Discretization of continuous model with white noise to use Kalman filter later
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I have this system which describes dynamics of a car in 2D space. The dynamics are governed by Newton's law g(t) = ma(t). The final task is to use Kalman filter on discretized system to estimate it's position and velocity. The measurements are based on GPS signal with some covariance.
Unfortunately, I already got stucked at the beginning. I dont know how to incorporate the G matrix with w and e into discretization. Based on what I've learned, it should meant process and measurement noise.
Therefore it doesnt effect the dynamics of the system itself and I shouldnt count it during the discretization. Am I right? However based on the assignment, I should somehow edit w and e for the discretized model. In that case, why Gc dissappears? Of course, then the different time steps confuse me as well :(
In order to achieve this result, can I just use ss function in MATLAB to create system and then use c2d function to discretize it?
I just look at this already two days and since I'm just overall confused about the course of actions, I havent moved a bit.
Description of the problem
If I could ask you for some advice how to proceed I would really appreciate a lot!! Thanks in advance
dynamical-systems matlab discontinuous-functions kalman-filter discrete-calculus
asked Dec 9 '18 at 21:26
BlahriBlahri
61
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add a comment |
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I have this system which describes dynamics of a car in 2D space. The dynamics are governed by Newton's law g(t) = ma(t). The final task is to use Kalman filter on discretized system to estimate it's position and velocity. The measurements are based on GPS signal with some covariance.
Unfortunately, I already got stucked at the beginning. I dont know how to incorporate the G matrix with w and e into discretization. Based on what I've learned, it should meant process and measurement noise.
Therefore it doesnt effect the dynamics of the system itself and I shouldnt count it during the discretization. Am I right? However based on the assignment, I should somehow edit w and e for the discretized model. In that case, why Gc dissappears? Of course, then the different time steps confuse me as well :(
In order to achieve this result, can I just use ss function in MATLAB to create system and then use c2d function to discretize it?
I just look at this already two days and since I'm just overall confused about the course of actions, I havent moved a bit.
Description of the problem
If I could ask you for some advice how to proceed I would really appreciate a lot!! Thanks in advance
dynamical-systems matlab discontinuous-functions kalman-filter discrete-calculus
asked Dec 9 '18 at 21:26
BlahriBlahri
61
$endgroup$
add a comment |
$begingroup$
I have this system which describes dynamics of a car in 2D space. The dynamics are governed by Newton's law g(t) = ma(t). The final task is to use Kalman filter on discretized system to estimate it's position and velocity. The measurements are based on GPS signal with some covariance.
Unfortunately, I already got stucked at the beginning. I dont know how to incorporate the G matrix with w and e into discretization. Based on what I've learned, it should meant process and measurement noise.
Therefore it doesnt effect the dynamics of the system itself and I shouldnt count it during the discretization. Am I right? However based on the assignment, I should somehow edit w and e for the discretized model. In that case, why Gc dissappears? Of course, then the different time steps confuse me as well :(
In order to achieve this result, can I just use ss function in MATLAB to create system and then use c2d function to discretize it?
I just look at this already two days and since I'm just overall confused about the course of actions, I havent moved a bit.
Description of the problem
If I could ask you for some advice how to proceed I would really appreciate a lot!! Thanks in advance
dynamical-systems matlab discontinuous-functions kalman-filter discrete-calculus
asked Dec 9 '18 at 21:26
BlahriBlahri
61
$endgroup$
I have this system which describes dynamics of a car in 2D space. The dynamics are governed by Newton's law g(t) = ma(t). The final task is to use Kalman filter on discretized system to estimate it's position and velocity. The measurements are based on GPS signal with some covariance.
Unfortunately, I already got stucked at the beginning. I dont know how to incorporate the G matrix with w and e into discretization. Based on what I've learned, it should meant process and measurement noise.
Therefore it doesnt effect the dynamics of the system itself and I shouldnt count it during the discretization. Am I right? However based on the assignment, I should somehow edit w and e for the discretized model. In that case, why Gc dissappears? Of course, then the different time steps confuse me as well :(
In order to achieve this result, can I just use ss function in MATLAB to create system and then use c2d function to discretize it?
I just look at this already two days and since I'm just overall confused about the course of actions, I havent moved a bit.
Description of the problem
If I could ask you for some advice how to proceed I would really appreciate a lot!! Thanks in advance
dynamical-systems matlab discontinuous-functions kalman-filter discrete-calculus
dynamical-systems matlab discontinuous-functions kalman-filter discrete-calculus
asked Dec 9 '18 at 21:26
BlahriBlahri
61
asked Dec 9 '18 at 21:26
BlahriBlahri
61
asked Dec 9 '18 at 21:26
BlahriBlahri
61
asked Dec 9 '18 at 21:26
BlahriBlahri
61
asked Dec 9 '18 at 21:26
BlahriBlahri
61
61
add a comment |
add a comment |
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