KalmanFilter | An exercise to explain/understand a kalman filter

Based on your model your state vector is the following: [x, y, v_x, v_y] and you are observing (measuring) only [x, y]. So you need to properly define also measurement matrix H, which maps the true state space into the observed space: z=Hx + noise. So in your case, it is very simple:

The problem is probably for the second function, update(), it couldn't infer the type of B, since it does not refer to the type B in the function signature. Looking at the signature for predict, you probably want to use the type B for covariances in the update function.

You have to set the proper type for the numpy.arrays errorCovPost and statePost:

errorCovPost = 1. * np.array([0.])
statePost = 1. * np.array([0.])

The Kalman Filter is a linear filter that is optimal for linear systems with gaussian noise. Assume there is no noise and your system is perfectly linear. The transition matrix hence describes how the state changes and is not updated by the kalman filter. If the transition matrix is just the identity it means the state never changes. The transition matrix for your case should be an identity with an entry of dt in (0,4) and (1,5) (since given the last state of your rectangle the next state is the current position (x,y) + dt *(vx,vy). It depends on the application whether you have more information about the change in your state (what happen with your width and height).

The reality is influenced by noise. There are two different kinds considered in the kalman filter. Structural /process noise and measurement noise. Both influence the gain matrix. The gain matrix is not given by the user but calculated through the history, the measurement covariance and the process covariance. If the measurement is not noisy you might decrease the measurement covariance (it might be worthwhile to check at least in which range your variances are), By "increasing" the measurement matrix on decreases the influence of the observation in the current estimation. The other part is the process noise covariance. This part influences the P'(k). This is the covariance of the current state given the last state (and its covariance). If you know perfectly how your system behaves (which means you know your transition matrix), you can assume the process noise as zero. If you increase the process noise covariance you are saying, that there is an error in the propagation between two time stamps, that is not explained by the transition matrix and is random. (Maybe you know how much the width or height change on average. This variance can be used in the diagonal element, that corresponds to w and h (2 and 3)). So to make the filter more responsive you have to tell him, that you are unsure about the actual change and hence you have to increase the process noise. For parameter tuning i suggest you have a closer look at your data. So you have to increase the process noise AND decrease the measurement noise to make the filter more responsive.

There is no show method on plots in Bokeh, and never has been. There is a show function that you can pass plots (or layouts of plots and widgets) to.

EDIT: Turns out that the stability was just that I'd found a set of values that didn't show spikes in that dataset. The instability is still there. Using this initialisation pattern does match the expected pattern until instability sets in though. So it looks like a bug in the underlying Kalman filter.

So after searching more, I found a closed issue in EMGU that pointed to the updated unit tests for the Kalman filter. Using their way of initialising, I've managed to get something that seems a lot more stable.

I figured it out! Data['y'].values is a numpy array with dtype=object. All I had to do is to change the type of the array to float using .astype(float). This has to be done with everything that goes into the kalman filter object of pykalman, so I also had to change the type of the H matrix.

Hope this helps somebody in the future!

Here is what the final working code looks like:

This has already been answered here: Kalman filter always predicting origin

OpenCV Kalman filter implementation does not let you set the an initial state. You have to save your initial state and then when you call kalman.correct you have to subtract the initial state. And when you call kalman.predict you have to add your initial state.

Something like this pseudo-code:

This is due to eulerangles being in a modulo space (bad terminology probably) over [0,360).

I don't know anything about Kalman Filters, but here's a possible partial solution. Maybe it will guide you to an answer

Use 2 filters to estimate the local transform.up and the transform.forward direction and then get the rotation from the estimates with Quaternion.LookRotation