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I am doing the robot localisation project. Now I stuck on the effect of measurement and process noise in Kalman filtering. Could you please explain what impacts they have while estimating the position of the robot?! I mean how the error ellipsoid(which shows the pose uncertainty) changes with respect to changes in process and measurement noise?!

To estimate the pose of the robot, the two sources of information (dead-reckoning estimation and sensor measurements) are combined with Kalman filter.

Cheers, nekromant

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Basically, the relative magnitude between process and measurement noise determines how much to trust a new sensor measurement. In one extreme, if the process noise is zero the kalman filter will effectively ignore new sensor measurements because you've told it the process model is perfect (i.e. zero noise).

At the other extreme, if you set the process noise very large and the sensor noise very small it is like resetting the state to match the sensor reading. If your time updates happen at the same time as sensor updates, then this is effectively the same as just using the sensor without a filter. If your time updates happen faster than sensor readings, then you'll see the state drift according to your model during time updates and then do a sharp reset when the sensor reading arrives.

In practice you likely have a noisy sensor and probably don't want to follow it exactly so you need to keep the sensor noise magnitude sufficiently large. If the system is drifting too much because of inaccuracies in the process model you add more process noise until you hopefully reach a happy medium.

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  • $\begingroup$ cheers! What You mean by "time updates happen at the same time as sensor updates"? $\endgroup$
    – Nekromant
    Aug 20, 2017 at 3:40
  • $\begingroup$ Sometimes people run time updates (i.e. just the prediction step of the filter) faster than sensor updates so, for example, you might have 5 time updates for every 1 sensor update. $\endgroup$
    – ryan0270
    Aug 20, 2017 at 14:24
  • $\begingroup$ cheers, @ryan0270! So, could you please correct the results of these cases: 1. If PN(process noise) is small and MN(measurement noise) is big, then the Kalman filter ignores the measurement results, and error ellipsoid will be as same as in dead-reckoning? 2. If PN is big and MN is small, then Kalman filter believes more to measurement results, depending on the measurement noise, we can see the corresponding error ellipsoid? Are these assumptions true?! $\endgroup$
    – Nekromant
    Aug 21, 2017 at 4:40

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