Method for calculating detected probability of penetration aircraft based on three-coordinate radar reverse modeling

Abstract

The invention provides a three-coordinate radar reverse modeling-based penetration aircraft detected probability calculation method, relates to the technical field of three-coordinate radar reverse modeling, and provides a multipath propagation factor dynamic correction model and an adaptive clutter suppression method through reverse modeling ship-borne radar power distribution characteristics and an environment coupling effect. And the calculation precision of the detection probability in a complex electromagnetic environment is improved. Based on a directional diagram propagation factor quantization radar wave attenuation law, and in combination with a sub-beam system constant inversion technology, the dependence of a traditional model on confidential parameters is broken through, and high-reliability simulation based on public parameters is realized. Through pre-generation of a typical scene database and cubic spline interpolation, dynamic response of a penetration strategy is supported, a multi-radar networking cooperative detection correction model is introduced, and a global detection blind area is identified.

Description

Technical Field

[0001] The present invention relates to the technical field of reverse modeling of three - coordinate radars, and specifically to a method for calculating the detection probability of a penetration aircraft based on reverse modeling of three - coordinate radars. Background Art

[0002] In the offensive - defensive simulation of radar against stealth penetration aircraft, existing methods usually rely on the single - beam radar equation, ignoring the influence of the interaction between electromagnetic waves and the environment (such as multipath interference, earth diffraction) and complex interferences (sea clutter, chaff) on the detection probability. Especially in the low - altitude penetration scenario, the penetration aircraft is long - term within the first elevation beam of the radar. Due to the traditional model not quantifying the pattern propagation factor and the dynamic power distribution effect, the deviation of the detection probability assessment is significant.

[0003] In the prior art, the publication number CN114781190A discloses a method and device for simulating radar detection capabilities. Specifically: grid the plane of a preset altitude layer to obtain multiple grid points; take all grid points that the radar can detect as targets; calculate the target echo power based on the total radar cross - section area and the pattern propagation factor of each target; calculate the total interference power of several jammers on the radar according to the three - dimensional pattern of the radar antenna; subtract the radar receiver noise and the total interference power from the target echo power to obtain the radar signal - to - noise ratio of the target; if the radar signal - to - noise ratio of the target is greater than the radar receiving sensitivity, it is determined that the radar can detect the target in the interference environment; plot the radar signal - to - noise ratios of all targets in the preset altitude layer to obtain the radar power coverage map of the preset altitude layer. Although it can achieve radar detection simulation, it does not dynamically quantify the multipath attenuation and clutter interference effects, relies on geometric decomposition to simplify the RCS calculation, ignores power distribution and adaptive filter design, resulting in insufficient accuracy of detection probability assessment in complex environments, and lacks the ability of multi - radar collaborative correction. In addition, it depends on complete radar parameters (such as system loss, noise temperature), making it difficult to adapt to the confidentiality parameter limitations of foreign active radars, and the clutter suppression model mostly uses fixed filter design, unable to dynamically respond to complex sea conditions and interference environments. These problems lead to low credibility and poor real - time performance of the simulation results, and it is difficult to support the stealth optimization and flight path planning of penetration aircraft.

[0004] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present disclosure, so it may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the detection probability of a penetration aircraft based on reverse modeling of three - coordinate radars to solve the problems raised in the above - mentioned background art.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three - coordinate radar, the specific steps include:

[0008] S1: Collect the beam parameters, operating parameters, antenna size, and operating wavelength of the radar, and construct the antenna pattern;

[0009] S2: Calculate the maximum detection range of the radar based on the search radar equation, and construct an ideal radar vertical power diagram in free space by combining the antenna pattern and the radar altitude;

[0010] S3: Calculate the system constant of each radar beam based on the beam parameters through the power resource allocation principle;

[0011] S4: Calculate the pattern propagation factor based on the antenna pattern, detection target parameters, environmental parameters, and beam parameters to quantify the attenuation and interference of the radar wave propagation path;

[0012] S5: Based on the system constant, pattern propagation factor, and real - time interference conditions, use a preset detection model to output the detection probability of the penetration aircraft under the corresponding interference conditions, and generate a visualization curve of the detection probability varying with distance.

[0013] Preferably, in the step S1, the Taylor synthesis method is used to construct the antenna pattern, and its expression is:

[0014]

[0015] In the formula, θ and λ respectively represent the elevation angle of the radar ray and the operating wavelength, F(θ) represents the radiation intensity of the radar at the elevation angle θ of the ray, J1(·) represents the first - order Bessel function, D represents the diameter of the radar antenna aperture, u n represents an intermediate parameter, the subscript n represents the term number index of the Taylor distribution, and N represents the total number of terms of the Taylor distribution;

[0016] Among them, the calculation method of the intermediate parameter u n is:

[0017]

[0018] In the formula, A represents the control parameter of the sidelobe level, and σ represents the beam broadening coefficient.

[0019] Preferably, in the step S2, when constructing the ideal radar vertical power diagram, the calculation method of the maximum detection range is:

[0020]

[0021] In the formula, R mrepresents the maximum detection range, P av , T s , L s , A r , D0(1) represent the average power of the radar, the noise temperature, the system loss, the aperture area of the receiving antenna, and the minimum detectable factor of a single pulse for the detected target respectively, t s represents the frame time, ψ s represents the solid angle of the search airspace, σ t0 represents the radar cross section of the detected target, k B represents the Boltzmann constant;

[0022] Among them, the calculation methods of the aperture area of the receiving antenna and the solid angle of the search airspace are respectively:

[0023]

[0024] In the formula, η a represents the aperture efficiency, θ a , θ b , N b represent the azimuth beam width and the elevation beam width in the radar beam respectively, N b represents the total number of beams.

[0025] Preferably, in the step S3, the calculation method of each radar beam system constant is:

[0026]

[0027] In the formula represents the system constant of the k-th group of radar beams, and the superscript k represents the index of the radar beam, represents the peak power when the radar emits the k-th group of radar beams, represent the main lobe gains of the radar transmitting antenna and the receiving antenna when emitting the k-th group of radar beams respectively, represents the system loss when the radar emits the k-th group of radar beams, the noise temperature when the radar emits the k-th group of radar beams.

[0028] Preferably, in the step S4, the pattern propagation factor adopts different calculation methods according to the type of the detection area:

[0029] When the detection area is an interference area, the calculation method is:

[0030]

[0031] When the detection area is a diffraction area, the calculation method is:

[0032]

[0033] In the formula, F represents the pattern propagation factor, ρ0 represents the specular reflection coefficient, τ represents the spherical ground diffusion factor, Γ represents the surface roughness correction factor, φ1 represents the phase delay of the reflected wave, φ2 represents the additional phase lag caused by reflection, Ai(·) represents the Airy function, V represents the diffraction parameter, and j represents the imaginary unit;

[0034] Among them, the calculation method of the surface roughness correction factor is:

[0035]

[0036] In the formula, σ h represents the root mean square height deviation of the water surface, and ψ represents the grazing angle of the radar;

[0037] The calculation method of the diffraction parameter is:

[0038]

[0039] In the formula, h t represents the flight height of the penetration aircraft, and R e represents the equivalent earth radius.

[0040] Preferably, in the step S5, the preset detection model is divided into a noise limit detection model and a clutter limit detection model, where the noise limit detection model is a Swerling-1 type detection model;

[0041] The calculation method of using the Swerling-1 type noise limit detection model to output the detection probability of the penetration aircraft under the corresponding interference conditions is:

[0042]

[0043] Among them, SNR and CNR respectively represent the signal-to-noise ratio and clutter-to-noise ratio, P fa represents the false alarm rate, P d represents the detection probability, and the calculation methods of the signal-to-noise ratio and clutter-to-noise ratio are respectively:

[0044]

[0045] In the formula, F t 、F r respectively represent the pattern propagation factors of the transmitting antenna and the receiving antenna, L p represents the two-way propagation loss between the radar and the detection target, P c 、P j 、P n respectively represent the clutter power, interference power and noise power, I(f) represents the interference improvement factor when the frequency of the radar beam is f, and R represents the real-time distance between the radar and the detection target.

[0046] Preferably, the clutter-limited detection model adopts the optimal MTI filter design method and uses the eigenvectors of the normalized clutter covariance matrix to generate the filter weight coefficients. Its frequency response function is:

[0047]

[0048] In the formula, H(f) represents the frequency response function, Q represents the total number of pulses, q represents the number of pulses, and w q is the filter weight coefficient at the q-th pulse, f represents the frequency of the radar beam, and T r represents the pulse period;

[0049] Then, according to the frequency response function, calculate the interference improvement factor when the frequency of the radar beam is f. The calculation method is:

[0050]

[0051] In the formula, f r represents the pulse frequency, S c (f) represents the Gaussian clutter power spectrum, and H0(f) represents the response of the ideal filter when the radar beam frequency is f.

[0052] Preferably, in step S5, the logic for generating the visualization curve of the detection probability varying with distance is as follows:

[0053] Pre-generate the typical values of the radar cross-section and flight altitude of the detection target, and set σ t0 ∈[0.01, 10], with the unit of m 2 , h t ∈[0.1, 25], with the unit of km. Use the typical values to calculate and generate the detection probability database under various combined conditions, and quickly obtain the detection probability in the dynamic scenario through the cubic spline interpolation method;

[0054] Use multiple radar networks for detection, and correct the detection probability generated by a single radar to the global detection probability. The calculation method is:

[0055]

[0056] In the formula, P net represents the global detection probability, ε represents the radar index, M represents the total number of radars, represents the probability that the penetration aircraft is detected by the ε-th group of radars.

[0057] Compared with the prior art, the beneficial effects of the present invention are:

[0058] The present invention proposes a dynamic correction model for the multipath propagation factor and an adaptive clutter suppression method by reverse modeling the radar power distribution characteristics and the environmental coupling effect, significantly improving the calculation accuracy of the detection probability in a complex electromagnetic environment. Based on the pattern propagation factor to quantify the attenuation law of radar waves and combined with the sub-beam system constant inversion technology, it breaks through the dependence of traditional models on confidential parameters and realizes high-confidence simulation only relying on public parameters. Through pre-generating a typical scenario database and cubic spline interpolation, it supports millisecond-level dynamic response of penetration strategies, and introduces a multi-radar networking collaborative detection correction model to accurately identify the global detection blind area. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the overall method flow of the present invention;

[0060] Figure 2 It is a data simulation diagram of the pattern propagation factor;

[0061] Figure 3 It is a data simulation diagram of the detection rate. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with specific embodiments.

[0063] It should be noted that unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meaning understood by those of ordinary skill in the field to which the present invention belongs. The "first", "second", and similar terms used in the present invention do not indicate any order, quantity, or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right", etc. are only used to represent relative position relationships, and when the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0064] Embodiment:

[0065] Please refer to Figures 1 to 3 , the present invention provides a technical solution:

[0066] A method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three-coordinate radar, the specific steps include:

[0067] S1: Collect the beam parameters, operating parameters, antenna size, and operating wavelength of the radar, and construct the antenna pattern;

[0068] In step S1, the Taylor synthesis method is used to construct the antenna pattern, and its expression is:

[0069]

[0070] In the formula, θ and λ represent the elevation angle of the radar ray and the operating wavelength respectively, F(θ) represents the radiation intensity of the radar at the elevation angle θ of the ray, j1(·) represents the first-order Bessel function, D represents the diameter of the radar antenna aperture, u n represents an intermediate parameter, the subscript n represents the term number index of the Taylor distribution, and N represents the total number of terms of the Taylor distribution.

[0071] Among them, the intermediate parameter u n is calculated as follows:

[0072]

[0073] In the formula, A represents the control parameter of the sidelobe level, and σ represents the beam broadening coefficient.

[0074] In this step, the antenna aperture diameter can be obtained from the radar technical manual, the control parameter of the sidelobe level is set according to the design requirements. For example, when the control signal of the sidelobe level is set to -45 dB, the control parameter A = 1.5, and the beam broadening coefficient can be optimized by the Taylor synthesis method, and its typical value is 1.2. In practical applications, clutter and chaff interference are the contents that must be considered emphatically when evaluating the penetration effectiveness of military aircraft against shipborne radars, and the antenna pattern directly affects the intensity of clutter and chaff interference. Therefore, the antenna pattern modeling has an important impact on the scientific nature of the evaluation results. Since the Taylor synthesis can achieve a lower sidelobe level at the cost of a smaller beam broadening, and its feed network has good realizability, it is widely used in phased array radars and can well simulate the internal radiation intensity of the radar antenna at different elevation angles of the ray, thereby reflecting the energy distribution characteristics of the main lobe and the sidelobe.

[0075] S2: Calculate the maximum detection range of the radar based on the search radar equation, and construct an ideal radar vertical power diagram in free space by combining the antenna pattern and the radar altitude.

[0076] In step S2, when constructing the ideal radar vertical power diagram, the maximum detection range is calculated as follows:

[0077]

[0078] In the formula, R m represents the maximum detection range, P av , T s , L s , A r, D0(1) represent the average power, noise temperature, system loss, aperture area of the receiving antenna, and the minimum detectable factor of a single pulse for the detected target of the radar, respectively, and t s represents the frame time, and ψ s represents the solid angle of the search airspace, and σ t0 represents the radar cross-section of the detected target, and k B represents the Boltzmann constant.

[0079] Among them, the calculation methods of the aperture area of the receiving antenna and the solid angle of the search airspace are respectively:

[0080]

[0081] ψ s = θ a ·θ e ·N b

[0082] In the formula, η a represents the aperture efficiency, θ a , θ b , N b respectively represent the azimuth beam width and elevation beam width in the radar beam, and N b represents the total number of beams.

[0083] In the existing technology, when performing offense-defense confrontation simulation, the single-beam single-pulse radar equation is usually used for calculation, and its expression is as follows:

[0084]

[0085] Here, G t , G r , h are respectively the main lobe gain of the radar transmitting antenna, the main lobe gain of the receiving antenna, and the pulse width. F t , F r respectively represent the propagation factors of the radiation patterns of the transmitting antenna and the receiving antenna. If the transmitting antenna and the receiving antenna are the same one, then F t , F r can both be represented by F. In the current simulation, generally, the influence of the interaction between electromagnetic waves and the environment on the radar detection probability is not considered, that is, let F t = F r = 1. However, when the penetration vehicle is within the first elevation beam, the fluctuations of F t and F r will have a greater impact on the detection probability. Since the flight altitude of the aerodynamic vehicle is much lower than that of the ballistic vehicle, during the penetration process of the shipborne three-coordinate radar, about half of the time is within the first elevation beam. Therefore, it is necessary to consider F t and F rImpact on the detection probability of aerodynamic aircraft.

[0086] Therefore, in order to more realistically reflect the detection probability of the radar for aerodynamic penetration aircraft, it is necessary to model the antenna pattern, the spectrum of clutter / chaff interference, and the filter to reflect the constraints of power resources and search airspace on the maximum detection range, that is, the model given in step S2 of the present invention. Based on the calculated maximum detection range and the radar altitude, the radar vertical power diagram under ideal conditions can be generated.

[0087] In this step, the average power and the aperture area of the receiving antenna in the calculation formula can be directly obtained from the technical manual of the radar. As for the single-pulse minimum detectable factor, frame time, and propagation factors of the transmitting and receiving antenna patterns, these can all be regarded as constants. It can be seen from the calculation formula of the maximum detection range that the maximum detection range of the radar for the nominal target is related to P av 、A r and ψ s and has no direct relationship with the waveform parameters and filter types adopted by the radar. Therefore, without knowing the detailed radar parameters, the radar vertical power diagram under ideal conditions can still be drawn according to the power distribution principle in the air defense warning mode, so as to realize reverse modeling and facilitate the subsequent calculation of the detection probability.

[0088] S3: Based on the beam parameters, calculate the system constants of each radar beam through the power resource allocation principle.

[0089] In step S3, the calculation method of the system constants of each radar beam is as follows:

[0090]

[0091] In the formula represents the system constant of the kth group of radar beams, and the superscript k represents the index of the radar beam. represents the peak power of the radar when transmitting the kth group of radar beams. respectively represent the main lobe gains of the transmitting and receiving antennas of the radar when transmitting the kth group of radar beams. represents the system loss of the radar when transmitting the kth group of radar beams. The noise temperature of the radar when transmitting the kth group of radar beams, where the superscript k is only used to index the radar beam in the subsequent cases where it is not specifically stated, and its definition will not be elaborated later.

[0092] It can be seen from the radar beam system constant and the calculation formula of the single-beam single-pulse radar equation in the prior art that the two can be equivalently replaced, that is, the system constant can be equivalently replaced with a function of R i of, and because R herem and is replaced by the newly proposed calculation model of the present invention, so it can be equivalently regarded as the following model:

[0093]

[0094] After the ideal radar vertical power diagram is drawn in step S2, the system constants of each radar beam can be calculated. It can be seen from this equivalent model that h (k) , σ t0 can all be obtained from the public literature or other similar radars, and the monopulse signal-to-noise ratio can also be simply fitted. The advantage of doing this is that it can avoid some relatively confidential radar parameters, and only use some public radar performance parameters to perform inverse deduction, so as to simulate the detection probability.

[0095] In this step, through the system constant integration and sub-beam power distribution modeling, the complex radar internal parameter problem is transformed into a quantifiable intermediate variable problem, solving the parameter confidentiality limitation and environmental coupling problem in traditional radar modeling, and significantly improving the engineering practicability and tactical guiding value of the detection probability calculation.

[0096] S4: Based on the antenna pattern, detection target parameters, environmental parameters and beam parameters, calculate the pattern propagation factor to quantify the attenuation and interference of the radar wave propagation path.

[0097] In step S4, different calculation methods are adopted for the pattern propagation factor according to the type of detection area:

[0098] When the detection area is the interference area, the calculation method is:

[0099]

[0100] When the detection area is the diffraction area, the calculation method is:

[0101]

[0102] In the formula, F represents the pattern propagation factor, ρ0 represents the specular reflection coefficient, τ represents the spherical ground diffusion factor, Γ represents the surface roughness correction factor, φ1 represents the phase delay of the reflected wave, φ2 represents the additional phase lag caused by reflection, Ai(·) represents the Airy function, V represents the diffraction parameter, and j represents the imaginary unit.

[0103] It is understandable that the interference area and diffraction area here mainly refer to the water surface and land. For the interference area, the specular reflection coefficient is used to quantify the reflection ability of an ideal smooth surface (such as a calm sea surface), which is calculated from the complex dielectric constant, and its specific value can be obtained by fitting the seawater temperature / salinity parameters into the Debye relaxation model; the spherical ground diffusion factor is inversely proportional to the real-time distance between the radar and the detection target, and is used to correct the influence of the earth's curvature on the energy diffusion of the reflected wave. The smaller the value, the greater the diffusion loss, and its value can be set according to expert experience or approximated by τ = 1 / (1 + R / R ck ), where R represents the real-time distance between the radar and the detection target, and R ck represents the reference distance, which is generally set between 50 and 80 KM; the surface roughness correction factor is used to reflect the attenuation of the reflected wave by the roughness of the actual surface (such as a wavy sea surface), so as to overall quantify the enhancement or cancellation effect of the multipath interference effect on the radar wave. Similarly, for the diffraction area, it is used to calculate the attenuation of the radar wave caused by diffraction due to the earth's curvature. When the target is below the radar horizon (diffraction area), the diffraction loss increases exponentially with distance, significantly reducing the detection probability.

[0104] The calculation method of the surface roughness correction factor is as follows:

[0105]

[0106] In the formula, σ h represents the root mean square height deviation of the water surface, which is used to reflect the wave height distribution of the sea surface or water surface. ψ represents the grazing angle of the radar, which is the angle between the radar wave and the sea surface or water surface. This factor is used to correct the destructive effect of the rough surface on the specular reflection. The larger its value, the rougher the water surface or sea surface, and the larger the angle between the radar wave and the sea surface or water surface, the stronger the destruction of the specular reflection, and the energy of the reflected wave is almost completely scattered.

[0107] The calculation method of the diffraction parameter is as follows:

[0108]

[0109] In the formula, h t represents the flight height of the penetration vehicle, and R e represents the equivalent earth radius.

[0110] Reference Figure 2The three-dimensional scatter plot shows 8 groups of classical values of the root mean square height deviation and 8 groups of classical values of the real-time distance selected from actual simulations. The X and Y axes represent the root mean square height difference of the water surface and the real-time distance between the radar and the detection target respectively, and the Z axis represents the value of the pattern propagation factor. The red dots represent the pattern propagation factor, the green dots represent the projection of the pattern propagation factor on the ZX plane, which is used to reflect the change of the pattern propagation factor with the root mean square height difference of the water surface, and the blue dots represent the projection of the pattern propagation factor on the YZ plane, which is used to reflect the change of the pattern propagation factor with the real-time distance. The specific data of the calculated pattern propagation factor are shown in the following table:

[0111] <![CDATA[σ h (m) / R(Km)]]> 20 30 40 50 60 70 80 90 0.1 1.32 1.27 1.21 1.15 1.09 1.04 0.99 0.95 0.3 1.18 1.12 1.06 1.01 0.96 0.92 0.88 0.84 0.5 0.94 0.89 0.85 0.81 0.78 0.75 0.72 0.69 0.8 0.72 0.69 0.66 0.63 0.61 0.59 0.57 0.55 1.0 0.61 0.59 0.57 0.55 0.53 0.51 0.49 0.47 1.2 0.53 0.51 0.49 0.47 0.45 0.44 0.42 0.40 1.5 0.44 0.42 0.40 0.39 0.38 0.36 0.35 0.34 2.0 0.35 0.34 0.33 0.32 0.31 0.30 0.29 0.28

[0112] From the data in the above table and Figure 2 the projections in each direction of the three-dimensional scatter plot, it can be seen that the pattern propagation factor is mainly affected by the root mean square height deviation of the water surface and shows a negative correlation. That is, the calmer the sea surface, the more coherent the direct wave and the reflected wave of the radar, and they are superimposed in the same phase, so the pattern propagation factor is larger. The rougher the sea surface, the more scattered the reflected energy and the coherence is destroyed, and the pattern propagation factor decreases significantly. The pattern propagation factor is also affected by the real-time distance and shows a negative correlation, but it can be seen that its change amount is very weak compared with the influence caused by the root mean square height deviation. Since the pattern propagation factor also follows this trend in the diffraction region, only the typical values in the interference region are shown here.

[0113] In this step, through the joint modeling of multipath interference and diffraction and the coupling of dynamic environmental parameters, it can automatically adapt to different meteorological, oceanic and terrain conditions, and still maintain the model accuracy in scenarios such as rainfall and chaff interference, achieving the effect of improving the simulation accuracy of the attenuation of the radar wave propagation path.

[0114] S5: Based on the system constants, the pattern propagation factor and the real-time interference conditions, use the preset detection model to output the detection probability of the penetration aircraft under the corresponding interference conditions, and generate a visualization curve of the detection probability changing with the distance.

[0115] In step S5, the preset detection model is divided into a noise-limited detection model and a clutter-limited detection model, where the noise-limited detection model is the Swerling-1 type detection model;

[0116] The calculation method of using the Swerling-1 type noise-limited detection model to output the detection probability of the penetration aircraft under the corresponding interference conditions is:

[0117]

[0118] where SNR and CNR represent the signal-to-noise ratio and the clutter-to-noise ratio respectively, P fa represents the false alarm rate, Pd Denote the detected probability, the calculation methods of the signal-to-noise ratio and the clutter-to-noise ratio are respectively as follows:

[0119]

[0120] In the formula, L p denotes the two-way propagation loss between the radar and the detected target, P c , P j , P n respectively denote the clutter power, the interference power and the noise power, I(f) denotes the interference improvement factor when the frequency of the radar beam is f, and R denotes the real-time distance between the radar and the detected target.

[0121] The general formula of the traditional Swerling-1 type detection model is as follows:

[0122]

[0123] In the present invention, since shipborne three-coordinate radars usually adopt single-pulse accumulation numbers, that is, usually n = 1, it is simplified, and a new interference improvement factor and clutter-to-noise ratio are introduced to optimize it. It can be seen that when there is no clutter interference and the interference improvement factor is 1, the simplified model is equivalent to the original model. The advantage of this is that the detection threshold can be dynamically corrected by CNR, supporting the penetration efficiency evaluation in complex electromagnetic environments. The interference improvement factor can reflect the actual clutter rejection ability of the radar, avoiding overestimating or underestimating the detection probability, so that the applicable scenario of the traditional Swerling-Ⅰ type model is extended from pure noise to multi-interference conditions. At the same time, through model simplification and parameter transparency design, the efficient and accurate calculation of the detection probability in complex interference environments is realized.

[0124] Refer to Figure 3 , similar to Figure 2 , where the X and Y axes are respectively the root mean square height difference of the water surface and the real-time distance between the radar and the detected target, the Z axis represents the value of the detected probability, the red dots represent the detected probability, the green dots represent the projection of the detected probability on the ZX plane, used to reflect the change of the detected probability with the root mean square height difference of the water surface, and the blue dots represent the projection of the detected probability on the YZ plane, used to reflect the change of the detected probability with the real-time distance. From the actual simulation, 8 sets of classical values of the root mean square height deviation and 8 sets of classical values of the real-time distance are respectively selected for display. The specific data of the calculated detected probability are shown in the following table:

[0125] <![CDATA[σ h (m) / R(Km)]]> 20 30 40 50 60 70 80 90 0.1 0.998 0.987 0.951 0.882 0.787 0.683 0.581 0.491 0.3 0.995 0.973 0.925 0.841 0.738 0.634 0.535 0.450 0.5 0.982 0.945 0.880 0.789 0.683 0.577 0.482 0.402 0.8 0.954 0.894 0.810 0.711 0.605 0.506 0.420 0.348 1.0 0.927 0.852 0.760 0.655 0.551 0.457 0.377 0.311 1.2 0.892 0.803 0.705 0.599 0.498 0.409 0.335 0.275 1.5 0.841 0.741 0.636 0.533 0.439 0.357 0.290 0.237 2.0 0.773 0.663 0.556 0.458 0.374 0.303 0.245 0.199

[0126] From the data in the above table, and Figure 3From the projections in all directions of the 3D scatter plot, it can be seen that the detected probability is negatively correlated with the root mean square height difference and the real-time distance, and positively correlated with the pattern propagation factor. From the blue projection points, it can be seen that the farther the real-time distance, the easier it is to enter the detection blind area and the smaller the detected probability; from the green projection points, it can be seen that when there are waves on the sea surface, the root mean square height difference of the water surface becomes larger, and the surface undulation causes the phase of the reflected wave to randomize, destroying the coherence. The multipath effect degrades into incoherent superposition, and the energy of the reflected wave is dispersed in multiple directions, and only a small amount of energy returns to the radar receiver, resulting in a decrease in the detection rate.

[0127] The clutter-limited detection model adopts the optimal MTI filter design method and uses the eigenvectors of the normalized clutter covariance matrix to generate the filter weight coefficients. Its frequency response function is:

[0128]

[0129] In the formula, H(f) represents the frequency response function, Q represents the total number of pulses, q represents the pulse number, w q is the filter weight coefficient at the q-th pulse, f represents the frequency of the radar beam, and T r represents the pulse period.

[0130] The clutter power spectrum here can be directly collected, normalized, and then the normalized clutter covariance function can be obtained through the discrete inverse Fourier transform. According to the normalized clutter covariance function, the corresponding normalized clutter covariance matrix can be obtained. This calculation method is a mature existing technology, so it will not be elaborated here.

[0131] Then, according to the frequency response function, calculate the interference improvement factor when the frequency of the radar beam is f. The calculation method is:

[0132]

[0133] In the formula, f r represents the pulse frequency, S c (f) represents the Gaussian clutter power spectrum, and H0(f) represents the response of the ideal filter when the radar beam frequency is f.

[0134] The interference improvement factor is used to dynamically evaluate the performance of the MTI filter and support the online optimization of filter parameters. Compared with the method of using fixed weight coefficients or empirical models in the existing technology, it can better adapt to the dynamic clutter environment, and through the eigenvalue decomposition of the covariance matrix, it realizes closed-loop feedback optimization, playing a role in improving the clutter suppression performance.

[0135] In step S5, the logic when generating the visualization curve of the detected probability varying with distance is:

[0136] Pre - generate typical values of the radar cross - section and flight altitude of the detection target, and set σ t0 ∈[0.01, 10], with the unit of m 2 , h t ∈[0.1, 25], with the unit of km. Calculate and generate a detection probability database under various combined conditions using the typical values, and quickly obtain the detection probability in the dynamic scenario through cubic spline interpolation method;

[0137] Use multiple radar networks for detection, and correct the detection probability generated by a single radar to the global detection probability. The calculation method is as follows:

[0138]

[0139] In the formula, P net represents the global detection probability, ε represents the radar index, M represents the total number of radars, represents the probability that the penetration aircraft is detected by the ε - th group of radars.

[0140] In this step, through the adaptive MTI filtering design and efficient visualization generation logic, upgrade the static empirical model of traditional clutter suppression to a dynamic closed - loop optimization system, and achieve tactical - level simulation efficiency through pre - calculation and network correction, improving the calculation accuracy and real - time performance of the detection probability in complex interference environments.

[0141] In summary, the present invention proposes a dynamic correction model for the multipath propagation factor and an adaptive clutter suppression method by reverse - modeling the radar power distribution characteristics and environmental coupling effects, significantly improving the calculation accuracy of the detection probability in complex electromagnetic environments. Quantify the radar wave attenuation law based on the pattern propagation factor, and combine the sub - beam system constant inversion technology to break through the dependence of traditional models on confidential parameters and achieve high - credibility simulation only based on public parameters. Support millisecond - level dynamic response of penetration strategies through pre - generation of typical scenario databases and cubic spline interpolation, and introduce a multi - radar network collaborative detection correction model to accurately identify global detection blind spots.

[0142] The above formulas are all dimensionless and take their numerical values for calculation. The formulas are obtained by collecting a large amount of data for software simulation to get a formula closest to the actual situation. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0143] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art will realize that the units and algorithm steps of the examples described in connection with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0144] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units. They may be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0145] As described above, the above are only specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed in the present application, and all of them should be covered by the protection scope of the present application.

Claims

1. A method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three - coordinate radar, characterized in that, The specific steps include: S1: Collect the beam parameters, operating parameters, antenna size, and operating wavelength of the radar, and construct the antenna pattern; S2: Calculate the maximum detection range of the radar based on the search radar equation, and construct the ideal radar vertical power pattern in free space by combining the antenna pattern and the radar altitude; S3: Calculate the system constants of each radar beam based on the beam parameters through the power resource allocation principle; S4: Calculate the pattern propagation factor based on the antenna pattern, detection target parameters, environmental parameters, and beam parameters to quantify the attenuation and interference of the radar wave propagation path; S5: Based on the system constants, pattern propagation factor, and real-time interference conditions, use the preset detection model to output the detection probability of the penetration aircraft under the corresponding interference conditions, and generate a visualization curve of the detection probability varying with distance.

2. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three-coordinate radar according to claim 1, characterized in that: In the step S1, the Taylor synthesis method is used to construct the antenna pattern, and its expression is: where θ and λ respectively represent the elevation angle of the radar beam and the operating wavelength, F(θ) represents the radiation intensity of the radar at the elevation angle θ of the beam, J1(·) represents the first-order Bessel function, D represents the diameter of the radar antenna aperture, u n represents an intermediate parameter, the subscript n represents the index of the number of terms of the Taylor distribution, and N represents the total number of terms of the Taylor distribution; where the intermediate parameter u n is calculated as follows: In the formula, A represents the control parameter of the sidelobe level, and σ represents the beam broadening coefficient.

3. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three-coordinate radar according to claim 2, characterized in that: In the step S2, when constructing the ideal radar vertical power pattern, the calculation method of the maximum detection range is: where r m represents the maximum detection range, P av , T s , L s , A r , D0(1) respectively represent the average power of the radar, the noise temperature, the system loss, the aperture area of the receiving antenna, and the monopulse minimum detectable factor for the detected target, t s represents the frame time, ψ s represents the solid angle of the search airspace, σ t0 represents the radar cross section of the detected target, k B represents the Boltzmann constant; Among them, the calculation methods of the aperture area of the receiving antenna and the solid angle of the search airspace are respectively: ψ s = θ a · θ e · N b where η a represents the aperture efficiency, θ a , θ b , N b respectively represent the widths of the azimuth beam and the elevation beam in the radar beam, and N b represents the total number of beams.

4. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three - coordinate radar according to claim 3, wherein: In the step S3, the calculation method of the system constants of each radar beam is: where represents the system constant of the k-th group of radar beams, and the superscript k represents the index of the radar beam, represents the peak power when the radar emits the k-th group of radar beams, respectively represent the main lobe gains of the radar transmitting antenna and receiving antenna when emitting the k-th group of radar beams, represents the system loss when the radar emits the k-th group of radar beams, is the noise temperature when the radar emits the k-th group of radar beams.

5. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three-coordinate radar according to claim 4, wherein: In the step S4, different calculation methods are adopted for the pattern propagation factor according to the type of detection area: When the detection area is the interference area, the calculation method is: When the detection area is the diffraction area, the calculation method is: In the formula, F represents the pattern propagation factor, ρ0 represents the specular reflection coefficient, τ represents the spherical ground diffusion factor, Γ represents the surface roughness correction factor, φ1 represents the phase delay of the reflected wave, φ2 represents the additional phase lag caused by reflection, Ai(·) represents the Airy function, V represents the diffraction parameter, and j represents the imaginary unit; Among them, the calculation method of the surface roughness correction factor is: where σ h represents the root-mean-square height deviation of the water surface, and ψ represents the grazing angle of the radar; The calculation method of the diffraction parameter is: where h t represents the flight altitude of the penetration vehicle, and R e represents the equivalent earth radius.

6. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three-coordinate radar according to claim 5, wherein: In the step S5, the preset detection models are divided into the noise-limited detection model and the clutter-limited detection model, and the noise-limited detection model is the Swerling-1 type detection model; The calculation method of using the Swerling-1 type noise-limited detection model to output the detection probability of the penetration aircraft under the corresponding interference conditions is: where SNR and CNR represent the signal-to-noise ratio and the clutter-to-noise ratio respectively, and P fa represents the false alarm rate, and P d represents the detection probability. The calculation methods of the signal-to-noise ratio and the clutter-to-noise ratio are as follows: where F t and F r represent the pattern propagation factors of the transmitting antenna and the receiving antenna respectively, L p represents the two-way propagation loss between the radar and the detection target, P c and P j and P n represent the clutter power, interference power and noise power respectively, I(f) represents the interference improvement factor when the frequency of the radar beam is f, and R represents the real-time distance between the radar and the detection target.

7. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three - coordinate radar according to claim 6, characterized in that: The clutter-limited detection model adopts the optimal MTI filter design method, and uses the eigenvectors of the normalized clutter covariance matrix to generate the filter weight coefficients, and its frequency response function is: where \(H(f)\) represents the frequency response function, \(Q\) represents the total number of pulses, \(q\) represents the number of pulses, and \(w\) q is the filter weight coefficient at the \(q\)th pulse, \(f\) represents the frequency of the radar beam, and \(T\) r represents the pulse period; Then, according to the frequency response function, calculate the interference improvement factor when the frequency of the radar beam is f, and the calculation method is: where f r represents the pulse frequency, and S c (f) represents the Gaussian clutter power spectrum, and H0(f) represents the response of the ideal filter at the radar beam frequency f.

8. The method for calculating the detection probability of a penetration aircraft based on reverse modeling of a three - coordinate radar according to claim 7, characterized in that: In the step S5, the logic when generating the visualization curve of the detection probability varying with distance is: Pre-generate typical values of the radar cross-section and flight altitude of the detection target, and set σ t0 ∈[0.01, 10], with the unit of m 2 , h t ∈[0.1, 25], with the unit of km. Calculate and generate a detection probability database under various combined conditions using the typical values, and quickly obtain the detection probability in a dynamic scenario through cubic spline interpolation; Use multiple radar networks for detection, and correct the detection probability generated by a single radar to the global detection probability, and the calculation method is: Where P net represents the global detection probability, ε represents the radar index, and M represents the total number of radars. represents the probability that the penetration vehicle is detected by the ε-th group of radars.

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