Optimised low complexity localisation in wireless sensor networks

Wireless sensor networks (WSNs) consist of many small (up to several hundred) low powered sensing nodes. These nodes can be capable of sensing temperature, humidity, light intensity etc. In location aware WSNs, these nodes aside from sensing environmental conditions, can also locate themselves, thus promoting many new applications in the wireless communications industry. These applications may include firefighter tracking, cattle/wild life monitoring and logistics. One way to locate the nodes is to use global positioning system (GPS), however deploying a GPS chip on every sensor node is expensive and also they are power hungry. Moreover, GPS assisted nodes can only be located when a guaranteed line of sight (LoS) is present with the navigational satellites. On the other hand, nodes can also be located using low complexity and cheap local positioning systems (LPS). Various techniques can be found in literature to locate wireless sensor nodes. Location algorithms, which are based on the absolute distance between nodes are known as range based algorithms. On the other hand, algorithms that do not require determination of the inter-node distance for localisation are called rangefree positioning algorithms. Range free algorithms are based on the number of hops for communications between two nodes as a distance metric. Range based algorithms are however more accurate than range free algorithms. In the context of range based algorithm, distance can be estimated between nodes by making use of the angle of the impinging signal, this technique is more commonly known as the angle of arrival (AoA) technique. Apart from being very sensitive to errors due to multipath, AoA is not favored for low complexity WSN localisation as an array of antennas or microphones is required on the sensor nodes to estimate the angle of the incoming signal. This increases the complexity and cost of the system. Absolute distance can be estimated using either the delay or attenuation of the signal. Systems capitalizing on the delay are more commonly known as time of arrival (ToA) systems. ToA localisation, although more accurate, requires highly accurate clocks and hence are high in complexity. On the other hand, received signal strength (RSS) based systems require no additional hardware and hence are more suitable for WSNs. For location estimation via RSS (and ToA) the so called trilateration technique is used. A number of nodes, usually high in resources and with known locations known as anchor nodes (AN) are used to estimate the locations of target nodes (TN). The location of ANs can be determined using GPS or they can be placed at predetermined positions. Readings from the TN is received at the ANs and are transmitted to a central station for processing. Due to its straightforward implementation, RSS has been an advantageous approach for low cost localisation systems such as WSN localisation. Thus a major part of this thesis focuses on RSS based localisation. The accuracy of location estimates via RSS is highly dependent on knowledge of the distance-power gradient or the so called path-loss exponent (PLE). Thus, degraded system performance is expected with an inaccurate PLE assumption. Although the propagation model is difficult to characterize in uncertain environments, the majority of current studies assume to have exact knowledge of the PLE. This is a gross oversimplification and hence this thesis looks into methods that considers the PLE as an unknown variable in addition to the location coordinates of the target sensor node. Thus the first part of this thesis deals with joint estimation of the PLE and location based on maximum likelihood (ML) and linear least squares (LLS) methods respectively. Error analysis of location estimates with incorrect PLE assumptions for both ML and LLS technique is done in their respective chapters. Furthermore, novel ideas such as assuming the PLE as an unknown random variable and development of a maximum a posteriori (MAP) estimator has also been discussed. While the hybrid Cramer Rao bound (CRB) is derived as benchmark for the MAP estimator. To further optimize the performance of the LLS technique, optimization such as optimal AN selection and weighted least squares (WLS) methods have also been proposed. Finally, a new linear CRB has been derived as a benchmark for the performance of the LLS. The second part looks into another aspect of localisation that impacts the location accuracy i.e. AN/TN geometry. It is well known that the accuracy of TN location estimation depends on its relative angle with the ANs. Thus the placement of ANs has an impact on location accuracy. Optimal AN positions are achieved that guarantees best accuracy for the entire network area via extensive simulation. This is done via choosing the placement of ANs that offers the minimum mean CRB. Finally, the impact of localisation error on upper layer applications i.e. routing of packets is studied. For location based routing, the fundamental assumption until recently was the absolute knowledge of the location of the forwarding nodes. This becomes unrealistic in localised networks and hence algorithms that are resilient to location error need to be developed. However, the first step is to recognise the impact of location on geographic routing parameters such as the packet delivery ratio (PDR) and loss rate (LR). Thus, via simulation, error analysis is done for location error induced by ToA and RSS localisation. Furthermore, an algorithm is developed that reduces the performance degradation due to location error. The ascendancy of the proposed algorithm is proven via simulation