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* work for additional information regarding copyright ownership. The ASF
* licenses this file to You under the Apache License, Version 2.0 (the
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* http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law
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package org.apache.commons.math4.userguide.filter;
import java.awt.Color;
import java.awt.Component;
import java.awt.Font;
import java.util.ArrayList;
import java.util.List;
import javax.swing.BorderFactory;
import javax.swing.BoxLayout;
import javax.swing.JComponent;
import javax.swing.JPanel;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.rng.simple.RandomSource;
import org.apache.commons.math4.filter.DefaultMeasurementModel;
import org.apache.commons.math4.filter.DefaultProcessModel;
import org.apache.commons.math4.filter.KalmanFilter;
import org.apache.commons.math4.filter.MeasurementModel;
import org.apache.commons.math4.filter.ProcessModel;
import org.apache.commons.math4.linear.MatrixUtils;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.linear.RealVector;
import org.apache.commons.math4.random.GaussianRandomGenerator;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.math4.userguide.ExampleUtils;
import org.apache.commons.math4.userguide.ExampleUtils.ExampleFrame;
import com.xeiam.xchart.Chart;
import com.xeiam.xchart.ChartBuilder;
import com.xeiam.xchart.Series;
import com.xeiam.xchart.SeriesLineStyle;
import com.xeiam.xchart.SeriesMarker;
import com.xeiam.xchart.XChartPanel;
import com.xeiam.xchart.StyleManager.ChartType;
import com.xeiam.xchart.StyleManager.LegendPosition;
public class CannonballExample {
public static class Cannonball {
private final double[] gravity = { 0, -9.81 };
private final double[] velocity;
private final double[] location;
private final double timeslice;
private final double measurementNoise;
private final GaussianRandomGenerator rng;
public Cannonball(double timeslice, double angle, double initialVelocity, double measurementNoise, int seed) {
this.timeslice = timeslice;
final double angleInRadians = FastMath.toRadians(angle);
this.velocity = new double[] {
initialVelocity * FastMath.cos(angleInRadians),
initialVelocity * FastMath.sin(angleInRadians)
};
this.location = new double[] { 0, 0 };
this.measurementNoise = measurementNoise;
this.rng = new GaussianRandomGenerator(RandomSource.create(RandomSource.WELL_19937_C, seed));
}
public double getX() {
return location[0];
}
public double getY() {
return location[1];
}
public double getMeasuredX() {
return location[0] + rng.nextNormalizedDouble() * measurementNoise;
}
public double getMeasuredY() {
return location[1] + rng.nextNormalizedDouble() * measurementNoise;
}
public double getXVelocity() {
return velocity[0];
}
public double getYVelocity() {
return velocity[1];
}
public void step() {
// Break gravitational force into a smaller time slice.
double[] slicedGravity = gravity.clone();
for ( int i = 0; i < slicedGravity.length; i++ ) {
slicedGravity[i] *= timeslice;
}
// Apply the acceleration to velocity.
double[] slicedVelocity = velocity.clone();
for ( int i = 0; i < velocity.length; i++ ) {
velocity[i] += slicedGravity[i];
slicedVelocity[i] = velocity[i] * timeslice;
location[i] += slicedVelocity[i];
}
// Cannonballs shouldn't go into the ground.
if ( location[1] < 0 ) {
location[1] = 0;
}
}
}
public static void cannonballTest(Chart chart) {
// time interval for each iteration
final double dt = 0.1;
// the number of iterations to run
final int iterations = 144;
// measurement noise (m)
final double measurementNoise = 30;
// initial velocity of the cannonball
final double initialVelocity = 100;
// shooting angle
final double angle = 45;
// the cannonball itself
final Cannonball cannonball = new Cannonball(dt, angle, initialVelocity, measurementNoise, 1000);
// A = [ 1, dt, 0, 0 ] => x(n+1) = x(n) + vx(n)
// [ 0, 1, 0, 0 ] => vx(n+1) = vx(n)
// [ 0, 0, 1, dt ] => y(n+1) = y(n) + vy(n)
// [ 0, 0, 0, 1 ] => vy(n+1) = vy(n)
final RealMatrix A = MatrixUtils.createRealMatrix(new double[][] {
{ 1, dt, 0, 0 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, dt },
{ 0, 0, 0, 1 }
});
// The control vector, which adds acceleration to the kinematic equations.
// 0 => x(n+1) = x(n+1)
// 0 => vx(n+1) = vx(n+1)
// -9.81*dt^2 => y(n+1) = y(n+1) - 1/2 * 9.81 * dt^2
// -9.81*dt => vy(n+1) = vy(n+1) - 9.81 * dt
final RealVector controlVector =
MatrixUtils.createRealVector(new double[] { 0, 0, 0.5 * -9.81 * dt * dt, -9.81 * dt } );
// The control matrix B only update y and vy, see control vector
final RealMatrix B = MatrixUtils.createRealMatrix(new double[][] {
{ 0, 0, 0, 0 },
{ 0, 0, 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 1 }
});
// After state transition and control, here are the equations:
//
// x(n+1) = x(n) + vx(n)
// vx(n+1) = vx(n)
// y(n+1) = y(n) + vy(n) - 0.5 * 9.81 * dt^2
// vy(n+1) = vy(n) + -9.81 * dt
//
// Which, if you recall, are the equations of motion for a parabola.
// We only observe the x/y position of the cannonball
final RealMatrix H = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 0, 0, 0 },
{ 0, 0, 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 0 }
});
// This is our guess of the initial state. I intentionally set the Y value
// wrong to illustrate how fast the Kalman filter will pick up on that.
final double speedX = cannonball.getXVelocity();
final double speedY = cannonball.getYVelocity();
final RealVector initialState = MatrixUtils.createRealVector(new double[] { 0, speedX, 100, speedY } );
// The initial error covariance matrix, the variance = noise^2
final double var = measurementNoise * measurementNoise;
final RealMatrix initialErrorCovariance = MatrixUtils.createRealMatrix(new double[][] {
{ var, 0, 0, 0 },
{ 0, 1e-3, 0, 0 },
{ 0, 0, var, 0 },
{ 0, 0, 0, 1e-3 }
});
// we assume no process noise -> zero matrix
final RealMatrix Q = MatrixUtils.createRealMatrix(4, 4);
// the measurement covariance matrix
final RealMatrix R = MatrixUtils.createRealMatrix(new double[][] {
{ var, 0, 0, 0 },
{ 0, 1e-3, 0, 0 },
{ 0, 0, var, 0 },
{ 0, 0, 0, 1e-3 }
});
final ProcessModel pm = new DefaultProcessModel(A, B, Q, initialState, initialErrorCovariance);
final MeasurementModel mm = new DefaultMeasurementModel(H, R);
final KalmanFilter filter = new KalmanFilter(pm, mm);
final List<Number> realX = new ArrayList<Number>();
final List<Number> realY = new ArrayList<Number>();
final List<Number> measuredX = new ArrayList<Number>();
final List<Number> measuredY = new ArrayList<Number>();
final List<Number> kalmanX = new ArrayList<Number>();
final List<Number> kalmanY = new ArrayList<Number>();
for (int i = 0; i < iterations; i++) {
// get real location
realX.add(cannonball.getX());
realY.add(cannonball.getY());
// get measured location
final double mx = cannonball.getMeasuredX();
final double my = cannonball.getMeasuredY();
measuredX.add(mx);
measuredY.add(my);
// iterate the cannon simulation to the next timeslice.
cannonball.step();
final double[] state = filter.getStateEstimation();
kalmanX.add(state[0]);
kalmanY.add(state[2]);
// update the kalman filter with the measurements
filter.predict(controlVector);
filter.correct(new double[] { mx, 0, my, 0 } );
}
chart.setXAxisTitle("Distance (m)");
chart.setYAxisTitle("Height (m)");
Series dataset = chart.addSeries("true", realX, realY);
dataset.setMarker(SeriesMarker.NONE);
dataset = chart.addSeries("measured", measuredX, measuredY);
dataset.setLineStyle(SeriesLineStyle.DOT_DOT);
dataset.setMarker(SeriesMarker.NONE);
dataset = chart.addSeries("kalman", kalmanX, kalmanY);
dataset.setLineColor(Color.red);
dataset.setLineStyle(SeriesLineStyle.DASH_DASH);
dataset.setMarker(SeriesMarker.NONE);
}
public static Chart createChart(String title, LegendPosition position) {
Chart chart = new ChartBuilder().width(650).height(450).build();
// Customize Chart
chart.setChartTitle(title);
chart.getStyleManager().setChartTitleVisible(true);
chart.getStyleManager().setChartTitleFont(new Font("Arial", Font.PLAIN, 12));
chart.getStyleManager().setLegendPosition(position);
chart.getStyleManager().setLegendVisible(true);
chart.getStyleManager().setLegendFont(new Font("Arial", Font.PLAIN, 12));
chart.getStyleManager().setLegendPadding(6);
chart.getStyleManager().setLegendSeriesLineLength(10);
chart.getStyleManager().setAxisTickLabelsFont(new Font("Arial", Font.PLAIN, 10));
chart.getStyleManager().setChartBackgroundColor(Color.white);
chart.getStyleManager().setChartPadding(4);
chart.getStyleManager().setChartType(ChartType.Line);
return chart;
}
public static JComponent createComponent() {
JComponent container = new JPanel();
container.setLayout(new BoxLayout(container, BoxLayout.PAGE_AXIS));
Chart chart = createChart("Cannonball", LegendPosition.InsideNE);
cannonballTest(chart);
container.add(new XChartPanel(chart));
container.setBorder(BorderFactory.createLineBorder(Color.black, 1));
return container;
}
@SuppressWarnings("serial")
public static class Display extends ExampleFrame {
private JComponent container;
public Display() {
setTitle("Commons Math: Kalman Filter - Cannonball");
setSize(800, 600);
container = new JPanel();
JComponent comp = createComponent();
container.add(comp);
add(container);
}
@Override
public Component getMainPanel() {
return container;
}
}
public static void main(String[] args) {
ExampleUtils.showExampleFrame(new Display());
}
}