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Thanks for the detailed overview. I wish to work in real life situation and i know that my sensor updates the data at 0.25s and it has an uncertainty of +-0.3m. Choosing a value and working with robot_localization, i want to see how much this uncertainty grows with time.. Two things that are still confusing me. Is 0.3 is right value for this situation? 2, i will provide the initial value only, manually, then robot_localization calculate /predict the future values? or how will it behave?

OK, so the per-measurement uncertainty of 0.3 m should be encoded in your covariance matrix. The difficulty is in interpreting what "+/- 0.3m" means. Does that represent one standard deviation, or more? I'd suggest over-estimating the error in general, as probabilistic approaches seem to be more robust to over-reporting error than under-reporting. Also, is it 0.3 meters in the position estimate, or 0.3 meters in both X and Y?

If we assume it's overall position error and it's one standard deviation, and we assume equal error in X and Y, then you might do

```
x_error^2 + y_error^2 = 0.3^2
2 * x_error^2 = 0.09
x_error = 0.212132034355964
```

But that would be standard deviation. You want variance, so you have to square again that to get `0.045`

. That value should go in the XX and YY entries in you covariance matrix (0th and 7th index of the covariance vector in the message.

I didn't think about this too deeply, so there may be a better way to interpret that data, but it's a start.

Between position measurements, the EKF will predict where you are, and then correct that prediction with your measurement. However, I hope you have something measuring yaw or yaw velocity, or your state estimate will get very ugly very quickly.

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