How can i solve this "Matrix dimensions must agree" error?

I am getting error while run this code.

error:

Error using +

Matrix dimensions must agree.

Error in Untitled (line 77)

omega(:, :, i+1) = omega(:, :, i)+10 * x_hat2(:, i) * conj(e(i))';

clear all; close all; clc;
%  Isometric model Kalman filter simulation Kalman Filter
%% Initial condition
ts = 1;             %  Sampling interval
t = [0:ts:100];     %  Sampling moment
T = length(t);      %  Sampling points 
%% Initial state
x = [0 40 0 20]'; 

%%  Process Noise Covariance Process Noise Co - point Patrograph
q = 5;              %  Process noise covariance
Q1 = q*eye(4);       %  Process noise covariance matrix

%%  Measurement Noise Covariance Observation Noise Co-Tariation Matrix
r = 5;              %  Observation noise covariance
Q2 = r*eye(2);       %  Observation noise covariance matrix

%% Process and measurement noise
v1 = sqrt(Q1)*randn(4,T);   %  Process noise sequence dimension:4 x T
v2 = sqrt(Q2)*randn(2,T);   %  Observing noise sequence dimension:2 x T
%% Estimate error covariance initialization
p = 5;                  %  Estimation error covariance matrix
P(:,:,1) = p*eye(4);    %  Estimated covariance matrix

%========================================================================== 

%%  Continuous time status space model
A = [0 1 0 0;
       0 0 0 0;
       0 0 0 1; 
       0 0 0 0];
B = [0 0;
       1 0;
       0 0;
       0 1];
C = [1 0 0 0;
       0 0 1 0];
D = [1 0;
       0 1];

%%  Discrete time status space model
% F:State transfer matrix
% H:Observation matrix
sysc = ss(A,B,C,D);             %  Generate continuous time status space model
sysd = c2d(sysc, ts, 'zoh');    %  Continuous time state space model to discrete time status space model
[F G C I] = ssdata(sysd);       %  Remove the discrete time status space model; process equation F:State transfer matrix; observation equationH:Observation matrix
%% Practice state of target
for i = 1:T-1
    x(:,i+1) = F*x(:,i);
end
x = x + v1;    %  Estimation vector sequence under noise
y = C*x + v2;  %  Observation vector sequence under noise

%========================================================================== 

%% Kalman Filter 
%  bookP179  algorithm5.4.1  Kalman Adaptive Filter Algorithm
K = P;
x_hat = [0 0 0 0].';
% x_hat = x;
for i = 1:T-1   
    G = F * K * C'* inv(C * K * C' + Q2);               %  Book P179  formula5.4.24Defined algorithm5.4.1Present a calculation method
    alpha = y(:, i) - C * x_hat(:, i);                  
    x_hat(:, i + 1) = F * x_hat(:, i) + G * alpha;      %  Calculate the current state vector x_hat
    P = K - inv(F) * G * C * F;
    K = F * P * F' + Q1;                                %  Update Kalman Gain
end

%% LMS adaptive filter
%  bookP183  algorithm5.5.1 LMSAdaptive filtering and basic deformation
omega(:, :, 1) = zeros(4, 4);
x_hat2(:, 1) = x(:, 1);
for i = 1:T - 1
    x_hat2(:, i + 1) = omega(:, :, i)' * x_hat2(:, i);                       %  Get the current estimate
    e(:, i) = x(:, i + 1) - x_hat2(:, i + 1);                           %  Calculate the error of the estimated value and the actual value
    alpha = 1 / (0.5 + x(:, i)' * x(:, i));
    omega(:, :, i + 1) = omega(:, :, i) + 10 * x_hat2(:, i) * conj(e(i))';      %  Update weights
end

%==========================================================================

%% Estimate error
x_error = x-x_hat;
%% Graph 1 practical and tracking position
figure(1)
plot(x(1,:),x(3,:),'r');
hold on;
plot(x_hat(1,:),x_hat(3,:),'g.');
title('2D Target Position')
legend('Practical Position','Tracking Position')
xlabel('X axis [m]')
ylabel('Y axis [m]')
hold off;
%% Graph 2 
figure(2) 
plot(t,x(1,:)),grid on;
hold on;
plot(t,x_hat(1,:),'r'),grid on;
plot(t, x_hat2(1, :), 'k'), grid on
title('Practical and Tracking Position on X axis')
legend('Practical Position', 'Kalman Tracking Position', 'LMS Tracking Position')
xlabel('Time [sec]')
ylabel('Position [m]')
hold off;
%% Graph 3
figure(3) 
plot(t,x_error(1,:)),grid on;
title('Position Error on X axis')
xlabel('Time [sec]')
ylabel('Position RMSE [m]')
hold off;
%% Graph 4
figure(4)
plot(t,x(2,:)),grid on;
hold on;
plot(t,x_hat(2,:),'r'),grid on;
plot(t,x_hat2(2,:),'k'),grid on;
title('Practical and Tracking Velocity on X axis')
legend('Practical Velocity','Tracking Velocity')
xlabel('Time [sec]')
ylabel('Velocity [m/sec]')
hold off;
%% Graph 5
figure(5)
plot(t,x_error(2,:)),grid on;
title('Velocity Error on X axis')
xlabel('Time [sec]')
ylabel('Velocity RMSE [m/sec]')
hold off;

How can i solve this error?

[G A]

Your code works OK in command window as well as in script. No error.

Answer 1

[Jan]

omega(:, :, i + 1) = omega(:, :, i) + 10 * x_hat2(:, i) * conj(e(i))';

This works since Matlab R2016b due to the auto-expanding. Do you use an older version? Then you need bsxfun:

omega(:, :, i + 1) = bsxfun(@plus, omega(:, :, i), 10 * x_hat2(:, i) * conj(e(i))';

You calculate alpha one line above, but do not use it anywhere.

What is the purpose of conj(e(i))' ? The matrix e(:, i) is calculated in the loop also. So do you really want to use e(i) and not e(:, i)? The conjugate transpose operator ' is strange also for a scalar. In addition you conjugate twice by conj and ' , so conj(e(i))' is the same as e(i). Remember that the transposition is .' including a dot.The quote ' is the conjugate transposition already. Maybe you want (bold guessing and not tested):

omega(:, :, i + 1) = omega(:, :, i) + 10 * x_hat2(:, i) * e(:, i)';