A method for predicting a drop point based on matching terrain elevation

Abstract

The application discloses a landing point prediction method based on terrain elevation matching, which converts received aircraft track data into coordinates in a geocentric rectangular coordinate system, then performs polynomial fitting on an XYZ data linked list by using a least square method, then calculates intersection points of a fitted track and an earth ellipsoid after superimposing an elevation, iteratively calculates from the intersection points, finally verifies a time point between a time t1 when a target reaches a starting elevation and a predicted landing point time t0, and verifies N time points in a loop, and if the track elevation of each time point is greater than an altitude of the track point projected on a terrain, the verification is passed, and a final predicted landing point position is output. The method verifies the predicted landing point in view of real problems such as a complex terrain environment in a landing point area, finds a first intersection point of a track and a terrain, improves the accuracy of the predicted landing point, and provides a strong support for smoothly carrying out a target range flight test.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spaceflight measurement and control, and particularly relates to a flight vehicle landing point prediction method based on terrain elevation matching. BACKGROUND

[0002] Landing point prediction is a comprehensive technology. According to the purpose of use, there are two common ways for landing point prediction: the first way is to perform computer simulation prediction on the ballistic missile hit area according to the theoretical flight trajectory before the ballistic missile is launched; and the second way is to accurately predict the flight vehicle landing point by using real-time remote measurement data obtained during the flight of the ballistic missile. At present, the landing point prediction methods at home and abroad are mainly divided into two categories: the first category is an analytical method, that is, based on the elliptical trajectory or parabolic trajectory theory, the air resistance can be ignored during the free flight period of the flight vehicle, so that the trajectory is only affected by the gravity of the earth, and the trajectory is a standard elliptical arc inertial flight; under the influence of air resistance, the trajectory of the reentry section can be approximated as an elliptical trajectory under perturbation motion. Therefore, the trajectory landing point prediction of the ballistic missile can apply the elliptical trajectory theory; the second category is a numerical integration method, which performs detailed force analysis on the free flight section and the reentry section of the ballistic missile trajectory, comprehensively considers the influence of atmospheric dynamics, and performs numerical integration on the trajectory of the ballistic missile, and extrapolates the landing point prediction.

[0003] At present, the landing point prediction model usually does not consider the terrain undulation factor near the landing point, and the ground is approximately treated as a flat surface. If the terrain near the actual landing point is complex and the elevation changes rapidly, the landing point calculated by the approximate flat surface equivalent treatment will have a large error with the actual landing point. Moreover, due to the low angle of the flight vehicle at the end of the descent and the high speed, the external measurement data is difficult to guarantee the accuracy of the final landing point, the prediction landing point result is not ideal, and the effective implementation of the flight vehicle recovery and other tasks will be affected.

[0004] In summary, it is necessary to seek an effective flight vehicle landing point prediction method to provide effective support for target flight experiments. SUMMARY

[0005] The purpose of the application is to provide a landing point prediction method based on terrain elevation matching, so as to solve the technical problem that the final predicted landing point has a large gap with the actual landing point in the prior art flight vehicle landing point prediction method, because the terrain undulation factor is not considered and the ground is approximately treated as a flat surface.

[0006] The purpose of the application is achieved by adopting the following technical solutions:

[0007] A landing point prediction method based on terrain elevation matching comprises the following steps:

[0008] Step 1, pre-process the received N flight vehicle track data to form a track linked list of x, y, z about time t in the geocentric rectangular coordinate system;

[0009] Step 2, polynomial fitting of the track chain list by using least square algorithm;

[0010] Step 3, according to the terrain elevation data, the altitude H of the projection point of the latest track point in the track chain list on the ground is calculated, assuming that the earth is an ideal ellipsoid with altitude H everywhere, the intersection time t0 of the fitted track curve and the earth ellipsoid is calculated as the predicted landing time;

[0011] The track chain list is a 4xN array (X, Y, Z, T), and the matrix method is used to calculate the fitting curve coefficients P of X, Y, Z with respect to T ix ,P iy ,P iz i = 0, 1, 2, …, j (j is the order of the fitting curve)

[0012]

[0013] The intersection point of the second-order fitted track curve and the earth ellipsoid is calculated by the following method:

[0014] Simultaneous fitting of the track polynomial equation

[0015]

[0016] and the equation of the earth ellipsoid

[0017]

[0018] Where a, e are the long semi-axis and short semi-axis of the earth ellipsoid, H is the altitude corresponding to the last guide point latitude and longitude, and a fourth-order polynomial equation about t is obtained

[0019] P(t) = a1t 4 +a2t 3 +a3t 2 +a4t+a5=0 (4)

[0020] Where

[0021]

[0022] The eigenvalue of the adjoint matrix of the polynomial is the solution of the equation, that is, the intersection time t0 of the fitted track curve and the earth ellipsoid, as the predicted landing time.

[0023] Step 4, verify whether the track point elevation at time t0 meets the preset minimum height difference, if it meets the requirement, go to step 6, if it does not meet the requirement, go to step 5;

[0024] Step 5, iteration calculation is carried out on t0 under certain constraints, if the height of the track point corresponding to t0 is higher than the height of the terrain, the predicted drop point time is advanced, if the height of the track point corresponding to t0 is lower than the height of the terrain, the predicted drop point time is pushed back. Then the initial time of iteration is further iteratively optimized by using bisection method to obtain a new predicted drop point time, and step 4 is repeated. When using the height data to iteratively calculate, since the height data does not have a mathematical equation expression, certain constraints are required to make the fitting track and the height data have an optimal solution within a certain number of iterations, the constraints are as follows: (1) maximum iteration number, (2) minimum iteration time accuracy, (3) minimum iteration height difference. The priority of condition (1) is greater than condition (2) and condition (3);

[0025] Step 6, N time points are set between the target arrival verification starting height time t1 and the predicted drop point time t0, if the height of the track at any time point of the N time points is greater than the altitude of the track point projected on the terrain, the verification is passed, at this time t0 is the final predicted drop point time, otherwise the time that does not meet the condition is taken as a new predicted drop point time t0, and step 4 is repeated.

[0026] The drop point prediction method based on terrain height matching can obtain the following beneficial effects:

[0027] 1, the method solves the problem of mismatching between the conventional least square method and the field terrain, and can iteratively correct the predicted drop point in real time by pre-inputting the height data, thereby improving the drop point prediction accuracy.

[0028] 2, the method verifies the predicted drop point in view of the real problems such as complex terrain environment in the drop point area, finds the first intersection point of the track and the terrain, improves the accuracy of the predicted drop point, and provides strong support for the smooth development of the target flight test. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 It is a flowchart of the drop point prediction method based on terrain height matching.

[0030] Figure 2 It is a drop point prediction program screenshot.

[0031] Figure 3 It is a simulation track and drop point display schematic diagram. DETAILED DESCRIPTION

[0032] The method and implementation steps will be described in detail below in combination with the drop point prediction software. The time, place, aircraft state and other related information set in the software running are all hypothetical parameters and have nothing to do with the actual situation.

[0033] Before implementing the present application, a terrain elevation matching based drop point prediction method, algorithm parameters need to be configured in the drop point prediction software: the order of the rank least square algorithm fitting; minLength, the minimum number of points to start calculation; maxLength, the length of the cache linked list, i.e. the maximum number of points, and the oldest points will be deleted when the number of points exceeds; computeMaxLength, the maximum number of points, i.e. the sliding window size; MinStep, the minimum iteration time precision, when the iteration time precision is less than MinStep, the final result is output; MinDivH, the minimum height difference, when the height difference is less than MinStep, the final result is output; MaxNumb, the maximum number of iterations. Also, load the drop zone elevation data, load the drop zone DEM elevation information into the two-dimensional elevation array geography[i][j].

[0034] After the parameter configuration is completed, please refer to Figure 1 , the implementation process of the present application, a terrain elevation matching based drop point prediction method, is as follows:

[0035] First, receive aircraft track data, such as aircraft GPS data or radar external measurement data, or perform data fusion on the ranging values of the radar and the azimuth and pitch values measured by the photoelectric theodolite, and then uniformly convert the track data into coordinates in the geocentric rectangular coordinate system.

[0036] Second, use the least square method to perform polynomial fitting on the XYZ data linked list (as shown in Figure 2 ). Verify whether the fitted track exceeds the DEM file range.

[0037] Third, get the latest time aircraft latitude and longitude corresponding ground elevation through the geography variable, calculate the intersection point of the fitted track and the superimposed elevation on the earth ellipsoid, and start iteration calculation from the intersection point. The specific iteration calculation process is described in detail in Figure 1 .

[0038] Fourth, verify the drop point, loop the height segment Verify_time from the set verification starting height start_H to the altitude high corresponding to the drop point time final_t calculated in the last step, if each track point height h0 is higher than the altitude h1 on the ground where the track is projected, the verification is passed, and the predicted drop point position is output (see Figure 3 ).

Claims

1. A method of fall point prediction based on terrain elevation matching, characterized by The method comprises the following steps: Step 1, preprocessing the received N aircraft track data to form a track chain table of x, y, z with respect to time t in the geocentric rectangular coordinate system; Step 2, performing polynomial fitting on the track chain table by using a least square method; Step 3, according to the terrain elevation data, calculate the altitude H of the projection point of the latest track point in the track chain on the ground, assuming that the earth is an ideal ellipsoid surface with an altitude H everywhere, calculate the intersection time of the fitted track curve and the earth ellipsoid t 0 , as the predicted drop point time Step 4, verification t 0 Whether the height of the time track point meets the preset minimum height difference with the terrain height, if meeting the requirement, step 6 is performed, otherwise, step 5 is performed. Step 5, to t 0 Iterative calculation is carried out under certain constraints, if t 0 If the corresponding track point elevation is higher than the terrain elevation, the predicted impact point time is advanced, if t 0 If the corresponding track point elevation is lower than the terrain elevation, the predicted impact point time is delayed; then the predicted impact point time is further iteratively optimized by dichotomy to obtain a new predicted impact point time, and step 4 is repeated; The constraint conditions are: (1) maximum iteration number, (2) minimum iteration time accuracy, (3) minimum iteration height difference, and the priority of the conditions is condition (1) > condition (2) > condition (3); Step 6: When the target reaches the verification starting elevation t 1 and predicted landing time t 0 N time points are set. If the elevation of the flight path at any of the N time points is greater than the elevation of the projection of that flight path onto the terrain, then the verification is successful. t 0 This is the final predicted landing time; otherwise, the time that does not meet the condition is taken as the new predicted landing time. t 0 Repeat step 4; The calculation process of the intersection point of the fitted track curve and the earth ellipsoid is: The track chain table is an array of 4N (X, Y, Z, T), and the fitting curve coefficients of X, Y, Z about T are obtained by using matrix method P ix , P iy , P iz , i = 0,1,2,…,j,j is the order of the fitting curve, (1) simultaneously fitting the track polynomial equation (2) and the earth ellipsoid equation (3) wherein a and e are the long semi-axis and the short semi-axis of the earth ellipsoid, and H is the altitude corresponding to the last guide point longitude and latitude, and a fourth-order polynomial equation with respect to t is obtained: (4) wherein (5) the eigenvalue of the accompanying matrix of the polynomial is the solution of the equation, that is, the intersection time of the fitted track curve and the earth ellipsoid.

2. The method of claim 1, wherein The aircraft track data in step 1 is aircraft GPS data, or aircraft radar external measurement data, or data obtained by fusing the ranging value of the radar and the azimuth and pitch values measured by an optical-electric theodolite.

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