I am studying about system identification using Least Mean Square algorithm. I tried with some code using the equations for LMS. Based on the algorithm steps, the calculation of the error and weight updates looks alright. However, it fails to give the correct output. Can somebody please help in fixing the problem?
clear all;
mu=0.05;
b=fir1(10,0.5,'low');
x = rand(1,30);
d = filter(b,1,x);
w=zeros(1,15);
for n=1:length(x)-15-1
temp=x(n:n+15-1);
y=temp.*w(n);
e(n)=d(n)-y(n);
w(n+1)=w(n)+mu*e(n)*x(n)';
end
subplot(2,1,1);stem(b);
legend('Actual');
xlabel('coefficient #');
ylabel('coefficient value');
subplot(2,1,2);stem(w);
legend('estimated');
xlabel('coefficient #');
ylabel('coefficient value');
Related
I have a following lab where i was asked to write the command matlab lines for these questions:
If initial Conditions are: x(0)=[2;0].๐๐๐๐ ๐กโ๐ ๐๐๐ ๐๐๐๐ ๐ ๐ฆ(๐ก).
Find the response y(t) due to step input with Amplitude of
Find the Transfer Function for the above state space model
Derive back the state space model from (3).
a = [0,1;0,4];
b = [0;1];
c = [0 -5];
x0=[2;0];
sys = ss(a,b,c,2);
initial(sys,x0); % to get 1
[n,d]=ss2tf(a,b,c,0);
mySys_tf=tf(n,d) % to get 3
[num den] = tfdata(mySys_tf, 'v')
tf2ss(num,den) % to get 4
I have written this code but it seems like its not giving me any results in the response graph and thus i can't also solve 2 and it get error in 4 if you can help me out to check what is wrong
I believe that the error comes from the fact that the system is unstable. If you were to plot the system's reaction to a step input using step() then you will see how it goes to infinity. I also don't know how far you are into your controls course and if you've seen the root locus yet, but you can plot the root locus of the system via rlocus(sys) and you'll see that the real portion of the root is on the right half of the plane and therefore letting you know that the system is unstable.
The response is 0 and will stay zero as x(2) = 0. It requires an input u to get x(2) off zero. So the graph is totally fine.
use step(sys) and you will see the drop to -Inf. Optionally you can define the end-time. Call step(sys,1) to see a reasonable range.
You solved 3 & 4 yourself.
To check stability you simply need to ask MATLAB isstable(sys) (isn't it continent? Well, there is a danger that people will forget the theory behind it and how it is connected...)
To check observability: rank(obsv(sys)) and make sure that it is the same as the system matrix
assert(rank(obsv(sys)) == length(sys.A), 'System is not observable!')
I want to implement a part of article. The following explanations are expressed in it.
"we evaluate the performance of proposed localization method at varying degree of irregularity, where DOI defines the radio propagation irregularity per unit degree change in direction. The radio propagation irregularity model used in this paper is shown as follows:"
I have tried to write the code of this part but It doesn't work and can't get a result.
function Coeff=k(i)
Rand=rand(1,100);
DOI=0.02;
if(i==0)
Coeff=1; %Terminating condition
else
while i<360
Coeff=k(i-1)+Rand*DOI; %DOI=[0.01,0.02,0.03,0.04,0.05]
end
end
end
And The following figure has been shown in that article for DOI=0.02...I need to get an output like this, How can I do it
Thanks in advance.
It would help if you post a link to the article, but in this case they just generate a circular path with some noise.
DOI=0.05;
phi = linspace(0,2*pi,360); %360 angles
r=-DOI+2*DOI*rand([1,360]); %random values between -DOI and DOI
r=cumsum(r)+1; %add them to make a path, with mean value 1
while abs(r(end)-r(1))> DOI %start and finish must not be too far away from eachother
r=-DOI+2*DOI*rand([1,360]);
r=cumsum(r)+1;
end
plot(r.*cos(phi),r.*sin(phi),'r',cos(phi),sin(phi),'--b')
axis equal
Actually I have to calculate values of 3 variables from probably 8 or 9 non-linear equations(may be more for accuracy).
I was using lsqnonlin and fsolve.
Using lsqnonlin, it says solver stopped prematurely (mainly due to value of iteration, funEvals and tolerance) and the output is far away from exact solution. I tried but I don't know on what basis I should set those parameters.
Using fsolve, it says no solution found.
I also used LMFnlsq and LMFsolve but it gives the output nowhere near the exact solution? I tried to change other parameters too but I could not bring those solutions to my desired values.
Is there any other way to solve these overdetermined non-linear equations?
My code till now:
x0 = [20 40 275];
eqn = #(x)[((((x(1)-Sat(1,1))^2+(x(2)-Sat(1,2))^2+(x(3)-Sat(1,3))^2))-dis(1)^2);
((((x(1)-Sat(2,1))^2+(x(2)-Sat(2,2))^2+(x(3)-Sat(2,3))^2))-dis(2)^2);
((((x(1)-Sat(3,1))^2+(x(2)-Sat(3,2))^2+(x(3)-Sat(3,3))^2))- dis(3)^2);
((((x(1)-Sat(4,1))^2+(x(2)-Sat(4,2))^2+(x(3)-Sat(4,3))^2))- dis(4))^2;
((((x(1)-Sat(5,1))^2+(x(2)-Sat(5,2))^2+(x(3)-Sat(5,3))^2))- dis(5))^2;
((((x(1)-Sat(6,1))^2+(x(2)-Sat(6,2))^2+(x(3)-Sat(6,3))^2))- dis(6))^2;
((((x(1)-Sat(7,1))^2+(x(2)-Sat(7,2))^2+(x(3)-Sat(7,3))^2))- dis(7))^2;
((((x(1)-Sat(8,1))^2+(x(2)-Sat(8,2))^2+(x(3)-Sat(8,3))^2))- dis(8))^2;
((((x(1)-Sat(9,1))^2+(x(2)-Sat(9,2))^2+(x(3)-Sat(9,3))^2))- dis(9))^2;
((((x(1)-Sat(10,1))^2+(x(2)-Sat(10,2))^2+(x(3)-Sat(10,3))^2))- dis(10))^2];
lb = [0 0 0];
ub = [100 100 10000];
options = optimoptions('lsqnonlin','MaxFunEvals',3000,'MaxIter',700,'TolFun',1e-18);%,'TolX',1);
x= lsqnonlin(eqn,x0,lb,ub,options)
**Error:**
**Solver stopped prematurely.**
lsqnonlin stopped because it exceeded the iteration limit,
options.MaxIter = 700 (the selected value).
x = 20.349 46.633 9561.5
Hoping for some suggestions!
Thanks in advance!
I usually model this explicitly:
min w'w
f_i(x) = w_i
w is a free variable
L<=x<=U
It should be easy to calculate a feasible (but non-optimal) solution in advance. If you can find a "good" initial solution that would be even better. Then use a general purpose NLP solver (e.g. fmincon) and pass on your initial feasible solution (both x and w). The best thing is to use a modeling system that allows automatic differentiation. Otherwise you should provide correct and precise gradients (and if needed second derivatives). See also the advice here.
I am trying to solve a very large non-linear problem using the MatCont package. Due to the large number of dimensions, and the non-linear nature, I believe that supplying the Jacobian for my system to the MatCont algorithm will speed things up immensely. However, I cannot get it to recognise that it has a Jacobian to use!
As a minimal working example, I have modified the circle finder from the help documentation to include a Jacobian:
function out = curve()
out{1}=#curvefunc;
out{2}=#defaultprocessor;
out{3}=#options;
out{4}=#jacobian;
out{13}=#adapt;
end
function f=curvefunc(x)
f=x(1)^2+x(2)^2-1;
end
function J=jacobian(x)
disp('USE JACOBIAN')
J=[2*x(1) , 2*x(2)];
end
function varargout=defaultprocessor(varargin)
if nargin>2
varargout{3}=varargin{3};
end
varargout{2}=[0];
varargout{1}=0;
end
function option=options()
option=contset;
end
function [res,x,v]=adapt(x,v)
res=[];
end
I then try to run this program from the command line using
[x,v,s,h,f] = cont(#curve,[1;0]);
However, the response is
first point found
tangent vector to first point found
elapsed time = 0.2 secs
npoints curve = 300
Since I told it to output 'USE JACOBIAN' every time the Jacobian function was called, it is clear that MatCont is not using it.
How do I get the Jacobian to be used?
I solved my own problem! Seems I was quite close to getting it working. The below is a bit of a botch, so if anyone knows how to do it with options please post an answer also.
Firstly I edit the options settings so that when it performs the continuation it only locates the first point:
function option=options()
option = contset;
option = contset(option,'MaxNumPoints',1);
end
its fine for it to do this using numerical Jacobians, the first point is known very well in most problems. This is then called from a script or a function using the following:
[x,v,s,h,f] = cont(#curve,[1;0]);
global cds
cds.options.MaxNumPoints=[];
cds.symjac=1;
[x,v,s,h,f] = cont(x,v,s,h,f,cds);
The first line finds the initial point using numerical Jacobians, as it was set up to do. The continuer is then manually adjusted to firstly have no limit on the maximal number of points (this can be set to any appropriate number) and then the use of the user provided Jacobian is set to 1 (true). The continuer is then resumed with the new settings and uses the Jacobain properly.
Recently I'm doing some training of HMM, I used the HMM toolbox. But I have some problems and couldn't resolve them.
I train my hmm as shown below. There's no problems here.
[LL, prior1, transmatrix1, observematrix1] = dhmm_em(data, prior0, transmatrix0, observematrix0);
I use the Viterbi algorithm to find the most-probable path through the HMM state trellis.
function path = viterbi_path(prior, transmat, obslik);
Now there's a problem. I don't know what the "obslik" means. Is it the observematrix1?
I want to get the probability of a sequence, but I don't know whether I should use the "fwdback" function or not. If I should, what the "obslik" means then?
function [alpha, beta, gamma, loglik, xi_summed, gamma2] = fwdback(init_state_distrib, transmat, obslik, varargin);
Thanks!!!
I didn't understand the comments. Now I understand it.
The "obslik" here isn't equal to the observematrix1. Before using Viterbi_path function, we should compute the obslik:
obslik = multinomial_prob(data(m,:), observematrix1);
the data matrix is the observematrix0, observe-matrix before training.
Am I right?