Compressed sensing using hidden Markov models with application to vision based aircraft tracking

This paper investigates compressed sensing using hidden Markov models (HMMs) and hence provides an extension of recent single frame, bounded error sparse decoding problems into a class of sparse estimation problems containing both temporal evolution and stochastic aspects. This paper presents two optimal estimators for compressed HMMs. The impact of measurement compression on HMM filtering performance is experimentally examined in the context of an important image based aircraft target tracking application. Surprisingly, tracking of dim small-sized targets (as small as 5-10 pixels, with local detectability/SNR as low as − 1.05 dB) was only mildly impacted by compressed sensing down to 15% of original image size.

Degradation modeling and monitoring of machines using operation-specific hidden Markov models

In this paper, a novel data-driven approach to monitoring of systems operating under variable operating conditions is described. The method is based on characterizing the degradation process via a set of operation-specific hidden Markov models (HMMs), whose hidden states represent the unobservable degradation states of the monitored system while its observable symbols represent the sensor readings. Using the HMM framework, modeling, identification and monitoring methods are detailed that allow one to identify a HMM of degradation for each operation from mixed-operation data and perform operation-specific monitoring of the system. Using a large data set provided by a major manufacturer, the new methods are applied to a semiconductor manufacturing process running multiple operations in a production environment.

Assessment on the effect of pollution abatement on environmental efficiency with Markov chain Monte Carlo simulation

Both environmental economists and policy makers have shown a great deal of interest in the effect of pollution abatement on environmental efficiency. In line with the modern resources available, however, no contribution is brought to the environmental economics field with the Markov chain Monte Carlo (MCMC) application, which enables simulation from a distribution of a Markov chain and simulating from the chain until it approaches equilibrium. The probability density functions gained prominence with the advantages over classical statistical methods in its simultaneous inference and incorporation of any prior information on all model parameters. This paper concentrated on this point with the application of MCMC to the database of China, the largest developing country with rapid economic growth and serious environmental pollution in recent years. The variables cover the economic output and pollution abatement cost from the year 1992 to 2003. We test the causal direction between pollution abatement cost and environmental efficiency with MCMC simulation. We found that the pollution abatement cost causes an increase in environmental efficiency through the algorithm application, which makes it conceivable that the environmental policy makers should make more substantial measures to reduce pollution in the near future.

Adaptive estimation of hidden semi-Markov chains with parameterised transition probabilities and exponential decaying states

This paper develops maximum likelihood (ML) estimation schemes for finite-state semi-Markov chains in white Gaussian noise. We assume that the semi-Markov chain is characterised by transition probabilities of known parametric from with unknown parameters. We reformulate this hidden semi-Markov model (HSM) problem in the scalar case as a two-vector homogeneous hidden Markov model (HMM) problem in which the state consist of the signal augmented by the time to last transition. With this reformulation we apply the expectation Maximumisation (EM ) algorithm to obtain ML estimates of the transition probabilities parameters, Markov state levels and noise variance. To demonstrate our proposed schemes, motivated by neuro-biological applications, we use a damped sinusoidal parameterised function for the transition probabilities.

Reduced complexity on-line estimation of hidden Markov model parameters

In this paper we propose and study low complexity algorithms for on-line estimation of hidden Markov model (HMM) parameters. The estimates approach the true model parameters as the measurement noise approaches zero, but otherwise give improved estimates, albeit with bias. On a nite data set in the high noise case, the bias may not be signi cantly more severe than for a higher complexity asymptotically optimal scheme. Our algorithms require O(N3) calculations per time instant, where N is the number of states. Previous algorithms based on earlier hidden Markov model signal processing methods, including the expectation-maximumisation (EM) algorithm require O(N4) calculations per time instant.

Autonomous vehicle path planning for persistence monitoring under uncertainty using Gaussian based Markov decision process

One of the main challenges facing online and offline path planners is the uncertainty in the magnitude and direction of the environmental energy because it is dynamic, changeable with time, and hard to forecast. This thesis develops an artificial intelligence for a mobile robot to learn from historical or forecasted data of environmental energy available in the area of interest which will help for a persistence monitoring under uncertainty using the developed algorithm.

Cross database training of audio-visual hidden Markov models for phone recognition

Speech recognition can be improved by using visual information in the form of lip movements of the speaker in addition to audio information. To date, state-of-the-art techniques for audio-visual speech recognition continue to use audio and visual data of the same database for training their models. In this paper, we present a new approach to make use of one modality of an external dataset in addition to a given audio-visual dataset. By so doing, it is possible to create more powerful models from other extensive audio-only databases and adapt them on our comparatively smaller multi-stream databases. Results show that the presented approach outperforms the widely adopted synchronous hidden Markov models (HMM) trained jointly on audio and visual data of a given audio-visual database for phone recognition by 29% relative. It also outperforms the external audio models trained on extensive external audio datasets and also internal audio models by 5.5% and 46% relative respectively. We also show that the proposed approach is beneficial in noisy environments where the audio source is affected by the environmental noise.

Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

Linear programming for large-scale Markov decision problems

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest goal of competing with a low-dimensional family of policies. We use the dual linear programming formulation of the MDP average cost problem, in which the variable is a stationary distribution over state-action pairs, and we consider a neighborhood of a low-dimensional subset of the set of stationary distributions (defined in terms of state-action features) as the comparison class. We propose a technique based on stochastic convex optimization and give bounds that show that the performance of our algorithm approaches the best achievable by any policy in the comparison class. Most importantly, this result depends on the size of the comparison class, but not on the size of the state space. Preliminary experiments show the effectiveness of the proposed algorithm in a queuing application.

Ergodic control of partially observed Markov chains

The ergodic or long-run average cost control problem for a partially observed finite-state Markov chain is studied via the associated fully observed separated control problem for the nonlinear filter. Dynamic programming equations for the latter are derived, leading to existence and characterization of optimal stationary policies.

Asymptotic behaviour of point processes with Markov-dependent intervals

This splitting techniques for MARKOV chains developed by NUMMELIN (1978a) and ATHREYA and NEY (1978b) are used to derive an imbedded renewal process in WOLD's point process with MARKOV-correlated intervals. This leads to a simple proof of renewal theorems for such processes. In particular, a key renewal theorem is proved, from which analogues to both BLACKWELL's and BREIMAN's forms of the renewal theorem can be deduced.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.