Formulation and implementation of Kalman filter
Linear Dynamical System
State: is the true status of the system.
Measurement: is the measured status of the system.
is called transition matrix.
is called observation matrix.
e.g. an agent moving on a 2D plane. ,
KF steps
Initialize
At , we assume the state to be normal distribution.
Predict
Before we got the next measurement, we “guess” the next state distribution.
Posterior from previous steps:
Predictions for new step:
The mean and variance are computed by:
Update
When new measurement arrives, we “correct” the predicted state distribution.
We treat the prediction as prior, then incorporate measurement to get posterior .
The parameters are computed by: