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updateEKFQuatAtt.m
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updateEKFQuatAtt.m
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function [roll_deg, pitch_deg, yaw_deg] = updateEKFQuatAtt(gyr_rps, acc_mps2, mag_unit, Va_mps, magDecRad, T, NdivT)
persistent flag
persistent p
persistent q
persistent r
persistent ax
persistent ay
persistent az
persistent mx
persistent my
persistent mz
persistent Va
persistent lpfGyr
persistent lpfAcc
persistent lpfMag
persistent lpfVa
persistent x
persistent P
persistent Q
persistent R
persistent g
if isempty(flag)
flag = 1;
g = 9.81;
% Low-pass filtered measurements
p = 0.0; q = 0.0; r = 0.0;
ax = 0.0; ay = 0.0; az = 0.0;
mx = 0.0; my = 0.0; mz = 0.0;
Va = 0.0;
% Low-pass filter coefficients
lpfGyr = 0.7;
lpfAcc = 0.9;
lpfMag = 0.4;
lpfVa = 0.7;
% Initialise state estimate vector
x = zeros(7, 1);
x(1) = 1.0;
% Initialise covariance matrix
cAtt0 = 0.001;
cBias0 = 0.0001;
P = diag([[1 1 1 1] * cAtt0, [1 1 1] * cBias0] .^ 2);
% Process noise matrix
nProcAtt = 0.00005;
nProcBias = 0.000001;
Q = diag([[1 1 1 1] * nProcAtt, [1 1 1] * nProcBias] .^ 2);
% Measurement noise matrix
nMeasAcc = 0.05;
nMeasMag = 0.02;
R = diag([[1 1 1] * nMeasAcc, [1 1 1] * nMeasMag] .^ 2);
end
% Get measurements and low-pass filter them
p = lpfGyr * p + (1 - lpfGyr) * gyr_rps(1);
q = lpfGyr * q + (1 - lpfGyr) * gyr_rps(2);
r = lpfGyr * r + (1 - lpfGyr) * gyr_rps(3);
ax = lpfAcc * ax + (1 - lpfAcc) * acc_mps2(1);
ay = lpfAcc * ay + (1 - lpfAcc) * acc_mps2(2);
az = lpfAcc * az + (1 - lpfAcc) * acc_mps2(3);
mx = lpfMag * mx + (1 - lpfMag) * mag_unit(1);
my = lpfMag * my + (1 - lpfMag) * mag_unit(2);
mz = lpfMag * mz + (1 - lpfMag) * mag_unit(3);
mnorm = sqrt(mx * mx + my * my + mz * mz);
mx = mx / mnorm;
my = my / mnorm;
mz = mz / mnorm;
Va = lpfVa * Va + (1 - lpfVa) * Va_mps;
for it = 1 : NdivT
% Extract states
q0 = x(1); q1 = x(2); q2 = x(3); q3 = x(4);
bp = x(5); bq = x(6); br = x(7);
% State transition function, xdot = f(x, u)
C_body2qdot = 0.5 * [-q1, -q2, -q3; ...
q0, -q3, q2; ...
q3, q0, -q1; ...
-q2, q1, q0];
f = [ C_body2qdot * [p - bp; q - bq; r - br]; 0; 0; 0];
% Update state estimate
x = x + (T / NdivT) * f;
end
% Normalise quaternion
qNorm = sqrt(x(1) * x(1) + x(2) * x(2) + x(3) * x(3) + x(4) * x(4));
x(1) = x(1) / qNorm;
x(2) = x(2) / qNorm;
x(3) = x(3) / qNorm;
x(4) = x(4) / qNorm;
% Re-extract states
q0 = x(1); q1 = x(2); q2 = x(3); q3 = x(4);
bp = x(5); bq = x(6); br = x(7);
% Compute Jacobian of f, A(x, u)
A = [0, -0.5 * (p - bp), -0.5 * (q - bq), -0.5 * (r - br), 0.5 * q1, 0.5 * q2, 0.5 * q3; ...
0.5 * (p - bp), 0, 0.5 * (r - br), -0.5 * (q - bq), -0.5 * q0, 0.5 * q3, -0.5 * q2; ...
0.5 * (q - bq), -0.5 * (r - br), 0, 0.5 * (p - bp), -0.5 * q3, -0.5 * q0, 0.5 * q1; ...
0.5 * (r - br), 0.5 * (q - bq), -0.5 * (p - bp), 0, 0.5 * q2, -0.5 * q1, -0.5 * q0; ...
0, 0, 0, 0, 0, 0, 0; ...
0, 0, 0, 0, 0, 0, 0; ...
0, 0, 0, 0, 0, 0, 0];
% Update error covariance matrix
P = P + T * (A * P + P * A' + Q);
% Compute magnetic field unit vector estimate in body coordinates from
% quaternion estimates
smag = sin(magDecRad);
cmag = cos(magDecRad);
magUnitEstimate = [ smag * (2 * q0 * q3 + 2 * q1 * q2) - cmag * (2 * q2 * q2 + 2 * q3 * q3 - 1); ...
-cmag * (2 * q0 * q3 - 2 * q1 * q2) - smag * (2 * q1 * q1 + 2 * q3 * q3 - 1); ...
cmag * (2 * q0 * q2 + 2 * q1 * q3) - smag * (2 * q0 * q1 - 2 * q2 * q3)];
% Compute accelerometer output estimates
% Note: assuming here that u = Va, v = 0, w = 0
% Would be good to set u = Va * cos(theta), v = 0, w = Va * sin(theta)
% But need expressions for cos(theta) as quaternions...
accEstimate = [-2 * g * (q1 * q3 - q2 * q0); ...
Va * (r - br) - 2 * g * (q2 * q3 + q1 * q0); ...
-Va * (q - bq) - g * (1 - 2 * (q1 * q1 + q2 * q2))];
% Output function z(x, u) = [axhat, ayhat, azhat, mxhat, myhat, mzhat]
z = [accEstimate; ...
magUnitEstimate];
% Jacobian of z, C(x, u)
C = zeros(6, 7);
C = [ 2 * g * q2, -2 * g * q3, 2 * g * q0, -2 * g * q1, 0, 0, 0; ...
-2 * g * q1, -2 * g * q0, -2 * g * q3, -2 * g * q2, 0, 0, -Va; ...
0, 4 * g * q1, 4 * g * q2, 0, 0, Va, 0; ...
2 * q3 * smag, 2 * q2 * smag, 2 * q1 * smag - 4 * q2 * cmag, 2 * q0 * smag - 4 * q3 * cmag, 0, 0, 0; ...
-2 * q3 * cmag, 2 * q2 * cmag - 4 * q1 * smag, 2 * q1 * cmag, -2 * q0 * cmag - 4 * q3 * smag, 0, 0, 0; ...
2 * q2 * cmag - 2 * q1 * smag, 2 * q3 * cmag - 2 * q0 * smag, 2 * q0 * cmag + 2 * q3 * smag, 2 * q1 * cmag + 2 * q2 * smag, 0, 0, 0];
% Kalman gain
K = P * C' / (C * P * C' + R);
% Update error covariance matrix
P = (eye(length(x)) - K * C) * P;
% Update state estimate using measurements (accelerometer and
% magnetometer)
x = x + K * ([ax; ay; az; mx; my; mz] - z);
% Normalise quaternion
qNorm = sqrt(x(1) * x(1) + x(2) * x(2) + x(3) * x(3) + x(4) * x(4));
x(1) = x(1) / qNorm;
x(2) = x(2) / qNorm;
x(3) = x(3) / qNorm;
x(4) = x(4) / qNorm;
% Re-extract states
q0 = x(1); q1 = x(2); q2 = x(3); q3 = x(4);
% Store state estimates
roll_deg = atan2(2 * (q0 * q1 + q2 * q3), q0 * q0 + q3 * q3 - q1 * q1 - q2 * q2) * 180 / pi;
pitch_deg = asin (2 * (q0 * q2 - q1 * q3)) * 180 / pi;
yaw_deg = atan2(2 * (q0 * q3 + q1 * q2), q0 * q0 + q1 * q1 - q2 * q2 - q3 * q3) * 180 / pi;
end