The localization schemes that use reference nodes can be classified into two main categories: range-based schemes and range-free schemes. Range-based schemes mainly consist of two
basic phases: distance (or angle) estimation and distance (or angle) combining. Distance estimation handles how to estimate the distance or angle between two nodes. In the distance combining phase, this information is combined to derive the locations of unresolved nodes.
The most commonly used methods in distance estimation include received signal strength indicator (RSSI), time based methods (ToA, TDoA), and the angle-of-arrival (AoA) tech- nique [102]. RSSI measures the power of a signal at the receiver and derives the distance between the sender and receiver, based on the known transmission power and propagation model. Time based methods record the time of arrival (ToA) or time difference of arrival (TDoA) and translate it directly into the distance based on the known signal propagation speed. ToA and TDoA are used at GPS [103] and Cricket [104] for distance estimation. In the work described in [105], it is shown these location estimation problems can be solved by measuring the received signal strength from just one or two anchors in a two dimensional plane with directional antennas. If the antennas of a target sensor node are aligned, then the power received by multiple receiving antennas of the target from a single transmitting an- tenna on an anchor can be used to estimate the position of the target sensor node. Otherwise, received power at two different antennas of the target node from two transmitting antennas of one anchor node can be used for location discovery. The power received at antennas from two different anchor nodes using uncorrelated channels can be used to improve the location estimation accuracy. In these schemes, it is assumed that anchor nodes can talk to all other nodes in the network. Therefore, one node can estimate its location by communicating with anchor nodes directly.
Distributed positioning algorithms, in contrast, do not assume anchor nodes can talk to all other nodes in the network. In distributed positioning schemes, a small set of anchors randomly distributed over the network starts the location discovery process by communi- cating to immediate neighboring nodes. A sensor node, upon receiving messages from its neighboring nodes, computes the distance or angle between them and derives its own loca- tion from this information. After a node successfully estimates its own position, it becomes an anchor node and continues the location discovery process by sending messages to its neighboring nodes. The process continues until all nodes resolve their locations or no more sensor nodes can resolve their locations. In the distance combining phase, multi-lateration
techniques, such as atomic, collaborative and iterative multi-lateration, can be used to esti- mate sensor nodes’ location [106]. The N-Hop Multi-lateration scheme [107] discusses the conditions under which one-hop, two-hop and n-hop multi-lateration can uniquely determine nodes’ locations. Obviously, for successful one-hop multi-lateration, an unknown node must be neighbor to at least three nodes whose positions are known. In addition, it is necessary for an unknown node to use at least one reference point that is not collinear with the rest of its reference points in order to uniquely determine its location. Similar conditions are also defined for two-hop and n-hop multi-lateration. The Ad-hoc Positioning System (APS) [108] uses four different distance metrics, ranging from minimum hop count and sum of hop lengths to local geometric constructions to locate nodes in the network. A variant of APS utilizes angle-of-arrival of signals received from anchor nodes for location estimation [109]. These schemes rely on a high level of network connectivity so that each node can gain sufficient information in the distance combining phase for location estimation. Furthermore, a high percentage of anchor nodes must exist to achieve a small location error at each sensor node. The schemes presented in [110][111][112] use mobile beacons whose locations are always known to help location discovery in terrestrial sensor networks. The mobile beacon nodes traverse the sensor network and disseminate their locations to other nodes in the network. A sensor node keeps track of location of and distance to the mobile beacon when it is moving. This information can then be used to derive the unknown sensors’ location. Apparently, the trajectory of the mobile beacon and when the mobile beacon sends packets to other nodes are critical to the location discovery scheme. It is shown that all sensors can estimate their location as long as the trajectory of the beacon covers the entire deployment area in such a way that each point receives at least three non-collinear beacon messages [110]. In [111], a mobile user is used to collect inter-node distances between sensors and the mobile user. A movement strategy is carefully designed so that the collected distances can produce a globally rigid structure of known distances among the sensors in the network. In the perpendicular intersection scheme presented in [112], a sensor node keeps measuring received signal strength from a mobile beacon which moves in a specially designed trajectory. It is known the received signal strength depends on the distance between the sending sensor and receiving sensor, and reaches the highest value when the sender and receiver are closest to each other. When the
mobile beacon moves along a straight line, a sensor node receives the strongest signal when the line between the sensor node and mobile beacon is perpendicular with the trajectory line of the mobile beacon. By not directly mapping distance from signal strength, which usually introduces inaccuracy in distance estimation due to noise, the scheme can achieve high accuracy for location estimation in sensor networks.
Range free localization schemes, such as [113][114][115][116] do not use range or bearing information for location estimation purposes. As a result, these schemes are generally simpler than range-based schemes. However, on the other hand, these schemes only provide a coarse estimation of a sensor node’s location.
DV-Hop [113] employs a classical distance vector exchange protocol to maintain a node’s distance in terms of hops to all anchor nodes. The hop distance is translated into physical distance after an average distance per hop is estimated based on the hop distance and geographical distance among anchor nodes. The estimated distance to anchor nodes are then used to perform triangulation at each node for location estimation. The DV-Hop algorithm performs well only in networks that have uniform and dense node distribution.
A variant of DV-Hop, Density-aware Hop-count Localization (DHL) have been pro- posed to improve the accuracy of location estimation when the node distribution is not uniform [114]. DHL incorporates density of a node’s neighborhood into the average hop distance estimation. Consequently, it can estimate a more accurate location of sensor nodes than DV-Hop in real deployment scenarios of sensor networks.
Area Localization Scheme (ALS) [115] locates sensor nodes into a certain area instead of an exact coordinate. Each anchor node sends out beacon signals at a set of predefined power levels. The sensors measure the lowest power level that they can receive from each anchor node. The information is then synthesized into an n-dimensional coordinate, where ith coordinate represents the lowest power level from the ithanchor node. The granularity of
the scheme depends on the interval of power levels each anchor is configured at to broadcast its beacon signals.
Approximate Point In Triangle (APIT) [116] uses RSSI of beacon signals received from anchor nodes to determine if a sensor node is inside a given triangle. The APIT tests are carried out with all different combinations of audible anchor nodes. The test results are then
aggregated together and the location is estimated as the center of gravity of the intersections of all these triangles. This scheme requires a large level of node density to achieve a good level of accuracy of location estimation.
Several other schemes have been proposed to ensure robust location estimation against range estimation errors or erroneous reference information [117][118][119], to reduce the number of beacon signals needing to be used for location discovery [120], or to reduce location measurement error cumulation [121]. The localization problem in sparse networks has also drawn interest from researchers recently. In [122][123], the conditions for unique localization in networks are studied and used to identify all the localizable nodes in partially localizable networks to prevent flawed location estimations. Furthermore, a special class of sparse network, bilateration network, is investigated in [124]. The finite possible location sets of nodes are derived sequentially and some particular edges in the network are then used to sweep location possibilities. It is shown that nodes in a bilateration network can be finitely localized using the proposed scheme.