Kalman Filters

How to efficiently combine uncertain information to make predictions in a continuously changing 1D environment

In the Simple Robot Localization block, we saw how we combined uncertainty in a robot's position and robot's movement to eventually gain more confidence about the location of the robot.

But this was for discrete movement. In the real world, movement is continuous. Cars and ice skaters don't instantaneously teleport from one position to another — they drive gradually over a road or glide gracefully over ice.

In this block, we're going to introduce a simplified version of a very powerful algorithm that combines uncertainty of position and uncertainty of measurement to make predictions with increased confidence: the Kalman filter.

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Let's initialize a chart with the x-axis representing the position of the robot in our 100m-long world.

We're only working with one-dimension of position here — left and right — which is what makes this the simplified version.

Position (m)20406080100

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