Identification of the location of nodes distributed in ad hoc networks
a technology of ad hoc networks and nodes, applied in the field of locating nodes in networks, can solve the problems of no such unanimously accepted indoor environment model, gps scales poorly in dense urban areas or indoor locations, and major sources of errors, so as to reduce the size of the minimum region of residence and minimize the size of the node's region of residen
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case 1
[0058] A line segment (arc) in Eu0, u1, . . . , uj−1uj is parallel to some line segment (arc) in Eu0, u1, . . . , uj−2uj−1 (for j>1) or in Ru0 (for j=1).
case 2
[0059] An arc in Eu0, u1, . . . , uj−1uj is i) not parallel to any arc in Eu0, u1, . . . , uj−2uj−1 (for j>1) or in R″ (for j=1), ii) but is an arc of a circle with radius ruj−1,uj having a center at one point on the region R′uj−1 which is the point of intersection of two different arcs or two different line segments or an arc and a line segment, at least one of which must be in Eu0, u1, . . . , uj−2uj−1 (for j>1) or in Ru0 for (j=1).
[0060]The above is illustrated in FIG. 6 where the arcs α and β on R′uj−1 and R′uj, respectively, are parallel to each other, while the arc γ on R′uj is derived from the point Q on R′uj−1 (with Q as center and having a radius equal to ruj−1,uj). It can also be seen from FIG. 6 that, for every point on R′uj, there exists a unique point on R′uj−1 from which this point was derived. Thus, for the point T on R′uj, the corresponding point on R′uj−1 is Q, which is transitively derived from a point P on Ru0.
[0061]Lemma 4: Let T be any point on Eu0, u1, . . . , ...
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