Target Tracking Performance Evaluation A General Software Environment for Filtering

Rickard KarlssonIEEE Aerospace Conf 2007

Target Tracking Performance EvaluationA General Software Environment for Filtering

Rickard KarlssonGustaf Hendeby

Automatic ControlLinköping University, SWEDEN

rickard@isy.liu.se

Motivating Example

Range-Only Measurements

Two Sensors with range uncertainties

•Performance?•General Software for filtering

Outline

Nonlinear filtering using particle filters

Performace measure for nonlinear filteringKullback-Divergence vs RMSE

General Filtering SoftwareObject oriented designDesign Patterns

Examples

Filtering

STATE SPACE MODEL Process noise

Measurement noise

PROBABILISTIC DESCRIPTION

Bayesian Recursions: Probability Density Function (pdf)

Filter Evaluation: Mean Square Error (MSE)

Mean square error (MSE) Standard performance measure Approximates the estimation error covariance Bounded by the Cramér-Rao Lower Bound (CRLB)

Ignores higher-order moments!

Compare the true trajectory with the estimated!!!

What can we do instead?

Kullback-Leibler Information

Filter Evaluation: Kullback Divergence (KD)

Kullback Divergence (KD) Compares the distance between two distributions

Captures all moments of the distributions True PDF from a grid-based method True PDF from PF, compare sub-optimal filters Smoothing kernel needed for implementation

Compare the true PDF with the estimated PDF.

Generalized Gaussian

Generalized Gaussion Distribution Kullback Divergence

Example 1: One-dimensional Nonlinear System

Probability Density Function

Example 1: One-dimensional Nonlinear System

Kullback Divergence RMSE

KD for one realizationcomparing PF and EKF

RMSE for 400 MC simulations

Example 2: Range-Only Measurement

Estimate target position from range-only measurements Nonlinear measurements but Gaussian noise Posterior distribution: bimodal Point Estimate: EKF vs PF the same, i.e. same RMSE

Example 2: Simulation Results for Range-Only

MSE KD

No Difference! KD Indicates a Difference!

Calculating the probability

PF&True

Probability for target withinthe circle with radius R

F++ A General Filtering Environment in C++

MATLAB Easy to use Weak typing Somewhat slow Object oriented (not really)

C++ More complicated to use Fast Strong typing Object oriented Can be implemented !

F++: Fairly easy to use

Just provide models f(x), h(x), etc

Estimators:

EKF, PF, IMM, UKF

Open Source code available www.control.isy.liu.se/resources/f++

OOP & Design Patterns

Object Oriented Programming (OOP)

• Inheritance

• Encapsulation

• Overloading

Design Patterns – What is it?

• Smart Pointers• Singletons• Object factories•…

“Design patterns are general, programming language independent, conceptual high level solutions to common problems”

Example:

F++ A General Filtering Framwork in C++

Model Noise Estimator I/O

•LinModel•MultiModel•GenericModel <LinDyn,LinMeas>

•Gauss •SumNoise• …

• EKF • PF • IMM • UKF • MPF

• MATLAB • XML

Class: Model

• MATLAB • XML

Class: Noise

• MATLAB • XML

Class: Estimator

• MATLAB • XML

Ex: Linear Gaussian system with KF and MATLAB support

• MATLAB • XML

Ex: Non-Linear Gaussian system with PF and MATLAB support

Code: Main Estimation Loop

Estimator Time Update Meas. Update Estimate

This works for any estimator!

estimate

filter

Code: Main Program

MC-loop

True/Meas

Estimate

OUTPUT

Summary

Rickard KarlssonAutomatic ControlLinköping University, SWEDEN

rickard@isy.liu.se

www.control.isy.liu.se/~rickard

•Proposed KD as a performance measure

•General Filtering Software

Target Tracking Performance Evaluation A General Software Environment for Filtering

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