| 1 | function [A_k, C_k, pre_k, A_l] = assembDeriv(ksi, iab, ksi0, Q, R, ref_ome) |
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| 2 | a = 0.9898; |
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| 3 | b = 0.0072; |
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| 4 | c = 0.0361; |
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| 5 | d = 1.0; |
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| 6 | e = 0.0149; |
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| 7 | dt = 0.000125; |
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| 8 | |
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| 9 | ome = ksi(1); |
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| 10 | the = ksi(2); |
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| 11 | P = [ksi(3), ksi(4); ksi(4), ksi(5)]; |
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| 12 | ia = iab(1); |
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| 13 | ib = iab(2); |
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| 14 | A_k = zeros(5); |
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| 15 | A_l = zeros(6); |
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| 16 | |
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| 17 | |
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| 18 | %puvodni matice derivaci |
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| 19 | A = [d, -e*(ia*cos(the)+ib*sin(the)); dt, 1.0]; |
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| 20 | C = [b*sin(the), b*ome*cos(the); -b*cos(the), b*ome*sin(the)]; |
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| 21 | |
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| 22 | %dalsi matice EKF |
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| 23 | Pp = A*P*A' + Q; |
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| 24 | S = C*Pp*C' + R; |
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| 25 | K = Pp*C'/S; |
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| 26 | Pnew = (eye(2) - K*C)*Pp; |
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| 27 | |
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| 28 | %derivace zakladnich matic EKF stavu |
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| 29 | % dAdom = zeros(4); |
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| 30 | dAdth = [0, e*(ia*sin(the)-ib*cos(the)); 0, 0]; |
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| 31 | % dAdP = zeros(4); |
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| 32 | dCdom = [0, b*cos(the); 0, b*sin(the)]; |
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| 33 | dCdth = [b*cos(the), -b*ome*sin(the); b*sin(the), b*ome*cos(the)]; |
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| 34 | % dCdP = zeros(4); |
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| 35 | % dPdomth = zeros(4); |
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| 36 | dPdPo = [1, 0; 0, 0]; |
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| 37 | dPdPot = [0, 1; 1, 0]; |
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| 38 | dPdPt = [0, 0; 0, 1]; |
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| 39 | |
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| 40 | %derivace dalsich matic EKF stavu |
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| 41 | % dPpdom = zeros(4); |
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| 42 | dPpdth = dAdth*P*A' + A*P*dAdth'; |
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| 43 | dPpdPo = A*dPdPo*A'; |
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| 44 | dPpdPot = A*dPdPot*A'; |
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| 45 | dPpdPt = A*dPdPt*A'; |
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| 46 | |
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| 47 | dSdom = dCdom*Pp*C' + C*Pp*dCdom'; |
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| 48 | dSdth = dCdth*Pp*C' + C*dPpdth*C' + C*Pp*dCdth'; |
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| 49 | dSdPo = C*dPpdPo*C'; |
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| 50 | dSdPot = C*dPpdPot*C'; |
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| 51 | dSdPt = C*dPpdPt*C'; |
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| 52 | |
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| 53 | dKdom = Pp*dCdom'/S - Pp*C'/S*dSdom/S; |
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| 54 | dKdth = dPpdth*C'/S + Pp*dCdth'/S - Pp*C'/S*dSdth/S; |
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| 55 | dKdPo = dPpdPo*C'/S - Pp*C'/S*dSdPo/S; |
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| 56 | dKdPot = dPpdPot*C'/S - Pp*C'/S*dSdPot/S; |
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| 57 | dKdPt = dPpdPt*C'/S - Pp*C'/S*dSdPt/S; |
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| 58 | |
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| 59 | dPnewdom = - dKdom*C*Pp - K*dCdom*Pp; |
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| 60 | dPnewdth = dPpdth - dKdth*C*Pp - K*dCdth*Pp - K*C*dPpdth; |
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| 61 | dPnewdPo = dPpdPo - dKdPo*C*Pp - K*C*dPpdPo; |
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| 62 | dPnewdPot = dPpdPot - dKdPot*C*Pp - K*C*dPpdPot; |
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| 63 | dPnewdPt = dPpdPt - dKdPt*C*Pp - K*C*dPpdPt; |
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| 64 | |
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| 65 | A_k(1,1) = d; |
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| 66 | A_k(1,2) = -e*(ia*cos(the)+ib*sin(the)); |
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| 67 | % A_k(1,3) = 0; |
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| 68 | % A_k(1,4) = 0; |
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| 69 | % A_k(1,5) = 0; |
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| 70 | |
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| 71 | A_k(2,1) = dt; |
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| 72 | A_k(2,2) = 1.0; |
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| 73 | % A_k(2,3) = 0; |
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| 74 | % A_k(2,4) = 0; |
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| 75 | % A_k(2,5) = 0; |
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| 76 | |
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| 77 | A_k(3,1) = dPnewdom(1,1); |
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| 78 | A_k(3,2) = dPnewdth(1,1); |
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| 79 | A_k(3,3) = dPnewdPo(1,1); |
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| 80 | A_k(3,4) = dPnewdPot(1,1); |
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| 81 | A_k(3,5) = dPnewdPt(1,1); |
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| 82 | |
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| 83 | A_k(4,1) = dPnewdom(1,2); |
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| 84 | A_k(4,2) = dPnewdth(1,2); |
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| 85 | A_k(4,3) = dPnewdPo(1,2); |
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| 86 | A_k(4,4) = dPnewdPot(1,2); |
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| 87 | A_k(4,5) = dPnewdPt(1,2); |
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| 88 | |
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| 89 | A_k(5,1) = dPnewdom(2,2); |
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| 90 | A_k(5,2) = dPnewdth(2,2); |
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| 91 | A_k(5,3) = dPnewdPo(2,2); |
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| 92 | A_k(5,4) = dPnewdPot(2,2); |
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| 93 | A_k(5,5) = dPnewdPt(2,2); |
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| 94 | |
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| 95 | phi = zeros(5,1); |
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| 96 | phi(1) = d*ksi0(1) + e*(ib*cos(ksi0(2)) - ia*sin(ksi0(2))); |
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| 97 | phi(2) = ksi0(2) + dt*ksi0(1); |
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| 98 | phi(3) = Pnew(1,1); |
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| 99 | phi(4) = Pnew(1,2); |
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| 100 | phi(5) = Pnew(2,2); |
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| 101 | |
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| 102 | A_l(1:5,1:5) = A_k; |
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| 103 | A_l(1:5,6) = phi - A_k*ksi0; |
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| 104 | A_l(6,6) = 1.0; |
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| 105 | |
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| 106 | %%% |
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| 107 | A_l(1,2) = 0; %maze clen e*(...), ktery se prevede do B |
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| 108 | A_l(1:2,6) = [0;dt*ref_ome]; %zmena korekce, protoze je to tam uz linearni, ale posun |
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| 109 | %%% |
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| 110 | |
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| 111 | C_k = zeros(2,5); |
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| 112 | C_k(1:2,1:2) = C; |
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| 113 | |
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| 114 | pre_k = zeros(3,1); |
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| 115 | pre_k(1) = Pnew(1,1); |
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| 116 | pre_k(2) = Pnew(1,2); |
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| 117 | pre_k(3) = Pnew(2,2); |
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| 118 | end |
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