Sensor Fusion - Test Bench
+
+
+
+Table of Contents
+ +
+
+
+1 Experimental Setup
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+
+
+
+
+
+| + | + |
|---|---|
| Accelerometer | +PCB 393B05 - Vertical (link) | +
| Geophone | +Mark Product L4C - Vertical | +
+
+2 Huddle Test
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+
+
+
+
+2.1 Load Data
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+
+
+
+load('./mat/huddle_test.mat', 'acc_1', 'acc_2', 'geo_1', 'geo_2', 't');
+dt = t(2) - t(1);
+
+
+
+
+2.2 Data
+
+
+
+
+acc_1 = acc_1 - mean(acc_1); +acc_2 = acc_2 - mean(acc_2); +geo_1 = geo_1 - mean(geo_1); +geo_2 = geo_2 - mean(geo_2); ++
+
+
+2.3 Scale Data
+
+
++From raw data to estimated velocity. +This takes into account the sensibility of the sensor and possible integration to go from acceleration to velocity. +
+ +
+
+
+G0 = 1.02; % [V/(m/s2)] + +G_acc = tf(G0); ++
+
+
+T = 276; +xi = 0.5; +w = 2*pi; + +G_geo = -T*s^2/(s^2 + 2*xi*w*s + w^2); ++
+
+acc_1 = lsim(inv(G_acc), acc_1, t); +acc_2 = lsim(inv(G_acc), acc_2, t); +geo_1 = lsim(inv(G_geo), geo_1, t); +geo_2 = lsim(inv(G_geo), geo_2, t); ++
+
+
+2.4 Compare Time Domain Signals
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+
+
+
+figure; +hold on; +plot(t, acc_1); +plot(t, acc_2); +plot(t, geo_1); +plot(t, geo_2); +hold off; ++
+
+
+2.5 Compute PSD
+
+
++We first define the parameters for the frequency domain analysis. +
+
+
+
+Fs = 1/dt; % [Hz] + +win = hanning(ceil(1*Fs)); ++
+Then we compute the Power Spectral Density using pwelch function.
+
+
+
+[p_acc_1, f] = pwelch(acc_1, win, [], [], Fs); +[p_acc_2, ~] = pwelch(acc_2, win, [], [], Fs); +[p_geo_1, ~] = pwelch(geo_1, win, [], [], Fs); +[p_geo_2, ~] = pwelch(geo_2, win, [], [], Fs); ++
+
+
+figure;
+hold on;
+plot(f, sqrt(p_acc_1));
+plot(f, sqrt(p_acc_2));
+hold off;
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD Accelerometers $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+xlim([1, 5000]);
+
+
+
+figure;
+hold on;
+plot(f, sqrt(p_geo_1));
+plot(f, sqrt(p_geo_2));
+hold off;
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD Geophones $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+xlim([1, 5000]);
+
+
+
+
+2.6 Dynamical Uncertainty
+
+
+
+
+[T_acc, ~] = tfestimate(acc_1, acc_2, win, [], [], Fs); +[T_geo, ~] = tfestimate(geo_1, geo_2, win, [], [], Fs); ++
+
+2.7 Sensor Noise
+
+
+
+
+
+[coh_acc, ~] = mscohere(acc_1, acc_2, win, [], [], Fs); +[coh_geo, ~] = mscohere(geo_1, geo_2, win, [], [], Fs); ++
+
+
+pN_acc = p_acc_1.*(1 - coh_acc); +pN_geo = p_geo_1.*(1 - coh_geo); ++
+
+figure;
+hold on;
+plot(f, pN_acc, '-', 'DisplayName', 'Accelerometers');
+plot(f, pN_geo, '-', 'DisplayName', 'Geophones');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('ASD of the Measurement Noise $\left[\frac{m/s}{\sqrt{Hz}}\right]$');
+xlim([1, 5000]);
+legend('location', 'northeast');
+
+