Best baseline correction method for quasi-static response

Hi, im trying to create a code for removing drift in a peice of acceleration signal i have. The signal measure a quasi-static response and im integrating it twice to get displacment but of course there are issues with low frequency noise and drift. If there's any advice on what baseline correction methods would suit best id appreciate it. filtering the signal removes some of the displacement so isnt ideal for this type of signal.

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Answer 1

[Mathieu NOE]

hello

this seems to be a reccurent topic on this forum... so here we go again...

the best advice I can give are :

1/ make sure your sensor is correctly calibrated and correct for offset and sensivity error before you do any integration

2/ look at your acceleration signal spectrum (make a FFT of it) and look at the spectrum shape.

as you will probably do some high pass filtering to remove offset and drift , you have to choose the best corner frequency of your filter :

• not too low or you will integrate some portion of the drift / low freq noise
• not too high or your double integration will give an underestimated displacement

One possible code is to use cumtrapz for the integration followed by a dc wash out filter.

repeat that combo twice for double integration

I use filtfilt for forward and backward filtering so no phase distorsion (if that matters to you)

data file attached and code example below :

data = readmatrix('GEE Earthquake.txt'); % time , accel (g)
t = data(:,1);
dt = mean(diff(t));       % Average dt
fs = 1/dt;                  % Frequency [Hz] or sampling rate

% Acceleration data
acc = data(:,2)*9.81;         % gravity factor ( g to m/s²)

figure(1)
plot(t,acc)
ylabel('Accel [g]')
xlabel('Time [s]')
title('Earthquake Acceleration')


% fft of the Acceleration signal 
L = length(acc); % Length of signal
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
accSpectrum = fft(acc, NFFT)/L;  % detrend the signal before fft to remove the large DC (and near DC) fft output
f = fs/2*linspace(0,1,NFFT/2+1);

figure(2);
loglog(f, abs(accSpectrum(1:NFFT/2+1)))
title('FFT of acceleration')
xlabel('Frequency (Hz)')
ylabel('Amplitude')

% main code
fc = 0.25;  % Hz
displ = MN_double_int2(acc,fc,fs); % double integration (cumtrapz) with high pass filtering

figure(3)
plot(t,displ)
ylabel('Dis. [m]')
xlabel('Time [s]')
title('Estimated Displacement')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [ydintd] = MN_double_int2(x,fc,Fs)

    dt = 1/Fs;

    % DC blocking filter (discrete)
    fn = fc/(Fs/2);  % normalized cutt off frequency
    p = (sqrt(3) - 2*sin(pi*fn))/(sin(pi*fn) + sqrt(3)*cos(pi*fn));
    b = [1 -1];                                  % (numerator)
    a = [1 -p];                                  % (denominator)

    y = filtfilt(b,a,x);                  % filter the test data with filtfilt

    % accel to velocity integration
    yint = dt*cumtrapz(y);           % integration 
    yintd = filtfilt(b,a,yint);     % detrend data with filtfilt

    % velocity to displ integration
    ydint = dt*cumtrapz(yintd);           % integration
    ydintd = filtfilt(b,a,ydint);     % detrend data with filtfilt

end

[Emily Keys]

Thank you so much for this, would you have any codes that does not include a filter and are purely baseline correction apart from using detrend function? I am just looking for alternatives to filtering if there are any.

[Mathieu NOE]

hello

what you call baseline correction does exist but IMHO isnot suited to accelerometer signals

Raman Spectrum Baseline Removal - File Exchange - MATLAB Central (mathworks.com)

this will do a baseline correction but on data that are only positive values not an AC signal