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# bias_drift uses wrong std value?

See original GitHub issue

First, thanks for the amazing tool!

But, I suspect there is a bug here: https://github.com/Aceinna/gnss-ins-sim/blob/2d2ba0fac193afd10b4d7758cc85d14457f17001/gnss_ins_sim/pathgen/pathgen.py#L552

Should it be

``````b = drift[i] * np.sqrt(1. - np.exp(-2/(fs * corr_time[i])))
``````

or am I missing something?

With this scaling, then the drift[i] describes the standard deviation of the output process. Whereas, the original implementation just describes the standard deviation of the discretized white noise. Which means that the noise process will not be consistent if the sampling frequency is changed.

### Issue Analytics

• State:
• Created 3 years ago

2reactions
dxg-aceinnacommented, Oct 22, 2020

Note that `(1 - dt/corr_time)**2` is the Taylor expansion of `1 - exp(-2 * dt/corr_time)` upto the second order. Also, note that dt/corr_time must be less than or equal to unity to make physical sense. (corr_time > dt or the whole discretization kinda falls a part.)

Thank you for the explanation. It is clear to me now. A pull request will be much appreciated.

1reaction
ace-e4scommented, Oct 21, 2020

1. You are right, this is a typo from my part.
2. No, the variance is `dt`. See https://en.wikipedia.org/wiki/Euler–Maruyama_method (last sentence in the introduction).
3. Follows 2.

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