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70 lines
2.5 KiB
Matlab
70 lines
2.5 KiB
Matlab
% Generate the symbolic code for the kalman filter on altitude
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dT = sym('dT','real');
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A = [1 dT 0 0; 0 1 dT 0; 0 0 1 0; 0 0 0 1];
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%Nu = diag([sym('V[1]') sym('V[2]') sym('V[3]') sym('V[4]')]);
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%Nu = [sym('V[1][1]') 0 0 0; ...
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% 0 sym('V[2][2]') 0 0; ...
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% 0 0 sym('V[3][3]') sym('V[3][4]'); ...
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% 0 0 sym('V[4][3]') sym('V[4][4]')];
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Nu = [sym('V[1][1]') sym('V[1][2]') sym('V[1][3]') sym('V[1][4]'); ...
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sym('V[2][1]') sym('V[2][2]') sym('V[2][3]') sym('V[2][4]'); ...
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sym('V[3][1]') sym('V[3][2]') sym('V[3][3]') sym('V[3][4]'); ...
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sym('V[4][1]') sym('V[4][2]') sym('V[4][3]') sym('V[4][4]');];
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Gamma = diag([sym('G[1]') sym('G[2]') sym('G[3]') sym('G[4]')]);
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Sigma = diag([sym('S[1]') sym('S[2]')]);
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C = [1 0 0 0; 0 0 1 1];
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state = [sym('z[1]'); sym('z[2]'); sym('z[3]'); sym('z[4]')];
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measure = [sym('x[1]'); sym('x[2]')];
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P = simplify(A * Nu * A' + Gamma);
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K = simplify(P*C'*(C*P*C'+Sigma)^-1);
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% fill in the zeros from above equations to make next calculation sparse
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P_mat = [sym('P[1][1]') sym('P[1][2]') sym('P[1][3]') sym('P[1][4]'); ...
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sym('P[2][1]') sym('P[2][2]') sym('P[2][3]') sym('P[2][4]'); ...
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sym('P[3][1]') sym('P[3][2]') sym('P[3][3]') sym('P[3][4]'); ...
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sym('P[4][1]') sym('P[4][3]') sym('P[4][3]') sym('P[4][4]')];
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K_mat = [sym('K[1][1]') sym('K[1][2]'); ...
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sym('K[2][1]') sym('K[2][2]'); ...
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sym('K[3][1]') sym('K[3][2]'); ...
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sym('K[4][1]') sym('K[4][2]')];
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z_new = A * state + K_mat * (measure - C * A * state);
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V = (eye(4) - K_mat * C) * P_mat;
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ccode(P)
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ccode(K)
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ccode(z_new)
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ccode(V)
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%% For when there is no baro update
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% Generate the symbolic code for the kalman filter on altitude
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C = [0 0 1 1];
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Sigma = sym('S[2]');
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measure = [sym('x[2]')];
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P = simplify(A * Nu * A' + Gamma);
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K = simplify(P*C'*(C*P*C'+Sigma)^-1);
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% fill in the zeros from above equations to make next calculation sparse
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P_mat = [sym('P[1][1]') sym('P[1][2]') sym('P[1][3]') sym('P[1][4]'); ...
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sym('P[2][1]') sym('P[2][2]') sym('P[2][3]') sym('P[2][4]'); ...
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sym('P[3][1]') sym('P[3][2]') sym('P[3][3]') sym('P[3][4]'); ...
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sym('P[4][1]') sym('P[4][3]') sym('P[4][3]') sym('P[4][4]')];
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K_mat = [sym('K[1][1]'); ...
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sym('K[2][1]'); ...
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sym('K[3][1]'); ...
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sym('K[4][1]')];
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z_new = A * state + K_mat * (measure - C * A * state);
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V = (eye(4) - K_mat * C) * P_mat;
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ccode(P)
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ccode(K)
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ccode(z_new)
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ccode(V)
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