Radar System PPI polar display

I am trying to plot a radar Plan Position Indicator (PPI) slant range with the following code. This code is describing a scene with a radar at 2 km altitude scanning the area contained in a box. The x axis ranges from -90 to 0 degrees, and to 0 degrees to 90 degrees.The y axis ranges from 2 to 12km and the x axis is in respect 10 km split into two section of 0 to 5 km on either side. I tried this code and it worked and I was able to plot the B-scan slant range and true ground range. However, when I tried to plot the PPI slant range with a polar display which is supposed to look like a traditional radar screen, it looks like lines contained within the radar screen instead of dots representing point locations. I attached the code and the other script which has the two equations being used. The equations are phi = atan(x/y) and rho = sqrt(x^2 +y^2 +(h-H)^2) -(h-0.2). I set the polarplot in terms of phi and rho but my plot looks like lines instead of dots on the polar display. I also included a pic of the scene and my current polar plot. Any suggestions?

Script 1

% x = [5 5 5 5 4 4 4 4 4 3 3 3 3 3 3 0 0 0 0 0 0 2 5 5 5 5 5 5];

% y = [10 9 3 0 10 9 8 3 0 10 9 8 7 3 0 10 6 5 4 3 0 5 10 6 5 4 3 0];

% h = [1.8 2 2 2 2 1.8 2 2 2 2 2 1.8 2 2 2 2 2 1.8 2 2 2 1.8 2 2 1.8 2 2 2];

% phi = [-26.6 -29.1 -59.1 -90 -21.8 -24.0 -26.6 -53.1 -90 -16.7 -18.4 -20.6 -23.2 -45 -90 0 0 0 0 0 0 21.8 26.6 39.8 45 51.3 59.0 90];

% r = [11.32 10.49 6.16 5.39 10.95 10.01 9.17 5.39 4.47 10.63 9.70 8.73 7.87 4.69 3.61 10.20 6.32 5.32 4.47 3.61 2 5.59 11.36 8.06 7.30 6.71 6.16 5.39];

%% build scenario

box_x=[];

box_x=[box_x -5:0.5:5];

box_x=[box_x (zeros(1,21)+5)];

box_x=[box_x 5:-0.5:-5];

box_x=[box_x (zeros(1,21)-5)];

box_y=[];

box_y=[box_y zeros(1,21)];

box_y=[box_y 0:0.5:10];

box_y=[box_y (zeros(1,21)+10)];

box_y=[box_y 10:-0.50:0];

box_z=zeros(1,84);

%%

road_x=[];

road_x=[road_x -5:0.5:5];

road_y=[];

road_y=[road_y zeros(1,21)+3];

road_z=[];

road_z=[road_z (zeros(1,21))];

%%

radio_tower_x=[];

radio_tower_x=[radio_tower_x (zeros(1,31)+1.5)];

radio_tower_y=[];

radio_tower_y=[radio_tower_y (zeros(1,31)+5)];

radio_tower_z=[];

radio_tower_z=[radio_tower_z 0.2:0.01:0.5];

%%

ridgebasef_x=[];

ridgebasef_x=[ridgebasef_x 5:-0.25:0];

ridgebasef_x=[ridgebasef_x 0:-0.25:-5];

ridgebasef_y=[];

ridgebasef_y=[ridgebasef_y (zeros(1,21)+4)];

ridgebasef_y=[ridgebasef_y 4:0.25:9];

ridgebasef_z=[];

ridgebasef_z=[ridgebasef_z (zeros(1,42))];

%%

ridgetop_x=[];

ridgetop_x=[ridgetop_x 5:-0.25:0];

ridgetop_x=[ridgetop_x 0:-0.25:-5];

ridgetop_y=[];

ridgetop_y=[ridgetop_y (zeros(1,21)+5)];

ridgetop_y=[ridgetop_y 5:0.25:10];

ridgetop_z=[];

ridgetop_z=[ridgetop_z (zeros(1,42)+0.2)];

ridgebaseb_x=[];

ridgebaseb_x=[ridgebaseb_x 5:-0.25:0];

ridgebaseb_x=[ridgebaseb_x 0:-0.25:-5];

ridgebaseb_y=[];

ridgebaseb_y=[ridgebaseb_y (zeros(1,21)+6)];

ridgebaseb_y=[ridgebaseb_y 6:0.20:10];

ridgebaseb_z=[];

ridgebaseb_z=[ridgebaseb_z (zeros(1,42))];

% done with Scenario

%% Call conversion to PPI_SR

Radar_x = 0.0;

Radar_y = 0.0;

Radar_z = 2.0;

[box_Az box_Rng] = FN_PPI_SR(box_x,box_y,box_z,Radar_x,Radar_y,Radar_z);

[road_Az road_Rng] = FN_PPI_SR(road_x,road_y,road_z,Radar_x,Radar_y,Radar_z);

[ridgebasef_Az ridgebasef_Rng] = FN_PPI_SR(ridgebasef_x,ridgebasef_y,ridgebasef_z,Radar_x,Radar_y,Radar_z);

[tower_Az tower_Rng] = FN_PPI_SR(radio_tower_x,radio_tower_y,radio_tower_z,Radar_x,Radar_y,Radar_z);

[ridgetop_Az ridgetop_Rng] = FN_PPI_SR(ridgetop_x,ridgetop_y,ridgetop_z,Radar_x,Radar_y,Radar_z);

[ridgebaseb_Az ridgebaseb_Rng] = FN_PPI_SR(ridgebaseb_x,ridgebaseb_y,ridgebaseb_z,Radar_x,Radar_y,Radar_z);

figure(1)

polarplot(box_Az,box_Rng,'k');hold on; %'k' gives black

polarplot(road_Az,road_Rng,'b');%'b' gives blue

polarplot(ridgebasef_Az,ridgebasef_Rng,'.-g');%'.-g' gives dashed green line

polarplot(tower_Az,tower_Rng,'r');%'g' gives red line

polarplot(ridgetop_Az,ridgetop_Rng,'.-c');%'.-c' gives dashed cyan line

polarplot(ridgebaseb_Az,ridgebaseb_Rng,'y');%'y' gives yellow line

hold off;

xlim([-90 90])

ylim([2 12]);

grid on

xlabel('AZIMUTH (deg)')

ylabel('SLANT RANGE (km)')

title('BSCAN (SLANT RANGE)');

legend('FRAME','ROAD','RIDGEBASE-F','TOWER','RIDGETOP','RIDGEBASE-B');

% figure

% hold on

% plot(box_x,box_y,x,y)

% set(gca,'XTickLabel', [-90 -70 -50 -30 -10 0 10 30 50 70 90])

% set(gca, 'YTickLabel', [0 1 2 3 4 5 6 7 8 9 10])

Script 2

function [outaz outR] = FN_PPI_SR(tx,ty,tz,rx,ry,rz)

%UNTITLED2 Summary of this function goes here

% Detailed explanation goes here

outR = sqrt((tx-rx).^2+(ty-ry).^2+(tz-rz).^2)-(tz-0.2);

% x^2 y^2 (h-H)^2

outaz = 57.3*atan((tx-rx)./(ty-ry));

end

Answer 1

[William Rose]

@Jose Iglesias,

[Edited: Fixed a few typos in my text below. Code, figure unchanged.]

Angles should be in radians, not degrees, for polarplot().

I have changed atan() to atan2(), which is the better function to use if you have both x and y data.

I have changed the angle range from +-90 degrees to 0..180 degrees.

I use rlim() and thetalim() rather than xlim() and ylim().

I deleted the xlabel(), ylabel() commands since they do not work with polar plots.

I am showing just the ridgetop, road, and tower for simplicity. You can add the rest.

Your way of defining the target location vectors seems cumbersome to me. See how I have done it differently for the road, ridgetop, and tower. My way is clearer and uses a lot fewer lines of code.

I modfied the radius calculation in your function because I think it is a mistake to subtract tz-0.2 from every slant range.

[Jose Iglesias]

Thank you William!!

[William Rose]

@Jose Iglesias, you're welcome. Good luck with your work.