how to skip the measured object for certain time using kalman filter ?

r = 11.01541; % range 
phi = 103.6669; % azimuth
theta = 2.624099; % elevation
% 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);

%% implementation of kalman filter
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)+randn(3,N); % generated randm error the measurement of v
z = H*xt+v; % measured matrix
%% perform the kalman filter estimation
x = zeros(3,N);
x(:,1) = [-5.4493 0.0308 -11.0152];

%%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
%%plot the results
plot(t,z,'r-',t,xt(1,:),'g:',t,x(1,:),'b:','Linewidth',2)
xlabel('time');
ylabel('position');
title('position of x');
legend('measured object','predict the object','correct/update the object');

[Image Analyst]

I have no idea what you mean, unless you just want to put gaps (NaN's) in the curves where nothing plots, but I did format your code as code for you and attached the screenshot. You attached a .fig, and if I click that, it brings up a question about what program to use and if I say the latest MATLAB, it launches a whole new instance of MATLAB (so now I have two MATLABs running). Not convenient at all compared to just seeing the plot right here in Answers instantly.

Answer 1

[swathi]

how can we read a matrix loop column by column xt(:,k) = 3*50

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