84 research outputs found
Vehicle path verification using wireless sensor networks
Path Verification is a problem where a verifier would like to determine how closely a vehicle actually traversed a path that it claims to have traversed. This problem has critical significances in terms of vehicle mobility. Mobile nodes can be patrols officers or cab drivers, while respective verifiers can be police dispatchers or cab operators. In this paper, we design a sensor network assisted technique for vehicle path verification. In our design, a number of static wireless sensors placed in road segments will serve as witnesses and certify vehicles as they move. Post movement, these witness certificates will be utilized by the verifier to derive the actual path of a suspect vehicle. The challenge now is how to compare a Claimed Path as reported by the vehicle and the Actual Path derived from witness certificates. In this paper, we design a simple, yet effective technique for comparing similarity between two vehicle paths. Our technique extends from Continuous Dynamic Time Warping, which involves constructing a universal manifold from the two paths and then finding the geodesic on the resulting polygonal surface (shortest path along the surface) which is a diagonal from the origin of the surface to the terminal point. This distance is analogous to the Fréchet distance and yields a good measure of the similarity between two paths. Using simulations and real experiments, we demonstrate the performance of our technique from the perspective of detecting false paths claims from correct ones. We also design light-weight cryptographic techniques to prevent vehicle masquerading and certificate forging attacks. A proof of concept experiment was conducted on the streets of Rolla, Missouri. A sensor grid was established on a small section of Rolla and a vehicle with a transmitter was driven through the grid many times. The analysis of the data yielded results consistent with the expected ones --Abstract, page iii
On the complexity of range searching among curves
Modern tracking technology has made the collection of large numbers of
densely sampled trajectories of moving objects widely available. We consider a
fundamental problem encountered when analysing such data: Given polygonal
curves in , preprocess into a data structure that answers
queries with a query curve and radius for the curves of that
have \Frechet distance at most to .
We initiate a comprehensive analysis of the space/query-time trade-off for
this data structuring problem. Our lower bounds imply that any data structure
in the pointer model model that achieves query time, where is
the output size, has to use roughly space in
the worst case, even if queries are mere points (for the discrete \Frechet
distance) or line segments (for the continuous \Frechet distance). More
importantly, we show that more complex queries and input curves lead to
additional logarithmic factors in the lower bound. Roughly speaking, the number
of logarithmic factors added is linear in the number of edges added to the
query and input curve complexity. This means that the space/query time
trade-off worsens by an exponential factor of input and query complexity. This
behaviour addresses an open question in the range searching literature: whether
it is possible to avoid the additional logarithmic factors in the space and
query time of a multilevel partition tree. We answer this question negatively.
On the positive side, we show we can build data structures for the \Frechet
distance by using semialgebraic range searching. Our solution for the discrete
\Frechet distance is in line with the lower bound, as the number of levels in
the data structure is , where denotes the maximal number of vertices
of a curve. For the continuous \Frechet distance, the number of levels
increases to
Pedestrian Dead-Reckoning Algorithms For Dual Foot-Mounted Inertial Sensors
This work proposes algorithms for reconstruction of closed-loop pedestrian
trajectories based on two foot-mounted inertial measurement units (IMU). The
first proposed algorithm allows calculation of a trajectory using measurements
from only one IMU. The second algorithm uses data from both foot-mounted IMUs
simultaneously. Both algorithms are based on the Kalman filter and the
assumption that while a foot is on the ground its velocity is supposed to be
zero. Two methods for comparing the obtained trajectories are proposed,
advantages and disadvantages of each method are indicated and a way to optimize
the computation time is presented. In addition, a method is proposed for
constructing one generalized trajectory of human motion based on the
trajectories of each leg.Comment: The data used in the article are available for downloading at
http://gartseev.ru/projects/mkins201
Four Soviets Walk the Dog-Improved Bounds for Computing the Fr\'echet Distance
Given two polygonal curves in the plane, there are many ways to define a
notion of similarity between them. One popular measure is the Fr\'echet
distance. Since it was proposed by Alt and Godau in 1992, many variants and
extensions have been studied. Nonetheless, even more than 20 years later, the
original algorithm by Alt and Godau for computing the Fr\'echet
distance remains the state of the art (here, denotes the number of edges on
each curve). This has led Helmut Alt to conjecture that the associated decision
problem is 3SUM-hard.
In recent work, Agarwal et al. show how to break the quadratic barrier for
the discrete version of the Fr\'echet distance, where one considers sequences
of points instead of polygonal curves. Building on their work, we give a
randomized algorithm to compute the Fr\'echet distance between two polygonal
curves in time on a pointer machine
and in time on a word RAM. Furthermore, we show that
there exists an algebraic decision tree for the decision problem of depth
, for some . We believe that this
reveals an intriguing new aspect of this well-studied problem. Finally, we show
how to obtain the first subquadratic algorithm for computing the weak Fr\'echet
distance on a word RAM.Comment: 34 pages, 15 figures. A preliminary version appeared in SODA 201
Four Soviets walk the dog, with an application to Alt's conjecture
Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One measure that is extremely popular is the Fréchet distance. Since it has been proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original O(n^2 log n) algorithm by Alt and Godau for computing the Fréchet distance remains the state of the art (here n denotes the number of vertices on each curve). This has led Helmut Alt to conjecture that the associated decision problem is 3SUM-hard.In recent work, Agarwal et al. show how to break the quadratic barrier for the discrete version of the Fréchet distance, where one considers sequences of points instead of polygonal curves. Building on their work, we give a randomized algorithm to compute the Fréchet distance between two polygonal curves in time O(n^2 \sqrt log n (log log n)^{3/2}) on a pointer machine and in time O(n^2 (log log n)^2) on a word RAM. Furthermore, we show that there exists an algebraic decision tree for the decision problem of depth O(n^{2¿}), for some ¿ > 0. This provides evidence that the decision problem may not be 3SUM-hard after all and reveals an intriguing new aspect of this well-studied problem
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