pedro delima dimitri zarzhitsky daniel j. pack presented by: chad e. hager
DESCRIPTION
Improving the Performance of Out-of-Order Sigma-Point Kalman Filters for Cooperative Target Localization Using Multiple UAVs. Pedro DeLima Dimitri Zarzhitsky Daniel J. Pack Presented by: Chad E. Hager. Overall Goal Sensor network objectives Problems of out-of-order measurements - PowerPoint PPT PresentationTRANSCRIPT
HQ U.S. Air Force Academy
I n t e g r i t y - S e r v i c e - E x c e l l e n c e
Improving the Performance of Out-of-Order Sigma-Point Kalman
Filters for Cooperative Target Localization Using Multiple UAVs
Pedro DeLimaDimitri Zarzhitsky
Daniel J. PackPresented by: Chad E. Hager
I n t e g r i t y - S e r v i c e - E x c e l l e n c e
10/11/2009
Overview
Overall Goal Sensor network objectives Problems of out-of-order measurements Out-of-Order Sigma-Point Kalman Filter Proposed method for merging Triangulation and O3SPKF Simulation results Summary
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Overall Goal
Develop a cooperative, heterogeneous, persistent intelligence, surveillance, reconnaissance (ISR) UAV system
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I n t e g r i t y - S e r v i c e - E x c e l l e n c e
Target Localization Examples
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X (meters)
Y (
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ers)
Target Location Estimates
121416182085112114270282285473474476477478480485487575641720724121416182085112114270282285473474476477478480485487575641720724
True Target Location
UAV1 Location
UAV2 LocationTarget Location Estimate by UAV1
Target Location Estimateby UAV2
0 50 100 150 200 250 300 350 400-80
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time (sec)
Y lo
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Estimate on Y
True Target Location
Estimated Target Location
0 50 100 150 200 250 300 350 4000
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time (sec)
X lo
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Estimate on X
True Target Location
Estimated Target Location
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I n t e g r i t y - S e r v i c e - E x c e l l e n c e
10/11/2009
Multi-Sensor, Multi-UAV Sensor Network
Provides target detection and localization capabilities using distributed heterogeneous sensor platforms Capability of multiple sensor types: e.g., RF/VR/IR Capability of multiple sensor modalities: e.g., DOA,
TDOA Processed data sent to local and remote UAVs GPS synchronization in real time allows for sensor
readings to be time stamped at the sensing source in a common timeframe.
Provide quick and accurate estimation of the target’s states, as well as the uncertainty associated with those, based on heterogeneous sensor measurements that become available with different degrees of delays and out-of-order.
Sensor FusionObjectives:
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10/11/2009
The Out-Of-Order Sigma Point Kalman Filter
Target state (position and velocity) estimates are computed using O3SPKF Kalman-filter based method provides near-optimal state
estimate with constant computational complexity Nonlinear Kalman filter handles intrinsic nonlinearities
in conversion between measurement and state SPKF (a variant of the UKF) has better accuracy than
EKF, same computational complexity Handles asynchronous and out of order measurements
from local UAV and remote UAVs Fuses measurements from multiple sensor modalities
CommunicationLatency
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I n t e g r i t y - S e r v i c e - E x c e l l e n c e
10/11/2009
The Out-Of-Order Sigma Point Kalman Filter
The classical SPKF requires that measurements arrive in-order. How to deal with measurements that arrive out-of-order (O3)? “O3SPKF Approach”: Modify SPKF algorithm to
explicitly account for O3 measurementscorrectly estimate position and velocity despite latency of communication channel
No buffer memory requirements; no added latency; all measurements retained
O3SPKF
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10/11/2009
Generic Kalman Filtering
General Kalman filtering maintains an estimate of a “state” of a system using a two-step predict/correct process
The assumption is that the state and output-error densities are Gaussian, so can be characterized by their means and covariances
All Kalman filters employ the following equations:
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10/11/2009
Implementation
For linear systems, with certain assumptions on noises, KF implements these equations exactly
For nonlinear systems, EKF approximates these equations to get analytical algorithm: Assume E[f(x)] = f(E[x]), which is not generally true Linearize equations to get local linear model
Also for nonlinear systems, SPKF approximates in a different way to get empirical algorithm: Propagate “sigma points” X for variable x through f(x) to
get Y = f(X) and take E[Y] (similar for covariance) No need to linearize equations
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10/11/2009
The O3SPKF modifies the SPKF steps slightly. If t is the present time, tx is the state-estimate time and tm is the measurement time, (f(.) must be invertible)
For in-order measurements, O3SPKF = SPKF as t tx tm
For O3 measurements, t > tx > tm
Sigma points representing state at time tm are generated based on inverse dynamic equation
Output estimate & covariance at time tm are generated
Gain matrix computed and update applied
Modifications to SPKF Leading to O3SPKF
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O3SPKF Performance: Speed of Convergence
Localization progress: RMS localization error versus time for six methods, 1s nominal sampling period, two sensors per UAV, 500m orbit (500 simulations averaged)
Lower curves are better, O3SPKF outperforms standard SPKF and implementations with different buffer sizes (ideal case is not achievable)
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10/11/2009
Merging O3SPKF and Triangulation
Whenever two or more UAVs detect a same target within a second (discretization level), a triangulation point xt(t) is generated.
xt(t)
xt(t)
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10/11/2009
Merging O3SPKF and Triangulation
The O3SPKF state is then propagated to the time t
The following equation is then used to merge the current target position state of the filter, x(t), with the triangulation point xt(t) to the degree specified by wt
)(N
))((trace)(
N
))((trace1)( )2:1()2:1( tx
tPwtx
tPwtx t
xt
xt
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Performance Comparison
10/11/2009
O3SPKF
O3SPKF + triangulation
Average results of 100 independent trials
Team size = 3 UAVs UAV speed = 25m/s Sensor uncertainty
= 15o
Sensor rate = 3Hz wt = 0.5
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Summary
O3SPKF handles asynchronous and O3 measurements from local UAV and remote UAVs
Triangulation technique allows us to take advantage of episodic joint sensor measurements that are more accurate than individual sensor measurements
O3SPKF state can be improved by merging them with triangulation points based on the estimated uncertainty of the filter
O3SPKF augmented with triangulation techniques provides faster localization error reduction, with no loss of performance at steady state behavior
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HQ U.S. Air Force Academy
I n t e g r i t y - S e r v i c e - E x c e l l e n c e
Improving the Performance of Out-of-Order Sigma-Point Kalman
Filters for Cooperative Target Localization Using Multiple UAVs
Pedro DeLimaDimitri Zarzhitsky
Daniel J. Pack
I n t e g r i t y - S e r v i c e - E x c e l l e n c e
10/11/2009
For in-order measurements, t tx tm; t0 = tm tx
The following equations optimized for linear state equation and nonlinear output equation with additive noises
O3SPKF: In-Order Measurements
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10/11/2009
For out-of-order measurements, t > tx > tm; t0 = tx tm
O3SPKF:Out-of-Order Measurements
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