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**Table of contents**

- Samenvatting
- Hierarchical Voronoi Graphs - Spatial Representation and Reasoning for Mobile Robots
- Hierarchical Voronoi Graphs
- Jan Oliver Wallgrün - Google Scholar Citations

### Samenvatting

Since the Voronoi-based route graph still reflects irrelevant features of the environment, our proposed representation is a hierarchical structure consisting of route graph layers representing the environment at different levels of granularity. It is shown how the more abstract layers can be derived from the original route graph by using relevance measures to assess the significance of the vertices. We provide examples of how planning, spatial reasoning, and communication can benefit from this kind of representation. Documents: Advanced Search Include Citations.

Citations: 7 - 0 self. However, only orthogonal frequency division multiplexing OFDM -based wireless systems can extract the CSI because they use multiple subcarriers for data transmission; other modulation schemes such as direct sequence spread spectrum cannot provide this value. Trajectory tracking methods that make use of real-time acceleration information to track an object are described in [ 11 ].

A future position of an object can be inferred from knowledge of its present position, speed and real-time acceleration information. To measure acceleration and speed in real time, acceleration sensors and gyroscopes are used in robots or aircrafts. However, without real-time calibration in indoor environments, this method results in large accumulated errors. Trajectory tracking based on consecutive object recognition in videos has been one of the most active research topics in recent decades, particularly in the field of machine vision [ 12 ]. Visual tracking remains a challenging problem due to many factors, e.

This algorithm has robust performance due to the hierarchical nature of its object representation. However, this method requires special video capture infrastructure; consequently, it is impractical in WSNs. The continuous position fingerprint of a single object over time must correspond to its adjacent position in space.

This spatiotemporal correlation can be regarded as a constraint in the trajectory tracking procedure. Some heuristic information can be mined in conjunction with the deployment of reference nodes. The heuristic information of an RSSI time series includes some key factors for the trajectory tracking procedure. This study aims to design a novel trajectory tracking scheme that mines heuristic information to improve the accuracy of trajectory tracking.

In this paper, the position of a moving node on the boundary is determined according to the change tendency of RSSI , and the moving trajectory is determined according to the RSSI time series. TTDH combines range free localization algorithms with position fingerprint localization algorithms. Algorithms that extract heuristic information from RSSI time series are designed.

Heuristic information includes some key factors for the trajectory tracking procedure. The principle of heuristic information is strictly proven mathematically. The temporal information and spatial information in WSNs are fully utilized to mine the heuristic information. The moving trajectory of an object is formed by means of a dynamic time-warping-position-fingerprint-matching algorithm with heuristic information constraints.

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TTDH has a good robustness, and that error does not accumulate among the regions. Field experiments show that the average error distance of the tracked trajectory is less than 1. The rest of this paper is organized as follows. Section 2 first provides some related background information. Section 3 presents the TTDH scheme and the algorithm design.

In Section 4 , we provide the results of experiments and a discussion. Finally, we present conclusions in Section 5. Trajectory tracking is a continuous localization process. A conventional trajectory tracking method first locates an object and then forms a trajectory using moving-object data-mining techniques. This section introduces the basic theory of Delaunay triangulation.

We propose and prove the peak phenomenon on the boundary. Then, the approximate point in the triangulation APIT test principle is introduced to determine sequential triangular regions. After the nodes are deployed at random, using a Voronoi diagram, a two-dimensional localization plane is partitioned into Voronoi cells see Figure 1.

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A Voronoi cell is a region enclosed by real lines. An unknown node must belong to a Voronoi cell whose center is the nearest among all reference nodes. That is,. Delaunay triangulation is the dual graph of a Voronoi diagram.

## Hierarchical Voronoi Graphs - Spatial Representation and Reasoning for Mobile Robots

For example, Wu et al. Calculation of a Delaunay triangulation requires global information, namely, the exact positions of all the reference nodes in the WSN. As discussed above, RSSI measurements are easily affected by various factors. Our scheme mines some heuristic information, which reveals the spatiotemporal correlation in conjunction with the process of trajectory tracking. Based on the excellent features of Delaunay triangulation, a common side is a line segment between the two closest reference nodes. Our scheme considers a common side as a boundary between two adjacent triangular regions.

As an unknown node moves continuously, it will pass through every triangle along its moving trajectory; therefore, it will cross over the common side between adjacent triangles. As shown in Figure 2 , the common side j 1 j 2 must intersect with the moving trajectory. For example, assume that j 1 j 2 is a common side that represents a boundary. R b represents the RSSI time series related to boundary j 1 j 2. The time series element r b k is the mean of r j 1 k and r j 2 k , and k is the k th element.

As an unknown node gradually approaches, intersects, and moves away from the common side, R b will increase during the approach phase and decrease during the departing phase. These changes tend to coincide with the wireless signal transmission model. Provided there is no noise, the maximal value of R b will be located at the intersection between boundary j 1 j 2 and the moving trajectory.

## Hierarchical Voronoi Graphs

As shown in Figure 2 , boundary j 1 j 2 could be in an arbitrary direction. We first rotate and translate the coordinates to ensure that boundary j 1 j 2 is vertical. P k represents the k th position related to boundary j 1 j 2 time series R b. There are several wireless signal transmission models, including the free-space propagation model, the Rayleigh fading model and the logarithmic shadowing model.

## Jan Oliver Wallgrün - Google Scholar Citations

The logarithmic shadowing model considers the factors mentioned above synthetically and is both simpler and more accurate than other models in indoor environments [ 20 ]. We adopt this model for further discussion. The relationship between the RSSI and propagation distance can be described as follows:. R d 0 represents the RSSI at the reference node whose propagation distance is d 0.

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P d mw represents the mean received signal power related to the propagation distance d , and P d 0 represents the mean received signal power at the reference node whose propagation distance is d 0. As shown in Figure 3 , q is the length of boundary j 1 j 2. In view of this real problem, r b k will achieve its maximal value only at the stationary point, and this stationary point must be on boundary j 1 j 2.

The phenomenon illustrates a definite change tendency about R b.

The maximal value could occur at a small deviation relative to boundary j 1 j 2 due to discrete RSSI measurement errors. We will discuss this problem further in Section 4. Without loss of generality, the deployment of reference nodes can be eligible. The approximate point in the triangulation APIT [ 21 , 22 ] localization method is a typical range-free localization scheme and is widely used for position estimation in WSNs because of its robustness to irregular wireless transmission models and random node distributions.

We first introduce PIT. As shown in Figure 4 a, many triangular regions are formed by reference nodes.