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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?

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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

[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 filtering Kullback-Divergence vs RMSE
  • General Filtering Software Object oriented design Design 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
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
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
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
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
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
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

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