Forward-Scan Sonar Tomographic Reconstruction PHD Filter Multiple Target Tracking [email protected] Bayesian Multiple Target Tracking in Forward Scan Sonar

Forward-Scan Sonar Tomographic Forward-Scan Sonar Tomographic Reconstruction Reconstruction

PHD Filter Multiple Target TrackingPHD Filter Multiple Target Tracking

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Bayesian Multiple Target Tracking in Forward Scan Sonar Images Using The PHD Filter

Daniel Clark and Judith Bell



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Thesis Topic: “Tomographic Reconstruction of a Sequenceof Forward Scan Sonar Images”



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Problems to Address:



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Problems to Address:•Segment Sonar into Homogeneous Regions of Same Seabed Type



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Problems to Address:•Segment Sonar into Homogeneous Regions of Same Seabed Type•Locate Objects on the Seabed



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Problems to Address:•Segment Sonar into Homogeneous Regions of Same Seabed Type•Locate Objects on the Seabed•Align Images onto Global Co-ordinate System



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Problems to Address:•Segment Sonar into Homogeneous Regions of Same Seabed Type•Locate Objects on the Seabed•Align Images onto Global Co-ordinate System•Reconstruct Sonar Data into 3D Elevation Map of Seabed



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Why?



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Why?•To Aid Navigation and Path Planning



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Why?•To Aid Navigation and Path Planning•Obstacle Avoidance, mines etc.



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Principle of Sonar:Transmission of an acoustic pulse of energy into water andmeasure reflected energy:



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Principle of Sonar:Transmission of an acoustic pulse of energy into water andmeasure reflected energy:

The intensity of the energy reflected is measured against time to give information on the surface below:

distance to surface = (speed of sound in water)x(time to return)/2



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Forward Scan Sonar:•The acoustic energy from the sonar is transmitted in a radial sector.



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Forward Scan Sonar:•The acoustic energy from the sonar is transmitted in a radial sector.•The backscattered energy can be shown as a sonar image:



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Environmental ReconstructionMethods for creating elevation maps of the seabed have been implemented using Lambert's Law and knowledge of the Sonar's Position.



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Environmental ReconstructionMethods for creating elevation maps of the seabed have been implemented using Lambert's Law and knowledge of the Sonar's Position.

Lambert's Law relates the reflected energy from the surface to the anglebetween the direction of reflection and the surface normal.

I s I I cos2



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Local Propagation Technique:Each successive point is determined from the intersection ofthe circle centred at the sonar fish and the surface gradientdetermined from Lambert's Law.



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Sonar Image:



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Sonar Image:

Reconstructed Image:



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Multiple Target Tracking

This work will be used to address the issues of:•Detecting and Locating Objects on the Seabed•Aligning Images onto a Global Co-ordinate System



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Multiple Target Tracking

This work will be used to address the issues of:•Detecting and Locating Objects on the Seabed•Aligning Images onto a Global Co-ordinate System

Targets to be Tracked:Mines, metallic objects which have high reflectance property:

Measurements obtained by thresholding.



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Recursive Bayesian Estimation

To make inference about a dynamic system, two models are needed:

•Motion Model – describes evolution of state with time ie the motion of underwater vehicle.



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•Measurement Model – relates the measurements to the state ie the objects on the seabed.



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•Measurement Model – relates the measurements to the state ie the objects on the seabed.

These correspond to prediction and update stages when tracking.



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Single Target Inference

The tracking problem is governed by two functions:

These relate to the motion and measurement models respectively.

x t F t x t 1 , v t 1

zt H t x t , nt



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Single Target Inference

The tracking problem is governed by two functions:

These relate to the motion and measurement models respectively.•The process noise v reflects the unknown target motion •The measurement noise n reflects sensor errors

x t F t x t 1 , v t 1

zt H t x t , nt



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Bayesian Recursion

The prior distribution of a target location based on previous observationsis obtained from the motion model and the posterior at time t-1:

f t t 1 x t z1 :t 1 f t t 1 x t x t 1 f t 1 t 1 x t 1 z1: t 1 dx t 1



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Bayesian Recursion

The prior distribution of a target location based on previous observationsis obtained from the motion model and the posterior at time t-1:

When a new measurement is obtained, the posterior distribution at time tis obtained by Bayes' Law:

where g is the likelihood of observing z given target state x.

f t t 1 x t z1 :t 1 f t t 1 x t x t 1 f t 1 t 1 x t 1 z1: t 1 dx t 1

f t t x t z1. .t g t zt x t f t t 1 x t z1. .t 1



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Multiple Target Inference Model

The single target recursive state estimation can be directly extended to a multiple target model using Finite Set Statistics (FISST).



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A Random Finite Set (RFS) is used to represent a multiple-target state.The set of objects tracked at time t is an RFS containing :•Set of objects survived from time t-1.



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A Random Finite Set (RFS) is used to represent a multiple-target state.The set of objects tracked at time t is an RFS containing :•Set of objects survived from time t-1.•Set of object appearing at time t.



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The measurements at time t are modelled by an RFS containing:•Measurements generated from actual targets.



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The measurements at time t are modelled by an RFS containing:•Measurements generated from actual targets.•Spurious measurements from clutter.



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Multiple Target Bayesian Recursion

The single target Bayesian recursion can be extended to the multipletarget scenario using the calculus defined in FISST:

f t t 1 X t Z1 :t 1 f t t 1 X t X t 1 , Z1 :t 1 f t 1 t 1 X t 1 Z1 : t 1 X t 1

f t t X t Z 1: t gt Z t X t f t t 1 X t Z1:t 1



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PHD Filter

The Probability Hypothesis Density or PHD is defined as the first orderstatistical moment of the multiple target posterior distribution.The integral of the PHD in any region represents the expected numberof objects in that region.



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PHD Filter


Why bother?Computationally cheaper to calculate than full posterior.



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PHD Filter


Why bother?Computationally cheaper to calculate than full posterior.

Where are the targets?The locations of the targets can be found as peaks of this distribution.



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PHD Filter

Prediction Equation:

Dt t 1 x t Z1:t 1 b t x t PS x t 1 f t t 1 x t x t 1 Dt 1 t 1 x t 1 Z1 :t 1 x t 1



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PHD Filter

Prediction Equation:

Data Update Equation:

Dt t 1 x t Z1:t 1 b t x t PS x t 1 f t t 1 x t x t 1 Dt 1 t 1 x t 1 Z1 :t 1 x t 1

Dt t x t Z1:t F t Z t x t Dt t 1 x t Z1:t 1

F t Z t x t 1 PD zti Z t

PD gt zti x t

t c t zt PD Dt t , g t



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Particle Filter Algorithm

Particle filters were designed for implementing Bayesian recursionby representing probability distributions by random samples or particles rather than in their functional forms.



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Particle Filter Algorithm

Particle filters were designed for implementing Bayesian recursionby representing probability distributions by random samples or particles rather than in their functional forms.

The areas with higher probability will have a larger number of particles.



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Particle Filter Algorithm (Single Target)

•Step 1: Initialisation.N particles are uniformly distributed across the Field of View (FoV).



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•Step 2: Data Update.After a new measurement, weights are assigned to the particlesaccording to their likelihoods.



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•Step 3: ResamplingAn unweighted particle set is obtained by resampling from the weighted set.



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•Step 4: Estimation of Target LocationThe location of the target is estimated by calculating the mean positionof the particles.



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•Step 4: Estimation of Target LocationThe location of the target is estimated by calculating the mean positionof the particles.

•Step 5: PredictionThe location of the next target location is estimated using the motion model.



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Particle Filter Algorithm (Multiple Target)




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•Step 2: Data Update.After a new measurement, weights are assigned to the particlesaccording to the data update equation for the PHD.



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•Step 3: Estimation of Target LocationThe locations of the targets are estimated by fitting a Gaussianmixture model to the particles where the number of targets is the sum of the weights.



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•Step 5: PredictionThe locations of the next target locations are estimated using the PHDprediction equation.



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Implementation on Forward Scan Sonar Data

•n beams separated by k degrees



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•n beams separated by k degrees•Intensity vs time data



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•n beams separated by k degrees•Intensity vs time data•Tracks range and bearing of targets



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Measurements are obtained by thresholding the data:



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Measurements are obtained by thresholding the data:

The motion of the sonar is assumed to be linear Field of View in the range of 20m to 60m



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Sequence of Simulated Forward Scan Sonar Images with Objects



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Results on Simulated Data

Linear Tracking in Sonar Image Reference Frame



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Linear Tracking in Global Reference Frame



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Sinusoidal Tracking in Global Reference Frame



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Sequence of Real Forward-Scan Images



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Results on Real Data

Tracked Cylinder in Forward Direction



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Results on Real Data

Tracked Cylinder in Backward Direction



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Extensions To PHD Filter:

The multi-target state set does not give individual target identities.

How do we associate measurements between frames?

Two possible approaches:



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•Increase state vector with invariant attribute



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•Increase state vector with invariant attribute

•Data Association



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What do I do with it now?

The target tracks will be used for alignment by computinga geometric transform between the frames eg affine/similarity.



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What do I do with it now?

The target tracks will be used for alignment by computinga geometric transform between the frames eg affine/similarity.

This will be used as a preliminary step for 3D reconstruction of asequence of images.



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Future Work on Reconstruction

Segmentation into different seabed types.

Reconstructed 3D elevation map of sequence of images.



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References

R. Mahler:"Multitarget Bayes Filtering via First-Order Multitarget Moments",IEEE Transactions on Aerospace and Electronic Systems, 2003.

Vo, Singh and Doucet:“Sequential Monte Carlo Implementation of the PHD Filter for Multi-targetTracking”Proc. FUSION 2003

Sidenbladh and Wirkander:“Tracking random sets of vehicles in terrain”IEEE Workshop on Multi-Object Tracking, Madison, WI, USA, 2003

Documents

Forward-Scan Sonar Tomographic Reconstruction PHD Filter Multiple Target Tracking [email protected] Bayesian Multiple Target Tracking in Forward Scan Sonar