Adapting the Ranging Algorithm to the Positioning Technique in UWB Sensor Networks Mats Rydström, Erik G. Ström and Arne Svensson Dept. Signals and Systems Chalmers University of Technology Göteborg, Sweden Luca Reggiani Dip. Di Ellettronica ed Informazione Politechnico di Milano Milano, Italy

In this talk… Introduction and motivation –Measuring the distance of a wireless link –Two different positioning approaches A “soft” distance estimator Numerical results

Measuring distance If we know distances between transceivers, we can figure out their positions Propagation delay (a function of distance) can be found by correlating the received signal with a known transmitted signal The correlation is high when we have a signal component arriving at that time offset Will not give distance directly, since we need to account for unknown clock-offsets at both transmitter and receiver

Distance estimates will never be perfect… Chip-spaced sampling Noise (assumed Gaussian) Multi-path channels Which peak is the first signal component? Magnitude squared correlator output

A “classic” approach to positioning Obtain a model of measurements Find position by optimizing an objective function, e.g., ML Example: Local minima in the objective function Sensitive to outliers and poor covariance estimates

Positioning using projections onto convex sets (POCS) A distance estimate defines a disc (or sphere) in the space A difference of distances (TDOA) defines a hyperbola An uncertain angle defines a cone A room could define a rectangular area… etc. etc. POCS finds an estimate that lies in the intersection of the convex sets For k = 1, 2, … until convergence, iterate

“Circular” POCS pros and cons +No local minima problems, only the intersection of sets matter +Positive errors are discarded (NLOS!) +Low complexity –Affected by negative errors –Beacon convex hull

A “soft” distance estimator Different positioning approaches have different characteristics –POCS does not like negative errors –Other approaches do not care about error sign, but wants low variance, and perhaps few outliers An estimator that can be adapted to the positioning technique would be nice…

Not likely Could be LOS This one!

(2) is influenced by the MMSE estimator (3) is influenced by the ML estimator (4) is designed specifically for circular POCS (5) can be used to measure the ”quality” of estimates

Simulation set-up UWB-IR signaling (~500 MHz bandwidth) over IEEE a LDR channel models (CM1-CM9) Matched filter transceiver front-ends Varying preamble lengths, number of fixed beacons, and sensors LOS/NLOS channels drawn according to specified probabilities

Preamble length 16 Residential LOS (CM1) Four beacons (room corners), one sensor (room center)

Preamble length 32 Residential LOS (CM1) Four beacons (room corners), one sensor (room center)

Preamble length 32 CM1 / CM / beacons, 2 sensors Sensor often inside convex hull

Preamble length 32 CM1 / CM / beacons, 2 sensors Sensor often outside convex hull

Conclusions A ‘soft’ distance estimator was proposed and evaluated in an UWB- IR setting The different distance estimators behave robustly and as expected under different channel models and network parameters Circular POCS, together with the thresholded distance estimator, works well when sensors are located inside beacon convex hull. It does not need to know when links are NLOS Circular POCS performs especially well (compared to WLS) when we have many distance estimates, with a high NLOS percentage For scenarios with sensors outside beacon convex hull, a WLS approach performs better, but requires NLOS detection The performance of circular POCS in such scenarios can be increased if also hyperbolic sets are used in iterations

Thank you for listening! Contact: Mats Rydström,