Ballistic extrapolation method for estimating optimal ballistic coefficient based on RANSAC

Abstract

The invention provides a ballistic extrapolation method for estimating an optimal ballistic coefficient based on RANSAC (Random Sample Consensus). The method comprises the following steps: firstly, acquiring part of ballistic trajectory data of a flying projectile by using the emplacement reconnaissance and calibration radar, and carrying out secondary filtering on the part of ballistic trajectory data so as to reduce a measurement error generated in a radar measurement process and reduce a ballistic extrapolation distance; then, an RANSAC (Random Sample Consensus) algorithm is adopted to calculate different data parameter models for different ballistic coefficients and trace point data, and an optimal model is selected by utilizing a root-mean-square error, so that an optimal estimated ballistic coefficient is obtained; and finally, extrapolation is carried out by using the optimal estimation ballistic coefficient so as to improve the emplacement extrapolation precision. According to the method, the trajectory extrapolation precision can be greatly improved, and the shot point of emplacement extrapolation is more accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a trajectory extrapolation method based on RANSAC estimation of an optimal trajectory coefficient. Background Art

[0002] As the detection distance of the artillery position detection and calibration radar becomes longer and longer, the requirements for the accuracy of trajectory extrapolation become higher and higher. According to existing research results, the ballistic coefficient C n It is an important parameter that affects the trajectory extrapolation, and is used to characterize the characteristics of the projectile itself and its interaction with the air. Each type of bullet has its own characteristics, and the ballistic coefficients of different types of bullets are different. The ballistic coefficient values ​​of the same type of bullet will be slightly different at different launch angles. Therefore, improving the estimation error of the ballistic coefficient is also the key to improving the accuracy of trajectory extrapolation. The calculation process of the existing trajectory extrapolation method is generally: select 5-20 point trace data, then iteratively estimate the ballistic coefficient, and finally perform trajectory extrapolation. For example, the most common method is based on the Kalman filter method, which filters the radar measured data to obtain the filter value, obtains the relevant parameters required for the ballistic equation according to the filter value, obtains the ballistic coefficient by artificial estimation, and then uses the Runge-Kutta equation to perform gun position extrapolation. Due to the small number of data samples and the low accuracy of the ballistic coefficient estimation, the data measurement error and the ballistic coefficient estimation error will be further amplified by the iterative calculation method, and the accuracy of the gun position extrapolation will be greatly reduced. Summary of the invention

[0003] In order to overcome the shortcomings of the existing trajectory extrapolation methods, such as the long extrapolation distance and the low accuracy of gun position extrapolation caused by the error in ballistic coefficient estimation, the present invention provides a trajectory extrapolation method based on RANSAC estimation of the optimal ballistic coefficient. First, a gun position reconnaissance and calibration radar is used to obtain partial ballistic trajectory data of the flying projectile, and secondary filtering is performed on it to reduce the measurement error generated in the radar measurement process and reduce the trajectory extrapolation distance; then, the RANSAC algorithm is used to calculate different data parameter models for different ballistic coefficients and point trace data, and the optimal model is selected using the root mean square error to obtain the optimal estimated ballistic coefficient; finally, the optimal estimated ballistic coefficient is used for extrapolation to improve the accuracy of gun position extrapolation. The present invention can greatly improve the accuracy of trajectory extrapolation, making the firing point of gun position extrapolation more accurate.

[0004] A trajectory extrapolation method for estimating an optimal ballistic coefficient based on RANSAC, characterized by the following steps:

[0005] Step 1: Use the gun position detection radar to obtain the ballistic point data of N points on the ascending arc of the projectile flight, and filter it. Perform secondary filtering on the filtered point data, and use the secondary filtered point data and the ballistic equation to calculate the preliminary estimate of the ballistic coefficient C. n ; The value range of N is [20,30];

[0006] The specific process of the secondary filtering is: taking the end point of the origin trace data as the starting point of the filtered data, taking the starting point of the origin trace data as the end point of the filtered data, reversely arranging the coordinate vectors of each point, and inverting the velocity component of each point on each coordinate axis to obtain the point trace data after the secondary filtering;

[0007] Step 2: Use the RANSAC algorithm to calculate the initial estimate C of the point data and the ballistic coefficient n Processing is performed to obtain the initialization parameter model E;

[0008] Step 3: Set the initial value of the ballistic coefficient to C n -0.2, the ballistic coefficient gradually increases with a step size of 0.01, and the RANSAC algorithm is used to calculate the matching parameter model Y for each ballistic coefficient and point data i , where i represents the i-th ballistic coefficient. Then, the root mean square error between each parameter model and the initialization model E is calculated, and the model with the smallest root mean square error is taken as the optimal parameter model, and the ballistic coefficient value corresponding to the optimal parameter model is taken as the optimal ballistic coefficient estimate;

[0009] Step 4: Use the variable-step fourth-order Runge-Kutta iterative algorithm to perform trajectory extrapolation calculations to obtain the projectile's shooting point coordinates.

[0010] The beneficial effects of the present invention are as follows: due to the use of secondary filtering processing, the error generated in the radar data measurement process can be reduced and the ballistic extrapolation distance can be reduced, thereby improving the ballistic coefficient estimation accuracy and extrapolation accuracy; due to the use of the RANSAC algorithm for parameter model calculation, abnormal points or noise in the model can be effectively eliminated, and a more accurate ballistic coefficient estimation value can be obtained, thereby greatly improving the extrapolation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of a trajectory extrapolation method for estimating the optimal ballistic coefficient based on RANSAC of the present invention. DETAILED DESCRIPTION

[0012] The present invention is further described below in conjunction with the accompanying drawings and embodiments. The present invention includes but is not limited to the following embodiments.

[0013] As shown in the figure, the present invention provides a trajectory extrapolation method based on RANSAC to estimate the optimal ballistic coefficient, and its specific implementation process is as follows:

[0014] Step 1: Use the gun position detection radar to obtain the ballistic point data of N points on the ascending arc of the projectile flight, and filter it. Perform secondary filtering on the filtered point data, and use the secondary filtered point data and the ballistic equation to calculate the preliminary estimate of the ballistic coefficient C. n Among them, the value range of N is [20,30], and more sample data are selected to improve the extrapolation accuracy.

[0015] The traditional method obtains a preliminary estimate of the ballistic coefficient by filtering the measurement data of the gun position detection radar. Directly using this ballistic coefficient for trajectory extrapolation will result in excessive extrapolation errors. In addition, the accuracy of gun position extrapolation is proportional to the square of time. It can be concluded that the longer the gun position extrapolation distance, the lower the gun position extrapolation accuracy. Therefore, the present invention adopts a method of secondary filtering of the point trace data to reduce the error generated in the radar data measurement process and reduce the trajectory extrapolation distance, thereby improving the accuracy of the estimated value of the ballistic coefficient and the accuracy of gun position extrapolation. The specific process of the secondary filtering is: take the end point of the original point trace data as the starting point of the filtered data, take the starting point of the original point trace data as the end point of the filtered data, reversely arrange the coordinate vectors of each point, and invert the velocity component of each point on each coordinate axis to obtain the point trace data after secondary filtering.

[0016] Step 2: Use the RANSAC algorithm to calculate the initial estimate C of the point data and the ballistic coefficient n After processing, the initialization parameter model E is obtained.

[0017] Step 3: Assuming that the optimal ballistic coefficient value varies within ±0.2 of the initial estimate of the ballistic coefficient, set the initial value of the ballistic coefficient to C n -0.2, the ballistic coefficient gradually increases with a step size of 0.01, and the RANSAC algorithm is used to calculate the matching parameter model Y for each ballistic coefficient and point data i , where i represents the i-th ballistic coefficient. Then, the root mean square error between each parameter model and the initialization model E is calculated, and the model with the smallest root mean square error is taken as the optimal parameter model, and the ballistic coefficient value corresponding to the optimal parameter model is taken as the optimal ballistic coefficient estimate.

[0018] The original ballistic extrapolation algorithm estimates the ballistic coefficient by manual valuation, which results in too much human experience interference and inaccurate ballistic coefficient value. The RANSAC algorithm can not only remove abnormal points or noise in the model, but also obtain the optimal parameter model through the size of the root mean square error value. Through model matching, the model with the smallest root mean square error between models is the optimal parameter model, and the corresponding ballistic coefficient is the optimal ballistic coefficient, which can improve the estimation accuracy of the ballistic coefficient, thereby improving the accuracy of gun position extrapolation.

[0019] Step 4: Use the variable-step fourth-order Runge-Kutta iterative algorithm to perform trajectory extrapolation calculations to obtain the projectile's shooting point coordinates.

[0020] Through experiments using real radar measurement data, it is found that the method of the present invention can improve the accuracy of gun position extrapolation from the original 3‰ to 3.5‰ to 2‰, and has a better trajectory extrapolation effect.

Claims

1. A trajectory extrapolation method based on RANSAC to estimate the optimal ballistic coefficient, characterized in that Here are the steps: Step 1: Use the gun position detection radar to obtain the ballistic point data of N points on the ascending arc of the projectile flight, and filter it. Perform secondary filtering on the filtered point data, and use the secondary filtered point data and the ballistic equation to calculate the preliminary estimate of the ballistic coefficient C. n ; The value range of N is [20,30]; The specific process of the secondary filtering is: taking the end point of the origin trace data as the starting point of the filtered data, taking the starting point of the origin trace data as the end point of the filtered data, reversely arranging the coordinate vectors of each point, and inverting the velocity component of each point on each coordinate axis to obtain the point trace data after the secondary filtering; Step 2: Use the RANSAC algorithm to calculate the initial estimate C of the point data and the ballistic coefficient n Processing is performed to obtain the initialization parameter model E; Step 3: Set the initial value of the ballistic coefficient to C n -0.2, the ballistic coefficient gradually increases with a step size of 0.01, and the RANSAC algorithm is used to calculate the matching parameter model Y for each ballistic coefficient and point data i , where i represents the i-th ballistic coefficient. Then, the root mean square error between each parameter model and the initialization model E is calculated, and the model with the smallest root mean square error is taken as the optimal parameter model, and the ballistic coefficient value corresponding to the optimal parameter model is taken as the optimal ballistic coefficient estimate; Step 4: Use the variable-step fourth-order Runge-Kutta iterative algorithm to perform trajectory extrapolation calculations to obtain the projectile's shooting point coordinates.

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