Bayesian inference for wind field retrieval

In many problems in spatial statistics it is necessary to infer a global problem solution by combining local models. A principled approach to this problem is to develop a global probabilistic model for the relationships between local variables and to use this as the prior in a Bayesian inference procedure. We show how a Gaussian process with hyper-parameters estimated from Numerical Weather Prediction Models yields meteorologically convincing wind fields. We use neural networks to make local estimates of wind vector probabilities. The resulting inference problem cannot be solved analytically, but Markov Chain Monte Carlo methods allow us to retrieve accurate wind fields.

Using quantitative analysis to implement autonomic IT systems

The software underpinning today’s IT systems needs to adapt dynamically and predictably to rapid changes in system workload, environment and objectives. We describe a software framework that achieves such adaptiveness for IT systems whose components can be modelled as Markov chains. The framework comprises (i) an autonomic architecture that uses Markov-chain quantitative analysis to dynamically adjust the parameters of an IT system in line with its state, environment and objectives; and (ii) a method for developing instances of this architecture for real-world systems. Two case studies are presented that use the framework successfully for the dynamic power management of disk drives, and for the adaptive management of cluster availability within data centres, respectively.

CADS*: Computer-Aided Development of self-* systems

We present the prototype tool CADS* for the computer-aided development of an important class of self-* systems, namely systems whose components can be modelled as Markov chains. Given a Markov chain representation of the IT components to be included into a self-* system, CADS* automates or aids (a) the development of the artifacts necessary to build the self-* system; and (b) their integration into a fully-operational self-* solution. This is achieved through a combination of formal software development techniques including model transformation, model-driven code generation and dynamic software reconfiguration.

Bayesian analysis of the scatterometer wind retrieval inverse problem:Some new approaches

The retrieval of wind vectors from satellite scatterometer observations is a non-linear inverse problem. A common approach to solving inverse problems is to adopt a Bayesian framework and to infer the posterior distribution of the parameters of interest given the observations by using a likelihood model relating the observations to the parameters, and a prior distribution over the parameters. We show how Gaussian process priors can be used efficiently with a variety of likelihood models, using local forward (observation) models and direct inverse models for the scatterometer. We present an enhanced Markov chain Monte Carlo method to sample from the resulting multimodal posterior distribution. We go on to show how the computational complexity of the inference can be controlled by using a sparse, sequential Bayes algorithm for estimation with Gaussian processes. This helps to overcome the most serious barrier to the use of probabilistic, Gaussian process methods in remote sensing inverse problems, which is the prohibitively large size of the data sets. We contrast the sampling results with the approximations that are found by using the sparse, sequential Bayes algorithm.

Studies on the generalisation of Gaussian processes and Bayesian neural networks

The assessment of the reliability of systems which learn from data is a key issue to investigate thoroughly before the actual application of information processing techniques to real-world problems. Over the recent years Gaussian processes and Bayesian neural networks have come to the fore and in this thesis their generalisation capabilities are analysed from theoretical and empirical perspectives. Upper and lower bounds on the learning curve of Gaussian processes are investigated in order to estimate the amount of data required to guarantee a certain level of generalisation performance. In this thesis we analyse the effects on the bounds and the learning curve induced by the smoothness of stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the tightness of the bounds are also discussed. The analysis is supported by several numerical simulations. The generalisation error of a Gaussian process is affected by the dimension of the input vector and may be decreased by input-variable reduction techniques. In conventional approaches to Gaussian process regression, the positive definite matrix estimating the distance between input points is often taken diagonal. In this thesis we show that a general distance matrix is able to estimate the effective dimensionality of the regression problem as well as to discover the linear transformation from the manifest variables to the hidden-feature space, with a significant reduction of the input dimension. Numerical simulations confirm the significant superiority of the general distance matrix with respect to the diagonal one.In the thesis we also present an empirical investigation of the generalisation errors of neural networks trained by two Bayesian algorithms, the Markov Chain Monte Carlo method and the evidence framework; the neural networks have been trained on the task of labelling segmented outdoor images.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

Classification and contextual enhancement of remotely sensed data

The aims of the project were twofold: 1) To investigate classification procedures for remotely sensed digital data, in order to develop modifications to existing algorithms and propose novel classification procedures; and 2) To investigate and develop algorithms for contextual enhancement of classified imagery in order to increase classification accuracy. The following classifiers were examined: box, decision tree, minimum distance, maximum likelihood. In addition to these the following algorithms were developed during the course of the research: deviant distance, look up table and an automated decision tree classifier using expert systems technology. Clustering techniques for unsupervised classification were also investigated. Contextual enhancements investigated were: mode filters, small area replacement and Wharton's CONAN algorithm. Additionally methods for noise and edge based declassification and contextual reclassification, non-probabilitic relaxation and relaxation based on Markov chain theory were developed. The advantages of per-field classifiers and Geographical Information Systems were investigated. The conclusions presented suggest suitable combinations of classifier and contextual enhancement, given user accuracy requirements and time constraints. These were then tested for validity using a different data set. A brief examination of the utility of the recommended contextual algorithms for reducing the effects of data noise was also carried out.

An accurate and scalable analytical model for IEEE 802.15.4 slotted CSMA/CA networks

In this paper a Markov chain based analytical model is proposed to evaluate the slotted CSMA/CA algorithm specified in the MAC layer of IEEE 802.15.4 standard. The analytical model consists of two two-dimensional Markov chains, used to model the state transition of an 802.15.4 device, during the periods of a transmission and between two consecutive frame transmissions, respectively. By introducing the two Markov chains a small number of Markov states are required and the scalability of the analytical model is improved. The analytical model is used to investigate the impact of the CSMA/CA parameters, the number of contending devices, and the data frame size on the network performance in terms of throughput and energy efficiency. It is shown by simulations that the proposed analytical model can accurately predict the performance of slotted CSMA/CA algorithm for uplink, downlink and bi-direction traffic, with both acknowledgement and non-acknowledgement modes.

End-to-end versus hop-by-hop soft state refresh for multi-hop signalling systems

To ensure state synchronization of signalling operations, many signaling protocol designs choose to establish “soft” state that expires if it is not refreshed. The approaches of refreshing state in multi-hop signaling system can be classified as either end-to-end (E2E) or hop-by-hop (HbH). Although both state refresh approaches have been widely used in practical signaling protocols, the design tradeoffs between state synchronization and signaling cost have not yet been fully investigated. In this paper, we investigate this issue from the perspectives of state refresh and state removal. We propose simple but effective Markov chain models for both approaches and obtain closed-form solutions which depict the state refresh performance in terms of state consistency and refresh message rate, as well as the state removal performance in terms of state removal delay. Simulations verify the analytical models. It is observed that the HbH approach yields much better state synchronization at the cost of higher signaling cost than the E2E approach. While the state refresh performance can be improved by increasing the values of state refresh and timeout timers, the state removal delay increases largely for both E2E and HbH approaches. The analysis here shed lights on the design of signaling protocols and the configuration of the timers to adapt to changing network conditions.

Unified model for performance analysis of IEEE 802.11 ad hoc networks in unsaturated conditions

IEEE 802.11 standard has achieved huge success in the past decade and is still under development to provide higher physical data rate and better quality of service (QoS). An important problem for the development and optimization of IEEE 802.11 networks is the modeling of the MAC layer channel access protocol. Although there are already many theoretic analysis for the 802.11 MAC protocol in the literature, most of the models focus on the saturated traffic and assume infinite buffer at the MAC layer. In this paper we develop a unified analytical model for IEEE 802.11 MAC protocol in ad hoc networks. The impacts of channel access parameters, traffic rate and buffer size at the MAC layer are modeled with the assistance of a generalized Markov chain and an M/G/1/K queue model. The performance of throughput, packet delivery delay and dropping probability can be achieved. Extensive simulations show the analytical model is highly accurate. From the analytical model it is shown that for practical buffer configuration (e.g. buffer size larger than one), we can maximize the total throughput and reduce the packet blocking probability (due to limited buffer size) and the average queuing delay to zero by effectively controlling the offered load. The average MAC layer service delay as well as its standard deviation, is also much lower than that in saturated conditions and has an upper bound. It is also observed that the optimal load is very close to the maximum achievable throughput regardless of the number of stations or buffer size. Moreover, the model is scalable for performance analysis of 802.11e in unsaturated conditions and 802.11 ad hoc networks with heterogenous traffic flows. © 2012 KSI.

Investigation of a cross-layer link adaptation algorithm for IEEE 802.11n networks

Link adaptation is a critical component of IEEE 802.11 systems, which adapts transmission rates to dynamic wireless channel conditions. In this paper we investigate a general cross-layer link adaptation algorithm which jointly considers the physical layer link quality and random channel access at the MAC layer. An analytic model is proposed for the link adaptation algorithm. The underlying wireless channel is modeled with a multiple state discrete time Markov chain. Compared with the pure link quality based link adaptation algorithm, the proposed cross-layer algorithm can achieve considerable performance gains of up to 20%.

End-to-end versus hop-by-hop state refresh in soft state signaling protocols

The concept of soft state (i.e., the state that will expire unless been refreshed) has been widely used in the design of network signaling protocols. The approaches of refreshing state in multi-hop networks can be classified to end-to-end (E2E) and hop-by-hop (HbH) refreshes. In this article we propose an effective Markov chain based analytical model for both E2E and HbH refresh approaches. Simulations verify the analytical models, which can be used to study the impacts of link characteristics on the performance (e.g., state synchronization and message overhead), as a guide on configuration and optimization of soft state signaling protocols. © 2009 IEEE.

Performance analysis of ONOE protocol - an IEEE 802.11 link adaptation algorithm

Link adaptation (LA) plays an important role in adapting an IEEE 802.11 network to wireless link conditions and maximizing its capacity. However, there is a lack of theoretic analysis of IEEE 802.11 LA algorithms. In this article, we propose a Markov chain model for an 802.11 LA algorithm (ONOE algorithm), aiming to identify the problems and finding the space of improvement for LA algorithms. We systematically model the impacts of frame corruption and collision on IEEE 802.11 network performance. The proposed analytic model was verified by computer simulations. With the analytic model, it can be observed that ONOE algorithm performance is highly dependent on the initial bit rate and parameter configurations. The algorithm may perform badly even under light channel congestion, and thus, ONOE algorithm parameters should be configured carefully to ensure a satisfactory system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Coverage overlapping problems in applications of IEEE 802.15.4 wireless sensor networks

IEEE 802.15.4 standard is a relatively new standard designed for low power low data rate wireless sensor networks (WSN), which has a wide range of applications, e.g., environment monitoring, e-health, home and industry automation. In this paper, we investigate the problems of hidden devices in coverage overlapped IEEE 802.15.4 WSNs, which is likely to arise when multiple 802.15.4 WSNs are deployed closely and independently. We consider a typical scenario of two 802.15.4 WSNs with partial coverage overlapping and propose a Markov-chain based analytical model to reveal the performance degradation due to the hidden devices from the coverage overlapping. Impacts of the hidden devices and network sleeping modes on saturated throughput and energy consumption are modeled. The analytic model is verified by simulations, which can provide the insights to network design and planning when multiple 802.15.4 WSNs are deployed closely. © 2013 IEEE.

Coverage overlapping problems in applications of IEEE 802.15.4 wireless sensor networks

IEEE 802.15.4 standard is a relatively new standard designed for low power low data rate wireless sensor networks (WSN), which has a wide range of applications, e.g., environment monitoring, e-health, home and industry automation. In this paper, we investigate the problems of hidden devices in coverage overlapped IEEE 802.15.4 WSNs, which is likely to arise when multiple 802.15.4 WSNs are deployed closely and independently. We consider a typical scenario of two 802.15.4 WSNs with partial coverage overlapping and propose a Markov-chain based analytical model to reveal the performance degradation due to the hidden devices from the coverage overlapping. Impacts of the hidden devices and network sleeping modes on saturated throughput and energy consumption are modeled. The analytic model is verified by simulations, which can provide the insights to network design and planning when multiple 802.15.4 WSNs are deployed closely. © 2013 IEEE.