108 lines
2.3 KiB
Matlab
108 lines
2.3 KiB
Matlab
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%% ('NoiseDensity(<28>Ƕ<EFBFBD><C7B6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>)', N, 'RandomWalk(<28><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>)', K,'BiasInstability(<28><>ƫ<EFBFBD>ȶ<EFBFBD><C8B6><EFBFBD>)', B);
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% omega <20><><EFBFBD><EFBFBD>Ϊ rad/s(<28><><EFBFBD><EFBFBD>)<29><> <20><><EFBFBD>ٶȼ<D9B6>: m/s^(2)
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% see Freescale AN: Allan Variance: Noise Analysis for Gyroscopes
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function [avar, tau, N, K, B] = allan(omega, Fs)
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% t0 = 1/Fs;
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% theta = cumsum(omega, 1)*t0;
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%
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% maxNumM = 200;
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% L = size(theta, 1);
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% maxM = 2.^floor(log2(L/2));
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% m = logspace(log10(10), log10(maxM), maxNumM).';
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% m = ceil(m); % m must be an integer.
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% m = unique(m); % Remove duplicates.
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%
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% tau = m*t0;
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%
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% avar = zeros(numel(m), 1);
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% for i = 1:numel(m)
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% mi = m(i);
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% avar(i,:) = sum( ...
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% (theta(1+2*mi:L) - 2*theta(1+mi:L-mi) + theta(1:L-2*mi)).^2, 1);
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% end
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% avar = avar ./ (2*tau.^2 .* (L - 2*m));
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[avar,tau] = allanvar(omega, 'octave', Fs);
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adev = sqrt(avar);
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%% Angle Random Walk
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slope = -0.5;
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logtau = log10(tau);
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logadev = log10(adev);
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dlogadev = diff(logadev) ./ diff(logtau);
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[~, i] = min(abs(dlogadev - slope));
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% Find the y-intercept of the line.
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b = logadev(i) - slope*logtau(i);
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% Determine the angle random walk coefficient from the line.
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logN = slope*log10(1) + b;
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N = 10^logN;
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% Plot the results.
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tauN = 1;
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lineN = N ./ sqrt(tau);
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%% Rate Random Walk
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slope = 0.5;
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logtau = log10(tau);
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logadev = log10(adev);
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dlogadev = diff(logadev) ./ diff(logtau);
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[~, i] = min(abs(dlogadev - slope));
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% Find the y-intercept of the line.
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b = logadev(i) - slope*logtau(i);
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% Determine the rate random walk coefficient from the line.
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logK = slope*log10(3) + b;
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K = 10^logK;
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% Plot the results.
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tauK = 3;
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lineK = K .* sqrt(tau/3);
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%% Bias Instability
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slope = 0;
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logtau = log10(tau);
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logadev = log10(adev);
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dlogadev = diff(logadev) ./ diff(logtau);
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[~, i] = min(abs(dlogadev - slope));
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[~, i] = min(adev); %yandld added
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% Find the y-intercept of the line.
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b = logadev(i) - slope*logtau(i);
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% Determine the bias instability coefficient from the line.
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scfB = sqrt(2*log(2)/pi);
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logB = b - log10(scfB);
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B = 10^logB;
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% Plot the results.
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tauB = tau(i);
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lineB = B * scfB * ones(size(tau));
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tauParams = [tauN, tauK, tauB];
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params = [N, K, scfB*B];
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figure;
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loglog(tau, adev, '-*', tau, [lineN, lineK, lineB], '--', tauParams, params, 'o');
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title('Allan Deviation with Noise Parameters')
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xlabel('\tau')
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ylabel('\sigma(\tau)')
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legend('\sigma', '\sigma_N', '\sigma_K', '\sigma_B')
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text(tauParams, params, {'N', 'K', '0.664B'})
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grid on
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end
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