Project%20Course%20in%20Adaptive%20Signal%20Processing

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Project Course in Adaptive Signal Processing

• Acoustic Positioning

Daniel Aronsson
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Problem statement
We want to find the position of a microphone.
Measure travel times from fixed speakers to the
microphone. Based on these measurements,
calculate x,y,z for the microphone.
The speakers positions are known.
Initially we will use four speakers, but more can
be added for improved accuracy.
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Basic principle

• Let each speaker transmit a unique training
  sequence.
• Correlate the recorded signal with each training
  sequence to find the respective travel times.
• Each sequence should be as uncorrelated as
  possible with
• the other sequences
• itself for time lags other than zero

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Impact of training sequences
As a first attempt, we try using four different
tones
? good frequency resolution means bad time
resolution!
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Impact of training sequences
Instead, use wideband binary noise
? much better result!
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Finding the position

• Express measured distances in terms of z,y,z ?
  quadratic equations!
• Many solution methods, both numeric and
  analytic, but the method used need to be robust
  to imperfect measurements and noise.
• In the provided test code, I solve the problem
  by linearizations and iterations.

• Another, and better, idea is to use Extended
  Kalman Filtering (see next slide)

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Position tracking

• Noise in the range measurements can be suppressed
  by filtering. You may e.g. model each range
  measurement as a random walk plus noise.
• A better approach is to use an Extended Kalman
  Filter (EKF). Let x,y,z,t be the states and
  linearize the non-linear measurement equation.
  Using EKF makes the previous linearization
  obsolete.

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Problems

• Imprecise measurements
• EKF probably works well, but additional
  algorithms for discarding bad measurements might
  be needed.
• Potential non-line-of-sight
• Use many parallel filter, each measuring a unique
  subset if ranges, and keep only the best
  estimate?
• Moving microphone
• In the present code, the microphone need to be
  still during measurements.
• Reverberation
• Measure speaker impulse responses and
  deconvolute?

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Problems

• The near-far problem
• Speakers near the microphone become too dominant.
  Implement an algorithm that adjusts the speakers
  volumes (a crude algorithm is already
  implemented).
• Simultaneous training sequences
• Training sequences currently need to be
  transmitted one by one. Implement simultaneous
  training.
• Continuous training?

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References

• Atomic Clock Augmentation For Receivers Using
  the Global Positioning System, Paul A. Kline,
  PhD dissertation
• Basics of the GPS Technique Observation
  Equations, Geoffrey Blewitt
• Audio Signal Processing for Next Generation
  Multimedia Communication Systems, Yiteng Huang,
  Jacob Benesty, and Gary W. Elko, Kluwer 2004