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This is in the context of mobile device localization. The mobile device does not move.

All I have is the delay estimated from the signal sent by the mobile device ('measure' in blue).

With a simple Kalman filter (fixed covariance of process noise and measurement noise), I got the estimated distance ('kalman' in red).

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The Kalman filter seems behave correctly. However, as I know that the device position is static, I am concerned about the form of the blue measures. My theory is that there is some sort of clock drift and the mobile tried to compensate the drift by shifting its signal regularly. This brings me to the questions

  1. Does it make sense I add moving average to the Kalman estimates (the red one)? My understanding is that the Kalman filter is a combination of a prediction model and a measurement model. The latter is a sequential linear MMSE estimator and has already incorporate the notion of averaging.
  2. Is there any way to better model this device behavior?
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