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How does a decay factor not "trust your 'new' data more than really 'old' data"?

The Kalman filter is much more sophisticated. Typical re-estimation will be:

  x1 = x0 + alpha * (z - x0)
where alpha is static. The Kalman filter will make it dynamic, taking into account how you obtained the measurements, how old the last re-estimation was, how noisy the process is, etc. Want to do multi-variate analysis? Make alpha a matrix transform.

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