Estimation Problem Refresh

Refresh Estimation Problem

Definition of Variables

x is the mean state vector. For an extended Kalman filter, the mean state vector contains information about the object's position and velocity that you are tracking. It is called the "mean" state vector because position and velocity are represented by a gaussian distribution with mean x .
P is the state covariance matrix, which contains information about the uncertainty of the object's position and velocity. You can think of it as containing standard deviations.
k represents time steps. So x_k refers to the object's position and velocity vector at time k.
The notation k+1|k refers to the prediction step. At time k+1 , you receive a sensor measurement. Before taking into account the sensor measurement to update your belief about the object's position and velocity, you predict where you think the object will be at time k+1 . You can predict the position of the object at k+1 based on its position and velocity at time k . Hence x_{k+1|k} means that you have predicted where the object will be at k+1 but have not yet taken the sensor measurement into account.
x_{k+1} means that you have now predicted where the object will be at time k+1 and then used the sensor measurement to update the object's position and velocity.

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What should a Kalman Filter do if both the radar and laser measurements arrive at the same time, k+3 ? Hint: The Kalman filter algorithm predicts -> updates -> predicts -> updates, etc. If two sensor measurements come in simultaneously, the time step between the first measurement and the second measurement would be zero.

Predict the state to k+3, and then update the state with only one of those measurements, either laser or radar.

Predict the state to k+3, and then only update with the laser measurement because it is more accurate

Predict the state to k+3 then use either one of the sensors to update. Then predict the state to k+3 again and update with the other sensor measurement.

Skip the prediction step because we have two measurements. Just update the prior probability distribution twice.

SOLUTION:

Predict the state to k+3 then use either one of the sensors to update. Then predict the state to k+3 again and update with the other sensor measurement.