NDLI: Least squares range difference location

Content Provider	IEEE Xplore Digital Library
Author	Schmidt, R.
Copyright Year	1965
Abstract	An array of n sensors at known locations receives the signal from an emitter whose location is desired. By measuring the time differences of arrival (TDOAs) between pairs of sensors, the range differences (RDs) are available and it becomes possible to compute the emitter location. Traditionally geometric solutions have been based on intersections of hyperbolic lines of position (LOPs). Each measured TDOA provides one hyperbolic LOP. In the absence of measurement noise, the RDs taken around any closed circuit of sensors add to zero. A bivector is introduced from exterior algebra such that when noise is present, the measured bivector of RDs is generally infeasible in that there does not correspond any actual emitter position exhibiting them. A circuital sum trivector is also introduced to represent the infeasibility; a null trivector implies a feasible RD bivector. A 2-step RD Emitter Location algorithm is proposed which exploits this implicit structure. Given the observed noisy RD bivector /spl Delta/, (1) calculate the nearest feasible RD bivector /spl Delta//spl circ/, and (2) calculate the nearest point to the (/sub 3//sup n/) planes of position, one for each of the triads of elements of /spl Delta//spl circ/. Both algorithmic steps are least squares (LS) and finite. Numerical comparisons in simulation show a substantial improvement in location error variances.
Starting Page	234
Ending Page	242
Page Count	9
File Size	151751
File Format	PDF
ISSN	00189251
Volume Number	32
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1996-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Least squares methods Sensor arrays Circuit noise Vectors Time measurement Noise measurement Position measurement Iterative algorithms Linear algebra Numerical simulation
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Aerospace Engineering

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