63 lines
1.5 KiB
Mathematica
63 lines
1.5 KiB
Mathematica
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function [newRO, newRR] = mstep_update_rotation(P, S_bar, V, E_z, E_zz, RO, Tr)
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%[newRO, newRR] = mstep_update_rotation(P, S_bar, V, E_z, E_zz, RO, Tr)
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% Linearizes the expression in Eq 24 using exponential maps and
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% solves for an improved rotation
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% update step
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tw_step = 0.3;
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[K, T] = size(E_z);
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J = size(S_bar, 2);
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Pc = P - Tr(:)*ones(1,J);
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newRR = zeros(2*T,3);
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newRO = RO;
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for iter=1:1,
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for t = 1:T,
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A = zeros(3);
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B = zeros(2,3);
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zz_hat_t = [1 E_z(:,t)'; E_z(:,t) E_zz((t-1)*K+1:t*K,:)];
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for j=1:J,
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H_j = [S_bar(:,j) reshape(V(:,j), 3, K)];
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A = A + H_j*zz_hat_t*H_j';
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B = B + ([Pc(t,j); Pc(t+T,j)] * [1 E_z(:,t)'] * H_j');
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end
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oldRO_t = RO{t};
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C = oldRO_t*A;
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D = B - oldRO_t(1:2,:)*A;
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% now we solve the system: [1 0 0; 0 1 0]*twist*C = D
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CC = [0 C(3,1) -C(2,1)
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-C(3,1) 0 C(1,1)
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0 C(3,2) -C(2,2)
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-C(3,2) 0 C(1,2)
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0 C(3,3) -C(2,3)
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-C(3,3) 0 C(1,3)];
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DD = D(:);
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% twist optimization
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twist_vect = tw_step*pinv(CC)*DD;
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twh = [0 -twist_vect(3) twist_vect(2)
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twist_vect(3) 0 -twist_vect(1)
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-twist_vect(2) twist_vect(1) 0 ];
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dR = expm(twh);
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newRO_t = dR*oldRO_t;
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newRO{t} = newRO_t;
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newRR(t,:) = newRO_t(1,:);
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newRR(t+T,:) = newRO_t(2,:);
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end
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RO = newRO;
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end
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