How to fix altitude bias of fusionRadarSeneor detections?

When I simulate a geoTrajectory trackingScenario with fusionRadarSensor, I recive some bias in the altitude of the detections. Changing the biasFraction to 0.0 didn't help. If it happens because the radar simulates refraction, I would like to know how it can be disabled/corrected. I would like to use those detections for tracking algorithms development and this bias would interefere with performance evaluation of the trackers.

Thanks :)

Answer 1

[Elad Kivelevitch]

Hi Stav,

As they say in Hebrew: It's not a bug, it's a feature :-)

The altitude bias is indeed caused by atmospheric refraction. We included it in the model to provide exactly the kind of "difficult" test case for trackers that you have encountered. There is also a range bias simulated due to the refraction. Reference [1] in this doc page provides more information about the refraction model and how biases are added.

I believe that we do not have a way to disable atmospheric refraction in the radar model. However, one way to mitigate that is to take the detections returned by the fusionRadarSensor object and use refraction tables from a text book to "undo" the refraction and try to estimate where the detection should really be. From what I hear from my radar colleagues, this is the workflow that tracking/radar engineers are expected to follow when dealing with refraction biases from real radar systems.

FYI: The BiasFraction has nothing to do with simulating refraction biases. It is used to put a lower bound on the detection noise to satisfy the Cramer-Row Lower Bound for high SNR targets.

Elad

[Stav Danino]

Thanks for the fast reply! :)

In my research I assume that my input radar detections are corrected, and my focus in on sensor fusion and tracking performance. I would really appreciate it if there is a "fast" way to correct the simulated detections.

I came up from the doc with this solution. Is it an intended valid approximation? Thanks again.

% target.Position: [lat,lon,alt]
[~, N] = refractiveidx(target.Position(3), 'LatitudeModel', 'Mid', 'Season', 'Winter');
rexp = refractionexp(N);
% detection: [a,e,r]
Re = effearthradius(detection(3), tower.Position(3), target.Position(3));
tgthtCRPL = range2height(detection(3), tower.Position(3), detection(2), "Method", "CRPL", ...
    RefractionExponent=rexp, SurfaceRefractivity=N, EffectiveEarthRadius=Re);
[~, corrected_R, corrected_Elv] = height2range(tgthtCRPL, tower.Position(3), detection(2), ...
    "Method", "CRPL", RefractionExponent=rexp, SurfaceRefractivity=N, EffectiveEarthRadius=Re);

[Trevor Roose]

Hi Stav,

Your approach looks correct, though it will not completely remove the bias because a slightly different model (not the CRPL model) was used to model the bias.

I suspect what you may be more interested is just disabling the bias completely. While there is not a way to do that with the shipping features, here is a workaround which can disable it, though it does rely on internal properties which may at some point change. In other words, it will work for you today, but may stop working in a future release, since it is relying on internal functionality that is not documented.

What you can do is extend the fusionRadarSensor class with a new class, and add a method to that class which you can use to disable the internal atmospheric refraction model. Your class should look something like this. You can treat the new myRadar class just as you would the original fusionRadarSensor. It will have all of the same properties, methods, and functionality, but will have one new method disableRefraction that enables you to turn off the refraction bias model inside of fusionRadarSensor.

classdef myRadar < fusionRadarSensor

methods

function disableRefraction(obj)

obj.pHasAtmosphericRefraction = false;

end

end

end

You can verify that this disables the refraction bias using a simple example like this.

% Create a radar that detects everything without noise or false alarms

rdrOn = myRadar(1,'No scanning', ...

'FieldOfView',[360 180], ...

'RangeLimits',[0 1e6], ...

'DetectionProbability',1, ...

'HasElevation',true, ...

'HasNoise',false, ...

'HasFalseAlarms',false, ...

'DetectionCoordinates','Sensor spherical');

% Create a copy of the radar with the refraction bias disabled

rdrOff = clone(rdrOn);

disableRefraction(rdrOff);

% Create a bunch of targets to show variation of bias with range

grg = 10e3:10e3:500e3;

hgt = 10e3;

tgts = repmat(struct('PlatformID',1,'Position',[0 0 -hgt]),numel(grg),1);

for m = 1:numel(grg)

tgts(m).PlatformID = m;

tgts(m).Position(1) = grg(m);

end

% Generate detections using the two radar models

detsOn = rdrOn(tgts,0);

detsOff = rdrOff(tgts,0);

% Collect the measurements

measOn = cell2mat(cellfun(@(d)d.Measurement,detsOn(:)','UniformOutput',false));

measOff = cell2mat(cellfun(@(d)d.Measurement,detsOff(:)','UniformOutput',false));

% Compute the true slant range and elevation of the targets

pos = reshape([tgts.Position],3,[]);

[~,ph,srg] = cart2sph(pos(1,:),pos(2,:),pos(3,:));

el = rad2deg(ph);

% Plot the range and elevation biases

figure;

tiledlayout(2,1); nexttile;

plot(grg/1e3,measOn(3,:)-srg,'o',grg/1e3,measOff(3,:)-srg,'^');

ylabel('Range error (m)'); grid on; grid minor;

legend('Refraction on','Refraction off');

nexttile;

plot(grg/1e3,measOn(2,:)-el,'o',grg/1e3,measOff(2,:)-el,'^');

ylabel('Elevation error (deg)'); grid on; grid minor;

xlabel('Ground range (km)');

The folowing figure shows the range and elevation measurements from the radar with the refraction bias disabled in red.

[Stav Danino]

Thanks! its exactly the solution I hoped for.