The positioning technique is the key technique for developing geographic applications, like location based services. The Global Positioning System (GPS) is a common approach for positioning in vehicular navigations. Although GPS can provide absolute position information, the accuracy of GPS is not enough for personal navigations. What is worse, GPS does not work well indoors. Instead, Inertial Measurement Units (IMUs) can be used to track objects with high precision, but it provides relative position information. Thus, integration of GPS and IMU can do positioning indoors and outdoors. In this paper, combining our previous work, a pedestrian tracking system for handheld devices, with GPS leads to a personal navigation system for handheld devices. The position and heading information can be calculated from this system. The system also serves a platform for many applications related to the location.

In wireless ad hoc networks, relative neighborhood graphs (RNGs) are widely used for topology control. If every node has the same transmission radius, then an RNG can be locally constructed by using only one hop information if the transmission radius is set no less than the largest edge length of the RNG. The largest RNG edge length is called the critical transmission radius for the RNG. In this paper, we consider the RNG over a Poisson point process with mean density in a unit-area disk. Let 0 = √ 1/ (2 3 − √ 3 2) ≈ 1.6. We show that the largest RNG edge length is asymptotically almost surely at most √ ln for any fixed > 0 and at least √ ln for any fixed < 0. This implies that the threshold width of the critical transmission radius is (√ ln). In addition, we also prove that for any constant , the expected number of RNG edges whose lengths are not less than 0 √ ln + is asymptotically equal to 0 2 2 −. Index Terms-Wireless ad hoc networks, relative neighborhood graphs, critical transmission radii, Poisson point processes, thresholds.

In most inertial motion tracking systems, motion directions are detected and measured by direction sensors such as magnetometers and gyroscopes. In this paper, we propose a motion tracking system, called g-sensor constellations, in which only g-sensors but no direction sensors are used. The g-sensor constellation is a loose coupling g-sensor system with rigid geometric topology. As few as three g-sensors are needed for motion tracking, including direction detection. The system is easy to be installed. No complicated calibrations are needed and the necessary information is the distances between sensors. The proposed framework can improve the accuracy of dead reckoning systems and help in the analyzing of traffic accidents and developing new human-computer interfaces. In our experiments, a g-sensor constellation composed of three g-sensors, which are located at the vertices of an equilateral triangle with edges of 0.3m and communicate with the processing unit via Bluetooth links, is built to verify the proposed technique.

A wireless node is called isolated if it has no links to other nodes. The number of isolated nodes in a wireless network is an important connectivity index. However, most previous works on analytically determining the number of isolated nodes were not based on practical channel models. In this work, we study this problem using a generic probabilistic channel model that can capture the behaviors of the most widely used channel models, including the disk graph model, the Bernoulli link model, the Gaussian white noise model, the Rayleigh fading model, and the Nakagami fading model. We derive the expected number of isolated nodes and further prove that their distribution asymptotically follows a Poisson distribution. We also conjecture that the nonexistence of isolated nodes asymptotically implies the connectivity of the network, and that the probability of connectivity follows the Gumbel function.