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submodule_missile.m
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%% Declare Variables
Sim_length = length(Sim_time);
TGT_TurnCounter = zeros(1, 1);
TGT_HED = zeros(Sim_length, 1);
TGT_FPA = zeros(Sim_length, 1);
TGT_HED_cmd = zeros(Sim_length, 1);
TGT_FPA_cmd = zeros(Sim_length, 1);
TGT_vel_NED = zeros(Sim_length, 3);
TGT_pos_NED = zeros(Sim_length, 3);
MSL_Euler = zeros(Sim_length, 3);
MSL_HED = zeros(Sim_length, 1);
MSL_FPA = zeros(Sim_length, 1);
MSL_PQR = zeros(Sim_length, 3);
MSL_PQR_rate = zeros(Sim_length, 3);
MSL_Euler_rate = zeros(Sim_length, 3);
MSL_Euler_cmd = zeros(Sim_length, 3);
MSL_Torque = zeros(Sim_length, 3);
MSL_pos_NED = zeros(Sim_length, 3);
MSL_vel_NED = zeros(Sim_length, 3);
MSL_speed = zeros(Sim_length, 1);
MSL_vel_Body = zeros(Sim_length, 3);
MSL_vel_Wind = zeros(Sim_length, 3);
MSL_acc_cmd_NED = zeros(Sim_length, 3);
MSL_acc_cmd_Wind = zeros(Sim_length, 3);
MSL_acc_cmd_Body = zeros(Sim_length, 3);
MSL_acc_mod_Body = zeros(Sim_length, 3);
MSL_force_Body = zeros(Sim_length, 3);
MSL_acc_Body = zeros(Sim_length, 3);
MSL_acc_NED = zeros(Sim_length, 3);
MSL_acc_Wind = zeros(Sim_length, 3);
MSL_Thrust = zeros(Sim_length, 10);
MSL_FOV_Angle = zeros(Sim_length, 1);
MSL_FOV_InRange = zeros(Sim_length, 1);
MSL_Disp_Body_ax1 = zeros(Sim_length, 3);
MSL_Disp_Body_ax2 = zeros(Sim_length, 3);
MSL_Disp_Body_ax3 = zeros(Sim_length, 3);
MSL_Disp_LOS_long = zeros(Sim_length, 3);
MSL_Disp_LOS_short = zeros(Sim_length, 3);
MSL_Disp_Vel_long = zeros(Sim_length, 3);
MSL_Disp_Vel_short = zeros(Sim_length, 3);
MSL_Disp_Body = zeros(3, 8, Sim_length);
MSL_Disp_Thrust = zeros(3, 20, Sim_length);
MSL_Disp_FOV_long = zeros(3, 8, Sim_length);
MSL_Disp_FOV_short = zeros(3, 8, Sim_length);
MSL_Disp_FOV_circle_long = zeros(3, length(0 : 0.1 : 2.1*pi), Sim_length);
MSL_Disp_FOV_circle_short = zeros(3, length(0 : 0.1 : 2.1*pi), Sim_length);
Geom_range_NED = zeros(Sim_length, 3);
Geom_range = zeros(Sim_length, 1);
Geom_LOS = zeros(Sim_length, 2);
Geom_LOS_rotation = zeros(Sim_length, 3);
Geom_vel_relative = zeros(Sim_length, 3);
Geom_speed_closing = zeros(Sim_length, 1);
%% Target Initial Values
TGT_TurnCounter(1) = 1;
TGT_TurnTime = [0 TGT_TurnTime Sim_Tf];
TGT_HEDRate = [0 TGT_HEDRate];
TGT_FPARate = [0 TGT_FPARate];
TGT_HED(1) = TGT_HED0*Sim_D2R;
TGT_HED_cmd(1) = TGT_HED0*Sim_D2R;
TGT_FPA(1) = TGT_FPA0*Sim_D2R;
TGT_FPA_cmd(1) = TGT_FPA0*Sim_D2R;
TGT_MTX_N2W = [cos(TGT_FPA(1)) 0 -sin(TGT_FPA(1))
0 1 0
sin(TGT_FPA(1)) 0 cos(TGT_FPA(1))]...
*...
[cos(TGT_HED(1)) sin(TGT_HED(1)) 0
-sin(TGT_HED(1)) cos(TGT_HED(1)) 0
0 0 1];
TGT_MTX_W2N = TGT_MTX_N2W';
TGT_vel_NED(1, 1 : 3) = [TGT_vel0 0 0]*TGT_MTX_W2N';
TGT_pos_NED(1, 1 : 3) = TGT_pos_NED0;
%% Missile Initial Values
% Missile Attitude
MSL_Euler(1, 1 : 3) = [0 MSL_FPA0 MSL_HED0]*Sim_D2R;
MSL_MTX_N2B = [1 0 0
0 cos(MSL_Euler(1, 1)) sin(MSL_Euler(1, 1))
0 -sin(MSL_Euler(1, 1)) cos(MSL_Euler(1, 1))]...
*...
[cos(MSL_Euler(1, 2)) 0 -sin(MSL_Euler(1, 2))
0 1 0
sin(MSL_Euler(1, 2)) 0 cos(MSL_Euler(1, 2))]...
*...
[cos(MSL_Euler(1, 3)) sin(MSL_Euler(1, 3)) 0
-sin(MSL_Euler(1, 3)) cos(MSL_Euler(1, 3)) 0
0 0 1];
MSL_MTX_B2N = MSL_MTX_N2B';
% Missile Flight Path
MSL_HED(1) = MSL_Euler(1, 3);
MSL_FPA(1) = MSL_Euler(1, 2);
MSL_MTX_N2W = [cos(MSL_FPA(1)) 0 -sin(MSL_FPA(1))
0 1 0
sin(MSL_FPA(1)) 0 cos(MSL_FPA(1))]...
*...
[cos(MSL_HED(1)) sin(MSL_HED(1)) 0
-sin(MSL_HED(1)) cos(MSL_HED(1)) 0
0 0 1];
MSL_MTX_W2N = MSL_MTX_N2W';
% Missile Line of Sight
Geom_range_NED(1, 1 : 3) = TGT_pos_NED0 - MSL_pos_NED0;
Geom_range(1) = norm(Geom_range_NED(1, 1 : 3));
Geom_LOS_vert = -atan2(Geom_range_NED(1, 3), norm(Geom_range_NED(1, 1 : 2)));
Geom_LOS_horz = atan2(Geom_range_NED(1, 2), Geom_range_NED(1, 1));
Geom_LOS(1, 1 : 2) = [Geom_LOS_vert Geom_LOS_horz];
MSL_MTX_N2L = [cos(Geom_LOS(1, 1)) 0 -sin(Geom_LOS(1, 1))
0 1 0
sin(Geom_LOS(1, 1)) 0 cos(Geom_LOS(1, 1))]...
*...
[cos(Geom_LOS(1, 2)) sin(Geom_LOS(1, 2)) 0
-sin(Geom_LOS(1, 2)) cos(Geom_LOS(1, 2)) 0
0 0 1];
MSL_MTX_L2N = MSL_MTX_N2L';
% Missile Torque, Eq 3.16
MSL_PQR(1, 1 : 3) = zeros(1, 3);
MSL_Euler_rate(1, 1 : 3) = MSL_PQR(1, 1 : 3)...
*...
[1 sin(MSL_Euler(1, 1))*tan(MSL_Euler(1, 2)) cos(MSL_Euler(1, 1))*tan(MSL_Euler(1, 2))
0 cos(MSL_Euler(1, 1)) -sin(MSL_Euler(1, 1))
0 sin(MSL_Euler(1, 1))/cos(MSL_Euler(1, 2)) cos(MSL_Euler(1, 1))/cos(MSL_Euler(1, 2))]';
MSL_Euler_cmd(1, 1 : 3) = [0 Geom_LOS(1, 1) Geom_LOS(1, 2)];
MSL_Torque(1, 1 : 3) = MSL_Euler_kp.*sin(MSL_Euler_cmd(1, 1 : 3) - MSL_Euler(1, 1 : 3)) - MSL_Euler_kv.*MSL_Euler_rate(1, 1 : 3);
% Missile PQR with Moment of Inertia, Eq 3.17
MSL_Moment = MSL_Moment_Jxyz(1)*MSL_Moment_Jxyz(3);
MSL_Moment2 = (MSL_Moment_Jxyz(3) - MSL_Moment_Jxyz(2))/MSL_Moment_Jxyz(1);
MSL_Moment3 = 1/MSL_Moment_Jxyz(1);
MSL_Moment5 = (MSL_Moment_Jxyz(3) - MSL_Moment_Jxyz(1))/MSL_Moment_Jxyz(2);
MSL_Moment7 = (MSL_Moment_Jxyz(1) - MSL_Moment_Jxyz(2))/MSL_Moment_Jxyz(3);
MSL_Moment8 = 1/MSL_Moment_Jxyz(3);
MSL_PQR_rate(1, 1 : 3) = [MSL_Moment3*MSL_Torque(1, 1) MSL_Torque(1, 2)/MSL_Moment_Jxyz(2) MSL_Moment8*MSL_Torque(1, 3)];
% Missile Guidance Law, Eq 3.15
MSL_pos_NED(1, 1 : 3) = MSL_pos_NED0;
MSL_vel_NED(1, 1 : 3) = [MSL_vel0 0 0]*MSL_MTX_W2N';
MSL_speed(1) = norm(MSL_vel_NED(1, 1 : 3));
MSL_vel_Body(1, 1 : 3) = MSL_vel_NED(1, 1 : 3)*MSL_MTX_N2B';
MSL_vel_Wind(1, 1 : 3) = MSL_vel_NED(1, 1 : 3)*MSL_MTX_N2W';
Geom_vel_relative(1, 1 : 3) = TGT_vel_NED(1, 1 : 3) - MSL_vel_NED(1, 1 : 3);
Geom_speed_closing(1) = norm(Geom_vel_relative(1, 1 : 3));
Geom_LOS_rotation(1, 1 : 3) = cross(Geom_range_NED(1, 1 : 3), Geom_vel_relative(1, 1 : 3))/Geom_range(1)^2;
MSL_acc_cmd_NED(1, 1 : 3) = -MSL_nav_gain*norm(Geom_vel_relative(1, 1 : 3))/MSL_speed(1)*cross(MSL_vel_NED(1, 1 : 3), Geom_LOS_rotation(1, 1 : 3));
MSL_acc_cmd_Wind(1, 1 : 3) = MSL_acc_cmd_NED(1, 1 : 3)*MSL_MTX_N2W';
MSL_acc_cmd_Body(1, 1 : 3) = MSL_acc_cmd_NED(1, 1 : 3)*MSL_MTX_N2B';
MSL_acc_mod_Body(1, 1 : 3) = [0 MSL_acc_cmd_Body(1, 2 : 3)/cos(atan2(MSL_acc_cmd_Body(1, 1), norm(MSL_acc_cmd_Body(1, 2 : 3))))^2];
% Missile Acceleration w/ Torque, Eq 3.15
MSL_force_Body(1, 1 : 3) = MSL_Mass*MSL_acc_mod_Body(1, 1 : 3);
MSL_acc_Body(1, 1 : 3) = [MSL_PQR(1, 3)*MSL_vel_Body(1, 2) - MSL_PQR(1, 2)*MSL_vel_Body(1, 3)
MSL_PQR(1, 1)*MSL_vel_Body(1, 3) - MSL_PQR(1, 3)*MSL_vel_Body(1, 1)
MSL_PQR(1, 2)*MSL_vel_Body(1, 1) - MSL_PQR(1, 1)*MSL_vel_Body(1, 2)]'...
+...
MSL_force_Body(1, 1 : 3)/MSL_Mass...
+...
[0 0 Sim_G]*MSL_MTX_N2B';
MSL_acc_NED(1, 1 : 3) = MSL_acc_Body(1, 1 : 3)*MSL_MTX_B2N';
MSL_acc_Wind(1, 1 : 3) = MSL_acc_NED(1, 1 : 3)*MSL_MTX_N2W';
% DACS Thrust
MSL_Thrust_cmd = [MSL_force_Body(1, 2 : 3) MSL_Torque(1, 1 : 3)]';
MSL_Thrust_MTX = [0 1 0 1 1
1 0 1 0 0
0 0 0 Disp_Body_Size(3)/4 -Disp_Body_Size(3)/4
0 0 Disp_Body_Size(1)/2 0 0
0 0 0 -Disp_Body_Size(1)/2 -Disp_Body_Size(1)/2];
MSL_Thrust_temp = (MSL_Thrust_MTX\MSL_Thrust_cmd)';
MSL_MTX_Thrustmap = [1 0 0 0 0
0 -1 0 0 0
-1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 -1 0
0 0 0 0 -1
0 0 -1 0 0
0 0 0 0 1
0 0 0 1 0]';
MSL_Thrust(1, 1 : 10) = max(MSL_Thrust_temp*MSL_MTX_Thrustmap, 0);
% Missile Seeker
MSL_FOV_Body_ax = [1 0 0]*MSL_MTX_B2N';
MSL_FOV_LOS_ax = [1 0 0]*MSL_MTX_L2N';
MSL_FOV_Angle(1) = acos(dot(MSL_FOV_Body_ax, MSL_FOV_LOS_ax));
MSL_FOV_InRange(1) = max(sign(MSL_FOV/2*Sim_D2R - MSL_FOV_Angle(1)), 0);
%% Vector Visualization
% Body Axis
MSL_Disp_Body_ax1(1, :) = [Disp_Body_axlength 0 0]*MSL_MTX_B2N';
MSL_Disp_Body_ax2(1, :) = [0 Disp_Body_axlength 0]*MSL_MTX_B2N';
MSL_Disp_Body_ax3(1, :) = [0 0 Disp_Body_axlength]*MSL_MTX_B2N';
% LOS Axis
MSL_Disp_LOS_long(1, :) = [Geom_range(1) 0 0]*MSL_MTX_L2N';
MSL_Disp_LOS_short(1, :) = MSL_Disp_LOS_long(1, :)/Geom_range(1)*Disp_Body_axlength*2;
% Velocity Axis
MSL_Disp_Vel_long(1, :) = [MSL_speed(1) 0 0]*MSL_MTX_W2N';
MSL_Disp_Vel_short(1, :) = MSL_Disp_Vel_long(1, :)/MSL_speed(1)*Disp_Body_axlength*2;
% Body Shape
MSL_Disp_Body_temp(:, 1) = [ Disp_Body_Size(1)/2; -Disp_Body_Size(2)/2; Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 2) = [ Disp_Body_Size(1)/2; Disp_Body_Size(2)/2; Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 3) = [ Disp_Body_Size(1)/2; -Disp_Body_Size(2)/2; -Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 4) = [ Disp_Body_Size(1)/2; Disp_Body_Size(2)/2; -Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 5) = [-Disp_Body_Size(1)/2; -Disp_Body_Size(2)/2; Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 6) = [-Disp_Body_Size(1)/2; Disp_Body_Size(2)/2; Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 7) = [-Disp_Body_Size(1)/2; -Disp_Body_Size(2)/2; -Disp_Body_Size(3)/2];
MSL_Disp_Body_temp(:, 8) = [-Disp_Body_Size(1)/2; Disp_Body_Size(2)/2; -Disp_Body_Size(3)/2];
MSL_Disp_Body(:, :, 1) = MSL_MTX_B2N*MSL_Disp_Body_temp + MSL_pos_NED(1, 1 : 3)';
% Thruster Position
MSL_Disp_Thrust_temp(:, 1) = [ 0 0 -Disp_Body_Size(3)/2];
MSL_Disp_Thrust_temp(:, 2) = [ 0 Disp_Body_Size(2)/2 0 ];
MSL_Disp_Thrust_temp(:, 3) = [ 0 0 Disp_Body_Size(3)/2];
MSL_Disp_Thrust_temp(:, 4) = [ 0 -Disp_Body_Size(2)/2 0 ];
MSL_Disp_Thrust_temp(:, 5) = [-Disp_Body_Size(1)/2 0 -Disp_Body_Size(3)/2];
MSL_Disp_Thrust_temp(:, 6) = [-Disp_Body_Size(1)/2 Disp_Body_Size(2)/2 -Disp_Body_Size(3)/4];
MSL_Disp_Thrust_temp(:, 7) = [-Disp_Body_Size(1)/2 Disp_Body_Size(2)/2 Disp_Body_Size(3)/4];
MSL_Disp_Thrust_temp(:, 8) = [-Disp_Body_Size(1)/2 0 Disp_Body_Size(3)/2];
MSL_Disp_Thrust_temp(:, 9) = [-Disp_Body_Size(1)/2 -Disp_Body_Size(2)/2 Disp_Body_Size(3)/4];
MSL_Disp_Thrust_temp(:, 10) = [-Disp_Body_Size(1)/2 -Disp_Body_Size(2)/2 -Disp_Body_Size(3)/4];
% Thrust Vector
MSL_Disp_Thrust_temp(:, 11) = MSL_Disp_Thrust_temp(:, 1) + [0 0 -MSL_Thrust(1, 1)]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 12) = MSL_Disp_Thrust_temp(:, 2) + [0 MSL_Thrust(1, 2) 0 ]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 13) = MSL_Disp_Thrust_temp(:, 3) + [0 0 MSL_Thrust(1, 3)]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 14) = MSL_Disp_Thrust_temp(:, 4) + [0 -MSL_Thrust(1, 4) 0 ]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 15) = MSL_Disp_Thrust_temp(:, 5) + [0 0 -MSL_Thrust(1, 5)]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 16) = MSL_Disp_Thrust_temp(:, 6) + [0 MSL_Thrust(1, 6) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 17) = MSL_Disp_Thrust_temp(:, 7) + [0 MSL_Thrust(1, 7) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 18) = MSL_Disp_Thrust_temp(:, 8) + [0 0 MSL_Thrust(1, 8)]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 19) = MSL_Disp_Thrust_temp(:, 9) + [0 -MSL_Thrust(1, 9) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 20) = MSL_Disp_Thrust_temp(:, 10) + [0 -MSL_Thrust(1, 10) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust(:, :, 1) = MSL_MTX_B2N*MSL_Disp_Thrust_temp + MSL_pos_NED(1, 1 : 3)';
% Seeker FOV
MSL_Disp_FOV_temp(:, 1) = [cos(MSL_FOV/2*Sim_D2R) 0 -sin(MSL_FOV/2*Sim_D2R)];
MSL_Disp_FOV_temp(:, 2) = [MSL_Disp_FOV_temp(1, 1) -MSL_Disp_FOV_temp(3, 1)/sqrt(2) -MSL_Disp_FOV_temp(3, 1)/sqrt(2)];
MSL_Disp_FOV_temp(:, 3) = [MSL_Disp_FOV_temp(1, 1) -MSL_Disp_FOV_temp(3, 1) 0];
MSL_Disp_FOV_temp(:, 4) = [MSL_Disp_FOV_temp(1, 1) -MSL_Disp_FOV_temp(3, 1)/sqrt(2) MSL_Disp_FOV_temp(3, 1)/sqrt(2)];
MSL_Disp_FOV_temp(:, 5) = [MSL_Disp_FOV_temp(1, 1) 0 -MSL_Disp_FOV_temp(3, 1)];
MSL_Disp_FOV_temp(:, 6) = [MSL_Disp_FOV_temp(1, 1) MSL_Disp_FOV_temp(3, 1)/sqrt(2) MSL_Disp_FOV_temp(3, 1)/sqrt(2)];
MSL_Disp_FOV_temp(:, 7) = [MSL_Disp_FOV_temp(1, 1) MSL_Disp_FOV_temp(3, 1) 0];
MSL_Disp_FOV_temp(:, 8) = [MSL_Disp_FOV_temp(1, 1) MSL_Disp_FOV_temp(3, 1)/sqrt(2) -MSL_Disp_FOV_temp(3, 1)/sqrt(2)];
MSL_Disp_FOV_long(:, :, 1) = MSL_MTX_B2N*MSL_Disp_FOV_temp*Geom_range(1) + MSL_pos_NED(1, 1 : 3)';
MSL_Disp_FOV_short(:, :, 1) = (MSL_Disp_FOV_long(:, :, 1) - MSL_pos_NED(1, 1 : 3)')/Geom_range(1)*Disp_Body_axlength*2 + MSL_pos_NED(1, 1 : 3)';
MSL_Disp_FOV_circle_temp(2, :) = MSL_Disp_FOV_temp(3, 1)*cos(0 : 0.1 : 2.1*pi);
MSL_Disp_FOV_circle_temp(3, :) = MSL_Disp_FOV_temp(3, 1)*sin(0 : 0.1 : 2.1*pi);
MSL_Disp_FOV_circle_temp(1, :) = MSL_Disp_FOV_temp(1, 1);
MSL_Disp_FOV_circle_long(:, :, 1) = MSL_MTX_B2N*MSL_Disp_FOV_circle_temp*Geom_range(1) + MSL_pos_NED(1, 1 : 3)';
MSL_Disp_FOV_circle_short(:, :, 1) = (MSL_Disp_FOV_circle_long(:, :, 1) - MSL_pos_NED(1, 1 : 3)')/Geom_range(1)*Disp_Body_axlength*2 + MSL_pos_NED(1, 1 : 3)';
%% Loop Begins
for i = 2 : length(Sim_time)
%% Target Trajectory
if Sim_time(i) >= TGT_TurnTime(TGT_TurnCounter) && Sim_time(i) < TGT_TurnTime(TGT_TurnCounter + 1)
TGT_HED_cmd(i, 1) = TGT_HED_cmd(i - 1, 1) + Sim_dt*TGT_HEDRate(TGT_TurnCounter)*Sim_D2R;
TGT_FPA_cmd(i, 1) = TGT_FPA_cmd(i - 1, 1) + Sim_dt*TGT_FPARate(TGT_TurnCounter)*Sim_D2R;
elseif Sim_time(i) >= TGT_TurnTime(TGT_TurnCounter + 1)
TGT_HED_cmd(i, 1) = TGT_HED_cmd(i - 1, 1);
TGT_FPA_cmd(i, 1) = TGT_FPA_cmd(i - 1, 1);
TGT_TurnCounter = TGT_TurnCounter + 1;
end
TGT_HED(i, 1) = TGT_HED(i - 1, 1) + Sim_dt*TGT_BW*(TGT_HED_cmd(i, 1) - TGT_HED(i - 1, 1));
TGT_FPA(i, 1) = TGT_FPA(i - 1, 1) + Sim_dt*TGT_BW*(TGT_FPA_cmd(i, 1) - TGT_FPA(i - 1, 1));
TGT_MTX_N2W = [cos(TGT_FPA(i, 1)) 0 -sin(TGT_FPA(i, 1))
0 1 0
sin(TGT_FPA(i, 1)) 0 cos(TGT_FPA(i, 1))]...
*...
[cos(TGT_HED(i, 1)) sin(TGT_HED(i, 1)) 0
-sin(TGT_HED(i, 1)) cos(TGT_HED(i, 1)) 0
0 0 1];
TGT_MTX_W2N = TGT_MTX_N2W';
TGT_vel_NED(i, 1 : 3) = [TGT_vel0 0 0]*TGT_MTX_W2N';
TGT_pos_NED(i, 1 : 3) = TGT_pos_NED(i - 1, 1 : 3) + Sim_dt*TGT_vel_NED(i, 1 : 3);
%% Numerical Integration
if i == 2
MSL_pos_NED(2, 1 : 3) = 1.5*Sim_dt*MSL_vel_NED(1, 1 : 3) + MSL_pos_NED(1, 1 : 3);
MSL_vel_Body(2, 1 : 3) = 1.5*Sim_dt*MSL_acc_Body(1, 1 : 3) + MSL_vel_Body(1, 1 : 3);
MSL_Euler(2, 1 : 3) = 1.5*Sim_dt*MSL_Euler_rate(1, 1 : 3) + MSL_Euler(1, 1 : 3);
MSL_PQR(2, 1 : 3) = 1.5*Sim_dt*MSL_PQR_rate(1, 1 : 3) + MSL_PQR(1, 1 : 3);
else
MSL_pos_NED(i, 1 : 3) = Sim_dt/2*(3*MSL_vel_NED(i - 1, 1 : 3) - MSL_vel_NED(i - 2, 1 : 3)) + MSL_pos_NED(i - 1, 1 : 3);
MSL_vel_Body(i, 1 : 3) = Sim_dt/2*(3*MSL_acc_Body(i - 1, 1 : 3) - MSL_acc_Body(i - 2, 1 : 3)) + MSL_vel_Body(i - 1, 1 : 3);
MSL_Euler(i, 1 : 3) = Sim_dt/2*(3*MSL_Euler_rate(i - 1, 1 : 3) - MSL_Euler_rate(i - 2, 1 : 3)) + MSL_Euler(i - 1, 1 : 3);
MSL_PQR(i, 1 : 3) = Sim_dt/2*(3*MSL_PQR_rate(i - 1, 1 : 3) - MSL_PQR_rate(i - 2, 1 : 3)) + MSL_PQR(i - 1, 1 : 3);
end
%% Equation 3.14
MSL_MTX_N2B = [1 0 0
0 cos(MSL_Euler(i, 1)) sin(MSL_Euler(i, 1))
0 -sin(MSL_Euler(i, 1)) cos(MSL_Euler(i, 1))]...
*...
[cos(MSL_Euler(i, 2)) 0 -sin(MSL_Euler(i, 2))
0 1 0
sin(MSL_Euler(i, 2)) 0 cos(MSL_Euler(i, 2))]...
*...
[cos(MSL_Euler(i, 3)) sin(MSL_Euler(i, 3)) 0
-sin(MSL_Euler(i, 3)) cos(MSL_Euler(i, 3)) 0
0 0 1];
MSL_MTX_B2N = MSL_MTX_N2B';
MSL_vel_NED(i, 1 : 3) = MSL_vel_Body(i, 1 : 3)*MSL_MTX_B2N';
MSL_speed(i, 1) = norm(MSL_vel_NED(i, 1 : 3));
MSL_HED(i, 1) = atan2(MSL_vel_NED(i, 2), MSL_vel_NED(i, 1));
MSL_FPA(i, 1) = -atan2(MSL_vel_NED(i, 3), norm(MSL_vel_NED(i, 1 : 2)));
MSL_MTX_N2W = [cos(MSL_FPA(i, 1)) 0 -sin(MSL_FPA(i, 1))
0 1 0
sin(MSL_FPA(i, 1)) 0 cos(MSL_FPA(i, 1))]...
*...
[cos(MSL_HED(i, 1)) sin(MSL_HED(i, 1)) 0
-sin(MSL_HED(i, 1)) cos(MSL_HED(i, 1)) 0
0 0 1];
MSL_MTX_W2N = MSL_MTX_N2W';
MSL_vel_Wind(i, 1 : 3) = MSL_vel_NED(i, 1 : 3)*MSL_MTX_W2N';
%% Equation 3.15 & Acceleration Command
Geom_range_NED(i, 1 : 3) = TGT_pos_NED(i, 1 : 3) - MSL_pos_NED(i, 1 : 3);
Geom_range(i, 1) = norm(Geom_range_NED(i, 1 : 3));
Geom_LOS_vert = -atan2(Geom_range_NED(i, 3), norm(Geom_range_NED(i, 1 : 2)));
Geom_LOS_horz = atan2(Geom_range_NED(i, 2), Geom_range_NED(i, 1));
Geom_LOS(i, 1 : 2) = [Geom_LOS_vert Geom_LOS_horz];
MSL_MTX_N2L = [cos(Geom_LOS(i, 1)) 0 -sin(Geom_LOS(i, 1))
0 1 0
sin(Geom_LOS(i, 1)) 0 cos(Geom_LOS(i, 1))]...
*...
[cos(Geom_LOS(i, 2)) sin(Geom_LOS(i, 2)) 0
-sin(Geom_LOS(i, 2)) cos(Geom_LOS(i, 2)) 0
0 0 1];
MSL_MTX_L2N = MSL_MTX_N2L';
Geom_vel_relative(i, 1 : 3) = TGT_vel_NED(i, 1 : 3) - MSL_vel_NED(i, 1 : 3);
Geom_speed_closing(i, 1) = norm(Geom_vel_relative(i, 1 : 3));
Geom_LOS_rotation(i, 1 : 3) = cross(Geom_range_NED(i, 1 : 3), Geom_vel_relative(i, 1 : 3))/Geom_range(i, 1)^2;
MSL_acc_cmd_NED(i, 1 : 3) = -MSL_nav_gain*norm(Geom_vel_relative(i, 1 : 3))/MSL_speed(i, 1)*cross(MSL_vel_NED(i, 1 : 3), Geom_LOS_rotation(i, 1 : 3));
MSL_acc_cmd_Wind(i, 1 : 3) = MSL_acc_cmd_NED(i, 1 : 3)*MSL_MTX_N2W';
MSL_acc_cmd_Body(i, 1 : 3) = MSL_acc_cmd_NED(i, 1 : 3)*MSL_MTX_N2B';
MSL_acc_mod_Body(i, 1 : 3) = [0 MSL_acc_cmd_Body(i, 2 : 3)/cos(atan2(MSL_acc_cmd_Body(i, 1), norm(MSL_acc_cmd_Body(i, 2 : 3))))^2];
MSL_force_Body(i, 1 : 3) = MSL_Mass*(MSL_acc_mod_Body(i, 1 : 3));
MSL_acc_Body(i, 1 : 3) = [MSL_PQR(i, 3)*MSL_vel_Body(i, 2) - MSL_PQR(i, 2)*MSL_vel_Body(i, 3)
MSL_PQR(i, 1)*MSL_vel_Body(i, 3) - MSL_PQR(i, 3)*MSL_vel_Body(i, 1)
MSL_PQR(i, 2)*MSL_vel_Body(i, 1) - MSL_PQR(i, 1)*MSL_vel_Body(i, 2)]'...
+...
MSL_force_Body(i, 1 : 3)/MSL_Mass...
+...
[0 0 Sim_G]*MSL_MTX_N2B';
MSL_acc_NED(i, 1 : 3) = MSL_acc_Body(i, 1 : 3)*MSL_MTX_B2N';
MSL_acc_Wind(i, 1 : 3) = MSL_acc_NED(i, 1 : 3)*MSL_MTX_N2W';
%% Equation 3.16
MSL_Euler_rate(i, 1 : 3) = MSL_PQR(i, 1 : 3)...
*...
[1 sin(MSL_Euler(i, 1))*tan(MSL_Euler(i, 2)) cos(MSL_Euler(i, 1))*tan(MSL_Euler(i, 2))
0 cos(MSL_Euler(i, 1)) -sin(MSL_Euler(i, 1))
0 sin(MSL_Euler(i, 1))/cos(MSL_Euler(i, 2)) cos(MSL_Euler(i, 1))/cos(MSL_Euler(i, 2))]';
%% Equation 3.17
MSL_Euler_cmd(i, 1 : 3) = [0 Geom_LOS(i, 1) Geom_LOS(i, 2)];
MSL_Torque(i, 1 : 3) = MSL_Euler_kp.*(sin(MSL_Euler_cmd(i, 1 : 3) - MSL_Euler(i, 1 : 3))) - MSL_Euler_kv.*MSL_Euler_rate(i, 1 : 3);
MSL_PQR_rate(i, 1 : 3) = [MSL_Moment3*MSL_Torque(i, 1) MSL_Torque(i, 2)/MSL_Moment_Jxyz(2) MSL_Moment8*MSL_Torque(i, 3)];
%% DACS Thrust
MSL_Thrust_cmd = [MSL_force_Body(i, 2 : 3) MSL_Torque(i, 1 : 3)]';
MSL_Thrust_temp = (MSL_Thrust_MTX\MSL_Thrust_cmd)';
MSL_Thrust(i, 1 : 10) = max(MSL_Thrust_temp*MSL_MTX_Thrustmap, 0);
%% Seeker FOV
MSL_FOV_Body_ax = [1 0 0]*MSL_MTX_B2N';
MSL_FOV_LOS_ax = [1 0 0]*MSL_MTX_L2N';
MSL_FOV_Angle(i, 1) = acos(dot(MSL_FOV_Body_ax, MSL_FOV_LOS_ax));
MSL_FOV_InRange(i, 1) = max(sign(MSL_FOV/2*Sim_D2R - MSL_FOV_Angle(i, 1)), 0);
%% Vector Visualization
MSL_Disp_Body_ax1(i, 1 : 3) = [Disp_Body_axlength 0 0]*MSL_MTX_B2N';
MSL_Disp_Body_ax2(i, 1 : 3) = [0 Disp_Body_axlength 0]*MSL_MTX_B2N';
MSL_Disp_Body_ax3(i, 1 : 3) = [0 0 Disp_Body_axlength]*MSL_MTX_B2N';
MSL_Disp_LOS_long(i, 1 : 3) = [Geom_range(i, 1) 0 0]*MSL_MTX_L2N';
MSL_Disp_LOS_short(i, 1 : 3) = MSL_Disp_LOS_long(i, 1 : 3)/Geom_range(i, 1)*Disp_Body_axlength*2;
MSL_Disp_Vel_long(i, 1 : 3) = [MSL_speed(i, 1) 0 0]*MSL_MTX_W2N';
MSL_Disp_Vel_short(i, 1 : 3) = MSL_Disp_Vel_long(i, 1 : 3)/MSL_speed(i, 1)*Disp_Body_axlength*2;
MSL_Disp_Body(:, :, i) = MSL_MTX_B2N*MSL_Disp_Body_temp + MSL_pos_NED(i, 1 : 3)';
MSL_Disp_Thrust_temp(:, 11) = MSL_Disp_Thrust_temp(:, 1) + [0 0 -MSL_Thrust(i, 1)]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 12) = MSL_Disp_Thrust_temp(:, 2) + [0 MSL_Thrust(i, 2) 0 ]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 13) = MSL_Disp_Thrust_temp(:, 3) + [0 0 MSL_Thrust(i, 3)]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 14) = MSL_Disp_Thrust_temp(:, 4) + [0 -MSL_Thrust(i, 4) 0 ]'*Disp_Thrust_DCS_Scale;
MSL_Disp_Thrust_temp(:, 15) = MSL_Disp_Thrust_temp(:, 5) + [0 0 -MSL_Thrust(i, 5)]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 16) = MSL_Disp_Thrust_temp(:, 6) + [0 MSL_Thrust(i, 6) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 17) = MSL_Disp_Thrust_temp(:, 7) + [0 MSL_Thrust(i, 7) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 18) = MSL_Disp_Thrust_temp(:, 8) + [0 0 MSL_Thrust(i, 8)]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 19) = MSL_Disp_Thrust_temp(:, 9) + [0 -MSL_Thrust(i, 9) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust_temp(:, 20) = MSL_Disp_Thrust_temp(:, 10) + [0 -MSL_Thrust(i, 10) 0 ]'*Disp_Thrust_ACS_Scale;
MSL_Disp_Thrust(:, :, i) = MSL_MTX_B2N*MSL_Disp_Thrust_temp + MSL_pos_NED(i, 1 : 3)';
MSL_Disp_FOV_long(:, :, i) = MSL_MTX_B2N*MSL_Disp_FOV_temp*Geom_range(i, 1) + MSL_pos_NED(i, 1 : 3)';
MSL_Disp_FOV_short(:, :, i) = (MSL_Disp_FOV_long(:, :, i) - MSL_pos_NED(i, 1 : 3)')/Geom_range(i, 1)*Disp_Body_axlength*2 + MSL_pos_NED(i, 1 : 3)';
MSL_Disp_FOV_circle_long(:, :, i) = MSL_MTX_B2N*MSL_Disp_FOV_circle_temp*Geom_range(i, 1) + MSL_pos_NED(i, 1 : 3)';
MSL_Disp_FOV_circle_short(:, :, i) = (MSL_Disp_FOV_circle_long(:, :, i) - MSL_pos_NED(i, 1 : 3)')/Geom_range(i, 1)*Disp_Body_axlength*2 + MSL_pos_NED(i, 1 : 3)';
%% Save and Terminate
if Geom_range(i, 1) - Geom_range(i - 1, 1) > 0
Result.Time = Sim_time(1 : i)';
Result.Target_Traj = TGT_pos_NED(1 : i, :);
Result.Target_Vel = TGT_vel_NED(1 : i, :);
Result.Target_Heading = TGT_HED(1 : i, :);
Result.Target_FlightPath = TGT_FPA(1 : i, :);
Result.Target_Heading_cmd = TGT_HED_cmd(1 : i, :);
Result.Target_FlightPath_cmd = TGT_FPA_cmd(1 : i, :);
Result.Missile_Euler = MSL_Euler(1 : i, :);
Result.Missile_Heading = MSL_HED(1 : i, :);
Result.Missile_FPAngle = MSL_FPA(1 : i, :);
Result.Missile_Euler_PQR = MSL_PQR(1 : i, :);
Result.Missile_Euler_PQR_Rate = MSL_PQR_rate(1 : i, :);
Result.Missile_Euler_Rate = MSL_Euler_rate(1 : i, :);
Result.Missile_Euler_cmd = MSL_Euler_cmd(1 : i, :);
Result.Missile_Torque = MSL_Torque(1 : i, :);
Result.Missile_Traj = MSL_pos_NED(1 : i, :);
Result.Missile_Vel_NED = MSL_vel_NED(1 : i, :);
Result.Missile_Speed = MSL_speed(1 : i, :);
Result.Missile_Vel_Body = MSL_vel_Body(1 : i, :);
Result.Missile_Vel_Wind = MSL_vel_Wind(1 : i, :);
Result.Missile_Acc_Cmd_NED = MSL_acc_cmd_NED(1 : i, :);
Result.Missile_Acc_Cmd_Wind = MSL_acc_cmd_Wind(1 : i, :);
Result.Missile_Acc_Cmd_Body = MSL_acc_cmd_Body(1 : i, :);
Result.Missile_Acc_Cmd_Mod_Body = MSL_acc_mod_Body(1 : i, :);
Result.Missile_Force_Body = MSL_force_Body(1 : i, :);
Result.Missile_Acc_Body = MSL_acc_Body(1 : i, :);
Result.Missile_Acc_NED = MSL_acc_NED(1 : i, :);
Result.Missile_Acc_Wind = MSL_acc_Wind(1 : i, :);
Result.Missile_Thrust = MSL_Thrust(1 : i, :);
Result.Missile_FOV_Angle = MSL_FOV_Angle(1 : i, :);
Result.Missile_FOV_InRange = MSL_FOV_InRange(1 : i, :);
Result.Geometry_Range_NED = Geom_range_NED(1 : i, :);
Result.Geometry_Range = Geom_range(1 : i, :);
Result.Geometry_LOS = Geom_LOS(1 : i, :);
Result.Geometry_LOS_Rotation = Geom_LOS_rotation(1 : i, :);
Result.Geometry_Vel_Relative = Geom_vel_relative(1 : i, :);
Result.Geometry_Speed_Closing = Geom_speed_closing(1 : i, :);
Result.Display_Body_ax1 = MSL_Disp_Body_ax1(1 : i, :);
Result.Display_Body_ax2 = MSL_Disp_Body_ax2(1 : i, :);
Result.Display_Body_ax3 = MSL_Disp_Body_ax3(1 : i, :);
Result.Display_LOS_long = MSL_Disp_LOS_long(1 : i, :);
Result.Display_LOS_short = MSL_Disp_LOS_short(1 : i, :);
Result.Display_Vel_long = MSL_Disp_Vel_long(1 : i, :);
Result.Display_Vel_short = MSL_Disp_Vel_short(1 : i, :);
Result.Display_Body = MSL_Disp_Body(:, :, 1 : i);
Result.Display_Thrust = MSL_Disp_Thrust(:, :, 1 : i);
Result.Display_FOV_long = MSL_Disp_FOV_long(:, :, 1 : i);
Result.Display_FOV_short = MSL_Disp_FOV_short(:, :, 1 : i);
Result.Display_FOV_circle_long = MSL_Disp_FOV_circle_long(:, :, 1 : i);
Result.Display_FOV_circle_short = MSL_Disp_FOV_circle_short(:, :, 1 : i);
disp(' '); disp(['Flight Time : ' num2str(max(Result.Time)) ' [sec]']);
disp(['Miss Distance : ' num2str(min(Result.Geometry_Range)) ' [m]']);
disp(['Tracking Score : ' num2str(round(sum(Result.Missile_FOV_InRange)/i*100)) '/100']);
disp(' '); disp('=============================================='); disp(' ');
break;
end
end