BiologicallyInspired Gradient Source Localization

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Biologically-Inspired Gradient Source Localization
DNA
Protein Pathways
Function

• Gail Rosen
• CSIP Seminar
• Advisor Paul Hasler
• March 18th, 2005

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Presentation Outline

• Biological Signal Processing
• Gradient Source Localization Algorithm
• Implementation of Gradient Source Localizer
• Proposed Research

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Biological Signal Processing
Beginnings of Medicine 2000 B.C. (Asia), 500
B.C. (Hippocrates)
Function
Discovery of DNA 1950 (Wilkins and Franklin),
1953 (Watson and Crick)
DNA
Feedback Regulation in Metabolism 1957
(Umbarger, Brown) (Yates, Pardee) 1970s major
breakthroughs
Protein Pathways
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Reverse Engineering Biology
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Presentation Outline

• Biological Signal Processing
• Gradient Source Localization Algorithm
• Implementation of Gradient Source Localizer
• Proposed Research

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Function from Biology
How can we use function to help design systems?
Signal
Computation(ie chemotaxis)
Cellular Dynamics
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Cell-response in Gradient

• Equilibrium
• In gradient, receptors congregate towards side
  closest to the source
• Morphology of cell changes
• Polarized cell migrates towards the source.

J. Krishnan and P.A. Iglesias. Uncovering
directional sensing where are we headed? IEE
Systems Biology, June 2004.
Cells navigate well Immune response, food
tracking, etc.
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What is a Gradient Source?
Gradient Rate of change of one quantity in
relation to another
Gradient Source Source which emits gradient
field
Heat
Chemical
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Why Track Gradients?

• Gradient field source localization Applications
• Explosive vapors
• Illegal substances
• Volatile chemical/thermal leaks

State-of-the-Art
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Signal Processing Approaches

• Nehorai/Porat Near-Field sensor arrays (square
  example), optimal sensor placement, parameter
  estimation of vapor source location and magnitude
  (1995)
• Gershman/Turchin Uniform linear array (12),
  near-field, multiple underwater sources (1995)
• Kaiser Multiple far-field square sensor arrays
  of 4 sensors, assume time-delay detection, fire
  sources (2000)

So many problems, hard to compare methods!
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Current Approaches

• Single sensor strategy
• Parametric estimation and circle-and-attack
  strategy

Swarm-robotics and Flocking
Source Adam T. Hayes. Self-Organized Robotic
System Design and Autonomous Odor Localization,
Ph.D. Thesis. Caltech. 2002.
Source Jeremic, Nehorai. IEEE Transactions on
Signal Processing. 2000.
Hard to compare methods!
Biologically-inspired Lobsters and Moths
Picture courtesy of Ayers at Northeastern
University. Grasso at Brooklyn College has
developed the Robolobster.
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Bio-Inspiration Chemotaxis

• Amoebae track food via a chemical gradient

• Receptors detect chemical flux

• Directional Sensing

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Spatial Array Signal Processing

• Delay-and-sum Beamforming
• usually want to line waves up in time

• Non-wave field, Amplitude ONLY measurements

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2-D Gradient Field

• Model Gradient Field

µ rate of release D diffusion constant

• Sensor Measurements, v

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Array

• Symmetric sensor arrangement maximizes the
  perimeter of the board/chip

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Deterministic Solutions

• Simplest Non-memory time measurements

• With one-known source, filter/weight to
  amplify/attenuate the signal.

where
rewrite as
A amplitude steering yn output for particular
sensor direction
y1
y2
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Steering with A

• Gets more interesting with non-identity A
• yn is now based on weighted
• adjacent sensors

• Biology does this too!

• Now how to make the steering adjustable

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Gradient Source Localization Outline

• Steer the inputs using a weight matrix, A.

2. Update A using a variant to the LMS algorithm
-- step-size parameter
where R is the input covariance, vnvTn

• Intuitive explanation
• The weights in A increase when the weights
  correlate to the input corr matrix (Narrow focus
  to where source is).
• Similar to positive feedback in some biology.

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Gradient Source Localization Outline
3. Adjacent receptor constraints similar to
Chemotaxis
Ainit (banded form of spatial averaging)
Averager
Uniform-bands (Ex. Sc3)
Tapered-bands (Ex. Sc3)
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Gradient Source Localization Outline
4. Direction of Source calculation
where
Coordinates with respect to center of array
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Note on Chemotaxis Constraints

• Averager

e

• Unity Uniform-banded

e

• Tapered bands
• Attenuated side-sensor contributions

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Simulation Parameters

• Number of sensors, N 4, 8, 16, 32
• Sc (sensor cooperation) odd, 1 to N-1
• startingSNR -8 to 8 dB per 2 dB

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Example of Simulation
Biological Scale Starting position
(-0.01,0.01) Step size 1/100 (starting radius
from center)
Parameters N32, Sc5, startingSNR-1dB converge
d in 208 steps
Rosen and Hasler. GENSIPS 2004.
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Simulation of Algorithm
1000 Monte Carlo runs (4 dB startingSNR)
Localization Times over Sensor Array Sizes Median
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Simulation Results
The Ainit of Form 2 degrades performance as more
sensor cooperation levels are added to a 32
sensor array.
The effect of increasing the number of sensors on
the localization time vs. SNR.
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Sensor Cooperation Comparison
Form 1
Form 3
Form 2
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Presentation Outline

• Biological Signal Processing
• Gradient Source Localization Algorithm
• Implementation of Gradient Source Localizer
• Proposed Research

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Implementation Issues

• Temperature vs. Chemical
• Hard to get non-drift, linear chemical sensors
  such temperature sensors are cheap
• Temperature and Chemical diffuse via Ficks 2nd
  Law

• Heat diffuses rapidly measured experimentally

• Sensor Bias and Quantization effects

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Circuit Diagram
Temperature Sensors
Sensor Standard Deviation 0.4C
Micro- controller
G. Rosen, M.T. Smith, and P. Hasler. IEEE
Sensors 2004.
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Setup
Heat Source (60/100-Watt Bulb)
Sensor interface up to 16 sensors
TC74 Sensors
HP Badge IV
Adding Turbulence
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Environmental Scenarios

• Diffusive
• Turbulent
• Turbulent and Noisy

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Diffusive Results
Localization of 100º
a) 4 sensors b) 8 sensors
Best performance is the Uniform Sc N-1.
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Turbulent
Localization of 100º
a) 4 sensors b) 8 sensors
Best performance is the Uniform 5-band
Best performance is the Uniform 3-band
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Turbulent and Noisy
Localization of 100º
a) 4 sensors b) 8 sensors

• All algorithms do well in Gaussian noise.
• The best is the Uniform Sc N/2-1.

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Algorithm Comparison
4-sensor statistics of the last 60 seconds of
data for each algorithm over each scenario.
BFE3 Equal-bands of 3 (Uniform) BFT3
Tapered-bands of 3

• Uniform (N/2-1)-banded best
• Tracks true mean with the smallest variance
• All algorithms perform well in additive
• Gaussian noise

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Presentation Outline
phdcomics.com
Improving localizer performance

• Biological Signal Processing
• Gradient Source Localization Algorithm
• Implementation of Gradient Source Localizer
• Proposed Research

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Work Proposed

• Algorithm Optimization Stationary Array and
  Adaptive Step-sizes
• Chemotaxis Models Excitation/Inhibition and
  Frequency Response
• Chemical Sensor Implementation
• Evaluation Criteria of Chemical Localizers

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Chemotaxis

• Frequency Information (Janata and Weisburg)
• Hypothesized that crabs use frequencies to
  localize
• Use array signal processing

Chemotaxis Pathways in E. Coli
von Karman Vortex Street

• Tumble/Run/Sensory Adaptation (Kirby)
• Excitation/inhibition models derived by
  biologists
• Parallel to EE models

C.V. Rao, J. R. Kirby, and A. P. Arkin, Design
and diversity in bacterial chemotaxis A
comparative study in escherichia coli and
bacillus subtilis, PLoS Biology, vol. 2, no.2,
February 2004.
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Chemical Sensor Implementation

• Effects of sensors
• Noise
• Nonlinear
• Environmental factors
• Turbulence and sensor measurements
• Turbulence introduced by a mobile setup

T. Kikas, H. Ishida, D. R. Webster, and J.
Janata, Chemical plume tracking. 1. chemical
information encoding, Analytical Chemistry, vol.
73, no. 15, pp. 36623668, August 2001.
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Audience Questions
Thank you for coming!
Gary Larson
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Publications

• G. L. Rosen and P. E. Hasler, Biologically-inspir
  ed odor localization using beamforming, in IEEE
  Workshop on Genomic Signal Processing and
  Statistics, May 2004.
• G. L. Rosen, M. T. Smith, and P. E. Hasler,
  Circuit implementation of a 2-d gradient source
  localizer, in 3rd IEEE Conference on Sensors,
  October 2004. 2nd place in Best Student Paper
  Competition