Abstract
Continued advances in positioning technologies and mobile devices have increased the demand for location-based services (LBSs) in distributed sensor networks. Every LBS provider requires the sensor nodes to report their location information as the quality of service strongly depends on the information.
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Notes
- 1.
In this chapter, the set of points inside or on the circle \(C(O,r)\) is called the ball of center \(O\) and radius \(r\) and represented by \(B(O,r)\).
- 2.
The line segment between points \(A\in \mathbb {R}^2\) and \(B\in \mathbb {R}^2\) is represented by symbol \(\overline{AB}\).
- 3.
The line passing through points \(A,B\in \mathbb {R}^2\) is denoted by symbol \(\overleftrightarrow {AB}\).
- 4.
Permutation \(\pi \) on set \(M\) is a total, one-to-one function in the form \(\pi :\{1,2,\ldots ,|M|\}\mapsto M\) such that \(\pi _i\) denotes the member of \(M\) corresponding to integer \(i\le |M|\).
- 5.
Although it is possible that the three lines meet each other in one point, the probability of such event is zero. Henceforth, we do not consider such case.
- 6.
As the basic polygon is convex for every \(i\ge i_0\), its edges have at most two intersecting points with a straight line.
- 7.
Radius of the circumscribed circle.
- 8.
Running maximum \(M_t\) of the Brownian motion process \(B_t\) is a random process which has the following cumulative density function at the arbitrary time \(t>0\) (\(\sigma ^2\) represents the variance of process \(B_t\)): \(F_{M_t}(m)=\text{ erf }(\frac{m}{\sqrt{2t\sigma ^2}})\) for every \(m\ge 0\).
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Iyengar, S.S., Boroojeni, K.G., Balakrishnan, N. (2014). A Stochastic Preserving Scheme of Location Privacy. In: Mathematical Theories of Distributed Sensor Networks. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8420-3_6
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DOI: https://doi.org/10.1007/978-1-4419-8420-3_6
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