CN114136324A - Stealth aircraft flight path planning method based on radar detection probability cloud picture - Google Patents

Stealth aircraft flight path planning method based on radar detection probability cloud picture Download PDF

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CN114136324A
CN114136324A CN202111447780.0A CN202111447780A CN114136324A CN 114136324 A CN114136324 A CN 114136324A CN 202111447780 A CN202111447780 A CN 202111447780A CN 114136324 A CN114136324 A CN 114136324A
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radar
detection probability
stealth aircraft
radar detection
stealth
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张文远
裴彬彬
徐浩军
禹志龙
冯佩
徐文丰
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Air Force Engineering University of PLA
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Abstract

The invention provides a stealth aircraft track planning method based on a radar detection probability cloud chart, which belongs to the field of aviation track planning and comprises the following steps: step 1, calculating a static RCS (radar cross section) of a whole airspace of the stealth aircraft, and obtaining a dynamic RCS of the stealth aircraft through coordinate conversion; step 2, solving the radar detection probability of the stealth aircraft according to the dynamic RCS of the stealth aircraft to obtain radar detection probability cloud charts of a single radar battlefield and a networking radar battlefield; and 3, planning the flight path of the stealth aircraft according to the radar detection probability cloud picture under the conditions of single radar and networking radar respectively. The method has the advantages of low detection probability, strong realizability and intuition, provides a new idea for planning the flight path of the stealth aircraft, and has certain guiding significance.

Description

Stealth aircraft flight path planning method based on radar detection probability cloud picture
Technical Field
The invention belongs to the technical field of aviation track planning, and particularly relates to a stealth aircraft track planning method based on a radar detection probability cloud picture.
Background
The stealth aircraft plays an increasingly important role in a battlefield by virtue of low detectability, and becomes a powerful weapon which breaks through an enemy defense net, goes deep into the abdominal land of the enemy and strikes important targets of the enemy. However, the low detectability of stealth aircraft is not omnidirectional and full-band, and with the appearance of networking radar, optimization of radar deployment and the like, the traditional flight path planning method cannot effectively guarantee penetration.
Currently, most of research on flight path planning focuses on ordering threats and optimizing scientific and reasonable flight paths under the condition that various constraints (such as oil consumption and flight distance) of stealth airplanes are met. The prior art provides analysis and modeling for two key problems of dynamic RCS of an unmanned aerial vehicle and a radar discovery criterion in stealth penetration track planning, but the dynamic RCS only takes an RCS value of horizontal irradiation within a certain pitch angle range, and the track planning is only suitable for low altitude; in the flight path planning based on the weight-variable theory provided by the prior art, the threat state is converted into a weight function, but the threat parameters are defined to be vague, and the cost of a flight path is sacrificed; the prior art also proposes a stealth aircraft track planning method based on pseudo-spectral method, but does not consider dynamic RCS.
The radar detection probability cloud chart-based flight path optimization method for the stealth aircraft has the characteristics of intuition, quantification and easiness in implementation, and has guiding significance for the general probability defense of the stealth aircraft.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a stealth aircraft track planning method based on a radar detection probability cloud picture.
In order to achieve the above purpose, the invention provides the following technical scheme:
a stealth aircraft flight path planning method based on a radar detection probability cloud picture comprises the following steps:
step 1, calculating a static RCS (radar cross section) of a whole airspace of the stealth aircraft, and obtaining a dynamic RCS of the stealth aircraft through coordinate conversion;
step 2, solving the radar detection probability of the stealth aircraft according to the dynamic RCS of the stealth aircraft to obtain radar detection probability cloud charts of a single radar battlefield and a networking radar battlefield;
and 3, planning the flight path of the stealth aircraft according to the radar detection probability cloud picture under the conditions of single radar and networking radar respectively.
Preferably, the calculation process of the static RCS of the stealth aircraft in full airspace is as follows:
after CAD modeling is carried out on the stealth aircraft, the stealth aircraft is guided into a CADFEKO for mould repairing and correction processing;
performing static RCS simulation operation on the processed model by adopting electromagnetic simulation software FEKO;
and (4) obtaining a stealth aircraft full-airspace static RCS database by adopting a physical optical method for the simulated model.
Preferably, the calculation process of the dynamic RCS of the stealth aircraft is as follows:
obtaining the attitude angle of the stealth aircraft according to the flat flight track, wherein the attitude angle comprises a pitch angle theta and a yaw angle
Figure BDA0003384529920000021
Roll angle η, and trajectory P (x)p,yp,zp) (ii) a Wherein x isp、yp、zpCoordinates of an x axis, a y axis and a z axis of the track P are respectively;
obtaining a transformation matrix Q from a radar coordinate system to a body coordinate system shown in a formula (2) according to a coordinate transformation principle; thereby obtaining the coordinate (x) of the radar in the body coordinate system by the formula (1)4,y4,z4) Wherein (x)T,yT,zT) Coordinates of the radar in a ground coordinate system;
Figure BDA0003384529920000022
wherein the transformation matrix Q is:
Figure BDA0003384529920000023
thus, of stealth aircraftRadar line-of-sight angles, i.e. pitch angle theta' and azimuth angle
Figure BDA0003384529920000024
As shown in formula (3);
Figure BDA0003384529920000031
and solving a dynamic RCS sequence of the target by adopting a linear interpolation method according to the real-time radar line-of-sight angle of the stealth aircraft and the established full-airspace static RCS characteristic library.
Preferably, a swerlingI radar detection model is adopted to solve the stealth aircraft radar detection probability.
Preferably, the solving of the radar detection probability of the stealth aircraft under the condition of the single radar specifically includes:
the radar detection probability being the false alarm probability PfaAnd signal-to-noise ratio S/N:
Pd=f(Pfa,S/N) (4)
in the formula: S/N refers to the ratio of the average power of the transmitted signal to the average power of the additive noise; f represents different radar signal processing modes, corresponds to different target types and threshold detection modes, has different false alarm probabilities and detection probability expressions, and divides a fluctuating target into four different Swerling models by a Swerling radar detection model, wherein the Swerling I type target has constant amplitude in one antenna scanning period, and the fluctuating amplitude has constant amplitude according to two degrees of freedom chi in different scanning periods2The probability density function of the data acquisition system is independently changed, namely the RCS under each emission pulse is considered to be the same in the same scanning period; therefore, when multi-pulse coherent accumulation is considered, the post-accumulation signal-to-noise ratio is:
SNR=np×S/N (5)
in the formula, npAccumulating the number of pulses for phase coherence; when n ispAt a certain time, the signal-to-noise ratio SNR is only related to the RCS of the target and the radar distance R of the target and can be solved through a radar equation;
the formula of the detection probability is:
when n ispWhen the number is equal to 1, the alloy is put into a container,
Figure BDA0003384529920000032
when n ispWhen the pressure is higher than 1,
Figure BDA0003384529920000041
wherein
Figure BDA0003384529920000042
In the formula: vTFor detecting the threshold, the stealth aircraft radar detection probability can be solved by a recursive algorithm in a Newton-Raphson method.
Preferably, the solving of the stealth aircraft radar detection probability under the condition of the networking radar specifically includes:
each radar generates a judgment value q according to the intensity of a reflected electromagnetic wave signal generated by the stealth aircraft, and the judgment is based on whether a radar input signal is greater than a detection probability threshold value;
when the target is detected, q is '1', otherwise q is '0';
and then fusing all the single radar judgment results to generate a networking judgment value Q, wherein Q is Q1+q2+…+qn(ii) a When Q is larger than or equal to K, judging that the networking radar finds a target, otherwise, judging that the networking radar does not find the target;
therefore, the joint detection probability of the networking radar is as follows:
Figure BDA0003384529920000043
wherein p isiThe probability that the target is found by the ith radar is i, j, a., k, m, a.., N is N single radars;
likewise, the false alarm probability of the whole radar net is:
Figure BDA0003384529920000044
wherein p isfiThe false alarm probability of the ith radar is the following, and when the false alarm probabilities of all the radars are equal, the false alarm probability of the networking radar is as follows:
Figure BDA0003384529920000045
taking the false alarm probability as Pf=10-11
Preferably, the planning of the flight path of the stealth aircraft specifically includes:
calculating and drawing a radar detection probability cloud chart of multi-azimuth crossing of a battlefield;
processing the obtained radar detection probability cloud picture of multi-azimuth crossing battlefield, and selecting a preliminary defense penetration means;
selecting a proper path to enable the radar detection probability to be smaller than a set value;
and connecting the whole flight path to obtain a final flight path planning diagram.
Preferably, the radar detection probability of each position of the three or more directions passing through the battlefield is taken as the maximum value to obtain a composite radar detection probability cloud picture.
The stealth aircraft flight path planning method based on the radar detection probability cloud chart has the following beneficial effects:
the method has the advantages of low detection probability, strong realizability and intuition, provides a new idea for stealth aircraft track planning, and has certain guiding significance.
Drawings
In order to more clearly illustrate the embodiments of the present invention and the design thereof, the drawings required for the embodiments will be briefly described below. The drawings in the following description are only some embodiments of the invention and it will be clear to a person skilled in the art that other drawings can be derived from them without inventive effort.
FIG. 1 is a diagram of a stealth aircraft F35 full airspace static RCS;
FIG. 2 is a radar centroid coordinate system;
FIG. 3 is a schematic diagram of a rank K decision criterion;
FIG. 4 is a cloud chart of radar detection probabilities;
FIG. 5 is a comparison of radar detection probability clouds with altitude;
FIG. 6 is a drawing of a stretcher maneuver trajectory plan;
FIG. 7 is a comparison of radar detection probabilities;
FIG. 8 is a cloud chart of detection probabilities of three azimuth radars;
FIG. 9 is a cloud graph of composite radar detection probabilities;
FIG. 10 is a primary track planning diagram;
FIG. 11 is a fine track planning diagram;
FIG. 12 is a final track planning diagram.
Detailed Description
In order that those skilled in the art will better understand the technical solutions of the present invention and can practice the same, the present invention will be described in detail with reference to the accompanying drawings and specific examples. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
The invention provides a stealth aircraft track planning method based on a radar detection probability cloud picture, which comprises the following steps:
step 1, calculating the static RCS of the stealth aircraft in a full airspace through electromagnetic simulation software FEKO, and obtaining the dynamic RCS of the stealth aircraft through coordinate conversion; RCS is a Radar scattering Cross-Section (abbreviated as RCS), which is an effective reflection area of an airplane to Radar waves.
The specific solving process is as follows:
step 1.1, after accurate CAD modeling is carried out on the stealth aircraft, the stealth aircraft is guided into a CADFEKO for mould repairing and correction processing.
And step 1.2, performing static RCS simulation operation on the magnetic resonance imaging system by adopting electromagnetic simulation software FEKO. And obtaining a full-airspace static RCS database of the target by using the conventional physical optics method. The simulation condition is that the incidence angle of 181 degrees multiplied by 361 degrees in a full airspace is adopted, the angle interval is 1 degree, the frequency band is an L wave band, and a vertical polarization mode is adopted. The obtained target static full spatial domain RCS is shown in fig. 1. Establishing a radar center coordinate system as shown in fig. 2, taking the radar center as an origin, taking the horizontal east as an X axis and the horizontal north as a y axis, and obtaining a z axis according to the right-hand spiral theorem. Under a single-station radar, taking the example that when a stealth aircraft is at H of 3000m, the stealth aircraft flies from east to west and passes through a battlefield, in a simulation program, 250 flat flight paths are set, the flight speed is 300m/s, the distance between every two flight paths is 800 m, and the flat flight starting point x is 60 km.
Step 1.3, obtaining the attitude angle (pitch angle theta and yaw angle) of the stealth aircraft according to the flat flight track
Figure BDA0003384529920000071
Roll angle η) and trajectory P (x)p,yp,zp). From the coordinate conversion principle, a transformation matrix Q from the radar coordinate system to the body coordinate system shown in equation (2) is obtained. Thereby obtaining the coordinate (x) of the radar in the body coordinate system by the formula (1)4,y4,z4) Wherein (x)T,yT,zT) The coordinates of the radar in a ground coordinate system.
Figure BDA0003384529920000072
Wherein the transformation matrix Q is:
Figure BDA0003384529920000073
thus, the radar line-of-sight angle, i.e. pitch angle θ' and azimuth angle, of the stealth aircraft
Figure BDA0003384529920000074
As shown in formula (3);
Figure BDA0003384529920000075
and step 1.4, solving out a dynamic RCS sequence of the target by adopting a linear interpolation method according to the real-time radar line-of-sight angle of the stealth aircraft and the established full-airspace static RCS characteristic library.
Step 2, solving radar detection probability of the stealth aircraft by adopting a swerlingI radar detection model to obtain radar detection probability cloud charts of a single radar battlefield and a networking radar battlefield, and specifically comprising the following steps:
step 2.1, calculating the radar detection probability under the condition of single radar
The radar detection probability being the false alarm probability PfaAnd signal-to-noise ratio S/N:
Pd=f(Pfa,S/N) (4)
in the formula: S/N refers to the ratio of the average power of the transmitted signal to the average power of the additive noise; f represents different radar signal processing modes. Corresponding to different target types and threshold detection modes, different false alarm probabilities and detection probability expressions are provided. The Swerling divides the fluctuating target into four different Swerling models, wherein the Swerling I type target has constant amplitude in one antenna scanning period, and the fluctuating amplitude is according to two freedom degrees chi in different scanning periods2The probability density function of (2) is changed independently, namely that RCS under each transmission pulse is the same in the same scanning period. Therefore, when multi-pulse coherent accumulation is considered, the post-accumulation signal-to-noise ratio is:
SNR=np×S/N (5)
in the formula, npAccumulating the number of pulses for phase coherence; when n ispAt a certain time, the signal-to-noise ratio SNR is only related to the RCS of the target and radar range R, and can be solved by radar equations.
The invention adopts a swerlingI type model to analyze the detection probability of the single radar. The formula of the detection probability is:
when n ispWhen the number is equal to 1, the alloy is put into a container,
Figure BDA0003384529920000081
when n ispWhen the pressure is higher than 1,
Figure BDA0003384529920000082
wherein
Figure BDA0003384529920000083
In the formula: vTFor detecting the threshold, the stealth aircraft radar detection probability can be solved by a recursive algorithm in a Newton-Raphson method.
Step 2.2, calculating the detection probability under the condition of the networking radar
The rank K judgment criterion is widely applied to radar network data fusion. The invention adopts a rank K judgment criterion for modeling the radar network.
Assuming that a certain radar network consists of N radars, according to a rank K fusion rule, namely when the number of radars finding a target in the radar network exceeds a detection threshold K, the target is determined to be found.
The principle of rank K decision criterion is shown in fig. 3. Each radar generates a judgment value q according to the intensity of a reflected electromagnetic wave signal generated by the stealth aircraft, and the judgment is based on whether a radar input signal is greater than a detection probability threshold value, wherein when a target is detected, the q is '1', otherwise, the q is '0'. And then fusing all the single radar judgment results to generate a networking judgment value Q, wherein Q is Q1+q2+…+qn. And when Q is larger than or equal to K, judging that the target is found by the networking radar, otherwise, judging that the target is not found by the networking radar.
Therefore, the joint detection probability of the networking radar is as follows:
Figure BDA0003384529920000091
wherein p isiFor the probability of finding a target by the ith radar, i, j, a.
Likewise, the overall radar net has a false alarm probability of
Figure BDA0003384529920000092
Wherein p isfiIs the false alarm probability of the ith radar. When the false alarm probabilities of all radars are equal, the false alarm probability of the networking radar is as follows:
Figure BDA0003384529920000093
the performance parameters of each radar adopted by the invention are consistent, and the false alarm probability is taken as Pf=10-11
And 3, respectively carrying out flight path planning on the stealth aircraft under the conditions of single radar and networking radar.
Step 3.1, flight path planning method under single radar condition
According to the obtained distribution cloud chart of the dynamic RCS, a swerlingI type radar detection model is adopted to obtain a detection probability cloud chart of the aircraft passing through the battlefield under different heights as shown in the following figure 4.
The detection cloud chart of the stealth aircraft presents different shapes along with the change of the height. As can be seen from the detection cloud images, when the airplane does not pass through the radar (X >0), the detection probability cloud image pair is shown in FIG. 5. Through comparison, the area of the detected region in the whole space is increased along with the increase of the flight path, and the effectiveness of the low-altitude penetration is also demonstrated. This is because the pitch angle of the radar line-of-sight angle of the stealth aircraft becomes smaller as the altitude decreases, and the RCS value becomes smaller as the pitch angle of the aircraft becomes smaller in the aircraft nose direction.
After the airplane passes through the radar (x is less than 0), the comparison shows that when the airplane flies back to the station (y is close to 0), the detection probability difference under different heights is obvious, and the exposure distance change is obvious. When the low altitude h is 1000m and the aircraft flies at a back station, the exposure distance of the stealth aircraft reaches 100km, and when the flight path height is increased to 9000m, the exposure distance is shortened to about 30 km. Referring to the RCS of fig. 4, this is because the cavity effect exists in the aircraft tail nozzle when flying at the low altitude back station, and the cavity effect is more obvious the lower the height is, resulting in the larger RCS. The hidden aircraft jet nozzle model is subjected to sealing treatment, the jet nozzle is sealed by a circular vertical surface, the effect of the vertical surface is similar to the cavity effect along with the scattering property of the height, the vertical surface is a strong scattering source, and the lower the height is, the stronger the electromagnetic scattering intensity is.
The invention plans three tracks according to the detected cloud picture.
First, take a level flight trajectory with y >80 km. Through the radar detection probability spectrum, when the vertical distance between the flight path of the airplane and the radar is more than 80km, the detection probability of the whole course of the airplane is 0.
Second, when a stealth aircraft is mission bound, it must take y <80 km. At this time, the aircraft is flown on the side of y of 80km as much as possible while keeping the low altitude flight as much as possible.
Thirdly, when the flight is bound by the mission, y must be 0km, namely, the station is flown. According to the characteristic that the radar detection probability cloud picture is 0km in y, the invention provides the penetration prevention mode: and keeping low-altitude flight when x is greater than 15km, and adopting a stretching maneuver when 15 is greater than x 0 to ensure that h is close to 9km when x is less than 0.
In order to verify the correctness of the third flight path planning method, the embodiment designs a flight path of low altitude level flight-stretching-high altitude level flight, and compares the flight path with the flight path of pure high altitude level flight and low altitude level flight. The designed trajectory plan is shown in figure 6 below.
By planning the flight path, the radar detection probability shown in the following fig. 7 is obtained by adopting the radar detection probability calculation method based on the dynamic RCS.
Through comparison, the stretching maneuver is adopted, so that the exposure distance and the exposure time of the airplane are reduced compared with the simple low-altitude flight; compared with high-altitude maneuvers, the method delays the exposure starting time of the radar (the time point at which the detection probability starts to be 1), the high-altitude maneuvers are found in about 130s, the exposure starting time of the stretching maneuver is 150s, and the average detection probability of the stretching maneuver for preventing penetration through the battlefield is 0.332743, and the average detection probability of the high-altitude maneuvers for penetration through the battlefield is 0.319113. The reason for this is that the actual detection probability of the stretch climbing maneuver at this position is 0 because the radar is also in the detection stage during 35s, but the actual detection probability is 0 because the radar has a blind spot at the radar search angle when the radar pitch angle is about 90 degrees during the search of the real radar.
Step 3.2, route planning method under networking radar
According to the drawing principle of the radar detection probability spectrum, the radar detection probability cloud picture is drawn when the flying height is 3000m and the rank K is 1 under the condition of 6 networking radars. Fig. 8 is a cloud diagram of radar detection probabilities of passing through a battlefield from east to west, north to south, and south to north, respectively. The operational background of the aircraft is set to cross the battlefield east to west with a lower probability of radar detection.
Finally, the obtained stealth aircraft track planning method based on the radar detection probability spectrum comprises the following steps:
calculating and drawing a radar detection probability cloud chart for traversing a battlefield from multiple directions, taking a flight path planning method under the networking radar as an example, and taking three penetration directions of east to west, north to south and south to north.
2, preliminary planning: and processing the obtained radar detection probability cloud pictures which penetrate through the battlefield from multiple directions, and selecting a preliminary defense penetration means. In this embodiment: the radar detection probability of each position of the three orientations crossing the battlefield is taken as the maximum value to obtain a composite radar detection probability cloud chart, which is shown in the following figure 9.
The physical meaning of the composite radar detection probability cloud picture is as follows: in the cloud picture, if a value at a certain position is 0, the detection probability of three azimuth penetration is 0. Based on the method, a preliminary segmented low detection probability flight path is designed, and points which are 0 in the composite radar detection probability cloud picture are sequentially connected according to three penetration directions. The preliminary track planning is shown in FIG. 10, and the primary route planning of A-B, C-D, E-F, H-I, J-K is obtained.
3, fine planning of the route: and selecting a proper path to ensure that the radar detection probability of B-C, D-E, F-H and I-J is smaller. Taking H-F as an example, referring to the detection probability distribution around H-F in the following diagram, as shown in fig. 11, comparing the detection probabilities of three directions, it is found that the radar detection probability from east to west is relatively small, and thus the fine route of F-M is planned. From the M-H process from north to south, the comparison shows that at this stage, the detection probability is 0. Therefore, fine track gauges of the F-M-H are planned in the F-H section.
And 4, connecting the whole flight paths according to the steps shown in the step 3 to obtain a final flight path planning diagram shown in the step 12.
The stealth aircraft track planning method based on the radar detection probability cloud chart respectively carries out track planning on a single-station radar and a networking radar, has the characteristics of intuition, visibility and easiness in implementation, and has certain guiding significance on stealth aircraft tactics.
The above-mentioned embodiments are only preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, and any simple modifications or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims (8)

1. A stealth aircraft flight path planning method based on a radar detection probability cloud picture is characterized by comprising the following steps:
step 1, calculating a static RCS (radar cross section) of a whole airspace of the stealth aircraft, and obtaining a dynamic RCS of the stealth aircraft through coordinate conversion;
step 2, solving the radar detection probability of the stealth aircraft according to the dynamic RCS of the stealth aircraft to obtain radar detection probability cloud charts of a single radar battlefield and a networking radar battlefield;
and 3, planning the flight path of the stealth aircraft according to the radar detection probability cloud picture under the conditions of single radar and networking radar respectively.
2. The stealth aircraft track planning method based on the radar detection probability cloud chart according to claim 1, wherein the calculation process of the all-airspace static RCS of the stealth aircraft is as follows:
after accurate CAD modeling is carried out on the stealth aircraft, the stealth aircraft is guided into a CADFEKO for mould repairing and correction processing;
performing static RCS simulation operation on the processed model by adopting electromagnetic simulation software FEKO; there are other calculation methods, but FEKO calculation is more accurate for the large size airplane model of the present invention.
And (4) obtaining a stealth aircraft full-airspace static RCS database by adopting a physical optical method for the simulated model.
3. The stealth aircraft trajectory planning method based on the radar detection probability cloud chart according to claim 2, wherein the calculation process of the dynamic RCS of the stealth aircraft is as follows:
obtaining the attitude angle of the stealth aircraft according to the flat flight track, wherein the attitude angle comprises a pitch angle theta and a yaw angle
Figure FDA0003384529910000011
Roll angle η, and trajectory P (x)p,yp,zp) (ii) a Wherein x isp、yp、zpCoordinates of an x axis, a y axis and a z axis of the track P are respectively;
obtaining a transformation matrix Q from a radar coordinate system to a body coordinate system shown in a formula (2) according to a coordinate transformation principle; thereby obtaining the coordinate (x) of the radar in the body coordinate system by the formula (1)4,y4,z4) Wherein (x)T,yT,zT) Coordinates of the radar in a ground coordinate system;
Figure FDA0003384529910000012
wherein the transformation matrix Q is:
Figure FDA0003384529910000021
thus, the radar line-of-sight angle, i.e. pitch angle θ' and azimuth angle, of the stealth aircraft
Figure FDA0003384529910000022
As shown in formula (3)Shown in the specification;
Figure FDA0003384529910000023
and solving a dynamic RCS sequence of the target by adopting a linear interpolation method according to the real-time radar line-of-sight angle of the stealth aircraft and the established full-airspace static RCS characteristic library.
4. The stealth aircraft flight path planning method based on the radar detection probability cloud chart is characterized in that a swerlingI radar detection model is adopted to solve the stealth aircraft radar detection probability, other methods can be adopted, and the model is adopted according to practical application.
5. The radar detection probability cloud atlas-based stealth aircraft flight path planning method according to claim 4, wherein the solving of the radar detection probability of the stealth aircraft under a single radar condition specifically comprises:
the radar detection probability being the false alarm probability PfaAnd signal-to-noise ratio S/N:
Pd=f(Pfa,S/N) (4)
in the formula: S/N refers to the ratio of the average power of the transmitted signal to the average power of the additive noise; f represents different radar signal processing modes, corresponds to different target types and threshold detection modes, has different false alarm probabilities and detection probability expressions, and divides a fluctuating target into four different Swerling models by a Swerling radar detection model, wherein the Swerling I type target has constant amplitude in one antenna scanning period, and the fluctuating amplitude has constant amplitude according to two degrees of freedom chi in different scanning periods2The probability density function of the data acquisition system is independently changed, namely the RCS under each emission pulse is considered to be the same in the same scanning period; therefore, when multi-pulse coherent accumulation is considered, the post-accumulation signal-to-noise ratio is:
SNR=np×S/N (5)
in the formula, npAccumulating the number of pulses for phase coherence; when n ispAt a certain time, the signal-to-noise ratio SNR is only related to the RCS of the target and the radar distance R of the target and can be solved through a radar equation;
the formula of the detection probability is:
when n ispWhen the number is equal to 1, the alloy is put into a container,
Figure FDA0003384529910000031
when n ispWhen the pressure is higher than 1,
Figure FDA0003384529910000032
wherein
Figure FDA0003384529910000033
In the formula: vTFor detecting the threshold, the stealth aircraft radar detection probability can be solved by a recursive algorithm in a Newton-Raphson method.
6. The radar detection probability cloud atlas-based stealth aircraft flight path planning method according to claim 4, wherein the solving of the radar detection probability of the stealth aircraft under the networking radar condition specifically comprises:
each radar generates a judgment value q according to the intensity of a reflected electromagnetic wave signal generated by the stealth aircraft, and the judgment is based on whether a radar input signal is greater than a detection probability threshold value;
when the target is detected, q is '1', otherwise q is '0';
and then fusing all the single radar judgment results to generate a networking judgment value Q, wherein Q is Q1+q2+…+qn(ii) a When Q is larger than or equal to K, judging that the networking radar finds a target, otherwise, judging that the networking radar does not find the target;
therefore, the joint detection probability of the networking radar is as follows:
Figure FDA0003384529910000034
wherein p isiThe probability that the target is found by the ith radar is i, j, a., k, m, a.., N is N single radars;
likewise, the false alarm probability of the whole radar net is:
Figure FDA0003384529910000041
wherein p isfiThe false alarm probability of the ith radar is the following, and when the false alarm probabilities of all the radars are equal, the false alarm probability of the networking radar is as follows:
Figure FDA0003384529910000042
taking the false alarm probability as Pf=10-11
7. The stealth aircraft trajectory planning method based on the radar detection probability cloud chart according to claim 5 or 6, wherein the performing of the trajectory planning on the stealth aircraft specifically comprises:
calculating and drawing a radar detection probability cloud chart of multi-azimuth crossing of a battlefield;
processing the obtained radar detection probability cloud picture of multi-azimuth crossing battlefield, and selecting a preliminary defense penetration means;
selecting a proper path to enable the radar detection probability to be smaller than a set value;
and connecting the whole flight path to obtain a final flight path planning diagram.
8. The method of claim 7, wherein the radar detection probability of each location across the battlefield at a plurality of orientations is maximized to obtain a composite radar detection probability cloud.
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