What is transition_matrices and observation_matrix in Kalman filter?

Question

Python

What is transition_matrices and observation_matrix in Kalman filter?

measurements = np.asarray(massgps)
    initial_state_mean = [measurements[0, 0],0,measurements[0, 1],0]
    transition_matrix = 
    observation_matrix = 
    kf1 = KalmanFilter(transition_matrices = transition_matrix,observation_matrices = observation_matrix,initial_state_mean = initial_state_mean)
    kf1 = kf1.em(measurements, n_iter=5)
    (smoothed_state_means, smoothed_state_covariances) = kf1.smooth(measurements)

There is a list with the last 5 GPS coordinates
How to enter the robot's movement model into the transition_matrix if the speed has not changed relative to the previous one, has increased or become zero?
How to enter a rover movement model if we do not know exactly how its coordinates change relative to the axes of latitude and longitude?

Answer 1

Take this image from the wiki
(The article itself)
This is a matrix representation of the equation of motion. The transition matrix is ​​this same Fk, i.e. a transition matrix that links the previous state vector x_k-1 and the current x_k.
For example, for the system diff. equations:
v1 = 3 * x1 + 0.1 * x2
v2 = 0.3 * x1 + 0.5 * x2
The transition matrix will be , where v1, v2 are the first derivatives of x1 and x2 respectively.
There is also a measurement verctor z, which is associated with the state vector X through the matrix H.
This Hk is the observation matrix.
How to get it if you only have a diff. equations? Well, substitute the current values ​​\u200b\u200binto the system, and look at the coefficients (in general, there are many ways to linearize)