In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multitarget filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multitarget posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multitarget filter. In addition, an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear nonGaussian dynamics. Convergence results for these filters are also established.

/pdf/sequential-monte-carlo-methods-for-multitarget-filtering-4bcv6t9roc.pdf

Sequential Monte Carlo methods for multitarget filtering with random finite sets

We evaluate the applicability of a biologically-motivated algorithm to select visually-salient regions of interest in video streams for multiply-foveated video compression. Regions are selected based on a nonlinear integration of low-level visual cues, mimicking processing in primate occipital, and posterior parietal cortex. A dynamic foveation filter then blurs every frame, increasingly with distance from salient locations. Sixty-three variants of the algorithm (varying number and shape of virtual foveas, maximum blur, and saliency competition) are evaluated against an outdoor video scene, using MPEG-1 and constant-quality MPEG-4 (DivX) encoding. Additional compression radios of 1.1 to 8.5 are achieved by foveation. Two variants of the algorithm are validated against eye fixations recorded from four to six human observers on a heterogeneous collection of 50 video clips (over 45 000 frames in total). Significantly higher overlap than expected by chance is found between human and algorithmic foveations. With both variants, foveated clips are, on average, approximately half the size of unfoveated clips, for both MPEG-1 and MPEG-4. These results suggest a general-purpose usefulness of the algorithm in improving compression ratios of unconstrained video.

/pdf/automatic-foveation-for-video-compression-using-a-6p2knaabr7.pdf

Automatic foveation for video compression using a neurobiological model of visual attention

This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as nonGaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR).

/pdf/multitarget-tracking-using-the-joint-multitarget-probability-2f40qfgbw2.pdf

Multitarget tracking using the joint multitarget probability density

Multi-armed bandit (MAB) problems are a class of sequential resource allocation problems concerned with allocating one or more resources among several alternative (competing) projects. Such problems are paradigms of a fundamental conflict between making decisions (allocating resources) that yield high current rewards, versus making decisions that sacrifice current gains with the prospect of better future rewards. The MAB formulation models resource allocation problems arising in several technological and scientific disciplines such as sensor management, manufacturing systems, economics, queueing and communication networks, clinical trials, control theory, search theory, etc. (see [88] and references therein).

Multi-Armed Bandit Problems

For many dynamic estimation problems involving nonlinear and/or non-Gaussian models, particle filtering offers improved performance at the expense of computational effort. This paper describes a scheme for efficiently tracking multiple targets using particle filters. The tracking of the individual targets is made efficient through the use of Rao-Blackwellisation. The tracking of multiple targets is made practicable using Quasi-Monte Carlo integration. The efficiency of the approach is illustrated on synthetic data.

Efficient particle filtering for multiple target tracking with application to tracking in structured images

Track-before-detect methods operate directly upon raw sensor signals without a separate, explicit detection stage. An efficient implementation of a Bayesian track-before-detect particle filter is described for tracking of a single target in a sequence of images. The filter produces a sample-based representation of the probability density function of the target state from raw pixel levels. An indication of the probability that the target is present is also provided. Spatial differentiation of the pixel array data allows objects to be tracked when viewed against a general scene with additive noise. Simulated results illustrate that a dim point target of unknown amplitude, which has become spatially blurred, may be tracked through a sequence of structured images. Detection sensitivity is established using simulated results. The novel aspect of the work is the efficient implementation - in particular, the calculation of the probability of the target being present.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-rsn.2017.0483

Particle filter for track-before-detect of a target with unknown amplitude viewed against a structured scene

During the terminal phase of an engagement an air to surface missile must ensure that it is on track to hit its target accurately and satisfy terminal conditions. This terminal guidance problem has been tackled for a missile carrying a Doppler beam sharpening (DBS) radar seeker. Emphasis is upon aspects affecting the trajectory shape which arise as a consequence of using measurements from a DBS sensor to remove an unknown error in the position of the target and a bias error in the velocity of the inertial navigation system (INS) carried by the missile. The conditions for high quality DBS imagery must be met and these are derived. It is shown that, by use of sequential estimation techniques, the uncertainty in the estimated spatial co-ordinates of the target’s position may be reduced to a few meters – compared with hundreds of meters if the measurements derived from only one image are processed independently in each time step. A theoretical bound on the performance of an estimator, as a function of image quality and trajectory shape, is given via computation of posterior Cramer-Rao lower bound (CRLB). Two novel estimators have been designed to overcome the heavily non-linear nature of the DBS measurement process and their performance is close to the CRLB.

Parameter estimation for terminal guidance using a doppler beam sharpening radar.

This paper discusses the use of constraints when super-resolving passive millimeter wave (PMMW) images A PMMW imager has good all-weather imaging capability but requires a large collection aperture to obtain adequate spatial resolution due to the diffraction limit and the long wavelengths involved A typical aperture size for a system operating at 94GHz would be 1m in diameter This size may be reduced if image restoration techniques are employed A factor of two in recognition range may be achieved using a linear technique such as a Wiener filter; while a factor of four is available using non-linear techniques These non-linear restoration methods generate the missing high frequency information above the pass band in band limited images For this bandwidth extension to generate genuine high frequencies, it is necessary to restore the image subject to constraints These constraints should be applied directly to the scene content rather than to any noise that might also be present The merits of the available super-resolution techniques are discussed with particular reference to the Lorentzian method Attempts are made to explain why the distribution of gradients within an image is Lorentzian by assuming that an image has randomly distributed gradients of random size Any increase in sharpness of an image frequently results in an increase in the noise present The effect of noise and image sharpness on the ability of a human observer to recognise an object in the scene is discussed with reference to a recent model of human perception

Malcolm Rollason

Papers

Efficient particle filtering for multiple target tracking with application to tracking in structured images

Efficient particle filtering for multiple target tracking with application to tracking in structured images

Particle filter for track-before-detect of a target with unknown amplitude viewed against a structured scene

Parameter estimation for terminal guidance using a doppler beam sharpening radar.

Use of constraints in the superresolution of passive millimeter-wave images