基于Matlab生成并可视化多架飞机轨迹仿真.rar

%% Benchmark Trajectories for Multi-Object Tracking % This example shows how to generate and visualize trajectories of multiple % aircraft using |trackingScenario| and |waypointTrajectory|. % % Copyright 2018 The MathWorks, Inc. %% Introduction % The six aircraft trajectories modeled in this example are described in % [1]. The aircraft fly in an arrangement intended to be received by a % radar located at the origin. %% Choice of Interpolant % Conceptually speaking, a trajectory is a curve through space which an % object travels as a function of time. To define the curve, you may think % of a curve through space that passes through a set of points called % _waypoints_ connected by an interpolating function called an % _interpolant_. An interpolant allows you to define the path between % waypoints via a continuous function. Common interpolants are polynomial % based (for example, piecewise linear or cubic splines). For a rapidly % changing trajectory, more waypoints are required to keep the interpolated % curve as close to the true curve as possible; however, we can reduce the % number of required points by choosing interpolants carefully. % % Many motion models used in track filters consist of "constant velocity," % "constant turn," or "constant acceleration" profiles. To accommodate % these motion models, the interpolant used in the |waypointTrajectory| % object is based on a piecewise clothoid spline (horizontally) and a cubic % spline (vertically). The curvature of a clothoid spline varies linearly % with respect to distance traveled; this lets us model straight and % constant turns with ease, having one extra degree of freedom to % transition smoothly between straight and curved segments. Similarly, % objects in the air experience the effects of gravity, following a % parabolic (quadratic) path. Having a cubic spline to model vertical % elevation allows us to model the path with a similar extra degree of % freedom. % % Once the physical path through space of an object is known (and set), % the speed of the object as a function of distance traveled is determined % via cubic Hermite interpolation. This is useful for modeling % trajectories of objects that accelerate through turns or straight % segments. % % The benchmark trajectories we are using consist of straight, constant-g % turns, and turns with acceleration. %% Waypoint Construction % The following file contains tables of waypoints and velocities (in units % of meters and meters per second) that can be used to reconstruct six % aircraft trajectories. Load it into MATLAB and examine the table % containing the first trajectory. load('benchmarkTrajectoryTables.mat', 'trajTable'); trajTable{1} %% Scenario Generation % The table contains a set of waypoints and velocities that the aircraft % passes through at the corresponding time. % % To use the control points, you can create a scenario with six platforms % and assign a trajectory to each: scene = trackingScenario('UpdateRate',10); for n=1:6 plat = platform(scene); traj = trajTable{n}; plat.Trajectory = waypointTrajectory(traj.Waypoints, traj.Time, 'Velocities', traj.Velocities); end %% Trajectory Visualization % Once you have the scenario and plotter set up, you can set up a % |theaterPlot| to create an animated view of the locations of the % aircraft as time progresses. helperPlot = helperBenchmarkPlotter(numel(scene.Platforms)); while advance(scene) % extract the pose of each of the six aircraft poses = platformPoses(scene); % update the plot update(helperPlot, poses, scene.SimulationTime); end %% % The trajectories plotted above are three-dimensional. You can rotate the % plot so that the elevation of the trajectories is readily visible. You % can use the |view| and |axis| commands to adjust the plot. Because the % trajectories use a NED (north-east-down) coordinate system, elevation % above ground has a negative z component. view(60,10); axis square grid minor set(gca,'ZDir','reverse'); %% Trajectory 1 % It may be instructive to view the control points used to generate the % trajectories. The following figure shows the first trajectory, which is % representative of a large aircraft. % % The control points used to construct the path are plotted on the leftmost % plot. Only a few waypoints are needed to mark the changes in curvature % as the plane takes a constant turn. % % The plots on the right show the altitude, magnitude of velocity (speed), % and magnitude of acceleration, respectively. The speed stays nearly % constant throughout despite the abrupt change in curvature. This is an % advantage of using the clothoid interpolant. [time, position, velocity, acceleration] = cumulativeHistory(helperPlot); helperTrajectoryViewer(1, time, position, velocity, acceleration, trajTable); %% Trajectory 2 % The second trajectory, shown below, represents the trajectory of a small % maneuverable aircraft. It consists of two turns, having several changes % in acceleration immediately after the first turn and during the second % turn. More waypoints are needed to adjust for these changes, however the % rest of the trajectory requires fewer points. helperTrajectoryViewer(2, time, position, velocity, acceleration, trajTable); %% Trajectory 3 % The third trajectory, shown below is representative of a higher speed % aircraft. It consists of two constant turns, where the aircraft % decelerates midway throughout the second turn. You can see the control % points that were used to mark the changes in velocity and acceleration in % the x-y plot on the left. helperTrajectoryViewer(3, time, position, velocity, acceleration, trajTable); %% Trajectory 4 % The fourth trajectory, also representative of a higher speed aircraft, is % shown below. It consists of two turns, where the aircraft accelerates % and climbs to a higher altitude. helperTrajectoryViewer(4, time, position, velocity, acceleration, trajTable); %% Trajectory 5 % The fifth trajectory is representative of a maneuverable high-speed % aircraft. It consists of three constant turns; however it accelerates % considerably throughout the duration of the flight. After the third turn % the aircraft ascends to a level flight. helperTrajectoryViewer(5, time, position, velocity, acceleration, trajTable); %% Trajectory 6 % The sixth trajectory is also representative of a maneuverable high-speed % aircraft. It consists of four turns. After the second turn the aircraft % decreases altitude and speed and enters the third turn. After the third % turn it accelerates rapidly and enters the fourth turn, continuing with % straight and level flight. helperTrajectoryViewer(6, time, position, velocity, acceleration, trajTable); %% Summary % This example shows how to use |waypointTrajectory| and % |trackingScenario| to create a multi-object tracking scenario. In % this example you learned the concepts behind the interpolant used inside % |waypointTrajectory| and were shown how a scenario could be reproduced % with a small number of waypoints. %% Reference % # W.D. Blair, G. A. Watson, T. Kirubarajan, Y. Bar-Shalom, "Benchmark for % Radar Allocation and Tracking in ECM." Aerospace and Electronic Systems % IEEE Trans on, vol. 34. no. 4. 1998