Localization Algorithms

In WSNs, the localization algorithm has been categorized into different cate- gories based on the limited resource and application requirements. A list of such categories for localization algorithms is listed below [65].

• Single-hop or Multi-hop localization:

A direct communication link between two nodes is commonly referred to as a hop. Networks where there is only a single link between nodes for location purposes are called single-hop. GPS is an example of a single-hop positioning systems. On the other hand, if the node that is desired to be localized is out of range of an anchor or BS, a communication link using intermediate nodes is established, this is known as multi-hop. Single hop algorithms are simple and accurate but are not scalable, multi-hop algo- rithms are more scalable due to their distributed nature. The problem of scalability in single-hop localization can be minimized by the cooperative localization, where to cover the entire field (i.e. subject nodes), localized nodes can behave as the pseudo-anchor nodes. This scheme is further dis- cussed and analysed in chapter 4.

• Centralized or Distributed Algorithms:

Centralized algorithms [12, 48, 66] are based on the central unit, which collects, process and sent back the processed data in a centralized manner. In such algorithms, the major problem is the scalability, intrinsic delay, however the accuracy stay better as they are less prone to error propa- gation but inefficiency increases as the network size increases, hence more communication cost and intrinsic delay.

On the other hand, distributed systems [49,67,68] can allow the processing to be performed at each node. Generally, distributed algorithms are more robust and energy capable since each node determines its position under the infrastructure (anchor based) or infrastructure less (connectivity based) networks, without the requirement of sending and receiving location infor- mation to and from a centralized unit. However, distributed algorithms are more complicated to implement due to the limited computational capabil- ities of sensor nodes. Distributed solutions tend to distribute and increase the error, cumulatively. This is because in multi-hop execution, there can be a considerable number of subject nodes that cannot directly communi- cate with any anchor node [65] and accumulate error while being localized using pseudo-anchor nodes in a cooperative way.

• With Infrastructure or Without Infrastructure:

Further classification of localization is based on the systems with infras- tructure and without infrastructure. Infrastructure based systems are those which are based on the anchor nodes (aka reference nodes). Anchor nodes are the special capability nodes who know their position usually either through a GPS receiver installed on them or through pre-programmed con- figuration. Other unknown subject nodes use these anchor nodes to cal- culate the location. One of the common examples of infrastructure based system is GPS. One of the most important factors to consider in infrastruc- ture based networks is the anchors geometry, which strongly affect the qual- ity of the localization. In GPS community, this problem has been studied extensively with respect to the Geometric Dilution of Precision (GDOP) [30–32, 35] metric but extendible to any range based localization system [55]. However, in the context of the WSN, GDOP study has been limited [69–71]. GDOP metric along with the lateration schemes is analyse thor- oughly in chapter 4. In [42] it is concluded that the one-hop distance-based localization mechanism has geometry as its foundation. However, the analy- sis was limited to 2-D as well as Cram´er-Rao lower bound (CRLB) metric is only used at different angles just to analyse the impact of 3 anchors geome- try on localization accuracy [42, 43]. Furthermore, the analysis was limited to the additive noise model and no optimal placement is suggested. A marginal degree of research has been done on optimal anchor placement. In [72,73], the authors obtained an analytical solution for the optimal anchor placement based on the CRLB. Where authors achieve optimality condition for 3 and 4 anchors only. The relation between lower bound and the Fisher Information Matrix (FIM) is given as (2.1):

σ2(ˆ_{s) ≥ [I(s)]}−1

jj (2.1)

where σ2_{(ˆs) can be given as σ}2_{(ˆs) = E(ˆs}

j − sj)(ˆsj − sj)T , (I(s)−1)jj is

the lower bound on the variance of (ˆs) and I(s) is the (FIM) and is defined as [72]: I(s) =       N X i=1 cos2_(α ij) σ2 ij N X i=1 cos(αij) sin(αij) σ2 ij N X i=1 cos(αij) sin(αij) σ2 ij N X i=1 sin2(αij) σ2 ij       (2.2)

Minimizing the inverse of the FIM is equivalent to maximizing its determi- nant. The determinant is given as:

det [I(s)] = 1 4σij " N2_{− (} N X i=1 cos(2αij))2− ( N X i=1 sin(2αij))2 # (2.3)

The upper bound can be bounded by _4σN22

ij, which is only achieved when:

N X i=1 cos(2αij) = 0, N X i=1 sin(2αij) = 0 (2.4)

As a consequence, the optimal anchor placement for 3 and 4 anchors is obtained if:

βij = βij =

2

Nπ (2.5)

where N is the number of anchors and βij is the angle subtended at the

MSE) for 3 and 4 anchors, each anchor should subtended the same angle on the target. For N > 5 anchors, the optimal anchor geometry is not unique. Furthermore, in both [72,73], the authors limited the analytical and simulation to 3 and 4 anchors with their own choice, i.e. without exploiting all possible combinations. The same approach is applied to TDoA [72] and RSS [74].

Without Infrastructure:

On the other hand, infrastructures less networks are those, which are with- out the anchor nodes. The communication in such systems is based on the connectivity with in-range nodes; hence they provide the location of sensor node relative to neighbour nodes. The nodes in the infrastructure less systems show more complexity due to the fact that each node has to communicate in hop count manner, hence nodes are required to have some way to access, prioritize the sequence of communication in order to provide quality of service (QoS).

• Range based or range free:

Range based approaches are discussed above under the process of range estimation phase in section 2.3.1, whereas range free approach is discussed below:

This course of localization systems is cost effective because it eliminates the need of high cost specialized hardware on each sensor node. The cal- culation in these systems is based on the radio connectivity information among neighbouring nodes and sensing capabilities (as they use the num- ber of hops between a node pair as a distance metric) that each sensor node posses [10, 56, 65]. One of the main problems with range-free localization is that, this type of localization is suitable for relative location instead of absolute location tracking. Example of range free localization schemes are approximate point in triangulation (APIT) [75], Secure Range-Independent Localization for Wireless Sensor Networks (SeRLoc) [76]. The accuracy of range-free methods is less than the range-based ones but they satisfy the requirements for many applications. Because of the hardware limitations of WSN devices, solutions in range-free localization are being pursued as a

simple and cost-effective alternative to range-based approaches. The most obvious disadvantage of this scheme is the fact that it performs poorly [65].