Target tracking performance evaluation a general software environment for filtering
This presentation is the property of its rightful owner.
Sponsored Links
1 / 29

Target Tracking Performance Evaluation A General Software Environment for Filtering PowerPoint PPT Presentation


  • 157 Views
  • Uploaded on
  • Presentation posted in: General

Target Tracking Performance Evaluation A General Software Environment for Filtering. Rickard Karlsson Gustaf Hendeby Automatic Control Linköping University, SWEDEN. [email protected] Motivating Example. Range-Only Measurements. Two Sensors with range uncertainties. Performance?

Download Presentation

Target Tracking Performance Evaluation A General Software Environment for Filtering

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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

[email protected]


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?


Kullback leibler information

Kullback-Leibler Information


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>


Class model

Class: Model


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>


Class noise

Class: Noise


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>


Class estimator

Class: Estimator


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

[email protected]

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


  • Login