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Named after Rudolph Kalman, the Kalman filter is one of the most powerful algorithms in signal processing, control engineering, and machine learning. It remains widely used from aerospace navigation to automotive systems and many industrial processes. The statistical foundations behind it, however, are complex and intimidating. Still, if we look past the mathematics, the Kalman filter is conceptually simple.

Note: Excluding the appendix at the end, this article is about a 10 min read.

Figure 1: Rudolph Kalman (Image source)

But what is a Kalman Filter?

Let’s start with some examples.

Example 1: Refining noisy measurements

A car’s GPS reports its location every second, but the readings are unreliable due to noise in the measurements. A Kalman filter combines these noisy measurements with a mathematical model of the car’s motion to produce a smoother, refined estimate of its true position.

This is the simplest use of a Kalman filter — cleaning up / refining sequential noisy measurements. That’s also where the term filter comes from.