I would like to apply Kalman smoothing to a series of data sampled at irregular time points. There is a claim on Stack Exchange that “For irregular spaced time series it’s easy to construct a Kalman filter”, but I haven’t been able to find any literature that specifically addresses this.

In my situation, I’d like to use a simple exponential covariance relationship to reflect the idea that the underlying continuous process is evolving as a linear dynamical system from which we irregularly receive samples.

So: is it simply OK to apply a Kalman filter with the “predict” step using a transition model and a process noise model whose “amplitude” depend on the amount of time that has elapsed since the last measurement?

**Answer**

Yes. In fact, this is how the Kalman Filter (KF) is also set up, at least implicitly. The assumptions in place when choosing the KF model, are that the movements and measurements compose a linear dynamical system. The transition matrix, $F_{t-1}$, (in the equation: $\hat{x}_{t|t-1} = F_tx_{t-1} + …$, where $\hat{x}$ is the predicted state estimate) is in fact indexed by time, so irregular observations shouldn’t be an issue.

For a more mathematically rigorous explanation of the KF, Max Welling has a really good tutorial that I highly recommend.

**Attribution***Source : Link , Question Author : Dan Stowell , Answer Author : Nick*