target's flight altitude; q B At a specific missile-target distance R n The optimal interception angle required to be achieved.

2. The ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to claim 1 is characterized in that: Determining the optimal interception angle of the environment specifically includes: Based on the radar illumination angle that minimizes the multipath scattering coefficient of the image, electromagnetic calculation is used to obtain the Brewster angle under different environmental types and parameters. The corresponding Brewster angle is selected according to the corresponding environmental conditions and determined as the optimal interception angle.

3. The ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to claim 1 is characterized in that: The optimization solution of the proportional guidance correction coefficient specifically includes: Establish response surface model, according to R0, Ma T 、H T ,q B The four parameters are expanded by power functions, and the expansion coefficients to be determined are determined by optimization calculation; Let q B =x1, R0=x2, M aT =x3、H T =x4, then formula (7) is written as: K x =f(x1,x2,x3,x4) (8) Select a set of simple elementary functions to construct a regression response model to simulate the true function Kx. Let the generalized model expression be: K x =c1X1(x1,x2,x3,x4)+c2X2(x1,x2,x3,x4)+....+c m X m (x1,x2,x3,x4)+ε (9) Where ε is the statistical error, assuming it satisfies the normal distribution with mean zero, that is, E(ε) = 0, so that it has no relationship with the free variable; X = (X1, X2, ...., X m ) is the basis function, m is the number of expansion terms, c=(c1,c2,...,c m ) are m undetermined coefficients, and a second-order polynomial is used as the response surface model (n=2). The basis function and formula (9) become: Retaining the constant term, first-order term, and second-order square term in formula (11), and discarding the second-order cross term, formula (11) becomes: make: And readjust the coefficient numbers, then transform Equation (11) into a linear model, namely: K x =c0+c1x1+c2x2+c3x3+c4x4 +c5x5+c6x6+c7x7+c8x8 +c9x9+c 10 x 10 +c 11 x 11 +c 12 x 12 +c 13 x 13 +c 14 x 14 +ε(14) Select at least 15 groups of sample points for testing to determine the value.

4. The ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to claim 3 is characterized in that: The calculation of the adaptive correction proportional guidance coefficient using typical sample points specifically includes: The response surface model is expressed in matrix form as: K x =Xc+ε(15)where K x ,ε is (n s ×1)-dimensional vector, X is n s ×15-dimensional matrix, c is a 15-dimensional vector, that is: c=(c0,c1,...,c 14 ) T (18) ε=(ε0,ε1,...,ε 14 ) T (19) The least squares estimate c obtained by solving the problem satisfies the following minimum: Expanding formula (20) yields: L=K x T K x -c T X T K x -K x T Xc+c T X T Xc (21) Analyze formula (21), c T X T K x is an lxl matrix or a scalar, so its transpose also has the same properties, then Equation (21) is simplified to: L=K x T K x -2c T X T K x +c T K x T Xc (22) Take the derivative of L with respect to c, and the vector c that makes the derivative zero is the desired vector: Simplify formula (23) to: X T Xc * =X T K x (24) Then the required parameter c * for: c * =(X T X) -1 X T K x (25) The covariance matrix of the coefficients obtained by the least squares method is: those(c i ,c j )=σ 2 (X T X) -1 (26) According to the preset criteria, appropriate samples are selected to reduce the covariance of the coefficients, the response surface model is obtained and response surface analysis is performed based on the covariance until the response model meets the accuracy requirements.

5. An ultra-low altitude trajectory optimization device based on proportional guidance rate correction, characterized by: The device comprises: a determination module configured to determine an environmentally optimal interception angle; a correction module configured to perform proportional seeker law correction; An optimization module is configured to optimize and solve a proportional guidance correction coefficient; a calculation module configured to calculate an adaptive modified proportional guidance coefficient through typical sample points; The correction module is further configured to: Based on the traditional proportional guidance law, a compensation amount is introduced for correction. The corrected guidance relationship is: Where x is the correction value, θ is the target rubbing angle, q is the sight angle between the missile and the target, K is the proportional coefficient, f is the guidance rate compensation, K f is the corrected proportional guidance coefficient; The correction value x is designed in sections, and the empirical formula is: in is the first-order derivative of the sight angle between the missile and the target, R n is the missile-target distance when the seeker is turned on, R is the missile-target distance, and R Mid is a constant, which represents the distance between the characteristic point at which the target intercept angle is expected to be reached after the turn is completed; Combining equations (1) and (2), we get: in is the intermediate derivation variable, K x is the correction coefficient, which is a dimensionless number. It is related to the state and target characteristics at the time of launch and is expressed as the following relationship: K x =f(q B ,R0,M aT ,H T ) (7) Where R0 is the distance between the missile and the target at the time of launch; Ma T is the target flight Mach number; H T is the target's flight altitude; q B At a specific missile-target distance R n The optimal interception angle required to be achieved.

6. The ultra-low altitude trajectory optimization device based on proportional guidance rate correction according to claim 5 is characterized in that: The optimization module is further configured to Establish response surface model, according to R0, Ma T 、H T ,q B The four parameters are expanded by power functions, and the expansion coefficients to be determined are determined by optimization calculation; Let q B =x1, R0=x2, M aT =x3、H T =x4, then formula (7) is written as: K x =f(x1,x2,x3,x4) (8) Select a set of simple elementary functions to construct a regression response model to simulate the true function Kx. Let the generalized model expression be: K x =c1X1(x1,x2,x3,x4)+c2X2(x1,x2,x3,x4)+....+c m X m (x1,x2,x3,x4)+ε (9) Where ε is the statistical error, assuming it satisfies the normal distribution with mean zero, that is, E(ε) = 0, so that it has no relationship with the free variable; X = (X1, X2, ...., X m ) is the basis function, m is the number of expansion terms, c=(c1,c2,...,c m ) are m undetermined coefficients, and a second-order polynomial is used as the response surface model (n=2). The basis function and formula (9) become: Retaining the constant term, first-order term, and second-order square term in formula (11), and discarding the second-order cross term, formula (11) becomes: make: And readjust the coefficient numbers, then transform Equation (11) into a linear model, namely: K x =c0+c1x1+c2x2+c3x3+c4x4 +c5x5+c6x6+c7x7+c8x8 +c9x9+c 10 x 10 +c 11 x 11 +c 12 x 12 +c 13 x 13 +c 14 x 14 +ε(14) Select at least 15 groups of sample points for testing to determine the value.

7. The ultra-low altitude trajectory optimization device based on proportional guidance rate correction according to claim 6 is characterized in that: The computing module is further configured to: The response surface model is expressed in matrix form as: K x =Xc+ε(15)where K x ,ε is (n s ×1)-dimensional vector, X is n s ×15-dimensional matrix, c is a 15-dimensional vector, that is: The least squares estimate c obtained by solving the problem satisfies the following minimum: Expanding formula (20) yields: L=K x T K x -c T X T K x -K x T Xc+c T X T Xc (21) Analyze formula (21), c T X T K x is an lxl matrix or a scalar, so its transpose also has the same properties, then Equation (21) is simplified to: L=K x T K x -2c T X T K x +c T K x T Xc (22) Take the derivative of L with respect to c, and the vector c that makes the derivative zero is the desired vector: Simplify formula (23) to: X T Xc * =X T K x (24) Then the required parameter c * for: c * =(X T X) -1 X T K x (25) The covariance matrix of the coefficients obtained by the least squares method is: those(c i ,c j )=σ 2 (X T X) -1 (26) According to the preset criteria, appropriate samples are selected to reduce the covariance of the coefficients, the response surface model is obtained and response surface analysis is performed based on the covariance until the response model meets the accuracy requirements.

8. A computer-readable storage medium, characterized in that: Computer-readable instructions are stored thereon, and when the computer-readable instructions are executed by a processor of a computer, the computer is caused to execute the ultra-low altitude trajectory optimization method based on proportional guidance rate correction according to any one of claims 1 to 4.

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