unweighted least square estimation with fminsearch

Hallo every one,

I have an equation or model which it must be fited to a part of a real signal (radar waveform) in order to estimate three parameter.

I should do an unweighted least-square estimation whose convergence is reachedt through the Nelder-Mead (NM) algorithm.

max nummber of iteration allowed is 600 , and the function toleranc is 10^-01

and wenn convergence is not met, i must widening the real signal that i have by one value until convergence is reached.

so far

• I wrote the equation with all the constansts
• took the sum of squares cost function and make it handle function
• tried to reach the convergence and get the parameters

%% Brown Modell fitting
k = size(n_1);
t = k* rt ;
% Constant Parameters
alt_20hz= lat_01(1,1);
off_nadir_angle_wf_20hz_ku = F_off_nadir_angle_wf_ocean_01_ku(1,1) ; 
c = 299792458 ; % speed of light m/s
Re = 6371000  ; % the earth raduis meters 
antenna_w =   rad2deg(1.28) ; % the antenna beam width           
rt = 3.125 * 10.^-6 ; % time resolution nano seoconds
sigma_p = 0.513 * rt   ; % width of the radar point target response

% the Equation
lamda = (sin(antenna_w).^ 2 )* (1 / ( 2 * log(2)));
a = (4 * c ) / (lamda .* alt_20hz * (1+ (alt_20hz / Re)));
b_offnadirangel = cos( 2 .* sqrt(off_nadir_angle_wf_20hz_ku)) - (( sin(2 * off_nadir_angle_wf_20hz_ku)) / lamda ) ;
c_offnadirangel = b_offnadirangel .* a ;
a_offnadirangel = exp(-4* sin(off_nadir_angle_wf_20hz_ku))./ (lamda);

% Parameter estimation
MaxIter =600 ;
f1 = n_1 ; % the real signal 
fun = @(P)sum(f1 - (a_offnadirangel .* P(1).^(( 1 + erf((t - P(2) - c_offnadirangel .* P(3).^2 )/...
    ( sqrt(2) .* P(3))) ) / 2) .* exp(-1 .*(c_offnadirangel .* ( t - P(2) - (0.5 .* c_offnadirangel .* P(3).^2)))) + Tn)).^2 % sum of squares cost function
% Start with the default options
options = optimset;
options = optimset(options,'Display', 'off');
options = optimset(options,'MaxIter', 600);
options = optimset(options,'MaxFunEvals', 600);
options = optimset(options,'TolFun', 10^-10);
options = optimset(options,'TolX', 10^-10);
x0 =[0,0,0]; % initial Parameter estimation
MaxIter = 600 ;
Tol_fun = 10^-10 ;
% wenn the convergence is not reach the stop gate is increased one (the estimation window is windend)
while c <= MaxIter 
P = fminsearch(fun,x0,options);  % Minimise 'cost P'
if abs(fun) < Tol_fun
break; 
else 
    stop_gate = stop_gate +1
    n_1 = waveform_norm(edge_foot(1):stop_gate(1))' ;
    P = fminsearch(fun, x0, options); 
    
end
c=c+1 ;
end

I seems like I am doing something wrong, I am getting the following error :

Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 1-by-2.

Error in fminsearch (line 200)
fv(:,1) = funfcn(x,varargin{:});

Can someone help me with this? Big thanks in advance!

Answer 1

[Star Strider]

You should be summing the squares, not squaring the sum.

Try this:

fun = @(P)sum((f1 - (a_offnadirangel .* P(1).^(( 1 + erf((t - P(2) - c_offnadirangel .* P(3).^2 )/...
    ( sqrt(2) .* P(3))) ) / 2) .* exp(-1 .*(c_offnadirangel .* ( t - P(2) - (0.5 .* c_offnadirangel .* P(3).^2)))) + Tn)).^2) % sum of squares cost function

I cannot run your code, so I cannot test this.

[Rima Habib]

Thank you for your help , you are right! I've fix it but i still get the same error with no results.

[Star Strider]

My pleasure.

‘... i still get the same error with no results.’

That could be because:

c = 299792458 ; % speed of light m/s

and:

MaxIter = 600 ;

so:

while c <= MaxIter 
P = fminsearch(fun,x0,options);  % Minimise 'cost P'
if abs(fun) < Tol_fun
break; 
else 
    stop_gate = stop_gate +1
    n_1 = waveform_norm(edge_foot(1):stop_gate(1))' ;
    P = fminsearch(fun, x0, options); 
    
end
c=c+1 ;
end

will never execute.

It may be necessary for you to choose another name for your counter than ‘c’.

[John D'Errico]

+1. As well, only 600 function evals were allowed, but with a fairly tight tolerance on the result. fminsearch is NOT an economical optimizer, in the sense that it has no nice quadratic convergence behavior as it gets near the optimum. This may be another reason why convergence will not occur. Of course, nothing can be known until you fix the bug. But without the data, it is difficult to say more.

[Rima Habib]

Star Strider, thanks again, I still have the same error. can I ask: do you have an idea why I am getting this particular error, I am not understanding what matlab means by : the size of the left side is 1-by-1 and the size of the right side is 1-by-2.

[Torsten]

What is the output if you insert the line

size(fun(x0))

after the line

while c <= MaxIter     

?

[Rima Habib]

John D'Errico , you are right, I thought about that too but unfortunately I can not edit the iterationnumber or the tolerance, they are constant values,I have been given from my professor. I know it is hard to say a point of view with out the data. I have attached a link to a mat file. hope it can clarify somethingmat. file

[Rima Habib]

Torsten, the output of size(fun(x0)) is an infinite loop with [1 2 ]

[Torsten]

Then something is wrong with your function "fun". It must return a scalar value (size must be [1 1 ]).

[Rima Habib]

Torsten, thank you for your hint, I will review my work to find out the error in the function