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I'm trying to estimate the state of a system that is changing linearly wrt time.

For a simple example, think of it as a car going at a constant speed: I want to measure both the distance traveled and the speed. I have as inputs noisy(unreliable) signals of the car's position and speed.

It has been suggested that I build a Kalman filter for this processing. But I am having a hard time seeing the benefit over just repeatedly averaging the speed and distance.

I understand that Kalman filter is good for complex paths with multiple inputs (velocity, acceleration, and further derivatives) (see An Explanation of the Kalman Filter).

But does this still apply to a simple model of constant speed? Is my problem too simple for a Kalman filter, or are there still benefits to it I'm not seeing?

abelenky
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The Kalman filter minimizes the mean square error. So, yes. The Kalman filter is "better" than averaging (at least in regards to the mean square error).

However, I am not sure how you would estimate the distance by averaging. The distance is changing, so you can't compute the average (or at least if you do, the result won't be accurate).

Ralff
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