Butterworth IIR Filtering of Gyroscope Data in a Two-Wheeled Self-Balancing Robot

Project info

• Field of studyRobotics and Mechatronics
• LevelMaster's thesis (S2)
• Method typeSignal Processing
• Estimated build time± 5 working days
• Toolsbutter, buttord, zp2sos, sosfilt, filtfilt (Signal Processing Toolbox)
• PriceUS$25 - US$166

Research goal

Apply Butterworth IIR filtering to the gyroscope angular rate to identify the filter order amid motor vibration noise through simulation.

Variables

Example result

• 6Filter order
• 47Cutoff (Hz)
• 60.448Attenuation at 3 fc (dB)
• 18.175Output SNR (dB)
• 0.092RMSE vs reference
• 0.927Max pole radius

The order-6 Butterworth filter (47 Hz cutoff) attenuates 60.4 dB at three times the cutoff and yields 18.2 dB SNR with an RMS error of 0.092 against Filter order; all poles stay inside the unit circle (max radius 0.927).

Computed from illustrative synthetic data, not from a real study.

About Butterworth IIR Filter

A Butterworth IIR filter gives the flattest passband magnitude response with a low order. It suits sensor or biomedical filtering when computational efficiency matters more than linear phase.

Steps

1. 1Define the filter type and cutoff frequency
2. 2Choose the order (buttord or trial)
3. 3Design with butter and convert to SOS for numerical stability
4. 4Check magnitude and phase response with freqz
5. 5Apply with filtfilt for zero phase or filter for causal use
6. 6Compute SNR improvement and plot

Assumptions to check

• Cutoff is normalised to Nyquist
• High orders should use SOS form for stability
• filter introduces phase distortion, filtfilt removes it but is non-causal

Reading and reporting the results

Report the order, cutoff, frequency response, and SNR improvement. Explain the choice between causal and zero-phase filtering according to the application.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(3);
fs = 500;
filter_order = (0:1/fs:4-1/fs)';
clean = sin(2*pi*5*filter_order) + 0.5*sin(2*pi*12*filter_order);
gyroscope_angular_rate = clean + 0.8*randn(size(filter_order));           % noisy signal

fc = 20;
[z, p, k] = butter(4, fc/(fs/2), 'low');
sos = zp2sos(z, p, k);
y_zero = sosfilt(sos, flipud(sosfilt(sos, flipud(gyroscope_angular_rate))));   % zero-phase (forward-backward)
y_caus = sosfilt(sos, gyroscope_angular_rate);                                  % causal

snr = @(x, ref) 10*log10(sum(ref.^2) / sum((x - ref).^2));
fprintf('SNR raw: %.2f dB\n', snr(gyroscope_angular_rate, clean));
fprintf('SNR causal: %.2f dB\n', snr(y_caus, clean));
fprintf('SNR zero-phase: %.2f dB\n', snr(y_zero, clean));

[h, w] = freqz(sos, 1024, fs);
figure;
subplot(2,1,1); plot(w, 20*log10(abs(h))); grid on;
xlabel('Frequency (Hz)'); ylabel('Magnitude (dB)'); ylim([-80 5]);
subplot(2,1,2);
idx = 1:500;
plot(filter_order(idx), gyroscope_angular_rate(idx), filter_order(idx), y_zero(idx), filter_order(idx), y_caus(idx), 'LineWidth', 1.1);
legend('Noisy', 'Zero-phase', 'Causal'); xlabel('Time (s)');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions