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I produced the "elevation vs distance" profile data and their PSD plots, I am trying to get the smartphone estimated profile close to the reference profile.

As you can see, the PSD of the smartphone estimated is100 times higher than that of the reference.

Judging from profile and PSD plots, what filters could I apply to the smartphone estimated profile so that the PSD of the two are in close magnitude.

Thank you all.

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    $\begingroup$ If the world is ending, it's not because of learning signal processing. $\endgroup$ Commented Apr 20, 2023 at 11:43

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The OP is measuring elevation and using a PSD to characterize the accuracy of the measurement. I am not sure that would be the best metric given we don't yet understand the stationarity of either the measurement system or what is being measured.

By understanding that first, we can then create optimum filters for tracking the result in the presence of noise. Further, this may also be a good application for using a Kalman filter depending on inputs available.

I recommend as a next step taking long duration measurements vs time with nothing else changing: a capture of reported elevation while we are at a fixed elevation. Processing that data to determine best filtering is then a great application for the Allan Deviation for all the reasons I mention already in the other posts listed further below. With that we can determine the optimum averaging time to minimize the noise in the measurement (determine for how long we can assume stationarity to our advantage in filtering out noise). Additionally evaluation of the frequency spectrum over shorter captures of the same can inform us if the noise is white (in which case a simple moving average is optimum) or if there is reason for more specialized filters to remove noise components more efficiently. Finally with very long captures, or repeated captures after long time gaps, we can assess total drift and if other inputs for calibration will be required and how often.

Once that is done, and importantly once we understand time durations where stationarity can be assumed, then power spectral density plots could be used to show noise performance (only over the durations where it is stationary)---the case for longer durations and non-stationary signals is what motivated the creation of the Allan Deviation charts! It will provide a consistent apples to apples noise performance metric.

With an optimized measurement at fixed elevation, then further measurements can be made by changing the elevation to referenced (known) locations and determined slope and offset error with the noise influence minimized.

ADEV Related Posts:

How to interpret Allan Deviation plot for gyroscope?

Allan deviation to determine averaging time

Allan varinace/ two-sample variance plot interpretation

Allan Variance vs Autocorrelation - Advantages

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