Nonlinear aiming line modeling method for target azimuth prediction

A technology of target orientation and modeling method, which is applied in the directions of measuring devices, measuring angles, surveying and navigation, etc., and can solve the problems of non-negligible model errors, errors, and affecting the accuracy of projectile hits, etc.

Active Publication Date: 2020-09-04
NORTHWESTERN POLYTECHNICAL UNIV
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AI-Extracted Technical Summary

Problems solved by technology

[0003]At present, the existing line-of-sight prediction technology mainly adopts the linear model of target azimuth and time. Although the model is simple and easy to use, it has errors compared with ...
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Method used

As can be seen from the results of Table 1, under the target motion condition in the simulation, there is a large error in the line of sight prediction linear model, and the projectile position error caused reaches 7.12m, which cannot reach the requirements of actual use at all. However, the angle error predicted by the nonlinear model is only 6.40′, which causes the position error of the emitter to be 0.97m, and the position error of the emitter is reduced to less than 1m. Compared with the linear model, the position accuracy is improved by more than 6m. Since the same motion conditions and inertial sen...
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Abstract

The invention provides a nonlinear aiming line modeling method for target azimuth prediction, which comprises the following steps that: a shooter aims at and locks a target when the target is closestto a launching point, so that an aiming line moves along with the target, and the target is ensured to be on the aiming line; the target is continuously tracked before the launcher launches, and the angle is updated by utilizing an inertia measurement assembly on the launcher, and time and the angle rotated by the aiming line are outputted; then an objective function of the aiming line predictionnonlinear model is established and solved; an optimal solution of parameters in the aiming line prediction nonlinear model then is calculated by utilizing a nonlinear least square algorithm; and the position of the virtual aiming line is estimated according to the aiming line prediction model after the launcher launches, so that the launcher tracks the target. According to the invention, the emitter aiming device is used for aiming at a target when a target motion trail is approximately vertical to the aiming line direction, the inertia measurement assembly of the emitter is used for measuringthe rotation angle of the aiming line, multiple times of aiming line angle measurement are completed in an aiming stage, and all angle data and corresponding time form measurement data.

Application Domain

Angle measurementNavigational calculation instruments +1

Technology Topic

Computational physicsLeast squares +4

Image

  • Nonlinear aiming line modeling method for target azimuth prediction
  • Nonlinear aiming line modeling method for target azimuth prediction
  • Nonlinear aiming line modeling method for target azimuth prediction

Examples

  • Experimental program(3)

Example Embodiment

[0047] Example 1:
[0048] This embodiment provides a non-linear line-of-sight modeling method for target azimuth prediction based on a non-linear least squares algorithm. When the trajectory of the target and the direction of the line-of-sight are close to perpendicular, the projectile targeting device is used to aim at the target. Time is the initial time of the line of sight prediction process. Keep the target on the line of sight. After a period of time, the target moves along a straight line for a certain distance, and the line of sight also turns to a certain angle with the target. The inertial measurement component of the projectile is used to measure the angle of the line of sight, and multiple lines of sight are completed during the aiming phase. Angle measurement, all angle data and corresponding time constitute measurement data.
[0049] When the line of sight angle is updated, the target advancing distance, the distance from the launch point to the target at the initial time, and the distance from the launch point to the target at the update time form a right triangle. Suppose the line-of-sight angle update time is t, the target movement speed is v, the distance from the launch point to the target at the initial moment is l, and the line-of-sight rotation angle is ψ, then
[0050]
[0051] Define model parameters Then the nonlinear model of line-of-sight prediction is
[0052] ψ(t)=arctan(μt).
[0053] Taking the line-of-sight angle and the corresponding time as the measurement data, the parameter μ can be calculated using the nonlinear least squares method to complete the establishment of the line-of-sight angle model. After the launcher is launched, the real-time orientation of the target can be calculated according to the established nonlinear model. , To achieve the tracking of the emitter to the target.

Example Embodiment

[0054] Example 2:
[0055] On the basis of the scheme disclosed in Example 1, figure 1 1 is the target position at the initial moment of aiming, 2 is the position of the target after a period of movement, 3 is the position of the launching point of the projectile, 4 is the angle that the line of sight tracks the target, 5 is the line of sight position at the moment, and 6 is the target Forward movement distance, 7 is the distance between the launch point and the target at the initial moment of aiming.
[0056] This embodiment presents the relationship between the angle of the line of sight and the time when the target moves along a straight line. The specific steps for modeling the line of sight are given below.
[0057] 1. The shooter aims and locks the target when the target is closest to the launch point, that is, when the target moves to position 1 in the figure, the launcher attitude matrix C 0 = I 3 , The angle of sight ψ(t 0 )=0°, make the line of sight to follow the target to ensure that the target is on the line of sight. In the process of tracking the target, the inertial measurement component on the launcher periodically outputs the increment of the attitude angle under the carrier system, denoted as t k Time angle incremental output
[0058] Δθ k =[Δθ x Δθ y Δθ z ] T , Then update the formula according to the pose matrix:
[0059]
[0060] The updated angle of sight, namely t k The target azimuth at time is:
[0061]
[0062] Where C k (i,j) represents the pose matrix C k The element in row i and column j. A set of measurements (t k ,ψ(t k )).
[0063] 2. Continue to track the target before the launcher is launched, and continuously use the inertial measurement component on the launcher to update the angle, output the time and the angle of the aiming line. Assuming that a total of N attitude updates are performed during the aiming process, the obtained measurement information is:
[0064] (t 1 ,ψ(t 1 )),(t 2 ,ψ(t 2 )),(t 3 ,ψ(t 3 )),…,(T N-1 ,ψ(t N-1 )),(t N ,ψ(t N )).
[0065] 3. Establish the objective function f(μ) for solving the nonlinear model of sight line prediction ψ(t)=arctan(μt) parameter μ. In the kth measurement, the line of sight angle output by the inertial measurement unit is ψ g (t k ), the line of sight angle ψ estimated by the line of sight prediction model m (t k ), the line-of-sight prediction error is:
[0066] δψ(t k )=ψ m (t k )-ψ g (t k )=arctan(μt k )-ψ g (t k ) (3)
[0067] Define the objective function:
[0068]
[0069] The independent variable μ that minimizes the objective function f(μ) * It is the optimal parameter of the line of sight prediction nonlinear model.
[0070] 4. Use nonlinear least squares algorithm to find the optimal solution of the line-of-sight prediction model parameters. Initial value μ of given parameter μ 0 , After the k-th line of sight angle is updated, the parameter update formula is:
[0071] μ k+1 =μ k +λd k (5)
[0072] In the formula, update direction:
[0073]
[0074] Where J k Is the function δψ(t k ) Jacobian matrix. Update step size:
[0075]
[0076] 5. After the launcher is launched, estimate the position of the virtual line of sight based on the line of sight prediction model determined in step 4, so that the launcher can track the target. The predicted aiming angle is:
[0077]
[0078] In the formula, t is the time relative to the start time of aiming.

Example Embodiment

[0079] Example 3:
[0080] This embodiment provides example simulation verification of the solutions of Embodiment 1 and Embodiment 2.
[0081] Assuming that the target moves in a straight line at a uniform speed, the speed is 20m/s, and the line of sight of the projectile points to the target. When the direction of the line of sight is nearly perpendicular to the direction of movement of the target, it starts to aim and track the target. The distance from the target to the launching point is 500m at the initial moment, the shooter will track the target for 5s after aiming, and then the launcher will launch. Assuming that the launcher hits the target after 4s flight, that is, it is necessary to estimate the 4s line of sight angle according to the line of sight prediction model after launch. The simulation time is 9s, the first 5s is based on the output of the inertial measurement component to estimate the line of sight prediction model parameters, and the last 4s is based on the model to predict the line of sight angle. Set the gyroscope sampling time t in the inertial measurement component during simulation s =0.01s, the device error parameter is: gyro zero offset ε=40°/h, gyro angle random walk coefficient
[0082] In the simulation, the nonlinear model of the present invention is compared with the linear model often used in the current line of sight prediction scheme. The relationship between angle and time in the linear model is ψ(t)=at+b, and the two parameters a and b respectively represent the rotational angular velocity and The initial angle.
[0083] The simulation data processing process is as follows:
[0084] 1. Solve the attitude matrix according to the angular velocity output by the inertial measurement component And calculate the target azimuth angle ψ(t);
[0085] 2. 500 attitude updates performed within 0-5s during the aiming process obtain 500 sets of time t and azimuth angle ψ(t) as measurements, and use the above measurements to solve the parameters of the two models;
[0086] 3. Use the least square method to solve the parameters a and b for the linear model. The calculation formula is:
[0087]
[0088] among them,
[0089] 4. Use nonlinear least squares for the nonlinear model to solve the parameter μ through numerical update, first set the initial parameter μ 0 =0, the model error δψ(t k ), calculate the update direction d k And update the step size λ, calculate the new parameter μ k+1 =μ k +λd k , Iterative update until the result meets the target accuracy;
[0090] 5. Perform target azimuth prediction in 5-9s, calculate the real-time azimuth of the target according to the two models established above, and calculate the predicted angle error and the resulting position error.
[0091] At the 9th second, the line-of-sight angle prediction error and the resulting position error of the projectile are listed in Table 1.
[0092] Table 1 Line of sight prediction simulation error
[0093] Predictive model Angle of sight error δψ(') Projectile position error (m) Traditional linear model (ψ(t)=at+b) 46.87 7.12 Non-linear model of the present invention (ψ(t)=arctan(μt)) 6.40 0.97
[0094] From the results in Table 1, it can be seen that under the target motion conditions in the simulation, the line-of-sight prediction linear model has a large error, and the resulting position error of the projectile reaches 7.12m, which completely fails to meet the requirements of actual use. The angle error predicted by the non-linear model is only 6.40', and the position error of the emitter is 0.97m. The position error of the emitter is reduced to less than 1m. Compared with the linear model, the position accuracy is improved by more than 6m. Because the same motion conditions and inertial sensor data are used for simulation, the linear model cannot express the nonlinear relationship between the line-of-sight angle and time, so the error in the linear model is caused by the model error. The simulation results also show that the line-of-sight prediction nonlinear model of the present invention is closer to the relationship between the line-of-sight angle changes with time in actual use, and more accurate line-of-sight angle prediction results can be obtained. Use this nonlinear line-of-sight prediction model for line-of-sight. Prediction can significantly improve the position accuracy of the emitter.

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