Introduction

In the synchronized multisensor-multitarget tracking problem, detections from multiple passive sensors are collected synchronously and are used to estimate the following:

This example demonstrates the use of the Static Fusion Before Tracking [1] architecture for tracking using passive measurements. The Static Fusion part of the architecture aims to triangulate the most likely set of detections and output fused detections containing estimated positions of targets. As measurements need to be fused together by static fusion, the sensors must report measurements synchronously.

With measurements containing only line-of-sight (LOS) information, at least 2 sensors are needed to find the position. However, with 2 sensors, the problem of ghosting (intersections at points with no targets) occurs when multiple targets lie in the same plane. With 2 targets and 2 sensors, it is impossible to identify the correct pair from a single frame of measurements as demonstrated in the figure below:

Therefore, one must use 3 or more sensors to reduce the problem of ghosting. Due to the presence of measurement noise and false measurements, it is difficult to eliminate the problem of ghosting completely. Ghost triangulations returned by static association are likely to be discarded by the dynamic association blocks as the geometry of targets and sensors changes during the scenario.

Define Scenario

The relative placement of sensors and targets in the scenario used here is taken from an example in [1]. The scenario consists of five equally-spaced targets observed by three to five passive sensors. The passive detections are modeled using radarEmitter and fusionRadarSensor with DetectionMode set to ESM. The HasNoise property of the sensors is set to false to generate noise-free detections along with false alarms. Noise is added to measurements in this example via a user-controlled variable. This is to simulate the effect of sensor noise on static fusion. Each sensor has a field of view of 180 degrees in azimuth and a FalseAlarmRate of 1e-3 per azimuth resolution cell. This results in 2 to 3 false alarms per scan. The scenario definition is wrapped inside the helper function helperGenerateFusionScenarioData.

[detectionBuffer,truthLog,theaterDisplay] = helperGenerateStaticFusionScenarioData;
showScenario(theaterDisplay);

showGrabs(theaterDisplay,[]);

Track with Three Sensors

In this section, only measurements from the inner three sensors are considered and measurement noise covariance for each sensor is set to 0.01 degrees squared.

The detections from each sensor are passed to a staticDetectionFuser. The MeasurementFusionFcn for passive triangulation is specified as triangulateLOS. The MeasurementFusionFcn allows specifying a function to fuse a given combination of detections (at most one detection from each sensor) and return the fused position and its error covariance. The parameters FalseAlarmRate, Volume and DetectionProbability are specified to reflect the parameters of sensors simulated in this scenario. These parameters are used to calculate the likelihood of feasible associations. The UseParallel property, when set to true, allows the fuser to evaluate the feasible associations using parallel processors.

The tracking is performed by GNN data association by using a trackerGNN.

The tracking performance is evaluated using trackAssignmentMetrics and trackErrorMetrics.

Setup

% Number of sensors
numSensors = 3;

% Create a detection fuser using triangulateLOS function as the
% MeasurementFusionFcn and specify parameters of sensors.
fuser = staticDetectionFuser('MeasurementFusionFcn',@triangulateLOS,...
    'MaxNumSensors',numSensors,...
    'UseParallel',true,...
    'FalseAlarmRate',1e-3,...
    'Volume',0.0716,...
    'DetectionProbability',0.99);

% Tracking using a GNN tracker
tracker = trackerGNN('AssignmentThreshold',45,...
    'ConfirmationThreshold',[3 5],'DeletionThreshold',[4 5]);

% Use assignment and error metrics to compute accuracy.
trackingMetrics = trackAssignmentMetrics('DistanceFunctionFormat','custom',...
    'AssignmentDistanceFcn',@trueAssignment,'DivergenceDistanceFcn',@trueAssignment);
errorMetrics = trackErrorMetrics;

Run simulation with three sensors

% Measurement noise
measNoise = 0.01;

time = 0; % simulation time
dT = 1; % 1 Hz update rate of scenario.

% Loop through detections and track targets
for iter = 1:numel(detectionBuffer)

    % Truth information
    sensorPlatPoses = truthLog{iter}(1:numSensors);
    targetPlatPoses = truthLog{iter}(6:end);
    groundTruth = [sensorPlatPoses;targetPlatPoses];

    % Generate noisy detections using recorded detections
    thisBuffer = detectionBuffer{iter};
    availableDetections = vertcat(thisBuffer{1:numSensors});
    noiseDetections = addNoise(availableDetections,measNoise);

    % Fuse noisy detections using fuser
    fusedDetections = fuser(noiseDetections);

    % Run a tracker on fused detections
    confTracks = tracker(fusedDetections,time);

    % Update track and assignment metrics
    trackingMetrics(confTracks,targetPlatPoses);
    [trackIDs,truthIDs] = currentAssignment(trackingMetrics);
    errorMetrics(confTracks,trackIDs,targetPlatPoses,truthIDs);

    % Update theater display
    detsToPlot = [noiseDetections(:);fusedDetections(:)];
    theaterDisplay(confTracks,detsToPlot,groundTruth);

    % Increment simulation time
    time = time + dT;
end
axes(theaterDisplay.TheaterPlot.Parent);

ylim([0 1.5]);

Results from tracking using three sensors with 0.01 degrees-squared of noise covariance can be summarized using the assignment metrics. Note that all tracks were assigned to the correct truths and no false tracks were confirmed by the tracker. These results indicates good static association accuracy.

assignmentTable = trackMetricsTable(trackingMetrics);
assignmentTable(:,{'TrackID','AssignedTruthID','TotalLength','FalseTrackStatus'})

ans =

  5×4 table

    TrackID    AssignedTruthID    TotalLength    FalseTrackStatus
    _______    _______________    ___________    ________________

       3             10               59              false      
       6              7               59              false      
       7              6               59              false      
      10              9               58              false      
      11              8               58              false      

The error in estimated position and velocity of the targets can be summarized using the error metrics. The errors in position and velocity are within 7 meters and 2 meters/sec respectively for all targets and the normalized errors are close to 1. The error metrics indicate good dynamic association and tracking performance.

disp(cumulativeTrackMetrics(errorMetrics));

    TrackID    posRMS    velRMS    posANEES    velANEES
    _______    ______    ______    ________    ________

       3       6.8821     1.595       2.51     0.80396 
       6       3.9895    1.1149     1.6409      0.5416 
       7       5.8195    1.3356     1.9041     0.66745 
      10       4.2425    1.2514     1.6719     0.62374 
      11       3.6443    1.1453      1.375     0.55326 

Effect of measurement accuracy

The fusion of passive detections to eliminate ghosting is highly dependent on the accuracy of passive measurements. As measurement noise increases, the distinction between ghost associations and true associations becomes less prominent, resulting in a significant drop in the accuracy of static association. With closely spaced targets, incorrect association of fused detections to tracks may also occur. In the next section, a helper function helperRunStaticFusionSimulation is used to re-run the scenario with a measurement noise covariance of 2 degrees squared.

Run the scenario again with a high measurement noise

numSensors = 3;
measNoise = 2; %standard deviation of sqrt(2) degrees
[trackingMetrics,errorMetrics] = helperRunStaticFusionSimulation(detectionBuffer,truthLog,numSensors,measNoise,theaterDisplay,false);
axes(theaterDisplay.TheaterPlot.Parent);

ylim([0 1.5]);

Note that a few tracks were confirmed and then dropped in this simulation. Poor static association accuracy leads to ghost target triangulations more often, which results in tracker deleting these tracks due to multiple misses.

assignmentTable = trackMetricsTable(trackingMetrics);
assignmentTable(:,{'TrackID','AssignedTruthID','TotalLength','FalseTrackStatus'})

ans =

  9×4 table

    TrackID    AssignedTruthID    TotalLength    FalseTrackStatus
    _______    _______________    ___________    ________________

       1              10              59              false      
       3             NaN               4              true       
       4             NaN               5              false      
       6               7              59              false      
       7               6              59              false      
      10               9              57              false      
      11               8              56              false      
      13             NaN               5              false      
      18             NaN               5              true       

The estimated error for each truth is higher. Notice that the track jumps in the theater display above.

disp(cumulativeTruthMetrics(errorMetrics));

    TruthID    posRMS    velRMS    posANEES    velANEES
    _______    ______    ______    ________    ________

       6       261.26     7.498     82.824      1.4568 
       7       54.822     3.226     3.9109     0.92307 
       8       50.606    4.6234     2.8907      1.1096 
       9       83.002    5.0335     7.1213      1.6252 
      10       206.17    7.0411     47.227      1.8917 

The association accuracy can be improved by increasing the number of sensors. However, the computational requirements increase exponentially with the addition of each sensor. The static fusion algorithm spends most of the time computing the feasibility of each triangulation. This part of the algorithm is parallelized when the UseParallel property of the staticDetectionFuser is set to true, which provides a linear speed-up proportional to the number of processors. To further accelerate execution, you can also generate C/C++ code which will also run in parallel execution on multiple processors. You can learn the basics of code generation using MATLAB® Coder™ at Get Started with MATLAB Coder (MATLAB Coder).

Accelerate MATLAB Code Through Parallelization and Code Generation

To accelerate MATLAB Code for simulation, the algorithm must be restructured as a MATLAB function, which can be compiled into a MEX file or a shared library. For this purpose, the static fusion algorithm is restructured into a function. To preserve the state of the fuser between multiple calls, it is defined as a persistent variable.

type('mexFuser');

function [superDets,info] = mexFuser(detections)

%#codegen
persistent fuser

if isempty(fuser)
    fuser = staticDetectionFuser('MeasurementFusionFcn',@triangulateLOS,...
        'MaxNumSensors',5,...
        'UseParallel',true,...
        'FalseAlarmRate',1e-3,...
        'Volume',0.0716,...
        'DetectionProbability',0.99);
end

[superDets,info] = fuser(detections);

MATLAB® Coder™ requires specifying the properties of all the input arguments. An easy way to do this is by defining the input properties by example at the command line using the -args option. For more information, see Define Input Properties by Example at the Command Line (MATLAB Coder). To allow variable number of detections, you will use the coder.typeof function to allocate data types and sizes for the inputs.

% Get a sample detection from the stored buffer
sampleDetection = detectionBuffer{1}{1}{1};

% Use the coder.typeof function to allow variable-size inputs for
% detections.
maxNumDets = 500;
inputDets = coder.typeof({sampleDetection},[maxNumDets,1],[1 0]);

h = msgbox({'Generating code for function. This may take a few minutes...';...
    'This message box will close when done.'},'Codegen Message');

% Use the codegen command to generate code by specifying input arguments
% via example by using the |-args| option.
codegen mexFuser -args {inputDets};

close(h);

Code generation successful.

You can verify the speed-up achieved by code generation by comparing the time taken by them for fusing one frame of detections

testDetections = addNoise(vertcat(detectionBuffer{1}{1:5}),1);
tic;mexFuser(testDetections);t_ML = toc;
tic;mexFuser_mex(testDetections);t_Mex = toc;
disp(['MATLAB Code Execution time = ',num2str(t_ML)]);
disp(['MEX Code Execution time = ',num2str(t_Mex)]);

MATLAB Code Execution time = 37.9316
MEX Code Execution time = 0.4011

Track with Five Sensors

In this section, detections from all five sensors are used for tracking and a measurement noise of 2 degrees squared is used.

measNoise = 2; % Same noise as 3 sensors
numSensors = 5;
[trackingMetrics,errorMetrics] = helperRunStaticFusionSimulation(detectionBuffer,truthLog,numSensors,measNoise,theaterDisplay,true);
axes(theaterDisplay.TheaterPlot.Parent);

ylim([0 1.5]);

The assignment results from tracking using five sensors show that all truths were assigned a track during the entire simulation. There were also no track drops in the simulation as compared to 4 track drops in the low-accuracy three sensor simulation.

assignmentTable = trackMetricsTable(trackingMetrics);
assignmentTable(:,{'TrackID','AssignedTruthID','TotalLength','FalseTrackStatus'})

ans =

  5×4 table

    TrackID    AssignedTruthID    TotalLength    FalseTrackStatus
    _______    _______________    ___________    ________________

       2             10               59              false      
       3              9               59              false      
       4              8               59              false      
       5              7               59              false      
       6              6               59              false      

The estimated errors for positions are much lower for each true target as compared to the three sensor simulation. Notice that the estimation results for position and velocity do degrade as compared to three sensors with high-accuracy measurements.

disp(cumulativeTruthMetrics(errorMetrics))

    TruthID    posRMS    velRMS    posANEES    velANEES
    _______    ______    ______    ________    ________

       6        34.74    3.0009     3.0358     0.75358 
       7       16.415    2.7014     1.3547     0.53336 
       8       16.555    2.5768     1.5645     0.49951 
       9       16.361    2.5381      1.474     0.55633 
      10       26.137    4.0457     2.3739      1.0349 

Summary

This example showed how to track objects using a network of distributed passive sensors. You learned how to use staticDetectionFuser to statically associate and fuse detections from multiple sensors. The example demonstrated how this architecture is depends parameters like number of sensors in the network and the accuracy of sensor measurements. The example also showed how to accelerate performance by utilizing parallel computing and automatically generating C code from MATLAB code.

Supporting Functions

trueAssignment Use ObjectAttributes of track to assign it to the right truth.

function distance = trueAssignment(track,truth)
tIDs = [track.ObjectAttributes.TargetIndex];
tIDs = tIDs(tIDs > 0);
if numel(tIDs) > 1 && all(tIDs == truth.PlatformID)
    distance = 0;
else
    distance = inf;
end
end

addNoise Add noise to detections

function dets = addNoise(dets,measNoise)
for i = 1:numel(dets)
    dets{i}.Measurement(1) = dets{i}.Measurement(1) + sqrt(measNoise)*randn;
    dets{i}.MeasurementNoise(1) = measNoise;
end
end

References

[1] Bar-Shalom, Yaakov, Peter K. Willett, and Xin Tian. "Tracking and Data Fusion: A Handbook of Algorithms." (2011).