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Tracking an Object in Space Using the Kalman Filter

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measurement interval
0
potential strength
2
constant negative acceleration
0
measurement noise variable
-3.5
number of data points
35
trajectory length
200
reconstructed trajectory length
150
MSE
plot range
velocity
plot range
pause/resume
reset
Tracking an object in space using the Kalman filter can reconstruct its trajectory and velocity from noisy measurements in real time. The object, indicated by a blue pentagon, undergoes motion in a gravitational
1/r
potential of adjustable magnitude created by an external mass, chosen as the Moon, whose position you can control by dragging. The boundary conditions at the box edge are reflective.
At regular intervals in time, measurements of the object's position are made with some additive measurement noise, drawn from a zero-mean Gaussian distribution. The Kalman filter is used to reconstruct both the trajectory of the object, shown in red, and the object's velocity, whose magnitude is indicated in the plot on the bottom left. The mean-square error (MSE) between the reconstructed and true state vectors is shown as an estimate of the filter's performance in the middle-left pane.
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