Warning: No se encontró frecuencia óptima; usando valor por defecto f_opt = 0.05
doble_integracion_ofi
performs the integral double of a sampled signal with the optimally filtered integration (OFI method).
Syntax
Description
pos=dinteg_oci(acc,freq) performs the integral double of a signal acc sampled at freq Hz with the the optimally filtered integration (OFI method).
To reduce the low frequency acceleration noise the acceleration signal is high-pass-filtered, with a 2nd order Butterworth filter with an fc Hz cut frequency, calculated from data of a given cycle with known equal initial and final velocities. After filtering, a first integration produced instantaneous velocity. The numerical method chosen to integrate the data is the Cavalieri–Simpson. If the so-estimated final velocity is close to the initial velocity, they are supposed as equal, and a weighted direct and reverse integration is applied, aimed to reduce the time drift in velocity.
Notice that this method, contrary to the LRI and MSI methods, did not need a general assumption about the velocity at the end of the integration time
More information:
Köse, A.; Cereatti, A.; Della Croce, U. Bilateral step length estimation using a single inertial measurement unit attached to the pelvis. J. NeuroEng. Rehabil. 2012, 9, 9.
Examples
% Simulamos una señal de acelerómetro que sube, baja y vuelve a reposo con ruido
fs = 100; % Frecuencia de muestreo [Hz]
t = 0:1/fs:3; % Duración de 3 segundos
n = length(t);
% Creamos una forma de aceleración: subida, bajada, reposo
fase1 = linspace(0, 3, round(n/3)); % subida
fase2 = linspace(3, -3, round(n/3)); % bajada
fase3 = linspace(-3, 0, n - 2*round(n/3));% vuelta a reposo
acc_real = [fase1 fase2 fase3]; % concatenamos
% Añadimos ruido gaussiano para simular el sensor
ruido = 0.2*randn(1, n);
acc = (acc_real + ruido)';
% Visualizamos la señal simulada
figure
plot(t, acc, 'b')
xlabel('Tiempo [s]')
ylabel('Aceleración [m/s²]')
title('Señal simulada de acelerómetro (sube, baja y vuelve a reposo)')
grid on
plot(doble_integracion_ofi(acc,100));
