Localization of multiple nodes based on correlated measurements and shrinkage estimation

Accurate covariance matrix estimation has applications in a wide range of disciplines. For many applications the estimated covariance matrix needs to be positive definite and hence invertible. When the number of data points is insufficient, the estimated sample covariance matrix has two fold disadvantages. Firstly, although it is unbiased, it consists of a large estimation error. Secondly, it is not positive definite. A shrinkage technique has been proposed in the fields of finance and life sciences to estimate the covariance matrix that is invertible and contains relatively a small estimation error variance. In this paper, we introduce the shrinkage covariance matrix concept in the area of multiple target localization in wireless networks with correlated measurements. For localization, we use the low cost received signal strength (RSS) measurements. Unlike most studies, where the links between sensor nodes (SNs) and targets nodes (TNs) are independent, we use a realistic model where these links are correlated. Optimization in location accuracy is achieved by weighting each link via the shrinkage covariance matrix. Simulation results show that using the estimated shrinkage covariance improves the location accuracy of the localization algorithm

Super resolution WiFi indoor localization and tracking

In this paper, we present a complete framework for accurate indoor positioning and tracking using the 802.11a WiFi network. Channel frequency response is first estimated via the least squares (LS) method using an orthogonal frequency division multiplexing (OFDM) pilot symbol. For accurate time of arrival (ToA) distance estimates in multipath environments, super resolution technique i.e. Multiple Signal Classification (MUSIC) is used which capitalizes on the autocorrelation matrix of the estimated channel frequency response. The estimated distances from the base stations (BSs) are then used in the observation model for particle filter (PF) tracking for which a constant velocity motion model is used, depicting indoor mobile movement. The tracking performance of the combined MUSIC-PF is compared with PF performance when a conventional cross correlator (CC) is used for delay estimates. It is shown via simulation that the MUSIC-PF performance is superior to the CC-PF performance

Sequential Markov Chain Monte Carlo for multi-target tracking with correlated RSS measurements

In this paper, we present a Bayesian approach to accurately track multiple objects based on Received Signal Strength (RSS) measurements. This work shows that taking into account the spatial correlations of the observations caused by the random shadowing effect can induce significant tracking performance improvements, especially in very noisy scenarios. Additionally, the superiority of the proposed Sequential Markov Chain Monte Carlo (SMCMC) method over the more common Sequential Importance Resampling (SIR) technique is empirically demonstrated through numerical simulations in which multiple targets have to be tracked

Tracking of wireless mobile nodes in he presence of unknown path-loss characteristics

Due to the difficult characterization of the propagation model, most studies on racking of mobile nodes assume the correct knowledge of the power-distance gradients or the path-loss exponents (PLEs). In this paper, we first investigate the impact of erroneous PLEs on positioning of a wireless nodes when both distance and bearing measurements are available. Thus, an analytical expression of the mean square error (MSE) in location estimation is derived in case of erroneous PLEs. Second, we propose a novel online PLE estimation and tracking algorithm in dynamic environments. The proposed algorithm estimates the PLE of individual links a every time-step using he generalized pattern search (GenPS) algorithm. The PLE estimates update the observation vector which is used in a Kalman filter (KF) and a particle filter (PF) for tracking. Simulation results show that the racking performance degrades drastically with an incorrect assumption for the PLE values. Further simulations show that tracking with PLE estimation performs considerably beer compared to tracking with incorrectly assumed PLEs

Gradient based sequential Markov chain Monte Carlo for multitarget tracking with correlated measurements

Measurements in wireless sensor networks (WSNs) are often correlated both in space and in time. This paper focuses on tracking multiple targets in WSNs by taking into consideration these measurement correlations. A sequential Markov Chain Monte Carlo (SMCMC) approach is proposed in which a Metropolis within Gibbs refinement step and a likelihood gradient proposal are introduced. This SMCMC filter is applied to case studies with cellular network received signal strength data in which the shadowing component correlations in space and time are estimated. The efficiency of the SMCMC approach compared to particle filtering, as well as the gradient proposal compared to a basic prior proposal, are demonstrated through numerical simulations. The accuracy improvement with the gradient-based SMCMC is above 90% when using a low number of particles. Thanks to its sequential nature, the proposed approach can be applied to various WSN applications, including traffic mobility monitoring and prediction

Tracking with Sparse and Correlated Measurements via a Shrinkage-based Particle Filter

This paper presents a shrinkage-based particle filter method for tracking a mobile user in wireless networks. The proposed method estimates the shadowing noise covariance matrix using the shrinkage technique. The particle filter is designed with the estimated covariance matrix to improve the tracking performance. The shrinkage-based particle filter can be applied in a number of applications for navigation, tracking and localization when the available sensor measurements are correlated and sparse. The performance of the shrinkage-based particle filter is compared with the posterior Cramer-Rao lower bound, which is also derived in the paper. The advantages of the proposed shrinkage-based particle filter approach are demonstrated via simulation and experimental results

An Improved Simulated Annealing Technique for Enhanced Mobility in Smart Cities

Vehicular traffic congestion is a significant problem that arises in many cities. This is due to the increasing number of vehicles that are driving on city roads of limited capacity. The vehicular congestion significantly impacts travel distance, travel time, fuel consumption and air pollution. Avoidance of traffic congestion and providing drivers with optimal paths are not trivial tasks. The key contribution of this work consists of the developed approach for dynamic calculation of optimal traffic routes. Two attributes (the average travel speed of the traffic and the roads’ length) are utilized by the proposed method to find the optimal paths. The average travel speed values can be obtained from the sensors deployed in smart cities and communicated to vehicles via the Internet of Vehicles and roadside communication units. The performance of the proposed algorithm is compared to three other algorithms: the simulated annealing weighted sum, the simulated annealing technique for order preference by similarity to the ideal solution and the Dijkstra algorithm. The weighted sum and technique for order preference by similarity to the ideal solution methods are used to formulate different attributes in the simulated annealing cost function. According to the Sheffield scenario, simulation results show that the improved simulated annealing technique for order preference by similarity to the ideal solution method improves the traffic performance in the presence of congestion by an overall average of 19.22% in terms of travel time, fuel consumption and CO2 emissions as compared to other algorithms; also, similar performance patterns were achieved for the Birmingham test scenario

Robustness analysis of Gaussian process convolutional neural network with uncertainty quantification

This paper presents a novel framework for image classification which comprises a convolutional neural network (CNN) feature map extractor combined with a Gaussian process (GP) classifier. Learning within the CNN-GP involves forward propagating the predicted class labels, then followed by backpropagation of the maximum likelihood function of the GP with a regularization term added. The regularization term takes the form of one of the three loss functions: the Kullback-Leibler divergence, Wasserstein distance, and maximum correntropy. The training and testing are performed in mini batches of images. The forward step (before the regularization) involves replacing the original images in the mini batch with their close neighboring images and then providing these to the CNN-GP to get the new predictive labels. The network performance is evaluated on MNIST, Fashion-MNIST, CIFAR10, and CIFAR100 datasets. Precision-recall and receiver operating characteristics curves are used to evaluate the performance of the GP classifier. The proposed CNN-GP performance is validated with different levels of noise, motion blur, and adversarial attacks. Results are explained using uncertainty analysis and further tests on quantifying the impact on uncertainty with attack strength are carried out. The results show that the testing accuracy improves for networks that backpropagate the maximum likelihood with regularized losses when compared with methods that do not. Moreover, a comparison with a state-of-art CNN Monte Carlo dropout method is presented. The outperformance of the CNN-GP framework with respect to reliability and computational efficiency is demonstrated

A Beamformer-Particle Filter Framework for Localization of Correlated EEG Sources

Abstract—Electroencephalography (EEG)-based brain computer interface (BCI) is the most studied non-invasive interface to build a direct communication pathway between the brain and an external device. However, correlated noises in EEG measurements still constitute a significant challenge. Alternatively, building BCIs based on filtered brain activity source signals instead of using their surface projections, obtained from the noisy EEG signals, is a promising and not well explored direction. In this context, finding the locations and waveforms of inner brain sources represents a crucial task for advancing source-based non-invasive BCI technologies. In this paper, we propose a novel Multi-core Beamformer Particle Filter (Multi-core BPF) to estimate the EEG brain source spatial locations and their corresponding waveforms. In contrast to conventional (single-core) Beamforming spatial filters, the developed Multi-core BPF considers explicitly temporal correlation among the estimated brain sources by suppressing activation from regions with interfering coherent sources. The hybrid Multi-core BPF brings together the advantages of both deterministic and Bayesian inverse problem algorithms in order to improve the estimation accuracy. It solves the brain activity localization problem without prior information about approximate areas of source locations. Moreover, the multi-core BPF reduces the dimensionality of the problem to half compared with the PF solution; thus alleviating the curse of dimensionality problem. The results, based on generated and real EEG data, show that the proposed framework recovers correctly the dominant sources of brain activity

Is doctor referral to a low energy total diet replacement programme costeffective for the routine treatment of obesity?

ABTRACT Objective To estimate the cost-effectiveness of a commercially provided low energy total diet replacement (TDR) programme versus nurse-led behavioural support. Methods We used a multi-state lifetable model and the weight reduction observed in a randomised controlled trial to evaluate the quality-adjusted life-years (QALYs) and direct healthcare costs (in UK 2017 prices) over a lifetime with TDR versus nurse-led support in adults who were obese, assuming that: i) weight returns to baseline over 5 years, and ii) a 1 kg weight loss is maintained after 5 years following TDR. Results The per-person costs of the TDR and nurse-led programmes were £796 and £34, respectively. The incremental cost-effectiveness ratio (ICER) of TDR was £12,955 (95% confidence interval: £8,082 to £17,827) assuming all weight lost is regained and £3,203 (£2,580 to £3,825) assuming that a 1 kg weight loss is maintained after 5 years. TDR was estimated to be more cost-effective (i.e. lower ICERs) in older adults and those with higher body mass index, with little difference by gender. Conclusions At current retail prices and with plausible long-term weight regain trajectories, TDR is projected to be cost-effective in obese adults and could be considered as an option to treat obesity in routine healthcare setting