We derive the posterior Cramér–Rao bound (PCRB) for tracking in anchorless dynamic networks consisting of static nodes at unknown locations and mobile nodes. We show that this is a type of PCRB under parametric constraints where the parameter space cannot be modeled by equation constraints. We propose a novel framework for modeling the constrained parameter manifold, as a factor manifold under the actions of a group. The approach we propose is generic, and can be used to derive lower error bounds for other parameter estimation problems where the parametric constraints cannot be optimally described by equation constraints.

The utility of wireless networks for many applications is increased if the locations of the nodes in the network can be tracked based on the measurements between communicating nodes. Many applications, such as tracking fire fighters in large buildings, require the deployment of mobile ad hoc networks. Real-time tracking in such environments is a challenging task, particularly combined with restrictions on computational and communication resources in mobile devices. In this paper, we present a new algorithm using the Bayesian framework for cooperative tracking of nodes, which allows accurate tracking over large areas using only a small number of anchor nodes. The proposed algorithm requires lower computational and communication resources than existing algorithms. Simulation results show that the algorithm performs well with the tracking error being close to the posterior Cramer-Rao lower bound that we derive for cooperative tracking. Experimental results for a network deployed in an indoor office environment with external global position system-referenced anchor nodes are presented. A computationally simple indoor range error model for measurements at the 5.8-GHz ISM band that yields positioning accuracy close to that obtained when using the actual range error distribution is also presented.

Location tracking is being increasingly used across many applications. While GPS is the most widely used location tracking technology, it is unavailable in many environments such as indoors and underground. Local positioning systems (LPS) that use time of arrival based ranging can provide high accuracy location tracking for many applications. Tracking location using range measurements is a non-linear state estimation problem and the measurement noise is often non-Gaussian in environments where LPS are typically used. Hence a particle filter is an appropriate state estimator for location tracking in LPS. Particle filters are computationally complex and have a serial bottleneck that prevents straightforward parallel implementation. In this paper we present a parallel architecture for the particle filter that can be efficiently implemented in a field programmable gate array or a fixed-point digital signal processor. We show that processing can be divided into up to twenty parallel particle filters to massively increase the processing speed. Mixing between the filters is essential and we present a new algorithm for this that minimises computational complexity and memory bandwidth. Finally, for efficient hardware implementation fixed point arithmetic should be used and we empirically determine the required precision.

This paper presents a method of determining the statistical positional accuracy of a moving object being tracked by any 2D (but particularly radiolocation) positioning system without requiring a more accurate reference system. Commonly for testing performance only static positional errors are measured, but typically for radiolocation systems the positional performance is significantly different for moving objects compared with stationary objects. When only the overall statistical performance is required, the paper describes a measurement technique based on determining 1D cross-track errors from a nominal path, and then using this data set to determine the overall 2D positional error statistics. Comparison with simulated data shows that the method has good accuracy. The method is also tested with vehicle tracking in a city and people tracking within a building. For the indoor case, static and dynamic measurements allowed the degrading effect of body-worn devices due to signal blockage to be determined. Error modeling is also performed and a Rayleigh-Gamma model is proposed to describe the radial positional errors. It is shown that this model has a good match with both indoor and outdoor field measurements.

We present a new method for anchorless localization of mobile nodes in wireless networks using only measured distances between pairs of nodes. The novelty of the algorithm lies in the method to complete the Euclidean distance matrix by inferring the unknown distances such as to align all nodes on a k-hyperplane, where typically k is 2 or 3. The relative locations of the nodes are then computed using multidimensional scaling. We also present experimental results with data collected using our WASP platform to verify the improvement in localization using our algorithm over previously published techniques.

Tracking nodes in a wireless network is beneficial for many applications. This is, however, a challenging task in multihop networks, particularly when combined with the limitations in processing power and communication capability of the nodes. The task is further complicated when rapid deployment of the network is required. In this paper we present a new algorithm for cooperative tracking of nodes, which allows accurate tracking over large indoor areas using only a small number of anchor nodes. The proposed algorithm is based on the multiple model particle filter and addresses several tracking issues not previously addressed in the literature. Further, we present a new indoor ranging error model based on our measurements that is simple, yet widely applicable, and gives much better localization accuracy compared to the standard Gaussian error model. Experimental results using a deployed wireless network, where GPS referenced nodes are used as anchors, demonstrate the effectiveness of the proposed algorithm.

In this paper, we present a low-cost wireless sensor network platform, called wireless ad hoc system for positioning (WASP), that has been developed for high-accuracy localization and tracking. This platform uses the time of arrival (TOA) of beacon signals periodically transmitted by the nodes at known times for localization. The system was designed to have a unique tradeoff between hardware complexity and processing complexity to provide high accuracy at minimal cost in complex radio propagation environments. To enable the system to perform well in realistic environments, it was also necessary to develop novel extensions to existing algorithms for the measurement of TOA, localization, and tracking. In this paper, we describe the architecture, hardware, and algorithms of WASP and present results based on field trials conducted in different radio propagation environments. The results show that WASP achieves a ranging accuracy of 0.15 m outdoors and 0.5 m indoors when around 12 anchor nodes are used. These accuracies are achieved with operating range of up to 200 m outdoors and 30 m indoors. This compares favorably to other published results for systems operating in realistic environments.

In complex propagation environments with multipath reflections determining the time-of-arrival (TOA) of the line-of-sight (LoS) signal, which is required for localization, is challenging. As a result the localization accuracy of TOA-based systems degrade in such environments. We are pursuing a novel approach where the TOA algorithm returns not one but multiple candidate TOA values as this list is more likely to contain the LoS TOA value and the localization algorithm uses all of these to form a more reliable estimate of the node location. In this paper we present a new algorithm for localization and tracking based on multiple candidate TOA values from each anchor. We show that this is similar to the well-known data association problem in target tracking and exploit this similarity to propose a particle filter based algorithm that has linear computational complexity in the number of anchors. The performance of the algorithm is validated using simulated data.

In many wireless sensor network (WSN) applications the location of the nodes in the network is required. Localization of nodes is difficult in cases where the use of Global Positioning System is not feasible. Such networks will usually contain a small number of anchors at known locations, but their density is sufficiently low that the other nodes cannot determine their location directly from the anchors. Hence cooperative localization within the network is required. In this paper we evaluate the performance of several cooperative localization algorithms using data collected in field trials and show that a modified version of the DV distance algorithm performs significantly better than the other algorithms considered.

In this paper, a secure communication system using chaotic systems and Markovian jump systems (MJS) is proposed. MJS evolve by switching from one model to another according to a finite state Markov chain. In the proposed system the chaotic transmitter jumps from one chaotic map (model) to another while transmitting. This feature makes it difficult for someone to track the transmitter, i.e., to eavesdrop, without knowing the exact map parameters. It is assumed that the Markov chain transition matrix is known. The Interacting Multiple Model (IMM) estimator is used at the intended receiver to track the transmitter state. It is also shown that the proposed receiver framework can be used to eavesdrop an unknown chaotic transmitter with limited success. It is shown further that the IMM based receiver structure improves the chaotic parameter modulation receiver based on the extended Kalman filter.