how can we read matrix step by step in kalman filter

my matrix size is 3*50 %% xt(:,k) = 3*50 having [r,phi,theta]

in this xt[3*50] matrix every time we can read single column by column r,phi,theta values

every time we read 3*1 matrix values ,,till 3*50

r = rand(1,50); % range

phi = rand(1,50); % azimuth

theta = rand(1,50); % elevation

xt = [r;phi;theta]; %% state matrix

% convert polar coordinates of (r,theta,phi) to cartessian coordinates of(x1,y1,z1)

x1 = r.*sin(theta).*cos(phi);

y1 = r.*sin(theta).*sin(theta);

z1 = r.*cos(theta);

v = [x1;y1;z1];

N = 50; % no of time steps

dt = 0.05; % time for one cycle

t = dt*(1:N); % time vector

A = [1 0 dt

0 1 0

0 0 1]; % state transition matrix

B = [0.5*dt^2

dt

1]; % control input matrix

H = [1 0 0]; % measured matrix

u = 9.8062; % gravitational force

Q = 0; %No noise assumed

I = eye(3);

w = 0;

% initialize the state vector

xt = zeros(3,N); % state vector

xt(:,1) = [x1;y1;z1]; % the first set of states are initial position(x,y,z)

%% set the true states are generated using prediction equations

for k = 2:N

xt(:,k) = A*xt(:,k-1)+B*u+w;

end

% generated noise measurements from the true states

R = 4; % error variance in measurement of position

V = sqrt(R)+v; % generated randm error the measurement of v

z = H*xt+V; % measured matrix

%% perform the kalman filter estimation

x = zeros(3,N);

x(:,1) = [0 0 0];

%%perform the kalman filter estimation

p = [0.01 0 0

0 0.01 0

0 0 0.01];

% perform the estimation of N steps

for k = 2:N

% predict the state vector

x(:,k) = A*x(:,k-1)+B*u;

% predict the covariance matrix

P = A*p*A'+Q;

% calculate the kalman gain matrix

K = P*H'/(H*P*H'+R);

% update / correct the state vector

x(:,k) = x(:,k)+K*(z(k)-H*x(:,k));

% update the covariance matrix

P1 = (I-K*H)*P;

end

[Totanly]

please clarify the question a bit.

[swathi]

xt = rand(3,50);

how can we read xt in every column by column,one column

if it reads (3*1) in xt position ,then after read (3*2) till (3*50)

reads xt file in for loop

A = [1 0 0

0 1 0

0 0 1]; %% 3*3 matrix size

dt = 0.5;

N = 50;

B = [0.5dt^2

dt

1]; %% 3*1 matrix size

u = 9.8;

w =0;

for k = 1:N

xt(:,k) = A*xt(:,k)+B*u+w;

end

Answer 1

[KALYAN ACHARJYA]

See you have mat variable xt = rand(3,50); if you wish to read thia xt variable matrix column by column then

1 Column=xt(:,1);
2 Column=xt(:,2);
3 Column=xt(:,3);
....
so on 

if you wish to do same using loop, to save the invididual column (vector data, not a sacalar), you have to use cell array

xt=rand(3,50);
col_data=cells(1,50)
for i=1:50
col_data{i}=xt(:,i)
end 

Multiple ways you can do the same, like splitting matrix to individual column vector etc. I have answered the question based on you comments.

Hope it helps! 🙂

[swathi]

how can we write that loop in given equation? can you help me

for k = 1:50

xt(:,k) = A*xt(:,k)+B*u+w;

end