Kalman Filter – Difference Between Kalman Filter and Moving Average

Question

I am computing a very simple Kalman filter (random walk + noise model).

I find that the output of the filter is very similar to a moving average.

Is there an equivalence between the two?

If not, what is the difference?

Answer 1

A random walk + noise model can be shown to be equivalent to a EWMA (exponentially weighted moving average). The kalman gain ends up being the same as the EWMA weighting.

This is shown to some details in Time Series Analysis by State Space, if you Google Kalman Filter and EWMA you will find a number of resources that discuss the equivalence.

In fact you can use the state space equivalence to build confidence intervals for EWMA estimates, etc.