# How to deal with Status: Inaccurate/Solved

hi, everyone, this is my problem

I try to solve it with CVX toolbox, the status is Inaccurate/Solved, the following is my code.
clc
clear all
close all

format long

%% Trajectory
T=10; % 信号发射周期
v=10*0.54444; % 在定位测量点时水面船的运动速度

ArcAngle=v
Angle=0:ArcAngle:(2pi+ArcAngle);

PosLoc=PosLoc’;
xShip=PosLoc(:,1)+10randn(size(PosLoc(:,1)));
yShip=PosLoc(:,2)+10
randn(size(PosLoc(:,1)));

zShip=0; % 发射换能器的入水深度

%% Target
Range=[800:100:1000];
xTar=Range/sqrt(2);
yTar=Range/sqrt(2);
NN=length(Range); % 阵元数目
zTar=50;

%% measurement error
detat=10.001; % 时延测量误差
tb=5
0.001;

c=1500+5*randn(size(xShip));
cb=5; % 声速测量的固定偏差
detac=1; % 声速测量 随机误差的标准差

detaa=1; % 节点位置的随机误差

%% solving
RmseCWLLS1=zeros(1,length(xTar));
xErr=zeros(1,length(xTar));
yErr=zeros(1,length(xTar));
for nn=1:NN
nn

``````for mc=1

mc

xShipMea=xShip+detaa*randn(size(xShip));
yShipMea=yShip+detaa*randn(size(yShip));

tMea=sqrt((xShip-xTar(nn)).^2+(yShip-yTar(nn)).^2+(zShip-zTar).^2)./c+detat*randn(size(xShip))+tb;

cMea=ones(size(xShip)).*(c+cb+detac*randn(size(xShip)));

%%  SDP
A=[2*xShipMea,2*yShipMea,ones(length(xShip),1),-2*tMea.^2.*cMea,tMea.^2,-2*tMea.*cMea.^2,4*tMea.*cMea,-2*tMea,cMea.^2,-2*cMea];
B=xShipMea.^2+yShipMea.^2+(zShip-zTar)^2-tMea.^2.*cMea.^2;

rk=sqrt((xTar(nn)-xShip).^2+(yTar(nn)-yShip).^2+(zTar-zShip)^2);
wt=detat^2*diag(4*rk.^2.*c.^2);
wxy=detaa^2*diag(4*rk.^2);
wc=detac^2*diag(4*rk.^2.*(rk./c).^2);
W=eye(length(tMea))/(wt+wxy+wc);

Coe=[A'*W*A -A'*W*B;-B'*W*A B'*W*B];

cvx_begin sdp
cvx_precision high
variable G(10,10) symmetric;
variable g(10);
minimize(trace([G g;g' 1]*Coe));
subject to
[G g;g' 1] >= 0;
g(3)-G(7,7)+G(1,1)+G(2,2) == 0;
g(5)-G(4,4) == 0;
g(7)-G(4,6) == 0;
g(8)-G(4,7) == 0;
g(9)-G(6,6) == 0;
g(10)-G(6,7) == 0;
cvx_end

X(1,1)=xTar(nn);
X(2,1)=yTar(nn);
X(3,1)=tb^2*cb^2-xTar(nn)^2-yTar(nn)^2;
X(4,1)=cb;
X(5,1)=cb^2;
X(6,1)=tb;
X(7,1)=tb*cb;
X(8,1)=tb*cb^2;
X(9,1)=tb^2;
X(10,1)=tb^2*cb;

xSDP_g(mc,nn)=g(1);
ySDP_g(mc,nn)=g(2);
xSDP_G(mc,nn)=sqrt(G(1,1));   %%%% 这块需要讨论使用G中数据还是g中的数据
ySDP_G(mc,nn)=sqrt(G(2,2));
end
``````

end

RmseSDP_g=sqrt(sum((xSDP_g-ones(mc,1)*xTar).^2+(ySDP_g-ones(mc,1)*yTar).^2,1)./mc);
RmseSDP_G=sqrt(sum((xSDP_G-ones(mc,1)*xTar).^2+(ySDP_G-ones(mc,1)*yTar).^2,1)./mc);

BiasSDP_g=sqrt((mean(xSDP_g-ones(mc,1)*xTar,1)).^2+(mean(ySDP_g-ones(mc,1)*yTar,1)).^2);
BiasSDP_G=sqrt((mean(xSDP_G-ones(mc,1)*xTar,1)).^2+(mean(ySDP_G-ones(mc,1)*yTar,1)).^2);
%% 绘图和保存数据
figure;
hold on
scatter(xShip,yShip,‘blue.’);
scatter(xTar,yTar,‘red.’);
legend(‘校阵节点’,‘水听器位置’)
xlabel(‘x(m)’);
ylabel(‘y(m)’);
xlim([-3000 3000])
ylim([-3000 3000])
axis equal
grid on
box on

figure;
hold on
plot(Range,RmseSDP_g,‘black-<’,‘LineWidth’,1.5)
plot(Range,RmseSDP_G,‘red->’,‘LineWidth’,1.5)
box on
grid on
set(gca,‘GridLineStyle’,‘–’)
xlabel(‘Distance(m)’)
ylabel(‘RMSE(m)’)

figure;
hold on
plot(Range,BiasSDP_g,‘black-<’,‘LineWidth’,1.5)
plot(Range,BiasSDP_G,‘red->’,‘LineWidth’,1.5)
box on
grid on
set(gca,‘GridLineStyle’,‘–’)
xlabel(‘Distance(m)’)
ylabel(‘Bias(m)’);

% for Num=1:NN
% figure;
% hold on
% scatter(xSDP_g(:,Num),ySDP_g(:,Num),‘black.’);
% scatter(xSDP_G(:,Num),ySDP_G(:,Num),‘black.’);
% scatter(xTar(Num),yTar(Num),‘green*’);
% end

Please show all the CVX and solver output. If you have Mosek available as solver, try that, and show us the output.

the following is the output. I currently do not have Mosek

The objective value has huge magnitude, which is indicative of bad scaling. Change units to try to get non-zero input data to be within a small number of orders of magnitude of 1, and so that optimal objective has magnitude no larger than 1e3 or 1e4.

I try the Mosek solver, the status is Solved, but the result is not the optimal, I can find another input value, which results in a smaller objective value.

@Michal_Adamaszek Why does Mosek report
Problem status : PRIMAL_AND DUAL_FEASIBLE,
Solution status : OPTIMAL,
when PRSTATUS does not appear to converge to + or -1?

The PRSTATUS is informational and does not participate in the termination criteria. The other residuals are small and the solution also has very small violations so all looks good. The wandering PRSTATUS could indicate it was hard to converge.

1 Like