target tracking performance evaluation a general software environment for filtering
DESCRIPTION
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? - PowerPoint PPT PresentationTRANSCRIPT
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Rickard KarlssonIEEE Aerospace Conf 2007
Target Tracking Performance EvaluationA General Software Environment for Filtering
Rickard KarlssonGustaf Hendeby
Automatic ControlLinköping University, SWEDEN
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Rickard KarlssonIEEE Aerospace Conf 2007
Motivating Example
Range-Only Measurements
Two Sensors with range uncertainties
•Performance?•General Software for filtering
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Rickard KarlssonIEEE Aerospace Conf 2007
Outline
Nonlinear filtering using particle filters
Performace measure for nonlinear filteringKullback-Divergence vs RMSE
General Filtering SoftwareObject oriented designDesign Patterns
Examples
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Rickard KarlssonIEEE Aerospace Conf 2007
Filtering
STATE SPACE MODEL Process noise
Measurement noise
PROBABILISTIC DESCRIPTION
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Rickard KarlssonIEEE Aerospace Conf 2007
Bayesian Recursions: Probability Density Function (pdf)
M.U.
T.U.
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Rickard KarlssonIEEE Aerospace Conf 2007
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?
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Rickard KarlssonIEEE Aerospace Conf 2007
Kullback-Leibler Information
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Rickard KarlssonIEEE Aerospace Conf 2007
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.
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Rickard KarlssonIEEE Aerospace Conf 2007
Generalized Gaussian
Generalized Gaussion Distribution Kullback Divergence
PD
F
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Rickard KarlssonIEEE Aerospace Conf 2007
Example 1: One-dimensional Nonlinear System
Probability Density Function
xTime
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Rickard KarlssonIEEE Aerospace Conf 2007
Example 1: One-dimensional Nonlinear System
Kullback Divergence RMSE
KD for one realizationcomparing PF and EKF
RMSE for 400 MC simulations
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Rickard KarlssonIEEE Aerospace Conf 2007
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
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Rickard KarlssonIEEE Aerospace Conf 2007
Example 2: Simulation Results for Range-Only
MSE KD
No Difference! KD Indicates a Difference!
EKF
PF
EKF
PF
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Rickard KarlssonIEEE Aerospace Conf 2007
Calculating the probability
EKF
PF&True
Probability for target withinthe circle with radius R
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Rickard KarlssonIEEE Aerospace Conf 2007
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
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Rickard KarlssonIEEE Aerospace Conf 2007
Object Oriented Programming (OOP)
• Inheritance
• Encapsulation
• Overloading
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Rickard KarlssonIEEE Aerospace Conf 2007
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:
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Rickard KarlssonIEEE Aerospace Conf 2007
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
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Rickard KarlssonIEEE Aerospace Conf 2007
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
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Rickard KarlssonIEEE Aerospace Conf 2007
Class: Model
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Rickard KarlssonIEEE Aerospace Conf 2007
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
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Rickard KarlssonIEEE Aerospace Conf 2007
Class: Noise
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Rickard KarlssonIEEE Aerospace Conf 2007
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
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Rickard KarlssonIEEE Aerospace Conf 2007
Class: Estimator
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Rickard KarlssonIEEE Aerospace Conf 2007
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
Ex: Linear Gaussian system with KF and MATLAB support
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Rickard KarlssonIEEE Aerospace Conf 2007
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
Ex: Non-Linear Gaussian system with PF and MATLAB support
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Rickard KarlssonIEEE Aerospace Conf 2007
Code: Main Estimation Loop
Estimator Time Update Meas. Update Estimate
This works for any estimator!
estimate
uy
filter
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Rickard KarlssonIEEE Aerospace Conf 2007
Code: Main Program
INPUT
MC-loop
True/Meas
Estimate
OUTPUT
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Rickard KarlssonIEEE Aerospace Conf 2007
Summary
Rickard KarlssonAutomatic ControlLinköping University, SWEDEN
www.control.isy.liu.se/~rickard
•Proposed KD as a performance measure
•General Filtering Software