{ } = t x ( t ), X x ( t ) | 0 t t i i State - PDF document

Data Fusion in Sensor Networks Hugh Durrant-Whyte ARC* Federation Fellow ARC* Centre of Excellence for Autonomous Systems The University of Sydney, Australia hugh@cas.edu.au *ARC=Australian Research Council 1 IPSN April 2005 Hugh Durrant-Whyte 2 IPSN April 2005 Hugh Durrant-Whyte Decentralised Sensor Networks Overview • Decentralised Sensor Networks • Endogenous Systems : • Data Fusion in Decentralised Networks • No central fusion • Structure of the problem Communications Medium • No central comms. • The essential DDF algorithm: SKIDS • Communication and Model Distribution: ISSS, OxNav • No global network • Timing and UAV demonstration: ANSER knowledge • The general Bayesian DDF: ANSER II • Probabilistic Algorithms • Management and Control in Sensor Networks • Tracking Sensor Node • Sensor Management • Navigation • Trajectory Control Sensor • Bayes estimation • Search and Exploration • Future Challenges Fusion Processor 3 4 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte Decentralised Data Fusion (DDF) Data Fusion: State { } = ≤ ≤ t x ( t ), X x ( t ) | 0 t t i i • State and state models • Observations and likelihood models • A track: of position and velocity for example • Distributed and decentralised estimation • A field property: temperature/pressure field for example • The DDF algorithm • A discrete property: Identity or label for example A State is a shared across sensor nodes 5 6 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte

Data Fusion: Observations Data Fusion: The Sensor Model ( ) { } t = ≤ ≤ z ( t ), Z z ( t ) | 0 t t P z ( t ) | x ( t ) j j i i j { } = ∈ t t Z Z | j N Model Inference Model Generation j ( ) ( ) • A track observation: range, bearing, velocity for example = = P z ( t ) | x ( t ) x ( t ) P z ( t ) z ( t ) | x ( t ) j j j • A local field observation: temperature/pressure for example • A discrete observation: presence/absence for example ( ) ( ) Λ z ( t ) j x ( t ) P z | x j j An Observation is local to a sensor node Sensor Model couples local observations to common global state 7 IPSN April 2005 Hugh Durrant-Whyte 8 IPSN April 2005 Hugh Durrant-Whyte Data Fusion: The State Model Data Fusion: The Essential Problem ( ) P x ( t ) | x ( t ) Observation Update − i i 1 ( ) ( ) ( ) ∏ = − = P x ( t ) | Z k C . P x ( t ) | Z k 1 P z z | x ( t ) Structural Encoding Temporal Encoding k k j j k j ( ) ( ) = Time/Structure Update P x ( t ) | x ( t 1 ) x = P x | x x − − i i i 1 j i i ( ) ) ( ) ( ∫ − = − k 1 k 1 P x ( t ) | Z P x ( t ) | x ( t ) P x ( t ) | Z d x ( t ) j i j i-1 − − − k k k 1 k 1 k 1 i Distributed and Decentralised versions of these Conditional Independence of Observations equations can be constructed with superficial ease State Model couples immediate states to global states Require Marginal State at current time 9 10 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte Data Fusion: Distributed Sensing Data Fusion: Distributed Fusion Fusion Centre P( x ) Fusion Centre k k-1 n P( x | Z n )=C P( x ) Π Λ i ( x ) n P( x k | Z n )=C P( x k-1 ) Π P i ( x k | z ) i=1 P( x k-1 | Z n ) i=1 Λ 1 ( x ) Λ i ( x ) Λ n ( x ) P 1 ( x k | z ) P n ( x k | z ) P( x k | Z n ) Sensor 1 Sensor i Sensor n P( x k | z 1 ) P( x k | z n ) Sensor n ...... ...... Sensor 1 P( z 1 | x ) P( z i | x ) P( z n | x ) ...... P( z 1 | x ) P( z n | x ) z 1 z n z 1 z i z n X X 11 12 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte

Decentralised Data Fusion: Data Fusion: Decentralised Fusion The Linear Gaussian Case ( ) : − P x ( k ) | x ( k 1 ) ( ) Fusion Centre Fusion Centre k k-1 k k-1 k → = − + w ( ) N 0 , Q x ( k ) Fx ( k 1 ) Gw ( k ) n n P( x k | Z n )=C P( x k-1 ) Π P i ( x k | z ) P( x k | Z n )=C P( x k-1 ) Π P i ( x k | z ) P( x k-1 | Z n ) P( x k-1 | Z n ) i=1 i=1 ( ) : P z ( k ) | x ( k ) j P 1 ( x k | z ) P n ( x k | z ) ( ) → = + v ( k ) N 0 , R z ( k ) H x ( k ) v ( k ) P( x k | z 1 ) P( x k | z n ) j j j j j P( x k | Z n ) P( x k | Z n ) Sensor 1 Sensor n ...... P( z 1 | x ) P( z n | x ) ( ) ( ) → P x ( p ) | Z q N x ( p ); x ˆ ( p | q ), P ( p | q ) z 1 z n X 13 IPSN April 2005 Hugh Durrant-Whyte 14 IPSN April 2005 Hugh Durrant-Whyte The Information Filter The Information Filter ( ) ( ) ( ) ∏ = − P x ( k ) | Z k C . P x ( k ) | Z k 1 P z ( k ) | x ( k ) Bayes: Observation updates are simple sums (unlike KF): j j ∑ = − + y ˆ ( k | k ) y ˆ ( k | k 1 ) i j k ( ) Log-Likelihood: j ∑ = − + ( ) ( ) ( ) Y ( k | k ) Y ( k | k 1 ) I j k ( ) ∑ = − + + ln P x ( k ) | Z k ln P x ( k ) | Z k 1 ln P z ( k ) | x ( k ) K j j j Time/Structure updates are Dual to state (KF) Observation Updates : (Fisher or Canonical) Information Form: [ ] + = + + y ˆ ( k 1 | k ) y ˆ ( k | k ) Ω y ˆ ( k | k ) Y ( k | k ) Bu ( k ) = − = T − 1 y ˆ ( k | k ) P 1 ( k | k ) x ˆ ( k | k ) i ( k ) H R z ( k ) j j j j + = − T − Y ( k 1 | k ) Y ( k | k ) Ω ( k ) Σ ( k ) Ω ( k ) = P 1 − Y ( k | k ) ( k | k ) = T 1 I j k ( ) H R H j j j 15 16 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte Implementation of the SKIDS Decentralised Information Filter • “European First Framework” Project 1986- 1991: Distributed/Decentralised Tracking in ^ Sensor node 2 y 2 (k|k-1), Y 2 (k|k-1) Σ k k-1 Civilian Environments Prediction z 2 (k) • Sensors { i 2 (k), I 2 (k) } ~ Σ ~ y 2 (k|k), Y 2 (k|k) H T R -1 2 2 • Multiple cameras each with embedded ^ Sensor node 1 processing y 1 (k|k-1), Y 1 (k|k-1) Σ k k-1 ~ Prediction [y 2 (k|k)-y 2 (k|k-1)] • Optical barriers, acoustic sensing z 1 (k) { i 1 (k), I 1 (k) } Σ • Algorithms ~ H T R -1 ~ ~ y 1 (k|k), Y 1 (k|k) 1 [y n (k|k)-y n (k|k-1)] 1 • DDF position/velocity tracking ~ ~ Σ y n (k|k), Y n (k|k) H T R -1 n n { i n (k), I n (k) } • Distributed data association and identification z n (k) ~ [y 1 (k|k)-y 1 (k|k-1)] • Fully connected Σ Prediction k k-1 ^ y n (k|k-1), Y n (k|k-1) Sensor node n 17 18 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte

SKIDS (1989 Demo) Three Issues Arising From SKIDS • Communication: • Non-fully connected networks • Time-varying and ad-hoc networks • Communications management • Modelling States: • Partial and distributed models at nodes • Estimation of field-like properties • Non-Gaussian posteriors • Control: • Sensor Placement • Sensor Management 19 IPSN April 2005 Hugh Durrant-Whyte 20 IPSN April 2005 Hugh Durrant-Whyte Operation of Channels Communication: Operation of Sensor Nodes • Nodes fuse information from: • Local observations, Local predictions, and • Communicated information • Focus on Channels (the Channel Filter): Z i • Communicate local information gain • Assimilate information gains from neighbourhood → ∩ I X Z ( | ) I X Z ( | Z ) i i j Channel Filters ∆ y qj (k|k) Sensor Node Channel I X Z ( | ) I X Z ( | ) Preprocess Manager ~ i i (k) i y i (k|k) Σ ∆ y pj (k|k) y i (k|k-1) Σ ∆ y pi (k|k) y i (k|k) Prediction 21 22 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte Operation of Channels Operation of Channels Z Z Z Z i j i j ∪ → ∩ I X Z ( | Z ) I X Z ( | Z ) ∩ I X Z ( | Z ) i j i j i j I X Z ( | ∪ ) ∪ ∪ − ∩ ∪ I X Z ( | ) I X Z ( | Z ) I X Z ( | Z ) I X Z ( | Z ) I X Z ( | Z ) I X Z ( | Z ) i j i j i i j i i j i j 23 24 IPSN April 2005 Hugh Durrant-Whyte IPSN April 2005 Hugh Durrant-Whyte