can your write a matlab code for simulating proportional navigation in matlab

main.m
% Proportional Navigation (PN) Guidance Simulation
clear all;
close all;

% Define parameters
target_pos = [0, 500];   % Target position [x, y]
initial_pos = [0, 0];   % Initial position [x, y]
initial_vel = [100, 0]; % Initial velocity [vx, vy]
t_end = 10;             % Simulation end time
dt = 0.01;              % Time step size

% Initialize variables
t = 0:dt:t_end;              % Time vector
num_steps = length(t);       % Number of simulation steps
guidance_cmd = zeros(1, num_steps);  % Guidance commands
miss_distance = zeros(1, num_steps); % Miss distance at each time step

% Simulate the guidance loop
for i = 1:num_steps
    pos_error = target_pos - initial_pos;  % Position error
    pos_error_unit = pos_error / norm(pos_error);  % Unit position error
    
    guidance_cmd(i) = cross(pos_error_unit, initial_vel);  % Compute guidance command
    
    % Update the positions and velocities
    initial_pos = initial_pos + initial_vel * dt;
    initial_vel = initial_vel + guidance_cmd(i) * dt;
    
    miss_distance(i) = norm(pos_error);  % Compute miss distance
end

% Plot the simulation results
figure;
subplot(2,1,1);
plot(t, guidance_cmd);
xlabel('Time (s)');
ylabel('Guidance Command');
title('Proportional Navigation Guidance Commands');

subplot(2,1,2);
plot(t, miss_distance);
xlabel('Time (s)');
ylabel('Miss Distance');
title('Miss Distance vs Time');

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