How does a Kalman Filter work?

Omkar Debadarshi Ray

Omkar Debadarshi Ray

Production Management | Autonomous Driving | Generative AI | NIT Trichy'21

Published Nov 7, 2020

 It's nearly incommunicable to grasp the total pregnant ofKalman Filter by starting from definitions and complicated equations (at to the lowest degree for us mere mortals). For well-nigh cases, the state matrices drop out and we obtain the below equation, which is much easier to kickoff with.

What is information technology?

You tin use a Kalman filter in whatsoever place where you haveuncertain data well-nigh some dynamic system, and you tin make aneducated guess about what the system is going to do next. Even if messy reality comes along and interferes with the make clean motility you guessed about, the Kalman filter will oftentimes practise a very good job of figuring out what really happened. And it can take advantage of correlations between crazy phenomena that you maybe wouldn't take thought to exploit!

Kalman filters are ideal for systems that arecontinuously irresolute. They have the advantage that they are light on retentivity (they don't demand to go on any history other than the previous state), and they are very fast, making them well suited for real-time problems and embedded systems.

The math for implementing the Kalman filter appears pretty scary and opaque in most places you find on Google. That's a bad state of affairs because the Kalman filter is actually super elementary and piece of cake to understand if you look at it in the right style.

A Quick Insight

Every bit I mentioned earlier, information technology's nigh impossible to grasp the total meaning ofKalman Filter by starting from definitions and complicated equations (at least for united states mere mortals). For most cases, the state matrices drop out and nosotros obtain the beneath equation, which is much easier to first with.

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Remember, thek's on the subscript are states. Hither we can treat it as detached time intervals, such as grand=1 means 1ms, k=ii ways 2ms. Our purpose is to discover, the gauge of the signalten. And nosotros wish to notice it for each consequent1000'south. Likewise here,  is the measurement value. Keep in mind that, we are not perfectly sure of these values. Otherwise, we won't be needing to do all these. And is called "Kalman Gain"(which is the cardinal betoken of all these), and is the estimate of the signal on the previous state.

The only unknown component in this equation is the  Kalman gain. Considering, we have the measurement values, and we already have the previously estimated bespeak. You should calculate this Kalman Gain for each consistent country. This is not easy of course, but we have all the tools to do information technology.

On the other hand, let'south presume exist 0.5, what do we get? It's a uncomplicated averaging! In other words, we should find smarter coefficients at each state.

The bottom line is :

Kalman filter finds the nearly optimum averaging factor for each consequent country. As well somehow remembers a little scrap about the past states.

Applications

The applications of a Kalman filter are numerous:

  • Tracking objects (e.grand., missiles, faces, heads, hands)
  • Plumbing fixtures Bezier patches to (noisy, moving, ...) point data
  • Economics
  • Navigation
  • Many figurer vision applications – Stabilizing depth measurements – Feature tracking – Cluster tracking – Fusing data from radar, laser scanner, and stereo-cameras for depth and velocity measurements – Many more

Reference: Kalman Filter for Dummies

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