Free Falling Body Kalman Filter Matlab

I have this data. The table shows free falling body examples. I have to plot a graph for "True values" Position, x1, Estimates Position x1(k), and Measurement z(k). How can I plot this table in MATLAB?

Answer 1

[Image Analyst]

plot(t, x1True, 'b.-', 'LineWidth', 2);
plot(t, x1Estimate, 'r.-', 'LineWidth', 2);
ylabel('x1', 'FontSize', 18);
xlabel('t', 'FontSize', 18)
grid on;
legend('x1 True', 'x1 Estimate');

I'm not sure what you're calling Measurement z, but you'd use the plot() function like above.

[HATIQAH ANIS]

Thank you for your answer. Act, I want the graph to look like this.

[HATIQAH ANIS]

Why I don't get the same as the above graph? Help. Here I attach my Matlab coding.

%% Simulate the true signal and measurement
% Define the system
N = 6; % number of time steps
dt = 1; % Sampling time (s)
t = dt*(1:N); % time vector (s)
F = [1, dt; 0, 1]; % system matrix - state
G = [-1/2*dt^2; -dt]; % system matrix - input
H = [1 0]; % observation matrix
Q = [0, 0; 0, 0]; % process noise covariance
u = -1; % input = acceleration due to gravity (m/s^2)
I = eye(2); % identity matrix
% Define the initial position and velocity
y0 = 100; % m
v0 = 0; % m/s
% Initialize the state vector (true state)
xt = zeros(2, N); % True state vector
xt(:, 1) = [y0; v0]; % True intial state
% Loop through and calculate the state
for k = 2:N 
 % Propagate the states through the prediction equations
 xt(:, k) = F*xt(:, k-1) + G*u; 
end
% Generate the noisy measurement from the true state
R = 1; % m^2/s^2
v = sqrt(R)*randn(1, N); % measurement noise
z = H*xt + v; % noisy measurement
%% Perform the Kalman filter estimation
% Initialize the state vector (estimated state)
x = zeros(2, N); % Estimated state vector
x(:, 1) = [105; 0]; % Guess for initial state
% Initialize the covariance matrix
P = [10, 0; 0, 0.01]; % Covariance for initial state error
% Loop through and perform the Kalman filter equations recursively
for k = 2:N 
 % Predict the state vector
 x(:, k) = F*x(:, k-1) + G*u; 
 % Predict the covariance
 P = F*P*F' + Q; 
 % Calculate the Kalman gain matrix
 K = P*H'/(H*P*H' + R); 
 % Update the state vector
 x(:,k) = x(:,k) + K*(z(k) - H*x(:,k)); 
 % Update the covariance
 P = (I - K*H)*P; 
end
%% Plot the results
% Plot the states
figure(1); 
plot(t, z, 'g-', t, x(1,:), 'b--', 'LineWidth', 2); 
hold on; plot(t, xt(1,:), 'r:', 'LineWidth', 1.5) 
xlabel('t (s)'); ylabel('x_1 = h (m)'); grid on; 
legend('Measured','Estimated','True'); 

[Image Analyst]

I'd guess that the first graph was made by an entirely different program. Do you have that code? Why do you think yours should look the same?

[HATIQAH ANIS]

Its because the first graph is the exact graph for the question (data given in the table). I don't have the code for the question.