2. Project Course in Adaptive Signal Processing Acoustic Positioning Daniel Aronsson

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

4. 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

5. Impact of training sequences As a first attempt, we try using four different tones: → good frequency resolution means bad time resolution!

6. Impact of training sequences Instead, use wideband binary noise: → much better result!

7. 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)

8. 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.

9. 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?

10. 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?

11. 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