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Target Tracking Performance Evaluation A General Software Environment for Filtering. Rickard Karlsson Gustaf Hendeby Automatic Control Linköping University, SWEDEN. rickard@isy.liu.se. Motivating Example. Range-Only Measurements. Two Sensors with range uncertainties. Performance?

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Target tracking performance evaluation a general software environment for filtering
Target Tracking Performance EvaluationA General Software Environment for Filtering

Rickard Karlsson

Gustaf Hendeby

Automatic Control

Linköping University,

SWEDEN

rickard@isy.liu.se


Motivating example
Motivating Example

Range-Only Measurements

Two Sensors with range uncertainties

  • Performance?

  • General Software for filtering


Outline
Outline

  • Nonlinear filtering using particle filters

  • Performace measure for nonlinear filteringKullback-Divergence vs RMSE

  • General Filtering SoftwareObject oriented designDesign Patterns

  • Examples


Filtering
Filtering

Process noise

STATE SPACE MODEL

PROBABILISTIC DESCRIPTION

Measurement noise

Method? Performance?

Implementation?


Bayesian recursions probability density function pdf
Bayesian Recursions: Probability Density Function (pdf)

M.U.

T.U.

Approx system

Approx pdf

Particle Filter

Extended Kalman Filter


Filter evaluation mean square error mse
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?



Filter evaluation kullback divergence kd
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 Gaussian

Generalized Gaussion Distribution

Kullback Divergence

PDF


Example 1 one dimensional nonlinear system
Example 1: One-dimensional Nonlinear System

Probability Density Function

x

Time


Example 1 one dimensional nonlinear system1
Example 1: One-dimensional Nonlinear System

RMSE

Kullback Divergence

KD for one realization

comparing PF and EKF

RMSE for 400 MC simulations


Example 2 range only measurement
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
Example 2: Simulation Results for Range-Only

KD

MSE

EKF

EKF

PF

PF

No Difference!

KD Indicates a Difference!


Calculating the probability
Calculating the probability

EKF

Probability for target within

the circle with radius R

PF&True


F a general filtering environment in c
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

OOP & Design Patterns

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


Object oriented programming oop
Object Oriented Programming (OOP)

  • Inheritance

  • Encapsulation

  • Overloading


Design patterns what is it
Design Patterns – What is it?

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

Example:

  • Smart Pointers

  • Singletons

  • Object factories


F a general filtering framwork in c
F++ A General Filtering Framwork in C++

Model

Noise

Estimator

I/O

  • EKF

  • PF

  • IMM

  • UKF

  • MPF

  • MATLAB

  • XML

  • Gauss

  • SumNoise

  • LinModel

  • MultiModel

  • GenericModel

  • <LinDyn,LinMeas>


F a general filtering framwork in c1
F++ A General Filtering Framwork in C++

Model

Noise

Estimator

I/O

  • EKF

  • PF

  • IMM

  • UKF

  • MPF

  • MATLAB

  • XML

  • Gauss

  • SumNoise

  • LinModel

  • MultiModel

  • GenericModel

  • <LinDyn,LinMeas>



F a general filtering framwork in c2
F++ A General Filtering Framwork in C++

Model

Noise

Estimator

I/O

  • EKF

  • PF

  • IMM

  • UKF

  • MPF

  • MATLAB

  • XML

  • Gauss

  • SumNoise

  • LinModel

  • MultiModel

  • GenericModel

  • <LinDyn,LinMeas>



F a general filtering framwork in c3
F++ A General Filtering Framwork in C++

Model

Noise

Estimator

I/O

  • EKF

  • PF

  • IMM

  • UKF

  • MPF

  • MATLAB

  • XML

  • Gauss

  • SumNoise

  • LinModel

  • MultiModel

  • GenericModel

  • <LinDyn,LinMeas>



F a general filtering framwork in c4
F++ A General Filtering Framwork in C++

Ex: Linear Gaussian system with KF and MATLAB support

Model

Noise

Estimator

I/O

  • EKF

  • PF

  • IMM

  • UKF

  • MPF

  • MATLAB

  • XML

  • Gauss

  • SumNoise

  • LinModel

  • MultiModel

  • GenericModel

  • <LinDyn,LinMeas>


F a general filtering framwork in c5
F++ A General Filtering Framwork in C++

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

Model

Noise

Estimator

I/O

  • EKF

  • PF

  • IMM

  • UKF

  • MPF

  • MATLAB

  • XML

  • Gauss

  • SumNoise

  • LinModel

  • MultiModel

  • GenericModel

  • <LinDyn,LinMeas>


Code main estimation loop
Code: Main Estimation Loop

u

y

filter

estimate

Estimator Time Update Meas. Update Estimate

This works for any estimator!


Code main program
Code: Main Program

INPUT

MC-loop

True/Meas

Estimate

OUTPUT

Same Code

for any Model


Summary
Summary

  • Proposed KD as a performance measure

  • General Filtering Software

Rickard Karlsson

Automatic Control

Linköping University,

SWEDEN

rickard@isy.liu.se

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


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