Dear friends,
I am implementing Kalman Filter on an Android device to get rid of noise generated due to double integration of accelerations from accelerometer. The aim of my project is to control the position of a model car so that it follows a specific trajectory. Kalman Filter predicts the position from some reference model to estimate the position in a recursive way. I can also take measuremets e.g from another sensor lets say, gyroscope, instead of car position from the physical model which could also be regarded as sensor fusion. The scenerio for first case could be as follows.
First step is to create the phycial model of the car. well as I am using an RC car. The input is the speed command to the wheels and output is the acceleration from the sensors. Which are the same as meaurements in the Kalman filter. I am not sure if this modelling approach is right? Does any one have experience in this area? The equations which I have created so far are as follows:
x(k) = x(k-1) + dt* derivative_of(x(k-1)) + velocity_of_car@(k)
derivative_of(x(k)) = derivative_of(x(k-1)) + dt/2* velocity_of_car@(k)
Where derivative_of(xt(k)) and xt(k) are the only two states of the car under considerations. Please first tell me if these equations are correct. and then if my approach towards Kalman Filter implementation is correct.
Regards,
Zahid Raza
The equations that you have written down simply seem like double integration itself, which is exactly what you want to avoid. In order for the Kalman filter implementation to work well, the actual model of the physical system (In this case the RC car) should be implemented. Now the model of the car is available in several resources, see for example chapter 2 of the following thesis,
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.2.6994&rep=rep1&type=pdf
specifically see Eq. 23. In your case the measurements should be \dot(v_u) which is the acceleration.
Hi Srikant,
First of all thanks for your answer. Well Eq 23 in the thesis you referred considers the steering angles etc. I am only interested in linear motion at start ignoring these angles stuff to make things simple. Could you please just tell me the equation in simple way
Just out of curiosity, how do you go about trajectory tracking without steering? Specifically, how this:
The aim of my project is to control the position of a model car so that it follows a specific trajectory.
matches with this:
I am only interested in linear motion at start ignoring these angles stuff to make things simple
?
Hi Pavel,
Thanks for your answer. Well in the start I will not follow a trajectory. Rather a straight path . Trajectory tracking is my last goal.
Hello. As it stands, your problem does not make sense. You have an intertial sensor only so you can integrate this twice in open loop to get position. But you do not have anything to close the loop and therefore control the motion of the car. You need some measurement of how far away from the actual trajectory the car is. If you only use inertial sensors, it won't work for very long since the position solution will lose accuracy.
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