• Neighborhood Measurement
– The radio connectivity measurement can be considered
economic since no extra hardware is needed. Perhaps the most basic positioning technique is that of one neighbor proximity, involving a simple decision of whether two nodes are within the reception range of each other.
– A set of reference nodes is placed in the network with some non-overlapping sub-regions. Reference nodes periodically emit
beacons including their location IDs. Unknown nodes use the received locations as their own location, achieving a course-grained localization. The major advantage of such a neighbor proximity approach is the simplicity of computation.
定位机制研究（Localization）
• Neighborhood Measurement
– The neighborhood information can be more useful when the density of reference nodes is sufficiently high so that there are often multiple
reference nodes within the range of an unknown node.
– Let there be k reference nodes
within the proximity of the unknown node. We use the centroid of the
polygon constructed by the k reference nodes as the estimated position of the unknown node.
定位机制研究（Localization）
• Comparative Study of Physical Measurements
定位机制研究（Localization）
• Network-Wide Localization
• Centralized algorithms
– Centralized algorithms are designed to run on a central machine with powerful computational capabilities. Network nodes collect environmental data and send back to a base station for analysis, after which the computed positions are delivered back into the network.
– Centralized algorithms resolve the computational limitations of nodes. This benefit, however, comes from accepting the
communication cost of transmitting data back to a base station.
Unfortunately, communication generally consumes more energy than computation in existing network hardware platforms.
定位机制研究（Localization）
• Centralized localization
• (a) Multi-Dimensional Scaling (MDS)
– The intuition behind MDS is straightforward. Suppose there are n points, suspended in a volume. We do not know the positions of the points, but we know the distances between each pair of points.
– MDS is an O(n3) algorithm that uses the law of cosines and linear algebra to reconstruct the relative positions of the points based on the pairwise distances.
定位机制研究（Localization）
• Centralized localization
• (b) SemiDefinite Programming (SDP)
– In SDP, geometric constraints between nodes are represented as linear matrix inequalities (LMIs). Once all the constraints in the network are expressed in this form, the LMIs can be combined to form a single semi-definite program, which is solved to produce a bounding region for each node.
– The advantage of SDP is its elegance on concise problem
formulation, clear model representation, and elegant mathematic solution.
– Solving the linear or semi-definite program has to be done centrally.
定位机制研究（Localization）
• Network-Wide Localization
• Distributed algorithms
– Distributed algorithms are designed to run in network, using massive parallelism and inter-node communication to
compensate for the lack of centralized computing power, while at the same time to reduce the expensive node-to-sink
communications.
– Distributed algorithms often use a subset of the data to locate each node independently, yielding an approximation of a
corresponding centralized algorithm where all the data are considered and used to compute the positions of all nodes simultaneously.
定位机制研究（Localization）
• Distributed algorithms
• (a)Beacon Based Localization (Top-down approach)
– Beacon based localization approaches utilize estimates of distances to reference nodes that may be several hops away.
These distances are propagated from reference nodes to
unknown nodes using a basic distance-vector technique. Such a mechanism can be seen as a top-down manner due to the
progressive propagation of location information from beacons to an entire network. There are three types as follows.
– 1) DV-hop: Each unknown node determines its distance from various reference nodes by multiplying the least number of hops to the reference nodes with an estimated average distance per hop that depends upon the network density.
定位机制研究（Localization）
• (a)Beacon Based Localization (Top-down approach)
– 2) DV distance: If inter-node distance estimates are directly available for each link in the graph, the distance-vector
algorithm is used to determine the distance corresponding to the shortest distance path between the unknown nodes and reference nodes.
– 3) Iterative localization: One variant of above approaches is indirect use of beacon nodes. Initially an unknown node is located based on its neighbors by multilateration or other positioning techniques. After being aware of its location, it
becomes a reference node to localize other unknown nodes in the subsequent localization process. This step continues iteratively, gradually turning the unknown nodes to the known.
定位机制研究（Localization）
• (a)Beacon Based Localization (Top-down approach)
– The process of iterative localization is illustrated as follows:
– Iterative trilateration only involves local information
(information within neighborhood) and accordingly reduces
communication cost. Nevertheless, the use of localized unknown nodes as reference nodes inherently introduces substantial
cumulative error.
定位机制研究（Localization）
• Distributed algorithms
• (b) Coordinate System Stitching
– It works in a bottom-up manner, in which localization is
originated in a local group of nodes in relative coordinates.
By gradually merging such local maps, it finally achieves entire network localization in global coordinates, as illustrated in the following figure.
定位机制研究（Localization）
• Comparative Study of Localization Algorithms
• (a) Beacon Nodes
– Higher localization accuracy can be achieved if beacons are placed in a convex hull around the network.
– Placing additional beacons in the center of the network is also helpful.
– Thus, it is necessary for system designers to plan the beacon layout before deploying a network.
• (b) Node Density
– Algorithms that depend on beacon nodes fail when the beacon density is not sufficiently high in a specific region.
– Thus when designing or analyzing an algorithm, it is important to consider its requirement on node density, since high density may not be always true.
定位机制研究（Localization）
• Comparative Study of Localization Algorithms
• (c) Accuracy
– Location accuracy is defined as the expected Euclidean distance between the location estimate and the actual location of an
unknown node, while location precision indicates the percentage of the results satisfying a pre-defined accuracy requirement.
– For a given localization result, location accuracy trades off with location precision. If we relax the accuracy requirement, we can increase precision, and vice versa.
– The error propagation demonstrates how location accuracy varies with the increase of measurement error. Intuitively,
localization error is linear with measurement error. However, it is not true for many localization systems.
定位机制研究（Localization）
• Comparative Study of Localization Algorithms
• (d) Cost
– In general, the cost of a localization system includes hardware cost and energy cost.
– Hardware cost consists of three parts: node density, beacon density, and measurement equipment.
– A localization procedure often involves inter-node measurement, computation and communication, among which communication consumes most energy. This is why distributed algorithms are often more compelling than centralized algorithms.
定位机制研究（Localization）
• Comparative Study of Localization Algorithms
• All approaches have their own merits and drawbacks, making them suitable for different applications.
• Hence, the design of a localization algorithm should sufficiently investigate application properties, as well as take into account algorithm generality and flexibility.
• In future study, obtaining a Pareto improvement is a major challenge.
That is, increasing the performance of one of the metrics without degradation on others.