matrix_optimal.m

自己做的毕设

function   [a1,segma]=matrix_optimal(a,b,Da,Dab,Wa,Wab)
%%%矩阵重复优化的核心计算程序，a是N个未知节点坐标矩阵，b是M个信标节点坐标矩阵，Da是未知节点之间的测距矩阵，Dab是未知节点和信标节点之间的测
%%%距矩阵，Wa是未知节点之间测距的权重函数，Wab是未知节点和信标节点之间测距的权重函数；a1是根据重复优化公式计算出来的下一个迭代的未知节点坐标
%%%矩阵，segma是当前未知节点坐标矩阵a作为定位坐标矩阵和实际的测距的总的平方误差和，也即优化函数的值
%%% 此函数综合了matrix_optimala()和matrix_optimalab()两个函数来迭代计算
%%% a(N*K) is the coordinates of the unknown nodes,N:is the number of the
%%% unknown nodes,K: is the dimensional(2 or 3 in fact)
%%% b(M*K) is the coordinates of the beacon nodes,M: is the number of the
%%% beacon nodes
%%% Da(N*N) is the measured distance matrix between the unknown nodes
%%% Wa(N*N) is the weight matrix of the unknown nodes
%%% Dab(N*M) is the measured distance matrix between the unknown node and the
%%% beacon node
%%% Wab(N*M) is the weight matrix between the unknown node and the beacon node
%%% a1(N*K) is the returned coordinate matrix according to the input a
%%% segma is the error value according to the measured distance Da and the
%%% estimated coordinates
%%% Author: Xie Dongfeng

row_a=size(a,1);
row_b=size(b,1);
calculated_disab=L2_distance(a',b');
calculated_disa=L2_distance(a',a');
 %%% calculated_disab is the distance between the unknown nodes  and beacon 
 %%% nodes by calculating  the estimated coordinates
 %%% calculated_disa is the distance between the unknown nodes  by
 %%% calculating
 V1=zeros(row_a,row_a);
 V2=zeros(row_a,row_a);
 V3=zeros(row_a,row_b);
 V4=zeros(row_b,row_b);
 
  for i=1:row_a
     for j=1:row_a
         if(i~=j)
             V1(i,j)=-Wa(i,j);
             V1(i,i)=V1(i,i)+Wa(i,j);
         end
     end
 end
 for i=1:row_a
     for j=1:row_b
         V2(i,i)=V2(i,i)+Wab(i,j);
     end
 end
 V3=Wab;
 for i=1:row_b
     for j=1:row_a
         V4(i,i)=V4(i,i)+Wab(j,i);
     end
 end
 elta=trace(a'*V2*a)-2*trace(a'*V3*b)+trace(b'*V4*b);
 
 B1X=zeros(row_a,row_a);
 B2X=zeros(row_a,row_a);
 B3X=zeros(row_a,row_b);
 B4X=zeros(row_b,row_b);
 lamata=zeros(row_a,row_b);
  for i=1:row_a
     for j=1:row_a
         if(i~=j&&calculated_disa(i,j)~=0)
             B1X(i,j)=-Wa(i,j)*Da(i,j)/calculated_disa(i,j);
         end
     end
 end
 for i=1:row_a
     for j=1:row_a
         if(j~=i)
             B1X(i,i)=B1X(i,i)-B1X(i,j);
         end
     end
 end
 for i=1:row_a
     for j=1:row_b
         if(calculated_disab(i,j)~=0)
             lamata(i,j)=Wab(i,j)*Dab(i,j)/calculated_disab(i,j);
         end
     end
 end
 for i=1:row_a
     for j=1:row_b
         B2X(i,i)=B2X(i,i)+lamata(i,j);
     end
 end
 B3X=lamata;
for i=1:row_b
     for j=1:row_a
         B4X(i,i)=B4X(i,i)+lamata(j,i);
     end
end
 sita=-2*(trace(a'*B2X*a)-2*trace(a'*B3X*b)+trace(b'*B4X*b));
 
 segma1=0;
 for i=1:row_a
     for j=1:row_b
         segma1=segma1+Wab(i,j)*Dab(i,j)*Dab(i,j);
     end
 end
 segmaXab=segma1+elta+sita;
 segma0=0;
 for i=1:row_a
     for j=i+1:row_a
         segma0=segma0+Wa(i,j)*Da(i,j)*Da(i,j);
     end
 end       
 segmaXa=segma0+trace(a'*V1*a)-2*trace(a'*B1X*a);
 segma=segmaXa+segmaXab;
 a1=inv(V1+V2)*((B1X+B2X)*a+(V3-B3X)*b);