WO2022241991A1 - Hypersonic vehicle trajectory tracking method - Google Patents

Abstract

Disclosed in the present invention is a hypersonic vehicle trajectory tracking method. In the method, a hypersonic vehicle is detected by a detection station having a radar; after the hypersonic vehicle is detected, a certain number of sampling points are continuously selected in a period of time, and target state information is correspondingly obtained for each sampling point moment, so as to form a motion pattern of the hypersonic vehicle in a period of time, thereby providing a data basis for subsequent research or trajectory prediction; a plurality of possible target states are solved at each sampling point, which are referred to as virtual target states; by comparing an azimuth angle obtained by means of real detection of the radar with azimuth angles corresponding to the virtual target states, the virtual target states having great deviation are removed, and the virtual target states having less deviation are added, so as to form a new virtual target state group; and a detection result corresponding to the sampling point, i.e., a detected target state, is obtained by means of the weighted average of the new virtual target state group.

Description

Hypersonic Vehicle Trajectory Tracking Method technical field

The invention relates to the technical field of defense and interception of non-cooperative hypersonic aircraft, in particular to a trajectory tracking method of a hypersonic aircraft.

Background technique

In order to realize the prediction of the trajectory of the hypersonic vehicle, no matter which method needs to use the motion state or aerodynamic parameters of the target, and these data come from the tracking of the target, that is, from the state change of the hypersonic vehicle over a period of time, This requires first obtaining the status information of the hypersonic vehicle.

The hypersonic aircraft generally refers to an aircraft with a flight speed of more than 5 times the speed of sound. Due to its high flight speed, traditional radar detection and other methods will produce large errors when calculating specific distances, and the detection results are not ideal. , there is an urgent need for a more accurate tracking and solving method for hypersonic vehicle trajectory. At the same time, this method also has high requirements for real-time performance, and the calculation results need to be obtained in time.

In view of the above problems, the inventors have conducted in-depth research on traditional tracking methods for hypersonic vehicles, hoping to design a new tracking method that can solve the above problems.

Contents of the invention

In order to overcome the above-mentioned problems, the present inventor has carried out intensive research and designed a hypersonic vehicle trajectory tracking method. In this method, a hypersonic vehicle is detected through a detection station with a radar. Continuously select a certain number of sampling points within a certain period of time, and obtain target state information correspondingly for each sampling point, so as to form the motion law of the hypersonic vehicle within a period of time, and provide a data basis for subsequent research or trajectory prediction. Among them, in each Sampling points are solved to calculate multiple possible target states, which are called virtual target states. Through the comparison relationship between the azimuth angle obtained by the real detection of the radar and the azimuth angle corresponding to the virtual target state, the virtual target state with excessive deviation is removed. Add a virtual target state with less deviation to form a new virtual target state group, and obtain the tracking result corresponding to the sampling point, that is, the tracked target state, through the weighted average of the new virtual target state group, thereby completing the present invention.

The object of the present invention is to provide a hypersonic vehicle trajectory tracking method based on virtual target state filtering, the method comprises the following steps:

Step 1, arrange a detection station, and continuously detect whether there is a target in the area through the detection station, and the target is a hypersonic aircraft;

Step 2, after the target is found, give the initial target state, and select the sampling point, start sampling, and obtain the observation value, the observation value includes the two coordinates of the target relative to the detection station in the northeast sky coordinate system obtained through detection station detection. azimuth;

Step 3, at each sampling point, a plurality of virtual target states are estimated according to the initial target state;

Step 4, resampling the virtual target state of each sampling point according to the observed value of the sampling point;

Step 5: Determine the target state corresponding to the sampling point according to the virtual target state obtained by resampling.

Among them, in step 3, each virtual target state is estimated by the following formula (1),

X(k)＝ΦX(0)+ΓB(k-1)+10ΓW(k) (one)

Among them, X(k) represents the virtual target state, X(0) represents the initial target state, B(k-1) represents the maneuvering acceleration of the target, W(k) represents the process noise, and both Φ and Γ represent matrix coefficients.

Wherein, when estimating the state of the virtual target, the value of the maneuvering acceleration B(k-1) of the target is:

B(k-1)＝[x _b x _b y _b y _b z _b z _b ] ^T

Among them, x _b randomly selects any number from 20m/s ² to 40m/s ² , y _b randomly selects any number from 7m/s ² to 13m/s ² , z _b randomly selects any number from 20m/s ² to 40m/s Any number from ² .

Wherein, when estimating the virtual target state, the value of the process noise W(k) is:

W(k)＝[s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ ] ^T

Among them, s ₁ , s ₂ , s ₃ , s ₄ , s ₅ and s ₆ are all random numbers conforming to a normal distribution with a mean of 0, a variance of 1, and a standard deviation of 1.

Among them, the matrix coefficients Φ and Γ are obtained by the following formulas (2) and (3):

Among them, T represents the sampling period.

Wherein, said step 4 includes the following sub-steps:

Sub-step 1: Solve the two azimuth angles of each virtual target state relative to the detection station in the northeast sky coordinate system;

Sub-step 2: Make a difference between the two azimuth angles of the virtual target state and the two azimuth angles in the observed value, and calculate the square root of the two difference values;

Sub-step 3: Substitute the square root of each virtual target state into the Gaussian distribution function to obtain the weight of each virtual target state;

In sub-step 4, the virtual target state with a smaller weight is deleted, and the virtual target state with a larger weight is copied, so that the total number of virtual target states remains consistent, thereby completing the resampling of the virtual target state.

Wherein, in step 5, the target state corresponding to the sampling point is obtained by performing a weighted average on all the virtual target states obtained by resampling in the sampling point.

Wherein, when the detection station is provided with one, the target state corresponding to each sampling point obtained in step 5 is the tracking result of the target;

When there are multiple detection stations, the average value of the target states obtained at the same sampling point among multiple detection stations is the detection result of the target.

Wherein, there are more than 50 sampling points, preferably 100 sampling points.

Wherein, the number of virtual target states set in each sampling point is all consistent with each other, preferably, the number of virtual target states set in each sampling point is more than 100; more preferably, 10000 virtual target states are set in each sampling point target state.

(1) The hypersonic vehicle trajectory tracking method provided by the present invention can realize real-time monitoring and tracking of the hypersonic vehicle, obtain its motion state information in real time, and its data acquisition speed is fast, real-time performance can be achieved, and the data obtained by it is accurate High, stable and reliable;

(2) In the hypersonic vehicle trajectory tracking method provided by the present invention, in the same detection station, the virtual target states obtained at different sampling points are all based on the same initial target state, which can reduce the amount of calculation and simplify the calculation process; at the same time, due to The process noise in the calculation process of the virtual target state is enlarged by ten times, and the coverage of the virtual target state is wide enough to offset the initial error caused by the initial target state, making the tracking results accurate and timely.

Description of drawings

Fig. 1 shows a logic diagram of the overall structure of the hypersonic vehicle trajectory tracking method in a preferred embodiment of the present invention; Fig. 2 shows a schematic diagram of the real trajectory and the measured trajectory in Embodiment 1 of the present invention; Fig. 3 shows the embodiment of the present invention Fig. 4 shows a schematic diagram of the change of the calculation time in Embodiment 1 of the present invention; Fig. 5 shows a schematic diagram of the real trajectory and the measurement trajectory in Embodiment 2 of the present invention; Fig. 6 shows the schematic diagram of the present invention A schematic diagram of the variation of the tracking error in Embodiment 2; FIG. 7 shows a schematic diagram of the variation of the calculation time in Embodiment 2 of the present invention; FIG. 8 shows a schematic diagram of the real trajectory and the measurement trajectory in Embodiment 3 of the present invention; A schematic diagram of the variation of the tracking error in the third embodiment of the invention; FIG. 10 shows a schematic diagram of the variation of the calculation time in the third embodiment of the invention; FIG. 11 shows a schematic diagram of the real track and the measurement track in the fourth embodiment of the invention; FIG. 12 shows Figure 13 shows a schematic diagram of the change of the calculation time in Embodiment 4 of the present invention; Figure 14 shows a schematic diagram of the real trajectory and the measurement trajectory in Embodiment 5 of the present invention; Fig. 15 shows a schematic diagram of the change of tracking error in Embodiment 5 of the present invention; FIG. 16 shows a schematic diagram of the change of calculation time in Embodiment 5 of the present invention; FIG. 17 shows a schematic diagram of real trajectory and measurement trajectory in Embodiment 6 of the present invention ; Figure 18 shows a schematic diagram of changes in tracking error in Embodiment 6 of the present invention; Figure 19 shows a schematic diagram of changes in calculation time in Embodiment 6 of the present invention; Figure 20 shows a schematic diagram of real trajectory and measurement in Embodiment 7 of the present invention Schematic diagram of trajectory; FIG. 21 shows a schematic diagram of the change of tracking error in Embodiment 7 of the present invention; FIG. 22 shows a schematic diagram of the displacement and speed change in the Middle East coordinate direction in Embodiment 7 of the present invention; FIG. Schematic diagram of the displacement and speed change in the coordinate direction; FIG. 24 shows a schematic diagram of the displacement and speed change in the sky coordinate direction in Embodiment 7 of the present invention; FIG. 25 shows a schematic diagram of the change in calculation time in Embodiment 7 of the present invention.

Detailed ways

The present invention will be further described in detail below by means of the accompanying drawings and preferred embodiments. Through these descriptions, the features and advantages of the present invention will become more apparent.

The present invention provides a hypersonic aircraft trajectory tracking method based on virtual target state filtering, as shown in Figure 1, the method includes the following steps:

Step 1, arrange a detection station, and continuously detect whether there is a target in the area through the detection station, and the target is a hypersonic aircraft;

The hypersonic vehicle mentioned in this application refers to an aircraft with a flight speed above Mach 5; the coordinate position of each detection station in this application is known, and the detection station includes a radar detector, that is, real-time detection by radar Target, find the target and obtain the azimuth, and directly read the target state without using the radar, so as to avoid the defect of excessive error when the traditional radar reads the distance of the high-speed object.

Step 2, after finding the target, give the initial target state, and select the sampling point, start sampling, and obtain the observed value;

The state described in this application includes position and speed, and the target state is the position and speed of the target. Since both position and speed have three components in the northeast sky coordinate system, the target state can be expressed as the following matrix:

[x _p (k) x _v (k) y _p (k) y _v (k) z _p (k) z _v (k)] ^T

Among them, x _p (k) represents the position component of the east in the northeast sky coordinate system, x _v (k) represents the velocity component of the east in the northeast sky coordinate system, and y _p (k) represents the position component of the north in the northeast sky coordinate system, y _v (k) represents the velocity component of the north in the northeast celestial coordinate system, z _p (k) represents the upper position component in the northeast celestial coordinate system, z _v (k) represents the upper velocity component in the northeast celestial coordinate system;

The sampling point described in this application is a concept of time. After the target is found, one sampling is performed at intervals of one sampling period T, and another sampling is performed after one sampling period T. The total number of sampling times is M, and the total sampling time _Ttotal =M×T, and the sampling includes observation by a detection station to obtain observed values, and also includes estimating the position of the virtual target.

The observations include two azimuths of the target in the northeast sky coordinate system relative to the detection station obtained through the detection of the detection station, specifically, one of the azimuths is the pitch angle θ(k), and the other azimuth is the heading angle φ(k).

The initial target state is a group of random target states given according to the speed characteristics of the hypersonic vehicle.

Step 3, at each sampling point, a plurality of virtual target states are estimated according to the initial target state;

In this application, each virtual target state is a virtual estimated value that does not actually exist. Specifically, it is a possible target state, which is matrix data including speed information and position information, and its position information is basically distributed in the real target position. around;

In step 3, each virtual target state is estimated by the following formula (1),

X(k)＝ΦX(0)+ΓB(k-1)+10ΓW(k) (one)

Among them, X(k) represents the virtual target state, X(0) represents the initial target state, B(k-1) represents the maneuvering acceleration of the target, W(k) represents the process noise, and both Φ and Γ represent matrix coefficients.

When estimating the state of the virtual target, the value of the maneuvering acceleration B(k-1) of the target is:

B(k-1)＝[x _b x _b y _b y _b z _b z _b ] ^T

Among them, x _b randomly selects any number from 20m/s ² to 40m/s ² , y _b randomly selects any number from 7m/s ² to 13m/s ² , z _b randomly selects any number from 20m/s ² to 40m/s Any number from ² .

When estimating the virtual target state, the value of the process noise W(k) is:

W(k)＝[s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ ] ^T

Among them, s ₁ , s ₂ , s ₃ , s ₄ , s ₅ and s ₆ are all random numbers conforming to a normal distribution with a mean of 0, a variance of 1, and a standard deviation of 1.

The matrix coefficients Φ and Γ are obtained by the following formulas (2) and (3):

Among them, T represents the sampling period.

Step 4, resampling the virtual target state of each sampling point according to the observed value of the sampling point;

Described step 4 comprises following sub-steps:

Sub-step 1: Solve the two azimuth angles of each virtual target state in the northeast sky coordinate system relative to the detection station, namely the azimuth angle of the virtual target state; the calculation of the azimuth angle is mainly by calling the virtual target state The coordinates of the target and the coordinates of the detection station are used to solve the problem;

Sub-step 2: Make a difference between the two azimuth angles of the virtual target state and the two azimuth angles in the observed value, and calculate the square root of the two differences; that is, the difference between the pitch angle of the virtual target state and the pitch angle of the observed value is obtained A difference value, the heading angle of the virtual target state and the heading angle of the observed value are differenced to obtain another difference, and then the square root of the two difference values is calculated.

Sub-step 3: Substituting the square root of each virtual target state into the Gaussian distribution function to obtain the weight of each virtual target state; in the Gaussian distribution function:

Where R represents the mean square error of the observation distance, R=0.01×π/180, |R| represents the determinant of R, z ₃ (k) represents the square root of the angle of the kth virtual target state, and 10 ^-99 is the adjustment coefficient;

In sub-step 4, the virtual target state with a smaller weight is deleted, and the virtual target state with a larger weight is copied, so that the total number of virtual target states remains consistent, thereby completing the resampling of the virtual target state.

Wherein, in sub-step 4, the size of the weight can be judged by setting a specific critical value, and specific copying conditions can be set according to the number of virtual target states to be deleted.

Preferably, the following operations can also be performed in sub-step 4:

Sub-sub-step 1, divide the weight of each virtual target state by the sum of all virtual target state weights in the sampling point to obtain the normalized weight of each virtual target state;

Sub-substep 2, accumulate the normalized weights of each virtual target state through the cumsum() function, and generate a set of random number sequences composed of N random numbers through the rand function, each number is between 0-1 , and use the sort function to complete the ascending order; the N is the number of virtual target states of the sampling point; thereby constructing a double loop function;

Sub-step 3, in the double loop function, the number of columns of the weight accumulation sequence cdf is the outer loop; the inner loop is: the number of random number columns, that is, the number of pointers is less than or equal to the number of virtual target states and when the number of random number columns corresponds to the number of elements is less than the number of elements corresponding to the weight accumulation sequence cdf, copy the column number of the weight accumulation sequence corresponding to cdf to the output index function outIndex, and add one to its pointer number. Specifically, when the random number sequence corresponds to the number of columns If the element is smaller than the corresponding column number element of the weight accumulation sequence cdf, it means that the weight value of the element weight value corresponding to the weight accumulation sequence cdf can accommodate a random number, and record the position of the sequence where the virtual target state with a large weight is located, so as to facilitate subsequent calls.

In sub-step 4, after completing the calculation of the double loop function, a new virtual target state combination can be obtained by performing column fetching on the output index function outIndex, thereby completing the resampling operation of the virtual target state.

Among them, in the double cycle function, the virtual target state with a large weight has a large value difference with the previous column in the weight accumulation sequence cdf, so it can be repeated in the comparison with the elements of the random sequence, which makes the virtual target The column number of the state is copied to the outIndex function multiple times; at the same time, the virtual target state with small weight will not or rarely be copied to the output index function outIndex. During the resampling process, because there is no pointer number, the virtual target state obtained by resampling The target state no longer includes the virtual target state with a small weight and no number of pointers; the total number of final virtual target states remains unchanged and is still N.

In this application, the weights of N virtual target states are obtained through weight normalization, which we call the weight sequence, and their ordering in the matrix is disorderly. The meaning of the cumsum() function is: if A is a vector, then cumsum(A) returns a vector, the elements of the mth row in the vector are the cumulative sum of all the elements from the 1st row to the mth row in A. After the weight sequence is calculated by the cumsum() function, it becomes the weight accumulation sequence cdf.

The double loop function described in this application is a form of loop, which refers to the loop statement of double loop in the program.

Step 5: Determine the target state corresponding to the sampling point according to the virtual target state obtained by resampling.

In step 5, the target state corresponding to the sampling point is obtained by performing a weighted average on all the virtual target states obtained by resampling in the sampling point.

When the detection station is provided with one, the target state corresponding to each sampling point obtained in step 5 is the detection result of the target;

When there are multiple detection stations, the average value of the target state obtained at the same sampling point among multiple detection stations is the detection result of the target.

In the actual working process, due to the synchronization problem of information transmission between various detection stations, the two sampling points whose absolute time is closest to each other on multiple detection stations can be identified as the same sampling point.

There are more than 50 sampling points, preferably 100 sampling points.

The number of virtual target states set in each sampling point is consistent with each other, preferably, the number of virtual target states set in each sampling point is more than 100; more preferably, 10000 virtual target states are set in each sampling point .

Example 1:

When the influence of maneuvering acceleration on the target is not considered, only the state of the target during hypersonic flight is observed, that is, the maneuvering acceleration of the target is defaulted to 0, and the initial speed is about five times the speed of sound;

The initial speed of the given target in the three directions of the northeast sky is V _x = 1000m/s, V _y = 900m/s, V _z = 1040m/s respectively, the combined speed is 1700.47m/s, and the given initial position x ₀ = 1m, y ₀ =20m, z ₀ =10m;

A 346-type active phased array radar is installed in the detection station, the number of sampling points is M=100, and the sampling period is T=1s.

There is only one detection station, and its number of virtual target states at each sampling point is N=100. The specific process is as follows:

Step 1. After the target is found at the detection station, the initial target state is given, namely: the initial velocities in the three directions of the northeast sky are V _x =1000m/s, V _y =900m/s, V _z =1000m/s, and the initial Position x ₀ =0m, y ₀ =0m, z ₀ =0m

Step 2, period T=1s, 100 sampling points are set, and when each sampling point is obtained by detection station detection, the target is in the northeast sky coordinate system relative to the two azimuth angles of the detection station;

Step 3, estimate 100 virtual target states by the following formula (1) at each sampling point;

X(k)＝ΦX(0)+10ΓW(k) (one)

Among them, X(k) represents the virtual target state, X(0) represents the initial target state, W(k) represents the process noise, and both Φ and Γ represent matrix coefficients;

Step 4, resampling the virtual target state of each sampling point according to the observed value of the sampling point;

Specifically, firstly, the two azimuth angles of each virtual target state relative to the detection station in the northeast sky coordinate system are solved separately;

Secondly, the two azimuth angles of the virtual target state are different from the two azimuth angles in the observation value, and the square root of the two difference values is calculated;

Again, the square root of each virtual target state is substituted into the Gaussian distribution function to obtain the weight of each virtual target state;

Finally, the virtual target state with a large weight is indexed multiple times, and the virtual target state with a small weight is indexed a few times or the index amount is 0, so that the total number of virtual target states remains consistent, thereby completing the resampling of the virtual target state.

In step 5, the weighted average value of the virtual target state obtained by resampling is used as the measurement target state corresponding to the sampling point.

Obtain the real trajectory and measurement trajectory of the target within the _total sampling time T = M × T time, that is, the real trajectory and measurement trajectory within 100 seconds, as shown in Figure 2, where the red solid line represents the target's real trajectory, and the blue dotted line represents the measurement trajectory ;

In addition, FIG. 3 shows the variation of the tracking error within 100 seconds, and FIG. 4 shows the variation of the time used to calculate the measurement target state in each sampling period.

According to the above results, the final flight position of the target is x- _end = 98500m, y- _end = 88450m, z- _end = 102500m, the distance from the initial position is 167410.0m, the maximum error is 11200m, the maximum tracking error rate is 6.69%, the unit sampling period The time required to obtain the measurement target state fluctuates around 0.0049s.

The tracking error basically remained stable in the first 60 sampling points, and the overall did not exceed or remained at 2000m, but the subsequent error showed a sharp increase, and the overall trend was also on the rise, because the target flight was affected by the state of the previous moment and the random error. However, the detection method in this application only tracks within the range of several times the random error according to the initial state, and the cumulative error of the simulated pre-flight target is not large and is within the filtering error range of the virtual target state, so it has better tracking results. However, as time goes by, the cumulative error is greater than the filtering error range of the virtual target state. Although the virtual target state takes the most deviated value within the range, it still has a large error with the actual state, so the error will show an upward trend over time. During the sampling point 50-60, the period error also dropped sharply, because the random error of the target had the opposite value, so that the range of the target flight state was included in the filtering range of the virtual target state, so it showed a downward trend. In addition, since the number of virtual target states is 100, it cannot completely cover the vicinity of the target state at a certain sampling point, so when the number of particles is 100, there is a probability that the error will be small, but in most cases the error is large.

Example 2

The experimental condition that is substantially consistent with embodiment 1 is set, adopts the experimental process that is substantially consistent with embodiment 1, and its difference is that 1000 virtual target states are set at each sampling point;

Obtain the real trajectory and measurement trajectory of the target within the total sampling time T _total = M × T time, that is, within 100 seconds, as shown in Figure 5, where the red solid line represents the real trajectory of the target, and the blue dotted line represents the measurement trajectory ;

In addition, FIG. 6 shows the variation of the tracking error within 100 seconds, and FIG. 7 shows the variation of the time used to calculate the measurement target state in each sampling period.

According to the above results, the final flight position of the target is x- _end = 98250m, y- _end = 88630m, z- _end = 102500m, the distance from the initial position is 167358.3m, the maximum error is 4134m, the maximum tracking error rate is 2.47%, the unit sampling period The time required to obtain the measurement target state fluctuates around 0.042s.

The overall tracking error is on the rise, and the simulation effect of 1000 particles on the state at the same time is still not ideal.

Example 3

The experimental conditions substantially consistent with embodiment 1 are set, and the experimental process substantially consistent with embodiment 1 is adopted, the difference being that 10,000 virtual target states are set at each sampling point;

Obtain the real trajectory and measurement trajectory of the target within the total sampling time T _total = M × T time, that is, within 100 seconds, as shown in Figure 8, wherein the red solid line represents the target's real trajectory, and the blue dotted line represents the measurement trajectory ;

In addition, FIG. 9 shows the variation of the tracking error within 100 seconds, and FIG. 10 shows the variation of the time used to calculate the measurement target state in each sampling period.

According to the above results, the final flight position of the target is at the _end of x = 99840m, _{at the end} of y = 89590m, _{at the end} of z = 103600m, the distance from the initial position is 169474.2m, the maximum error is 2277m, the maximum tracking error rate is 1.34%, and the unit sampling period The time required to obtain the measurement target state fluctuates around 0.42s.

Although the overall error is on the rise when the number of particles is 10000, most of the sampling point errors are controlled within 1000m. Compared with N=100 and N=1000, it can be concluded that the more the number of particles, the poorer the tracking distance. The smaller the value, the higher the tracking accuracy. However, the appearance of error accumulation still exists. In theory, when the ratio of particle simulation random error to target state random error is higher and the number of virtual target states is sufficiently large, the tracking error can be greatly reduced. But at the same time, since when N=100, 1000 and 10000, the single-step calculation time is 0.0049s, 0.042s and 0.40s respectively, that is, the calculation time gradually increases, so in the actual tracking process, the hardware computing power and error should be considered Between multiples and tracking effects, setting the number of virtual target states to 10,000 is the most cost-effective overall.

Example 4

The experimental condition that is basically consistent with embodiment 2 is set, adopts the experimental process that is basically consistent with embodiment 2, and its difference is to set two detection stations, the average value of the target state that same sampling point obtains between two detection stations is to The detection result of the target, that is, the measurement target state;

Obtain the real trajectory and measurement trajectory of the target within the _total sampling time T = M × T time, that is, the real trajectory and the measurement trajectory within 100 seconds, as shown in Figure 11, wherein the red solid line represents the target's real trajectory, and the blue dotted line represents the measurement trajectory ;

In addition, FIG. 12 shows the variation of the tracking error within 100 seconds, and FIG. 13 shows the variation of the time used to calculate the measurement target state in each sampling period.

According to the above results, the final flight position of the target is x- _end = 99310m, y- _end = 90240m, z- _end = 103200m, the distance from the initial position is 169263.4m, the maximum error is 2998m, the maximum tracking error rate is 1.77%, the unit sampling period The time required to obtain the measurement target state fluctuates around 0.1s.

Example 5

The experimental conditions that are basically consistent with Example 4 are set, and the experimental process that is basically consistent with Example 4 is adopted. The difference is that 4 testing stations are set, and the average value of the target state obtained at the same sampling point between the 4 testing stations is the same as The detection result of the target, that is, the measurement target state;

Obtain the real trajectory and measurement trajectory of the target within the total sampling time T _total = M × T time, that is, within 100 seconds, as shown in Figure 14, wherein the red solid line represents the target's real trajectory, and the blue dotted line represents the measurement trajectory ;

In addition, FIG. 15 shows the variation of the tracking error within 100 seconds, and FIG. 16 shows the variation of the time used to calculate the measurement target state in each sampling period.

According to the above results, the final flight position of the target is x- _end = 98800m, y- _end = 89570m, z- _end = 103400m, the distance from the initial position is 168730.4m, the maximum error is 1215m, the maximum tracking error rate is 0.72%, unit sampling period The time required to obtain the measurement target state fluctuates around 0.2s.

Example 6

The experimental condition that is basically consistent with embodiment 4 is set, and the experimental process that is basically consistent with embodiment 4 is adopted. The difference is that 6 detection stations are set, and the average value of the target state obtained at the same sampling point between the 6 detection stations is the same as The detection result of the target, that is, the measurement target state;

Obtain the real trajectory and measurement trajectory of the target within the _total sampling time T=M×T time, that is, the real trajectory and the measurement trajectory within 100 seconds, as shown in Figure 17, wherein the red solid line represents the target's real trajectory, and the blue dotted line represents the measurement trajectory ;

In addition, FIG. 18 shows the variation of the tracking error within 100 seconds, and FIG. 19 shows the variation of the time used to calculate the measurement target state in each sampling period.

According to the above results, the final flight position of the target is x- _end = 98790m, y- _end = 89400m, z- _end = 103200m, the distance from the initial position is 168511.8m, the maximum error is 663.7m, the maximum tracking error rate is 0.39%, unit sampling The time required to obtain the measurement target state within a cycle fluctuates around 0.28s.

When the number of detection stations is 2, 4, and 6, the maximum tracking error rates are 1.77%, 0.72%, and 0.39%, respectively, and the average error decreases in turn. Therefore, it can be concluded that with the increase of the number of monitoring stations, the tracking error value It can be gradually reduced because the increase in the number of monitoring stations can make the values obtained by each monitoring station after particle filter tracking obtain the mean value, thereby reducing the influence of observation errors. Compared with the number of virtual target states in Example 2 as 1000, when the number of detection stations is 1, the error is greatly reduced in turn, but at the same time, the single-step calculation time is gradually increased, and the requirements for hardware are increased. In summary, increasing the number of monitoring stations is an effective way to effectively reduce the error of tracking hypersonic targets.

Example 7

When considering the influence of maneuvering acceleration on the target, the target trajectory will no longer move according to the approximate straight line, and the trajectory is in the shape of a parabola. The basic data similar to those in Embodiment 1 are selected for use. The difference is that the number of virtual target states N=10000,

The experimental process similar to that in Example 1 is selected for use, the difference is:

The initial target state given in step 1 is: the initial velocities in the three directions of the northeast sky are V _x =100m/s, V _y =90m/s, V _z =104m/s, the initial position x ₀ =0m, y ₀ =0m, z ₀ =0m,

Estimate 100 virtual target states by following formula (-') at each sampling point in step 3;

X(k)＝ΦX(0)+ΓB(k-1)+10ΓW(k) (one’)

Among them, the value of the maneuvering acceleration B(k-1) of the target is:

B(k-1)＝[x _b x _b y _b y _b z _b z _b ] ^T

Among them, x _b randomly selects any number from 20m/s ² to 40m/s ² , y _b randomly selects any number from 7m/s ² to 13m/s ² , z _b randomly selects any number from 20m/s ² to 40m/s Any number from ² .

Obtain the real trajectory and measurement trajectory of the target within the _total sampling time T = M × T time, that is, the real trajectory and the measurement trajectory within 100 seconds, as shown in Figure 20, wherein the red solid line represents the target's real trajectory, and the blue dotted line represents the measurement trajectory ;

In addition, Figure 21 shows the change of tracking error within 100 seconds, Figure 22 shows the schematic diagram of the displacement and velocity change in the X direction within 100 seconds, that is, the east direction, and Figure 23 shows the displacement and velocity change in the Y direction within 100 seconds, that is, the north direction. Schematic diagram of displacement and velocity changes. Figure 24 shows a schematic diagram of displacement and velocity changes in the Z direction, that is, in the height direction within 100 seconds; through these three figures, it can be proved that the introduced maneuvering acceleration has a significant impact on the trajectory of the target. That is, linear motion with variable acceleration is performed in each of the three directions, which is different from the uniform linear motion in the first six embodiments. Fig. 25 shows the variation of the time used to calculate and measure the target state in each sampling period.

According to the above results, it can be seen that the final flight position of the target is x- _end =155200m, y- _end =54190m, z- _end =144700m, the distance from the initial position is 218989.3m, the maximum tracking error rate is 0.83%, and the measurement target state is obtained within the unit sampling period The required time fluctuates around 0.4s. It can be concluded that even after the maneuvering acceleration is introduced, the hypersonic vehicle trajectory tracking method provided by the present application still has a good tracking effect on the target.

The present invention has been described in detail above with reference to preferred embodiments and illustrative examples. However, it should be declared that these specific embodiments are only illustrative explanations of the present invention, and do not constitute any limitation to the protection scope of the present invention. Without departing from the spirit and protection scope of the present invention, various improvements, equivalent replacements or modifications can be made to the technical contents and implementation methods of the present invention, all of which fall within the protection scope of the present invention. The protection scope of the present invention shall be determined by the appended claims.

Claims (10)

1. A hypersonic vehicle trajectory tracking method, characterized in that:

   The method comprises the steps of:

   Step 1, arrange a detection station, and continuously detect whether there is a target in the area through the detection station, and the target is a hypersonic aircraft;

   Step 2, after the target is found, give the initial target state, and select the sampling point, start sampling, and obtain the observation value, the observation value includes the two coordinates of the target relative to the detection station in the northeast sky coordinate system obtained through detection station detection. azimuth;

   Step 3, at each sampling point, a plurality of virtual target states are estimated according to the initial target state;

   Step 4, resampling the virtual target state of each sampling point according to the observed value of the sampling point;

   Step 5: Determine the target state corresponding to the sampling point according to the virtual target state obtained by resampling.
2. The hypersonic vehicle trajectory tracking method according to claim 1, characterized in that:

   In step 3, each virtual target state is estimated by the following formula (1),

   X(k)＝ΦX(0)+ΓB(k-1)+10ΓW(k) (one)

   Among them, X(k) represents the virtual target state,

   X(0) represents the initial target state,

   B(k-1) represents the maneuvering acceleration of the target,

   W(k) represents the process noise,

   Both Φ and Γ represent matrix coefficients.
3. The hypersonic vehicle trajectory tracking method according to claim 2, characterized in that:

   When estimating the state of the virtual target, the value of the maneuvering acceleration B(k-1) of the target is:

   B(k-1)＝[x _b x _b y _b y _b z _b z _b ] ^T

   Among them, x _b randomly selects any number from 20m/s ² to 40m/s ² ,

   y _b randomly selects any number from 7m/s ² to 13m/s ² ,

   z _b Randomly select any number from 20m/s ² to 40m/s ² .
4. The hypersonic vehicle trajectory tracking method according to claim 2, characterized in that:

   When estimating the virtual target state, the value of the process noise W(k) is:

   W(k)＝[s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ ] ^T

   Among them, s ₁ , s ₂ , s ₃ , s ₄ , s ₅ and s ₆ are all random numbers conforming to a normal distribution with a mean of 0, a variance of 1, and a standard deviation of 1.
5. The hypersonic vehicle trajectory tracking method according to claim 2, characterized in that:

   The matrix coefficients Φ and Γ are obtained by the following formulas (2) and (3):

   

   

   Among them, T represents the sampling period.
6. The hypersonic vehicle trajectory tracking method according to claim 1, characterized in that:

   Described step 4 comprises following sub-steps:

   Sub-step 1: Solve the two azimuth angles of each virtual target state relative to the detection station in the northeast sky coordinate system;

   Sub-step 2: Make a difference between the two azimuth angles of the virtual target state and the two azimuth angles in the observed value, and calculate the square root of the two difference values;

   Sub-step 3: Substitute the square root of each virtual target state into the Gaussian distribution function to obtain the weight of each virtual target state;

   In sub-step 4, the virtual target state with a smaller weight is deleted, and the virtual target state with a larger weight is copied, so that the total number of virtual target states remains consistent, thereby completing the resampling of the virtual target state.
7. The hypersonic vehicle trajectory tracking method according to claim 1, characterized in that:

   In step 5, the target state corresponding to the sampling point is obtained by performing a weighted average on all the virtual target states obtained by resampling in the sampling point.
8. The hypersonic vehicle trajectory tracking method according to claim 1, characterized in that:

   When the detection station is provided with one, the target state corresponding to each sampling point obtained in step 5 is the tracking result of the target;

   When there are multiple detection stations, the average value of the target states obtained at the same sampling point among multiple detection stations is the detection result of the target.
9. The hypersonic vehicle trajectory tracking method according to claim 1, characterized in that:

   There are more than 50 sampling points, preferably 100 sampling points.
10. The hypersonic vehicle trajectory tracking method according to claim 1, characterized in that:

    The number of virtual target states set in each sampling point is consistent. Preferably, the number of virtual target states set in each sampling point is more than 100; more preferably, 10000 virtual target states are set in each sampling point.

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