Point estimation, stochastic approximation, and robust Kalman filtering

Caption title.Includes bibliographical references (p. 23-25).Supported by the U.S. Air Force Office of Scientific Research. AFOSR-85-0227 AFOSR-89-0276Sanjoy K. Mitter and Irvin C. Schick

Ultimate iterative UFIR filtering algorithm

Measurements are often provided in the presence of noise and uncertainties that require optimal filters to estimate processes with highest accuracy. The ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm presented in this paper is more robust in real world than the Kalman filter. It completely ignores the noise statistics and initial values while demonstrating better accuracy under the mismodeling and temporary uncertainties and lower sensitivity to errors in the noise statistics

Robust estimation for structural time series models.

This thesis aims at developing robust methods of estimation in order to draw valid inference from contaminated time series. We concentrate on additive and innovation outliers in structural time series models using a state space representation. The parameters of interest are the state, hyperparameters and coefficients of explanatory variables. Three main contributions evolve from the research. Firstly, a filter named the approximate Gaussian sum filter is proposed to cope with noisy disturbances in both the transition and measurement equations. Secondly, the Kalman filter is robustified by carrying over the M-estimation of scale for i.i.d observations to time-dependent data. Thirdly, robust regression techniques are implemented to modify the generalised least squares transformation procedure to deal with explanatory variables in time series models. All the above procedures are tested against standard non-robust estimation methods for time series by means of simulations. Two real examples are also included

Robust Techniques for Signal Processing: A Survey

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryU.S. Army Research Office / DAAG29-81-K-0062U.S. Air Force Office of Scientific Research / AFOSR 82-0022Joint Services Electronics Program / N00014-84-C-0149National Science Foundation / ECS-82-12080U.S. Office of Naval Research / N00014-80-K-0945 and N00014-81-K-001

Aspects of recursive Bayesian estimation

This thesis is concerned with the theoretical and practical aspects of some problems in Bayesian time series analysis and recursive estimation. In particular, we examine procedures for accommodating outliers in dynamic linear models which involve the use of heavy-tailed error distributions as alternatives to normality. Initially we discuss the basic principles of the Bayesian approach to robust estimation in general, and develop those ideas in the context of linear time series models. Following this, the main body of the thesis attacks the problem of intractibility of analysis under outlier accommodating assumptions. For both the dynamic linear model and the classical autoregressive-moving average schemes we develop methods for parameter estimation, forecasting and smoothing with non-normal data. This involves the theoretical examination of non-linear recursive filtering algorithms as robust alternatives to the Kalman filter and numerical examples of the use of these procedures on simulated data. The asymptotic behaviour of some special recursions is also detailed in connection with the theory of stochastic approximation. Finally, we report on an application of Bayesian time series analysis in the monitoring of medical time series, the particular problem involving kidney transplant patients

Numerical Optimisation of Building Thermal and Energy Performance in Hospitals

This thesis details the development and testing of a metamodel-based building optimisation methodology dubbed thermal building optimisation tool (T-BOT), designed as an information gathering framework and decision support tool rather than a design automator. Initial samples of building simulations are used to train moving least squares regression (MLSR) meta-models of the design space. A genetic algorithm (GA) is then used to optimise with the dual objectives of minimising time-averaged thermal discomfort and energy use. The optimum trade-off is presented as a Pareto front. Adaptive coupling functionality of the building simulation program ESP-r is used to augment the dynamic thermal model (DTM) with computational fluid dynamics (CFD), allowing local evaluation of thermal comfort within rooms. Furthermore, the disconnect between simulation and optimisation induced by the metamodeling is exploited to lend flexibility to the data gathered in the initial samples. Optimisations can hence be performed for any combination of location, time period, thermal comfort criteria and design variables, from a single set of sample simulations; this was termed a “one sample many optimisations” or OSMO approach. This can present substantial time savings over a comparable direct search optimisation technique. To the author’s knowledge the OSMO approach and adaptive coupling of DTM and CFD are unique among building thermal optimisation (BTO) models. Development and testing was focussed on hospital environments, though the method is potentially applicable to other environments. The program was tested by application to two models, one a theoretical test case and one a case study based on a real hospital building. It was found that variation in spatial location, time period and thermal comfort criteria can result in different optimum conditions, though seasonal variation had a large effect on this. Also the sample size and selection of design variables and their ranges were found to be critical to meta-model fidelity