Can someone explain about digital filters

[and-sh]

Pt1 low pass filter is simple iir filter
It defined by following equation
out=in * alpha+out * (1-alpha)
At sampling rate 2kHz and bandwidth about 100Hz alpha is about 1/4.

So 1/4 of 'in' is always translated to out.
This means that it can suppress noise only 4 times no matter of it frequency?

[and-sh]

some pictures
white noise source instead one gyro

After all filters

Moving averaging 14pts about 6kHz as aa filter

after all filters

[and-sh]

frequency and step response
red - unfiltered
blue - pt1 100Hz
green - moving average 7pts
pink - biquad 150Hz

pt1 & pt1 + 3 notch

[and-sh]

As always, I have to answer for myself.
As a result of the research of the frequency and step response of popular filters, the following was discovered:

1. Popular filters are generally not very suitable for gyroscope filtering, since they were designed to filter harmonic signals.
2. The step response and, accordingly, the delay do not depend on the filter type and are determined mainly by the frequency dependence. Thus, it makes no difference what type of filter to use. Therefore, it makes sense to give preference to the simplest and least processor-intensive algorithms.
3. The easiest way to reduce latency is to use a clean build and the stiffest frame possible and thus reduce the filtering required.
4. The usual moving average has very interesting characteristics.

Probably promising algorithms may be the use of AI or filtering based on drone motion modeling. However, modern processors can't handle this.

[and-sh]

Two stage avereging 30 and 21 points at 6kHz
All other filters are disabled
'real' delay about 1ms.

[and-sh]

Found error
4ms.

[and-sh]

Standard filtration
About the same or even more.