Rickard Karlsson IEEE Aerospace Conf 2007 Target Tracking Performance Evaluation A General Software Environment for Filtering Rickard Karlsson Gustaf Hendeby

Rickard KarlssonIEEE Aerospace Conf 2007

Target Tracking Performance EvaluationA General Software Environment for Filtering

Rickard KarlssonGustaf Hendeby

Automatic ControlLinköping University, SWEDEN

[email protected]


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)

M.U.

T.U.


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

PD

F


Example 1: One-dimensional Nonlinear System

Probability Density Function

xTime


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!

EKF

PF

EKF

PF


Calculating the probability

EKF

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







• 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

uy

filter


Code: Main Program

INPUT

MC-loop

True/Meas

Estimate

OUTPUT


Summary

Rickard KarlssonAutomatic ControlLinköping University, SWEDEN

[email protected]

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

•Proposed KD as a performance measure

•General Filtering Software

Documents

Rickard Karlsson IEEE Aerospace Conf 2007 Target Tracking Performance Evaluation A General Software Environment for Filtering Rickard Karlsson Gustaf Hendeby