# Unscented Kalman Filter - Multiple Consecutive Measurement Updates

In trying to implement an Unscented Kalman Filter (UKF), I have come across the issue of what to do when my measurement signals come in at a different rate than my control inputs, which I use in the prediction step of the UKF. In my implementation, I've tried working around this issue by forming a prediction each time I receive a new measurement, but I've been told that it's also possible and perhaps favorable to only form a prediction when I get a new control input and form a new measurement update when I get a new measurement.

The "standard" Kalman filter algorithm in most textbooks/papers that I've seen do not delve deeply into this issue of different data rates, and they usually just show a simple predict-update loop that occurs at each time step.

I see how it is possible to form multiple consecutive predictions. However, I don't fully understand how one could do an update without a prediction right before it at the same time step, since the computation of the Kalman gain relies on the sigma points passed through the state transition function. Any help would be greatly appreciated!

For reference, I am trying to implement my UKF using the FilterPy Python library: https://filterpy.readthedocs.io/en/latest/_modules/filterpy/kalman/UKF.html#UnscentedKalmanFilter

• Your question isn't clear. Could you show your model equations and we'll solve it together? – Royi Jul 13 '18 at 22:16
• @Royi, my model equation f(x, u, dt) for the state transition involves integrating velocities to yield change in position, and integrating acceleration control inputs u to yield change in velocity. Therefore, this equation has numerous dt terms. My measurement function h(x) does not have any dt terms. Does this help? – theo1010 Jul 16 '18 at 13:46
• Kalman Filter doesn't have to be implemented with fixed step size (What you call dt). I think if you give us the model, and a set of measurements, we'll be able to assist you. – Royi Apr 3 at 22:32