How to model Kalman filter for Projectile Motion ?

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Atishay Jain
Atishay Jain 2016년 12월 16일
I am experimenting with Kalman filter implementation of Matlab. I wish to model the motion of a ball tossed up by a child in the air using Kalman filter. I have manually annotated the position of the ball in the image frames to use as measurements (ground truth values) for initializing and updating the kalman filter. I have defined the state to be a 6-dimensional vector as follows:
[X Vx Ax Y Vx Ay]
I wish to use 'Constant Acceleration' model. However, I am having difficulty in forming the StateTransitionModel.
Currently the StateTransitionModel Matrix I am using is as follows:
As = [1, 1, 0 , 0, 0 , 0; 0, 1, 1 , 0 , 0 , 0; 0, 0, 1 , 0 , 0 , 0 ; 0, 0 , 0 , 1, 1, 0 ; 0 , 0 , 0 , 0, 1, 1 ; 0 , 0 , 0 , 0, 0, 1 ];
MeasurementModel Matrix is as follows :
Hs = [1, 0, 0 , 0 , 0 , 1];
I am currently not using ControlModel matrix.
The problem with this model is that the acceleration components are currently not being used correctly. If I am to include acceleration components (Ax , Ay) what modifications should I do ?
Also, using the fact that in this case Ay is constant and equal to acceleration due to gravity (g) , How to plug in the value of g ?

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