A SelfCalibrating System of Distributed Acoustic Arrays

1
A Self-Calibrating Systemof Distributed Acoustic
Arrays

• Public Defense
• 14 November 2005
• Lewis Girod
• CENS Systems Lab
• girod_at_cs.ucla.edu

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Distributed Acoustic SensingApplication
Requirements

• Acorn Woodpecker Localization
• Solution
• Surround trees with acoustic arrays
• Arrays detect woodpecker(s)
• Arrays estimate bearing to birds
• Cross-beam localization to estimate number and
  location of birds
• Key Problem
• Need 3D Array Position and Orientation
• Design constraints
• 3D birds are in trees, 3D terrain
• Spacing requirement 20 meters
• Accuracy requirement
• 2 bearing, ?25 cm position
• Resilient to environment
• Ground foliage
• Background noise
• Weather conditions

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Problem Statement
Goal Develop a self-calibrating system to
support collaborative acoustic sensing
applications, such as beam-forming and cross-beam
localization.

• Target System
• Input Node placement
• 3D, Outdoor, Foliage OK
• 20m Inter-node spacing
• Arrays are level
• Output Estimates
• XYZ Position 25cm
• Orientation 2
• Results in James Reserve
• Accurate Mean 3D Position Error 50 cm
• Precise Std. Dev. of Node Position 18 cm

70x50m
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Why is this hard?
Node 108

• Spacing / low node density requirement
• Requires high precision (10 µS) time
  synchronization
• Acoustic range often RF range ? multi-hop
  timesync
• Less range data available, larger impact of
  angular error
• 3D positioning vs. 2D
• Adds additional degree of freedom
• Topologies tend to be flat i.e. poorly
  constrained Z
• Orientation estimation
• Adds additional degree of freedom
• Accuracy of 2 degrees difficult with small
  baseline array
• Noise and interference rejection
• Ranging must acquire precise phase of first
  arrival
• Foliage often obstructs LOS
• Blocks/attenuates signal (esp. narrowband
  signals)
• Increases odds of ranging errors

Node 104
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Acoustic Position Estimation SystemA Vertical
Distributed Sensing Application
Acoustic Ranging and Positioning System

• Range and DOA Estimation (Ch 3)
• Multilateration Algorithms (Ch 4)
• Calibration Application (Ch 2,4,5)

Integration of Embedded Platform

• CPU and Microphone Array (Ch 2)
• Emstar Software Framework (Ch 6)
• Audio Server and Sync Support (Ch 7)
• Diagnostic and control tools (Ch 6)

Network Stack and Collaboration Primitives

• Multi-hop Time Synchonization (Ch 7)
• Topology discovery and control (Ch 8)
• Reliable State Dissemination (Ch 8)

6

Related Work
Studentized Residuals
Active Bat
Ultrasound
X Indoor Only
Ad-Hoc Acoustic
Audible
AHLoS
Cricket
X Accuracy
UCB (Whitehouse)
UIUC (Kwon)
X 2-D
Vanderbilt (Sallai)
Cricket Compass
Yao/Wang
Penn State (Ji)
X 2-D
OSU (Moses)
Microsoft (Rui)
MultiDim Scaling
X Accuracy
DOA
Network Services
X Wireless
ISIS
SRM
DOA Based Localization
Range Error Models
Hood
Trickle
USC (Chintalapudi)
X Mote-based
Slijepcevic/Potkonjak
X 2-D
X Accuracy
UCB (Doherty)
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Key Contributions Beyond Related Work

• Works well outdoors, even in obstructed
  environments
• Other systems tested at shorter range, no foliage
• Works for relatively sparse nets 20m spacing
  with foliage
• Others work well only at high densities and
  larger scales
• This is not always practical
• Achieves better accuracy and precision, in 3D
• The best competing system gives 50cm position
  error in 2D
• Our system gives 9cm error in 2D, 50cm error in
  3D with poorly constrained flat topology
• Precise orientation estimation
• Required to support cross-beam algorithms
• Does not require magnetic compass
• 3D DOA estimation
• Angular constraints are critical to good 3D
  performance, especially given that most
  topologies are relatively flat
• Multi-hop time synchronization with COTS 802.11
• Acoustic range RF range

Node 108
Node 104
8
Acoustic Position Estimation SystemA Vertical
Distributed Sensing Application
Acoustic Ranging and Positioning System

• Range and DOA Estimation (Ch 3)
• Multilateration Algorithms (Ch 4)
• Calibration Application (Ch 2,4,5)

Integration of Embedded Platform

• CPU and Microphone Array (Ch 2)
• Emstar Software Framework (Ch 6)
• Audio Server and Sync Support (Ch 7)
• Diagnostic and control tools (Ch 6)

Network Stack and Collaboration Primitives

• Multi-hop Time Synchonization (Ch 7)
• Topology discovery and control (Ch 8)
• Reliable State Dissemination (Ch 8)

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Position Estimation Application
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Acoustic Array Configuration

• 4 condenser microphones, arranged in a square
  with one raised
• 4 piezo tweeter emitters pointing outwards
• Array mounts on a tripod or stake, wired to CPU
  box
• Coordinate system defines angles relative to array

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Range and DOA Estimation

• Inputs
• The input signals from the microphones
• The time the signal was emitted (used to select
  from input signal)
• The PN code index used
• Outputs
• Peak phase (i.e. range)
• The 3-D direction of arrival ?, ?, and a scaling
  factor V
• Signal to Noise Ratio (SNR)

12
Filtering and Correlation Stage

• Synchronized Sampling Layer completely abstracts
  application from synchronization details
• Correlation
• Generate reference signal from PN code index
• Correlate against the incoming signal

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Correlation

• Signal detection via matched filter constructed
  from PN code
• Observed signal S is convolved with the reference
  signal
• Peaks in resulting correlation function
  correspond to arrivals
• Earliest peak is most direct path

Lag Time of Flight
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Detection Stage

• Want to detect first peak above noise floor
• Need to capture approx. peak region peak
  selection refined later
• Noise floor is time varying and must be estimated
• Use EWMA to compute continuous mean and variance
  estimate
• Selected a such that system adapts to 1 within
  5ms
• Define threshold to be a multiple of the standard
  deviation
• First value over threshold considered peak
• How to select threshold?

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Selecting a Peak Detection Threshold
Detection Peak.. 1st peak above threshold
Noise Peak.. max peak before detection

• Given a peak detection threshold, e.g. 12, we can
  determine for any given signal the noise peak
  and detection peak.
• To be certain not to detect noise, we want a wide
  gap between the distribution of rejected noise
  peaks and of detection peaks
• We selected a threshold of 12, and tested it with
  100,000 trials collected at the James Reserve.

12
Multiples of s
0
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Distribution of Noise Peaks
Distribution of Detection Peaks
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Zooming in.. 8x Interpolation

• Sub-sample phase comparison is critical to DOA
  estimation
• Otherwise, large quantization errors 1 sample
  offset 5
• Once a peak region is identified
• Zoom in by interpolating
• Use Fourier coefficients to expand the signal at
  higher resolution
• Equivalent to phase shift in FD
• But enables direct TD processing of correlation
  outputs

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DOA Estimation and Combining Stage

• 6-way cross-correlation of correlations ? DOA
  Estimator
• Filtered signals from each pair of microphones
  are correlated
• Offset of maximum correlation between pair
  (lag) recorded
• DOA Estimator uses least squares to fit lags to
  array geometry
• Key Resilient to perturbations in microphone
  placement
• DOA estimate used to recombine signals to improve
  SNR
• Final peak detection yields range estimate

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Position Estimation

• Problem
• Given pair-wise range and DOA estimates
• Estimate X,Y,Z locations and orientation T for
  each node

R,?,?
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Position Estimation Solution

• Two refinement algorithms
• R-? and NLLS
• Filtering out bad data is the key to good results
• Pre-filtering step
• Rejection of inconsistent data
• Metrics for assessment

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Use DOA for Initial Estimate
(Difference of forward and reverse DOA used to
estimate orientation)
R
?
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Two Refinement Methods R-? and NLLS

• R-? method extrapolates positions based on range
  and DOA
• Simpler results in linear system, e.g.
  (assuming T constant)
• Non-linear Least Squares (NLLS)
• Express range constraints separately from angle
  constraints
• Does not result in a linear system

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Comparison of R-? and NLLS
2-D Position errors from courtyard data

• NLLS outperforms R-? for our system
• Position error from ? scales with R
• R-? cant independently weight angle and range
  info
• R-? cant independently drop angle and range info
• Note, R-? works for very high node densities
• Given distributions of R and ? errors
• Uncertainty of R and ? is comparable for an
  inter-node spacing S such that
• S?? ?R
• For our system,
• ?? 1 0.017 rad,
• ?R 3.8 cm,
• so S 2.17 m

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Interleaved Orientation Estimation

• Orientation estimated in a separate, interleaved
  step
• Average difference between measured and computed
  angles
• Average represents bias caused by array
  orientation
• Values converge rapidly keep fixed after 10
  iterations while NLLS converges.

Measured
Computed
T
Node
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Rejecting Inconsistent Data

• Rejecting data from inconsistent angles
• Angular error likely caused by reflections
• Pre-filter data
• Perform multiple trials, keep data from median
  angle value
• After orientation converges
• Drop ranges associated with angles that differ
  significantly from angles computed from estimated
  positions
• Rejecting outlier constraints
• Use studentized residuals
• Divides each residual by its variance
• Intuition Large residuals with low variance are
  inconsistent

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Building the Position Estimation Application
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StateSync A Multi-hop Collaboration Primitive

• StateSync provides a simple Publish-Subscribe API
  and reliable, efficient data dissemination over
  multiple hops. It is designed to support
  applications publishing long-lived data.

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StateSync Achieves Low Quiescent Cost
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Without Sacrificing Latency Much
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StateSync Greatly Simplifies Position Estimation

• Ranging component publishes range estimates
• Position Estimation component subscribes to range
  estimates
• Processes current data
• If data is insufficient to achieve convergence
  and place our own node, requests local ranging
  component to emit ranging signals
• StateSyncs reliability layer unburdens the
  application
• Reliable
• Handles retransmission to achieve reliable
  delivery
• Brings late joiners up to date
• Nodes that lose connectivity can smoothly rejoin
  the network
• Stale data from rebooted nodes is dropped
• Efficient
• Leverages broadcasts
• Eliminates expensive soft-state refresh for low
  quiescent cost

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Experiments

• Component Testing
• Azimuth angle test
• Zenith angle test
• Range test

• System Testing
• Court of Sciences Test
• James Reserve Test

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Experimental Setup for Angular Tests
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Azimuth Errors as Function of Angle
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Overall Distribution of Azimuth Errors
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Zenith Errors as Function of Angle

• Negative angles are obstructed by the array
  itself, and have much worse variance.
• Zenith performance varies with the azimuth angle,
  perhaps a function of the array geometry. Our
  data only tested two azimuth angles.

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Overall distributions of Zenith Angle

• The zenith data does not fit well to a normal
  distribution (which is problematic because the
  position algorithms assume that).
• To improve things slightly, we computed
  statistics on subsets of the data. Both position
  algorithms can accept parameterized ? values.

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Experimental Setup for Range Tests
Semi-enclosed environment (lot 9). Tests at
different scales assess precision at a range of
distances.
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Range Measurements with Mean Error
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Anomalous Behavior at 50m

• Might be due to bug in time synchronization
  service that has since been fixed, or to
  environmental variables.

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Overall Distribution of Range Errors

• Not a particularly good fit to normal
  distribution
• Might improve under more controlled experiment
  (e.g. lot 4)

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System Tests

• Experimental Process
• Lay out 10 nodes, and run system to collect
  ranges and DOA
• Apply positioning algorithms to compute maps
• Compare to ground truth
• Metrics1
• Average Range Residual
• Measures quality of fit, useful when GT unknown
• Simple average of range residual values
• Average Position Error
• Absolute measure of performance, useful when GT
  known
• Fit estimated map to ground truth
• Then compute average distance between
  corresponding points

1. Modification of metrics presented in
Slijepcevic and Potkonjak, Characterization of
Location Errors in WSNs, Analysis and
Applications, IPSN 03.
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Fitting to Ground Truth to get Fair Position
Error
Ground Truth
Computed
Corresponding Points
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System Test Court of Sciences
N

• 10 nodes placed at yellow dots
• Yellow lines denote tall hedges
• Ground truth measured as carefully as possible
  and arrays aligned to point west.
• Z axis was difficult to measure used data from
  Google Earth, which is measured to the nearest
  foot.

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2D and 3D position error

• 3D position error for NLLS reflects low quality Z
  GT, flat topology
• NLLS did not converge for experiment 9
• R-? much worse, but shows improvement over time
  (env. cond.?)

44
Average Range Residuals and Position Err

• Average Range Residual metric is consistently
  low, except for the failed Experiment 9.

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Repeatability Per-node XY mean and std-dev
X cm
Y cm
Mean Std-dev X3.18, Y3.85
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Z and Orientation mean and std-dev
Mean Std-dev 1.37
Mean Std-dev 49.15

• Are non-zero means due to errors in ground truth
  or in measurements?
• X/Y estimates unclear. Ground truth
  incorporated cumulative errors and obstructions
  often blocked efforts to measure both axes.
• Z estimates likely inaccurate. The variation is
  larger than that expected from Google Earth data.
• Orientation estimates likely accurate They are
  generally low-variance and ground truth errors in
  alignment of 5 degrees are expected.

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James Reserve System Test

• Deployed 10 nodes in forested area.
• In many cases LOS was partially obstructed.
• Accurate ground truth difficult to measure
  because of blocked LOS and changes in elevation.
• Measurements were taken with a laser rangefinder
  and an altimeter with a output resolution of 1m.
• Nodes were aligned to point west with a compass.

N
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James Reserve per-node mean and std-dev
Mean Std-dev X3.48, Y3.78

• Errors in ground truth likely to be significant
  fraction of error in mean

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James Reserve Z and Orientation mean/std-dev
Mean Std-dev 17.1
Mean Std-dev 3.15

• For many nodes, the variance in Z values for the
  hilly JR data is considerably lower than those in
  the courtyard data.
• The orientation repeatability is comparable to
  the courtyard data. The errors in ground truth
  for JR are expected to be worse.
• All data taken from the 6 experiments that placed
  all 10 nodes. The location stakes are still in
  place.

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Range Consistency vs. Position Error

• This result shows that there are few cases where
  a good fit resulted in bad position error. The
  better fits at JR are likely due to more
  well-constrained Z axis which relies less on ?
  angles.

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Conclusions

• Acoustic ENSbox platform supports distributed
  acoustic sensing
• Implemented ranging and position estimation
  application.
• Highly accurate positioning in a challenging
  environment
• XYZ Position 50cm (likely considerably better)
• Orientation 2
• Nearly order of magnitude improvement upon prior
  work
• 9 cm XY error vs. 50 cm (UIUC)
• Supports XYZT estimation
• achieved with
• fewer nodes
• lower densities
• more difficult conditions.

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Review of Contributions
Acoustic Ranging and Positioning System

• Range and DOA Estimation (Ch 3)
• Multilateration Algorithms (Ch 4)
• Calibration Application (Ch 2,4,5)

Integration of Embedded Platform

• CPU and Microphone Array (Ch 2)
• Emstar Software Framework (Ch 6)
• Audio Server and Sync Support (Ch 7)
• Diagnostic and control tools (Ch 6)

Network Stack and Collaboration Primitives

• Multi-hop Time Synchonization (Ch 7)
• Topology discovery and control (Ch 8)
• Reliable State Dissemination (Ch 8)