PINTS Network

Multiple Target Tracking

Nonlinear Filtering

• Used for detection, tracking, and prediction of a target in a noisy environment

• Based entirely in probability– A filter won’t tell you exactly where a target is,

but it will tell you that there’s a 95% chance that it is within a certain region

Targets

• Targets are what filters work with• There are many different sorts of targets:

– Physical• Dinghy lost at sea• Performer on stage

– Financial• Investing• Fraud

– Other• Radio Frequencies• Port Scans

The Three Parts

• Filtering can be thought of as being divided into three parts:

– Signal Model (Target)– Observation Model (Noisy Environment)– Conditional Distribution (The Answer!)

Signal Model

• Model of how your target behaves

• Typical described using a Stochastic Differential Equation (SDE)

• Exists on some d-dimensional domain– For physical signals domain usually includes

dimensions for position, velocity, etc

• Basically tells you the probability that the target will move in any given way.

Boat Signal

• Domain is five dimensional:– X, Y position– Orientation– Speed– State (motoring, drifting, etc)

• Signal Model gives you the probabilistic distribution of what state the boat will be in at time t + 1, given it is currently at position Xt

• So, for example, the model might tell you that there’s a 40% chance that the boat will move north.

Observation Model

• Observation model tells about what information is available to the filter.

• Typically very poor:– Incomplete:

• Missing information• Might know location but not velocity or vice versa

– Corrupted:• Target might occasionally disappear completely from

observation

– Noisy:• Lots of false information on top of real target

Infra-red camera observation

• Observation model typically used with boat signal• Models infra-red satellite camera looking down at ocean• Not corrupted, but partial and very noisy!

– Only has position, no orientation, speed, or state

• Picture looks like TV static• To construct:

– Start with black picture– Add 1 to boat shaped area at location of boat– Add Normal Random Variable to each pixel– Colour each pixel according to the total number it ends up with

Conditional Distribution

• The output of the filter

• Used to answer various questions:– Where is the target now?– What are the chances that it’s within a certain

region?– Where will it be in 5 seconds?

• Just like a distribution for a random variable

Filtering Summary

• Filter has a model for both the signal it’s tracking and the type of observations it’s receiving.

• Input: Observations

• Output: Conditional Distribution

• Very powerful tool for a wide variety of applications

Surveillance (Lockheed Martin)

Communications(Optovation)

Automated Theatre Effects(APR Inc.)

Manufacturing(Visionsmart)

Filtering Applications

Network Security(Random Knowledge Inc.)

Medical Imaging

Pollution Monitoring

Fraud Detection(Random Knowledge Inc.)

Finance(Random Knowledge Inc.)

Fish Farming

Tracking a boat• Location : Where is the boat ? • Speed : How fast is the boat traveling ?• Orientation : Which way is the boat heading ?• Motion Type : Is the boat drifting, rowing, or motorized ?

Present Future Past

Tracking a performer on stage• Location : Where is the Performer ?

• Speed : How fast is the Performer traveling ?

• Orientation : Which way is the Performer heading ?

• Motion Type : Is the Performer in Walk or Pivot Mode?

Signal

(Port Scanner)

Observation

(Normal Traffic)

Port Scanner

Present

Port Scanner

Not Present

Detecting a port scanner