Estimation of discrete signals containing a nonrandom component

Ph.D.Roger P. Web

Review of Unbiased FIR Filters, Smoothers, and Predictors for Polynomial Signals

Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided

Optimum linear and adaptive polynomial smoothers

The design of optimum polynomial digital data smoothers (filters) is considered for linear and adaptive processing systems. It is shown that a significant improvement in performance can be obtained by using linear smoothers that take into account known a priori constraints or distributions of the input signal. The procedure for designing optimum (minimum mean square error) adaptive polynomial data smoothers is then discussed and analyzed. The optimum smoother makes use of a priori signal statistics combined with an adaptive Bayesian weighting of a bank of conditionally optimum smoothers. Use of this technique permits large improvements in performance with a minimum of additonal system complexity

Iterative Unbiased FIR State Estimation: A Review of Algorithms

In this paper, we develop in part and review various iterative unbiased finite impulse response (UFIR) algorithms (both direct and two-stage) for the filtering, smoothing, and prediction of time-varying and time-invariant discrete state-space models in white Gaussian noise environments. The distinctive property of UFIR algorithms is that noise statistics are completely ignored. Instead, an optimal window size is required for optimal performance. We show that the optimal window size can be determined via measurements with no reference. UFIR algorithms are computationally more demanding than Kalman filters, but this extra computational effort can be alleviated with parallel computing, and the extra memory that is required is not a problem for modern computers. Under real-world operating conditions with uncertainties, non-Gaussian noise, and unknown noise statistics, the UFIR estimator generally demonstrates better robustness than the Kalman filter, even with suboptimal window size. In applications requiring large window size, the UFIR estimator is also superior to the best previously known optimal FIR estimators

Façonnement de l'Interférence en vue d'une Optimisation Globale d'un Système Moderne de Communication

A communication is impulsive whenever the information-bearing signal is burst-like in time. Examples of the impulsive concept are: impulse-radio signals, that is, wireless signals occurring within short intervals of time; optical signals conveyed by photons; speech signals represented by sound pressure variations; pulse-position modulated electrical signals; a sequence of arrival/departure events in a queue; neural spike trains in the brain. Understanding impulsive communications requires to identify what is peculiar to this transmission paradigm, that is, different from traditional continuous communications.In order to address the problem of understanding impulsive vs. non-impulsive communications, the framework of investigation must include the following aspects: the different interference statistics directly following from the impulsive signal structure; the different interaction of the impulsive signal with the physical medium; the actual possibility for impulsive communications of coding information into the time structure, relaxing the implicit assumption made in continuous transmissions that time is a mere support. This thesis partially addresses a few of the above issues, and draws future lines of investigation. In particular, we studied: multiple access channels where each user adopts time-hopping spread-spectrum; systems using a specific prefilter at the transmitter side, namely the transmit matched filter (also known as time reversal), particularly suited for ultrawide bandwidhts; the distribution function of interference for impulsive systems in several different settings.Une communication est impulsive chaque fois que le signal portant des informations est intermittent dans le temps et que la transmission se produit à rafales. Des exemples du concept impulsife sont : les signaux radio impulsifs, c’est-à-dire des signaux très courts dans le temps; les signaux optiques utilisé dans les systèmes de télécommunications; certains signaux acoustiques et, en particulier, les impulsions produites par le système glottale; les signaux électriques modulés en position d’impulsions; une séquence d’événements dans une file d’attente; les trains de potentiels neuronaux dans le système neuronal. Ce paradigme de transmission est différent des communications continues traditionnelles et la compréhension des communications impulsives est donc essentielle. Afin d’affronter le problème des communications impulsives, le cadre de la recherche doit inclure les aspects suivants : la statistique d’interférence qui suit directement la structure des signaux impulsifs; l’interaction du signal impulsif avec le milieu physique; la possibilité pour les communications impulsives de coder l’information dans la structure temporelle. Cette thèse adresse une partie des questions précédentes et trace des lignes indicatives pour de futures recherches. En particulier, nous avons étudié: un système d'accès multiple où les utilisateurs adoptent des signaux avec étalement de spectre par saut temporel (time-hopping spread spectrum) pour communiquer vers un récepteur commun; un système avec un préfiltre à l'émetteur, et plus précisément un transmit matched filter, également connu comme time reversal dans la littérature de systèmes à bande ultra large; un modèle d'interférence pour des signaux impulsifs

Intraspecific trait variation and community assembly in old-field grasslands

Trait-based approaches are increasingly used in plant community ecology, but previous research has largely ignored functional trait variation within species. Here I investigated the role of intraspecific trait variation in community assembly and responses to spatial and temporal environmental variation in old-field plant communities in the eastern United States. In the first study I analyzed spatial patterns of functional divergence in old fields in central New York on spatial scales from 1-1500 m. Results showed that spatial divergence in functional traits at the community and intraspecific levels corresponded with spatial heterogeneity in edaphic variables, consistent with predicted patterns resulting from trait-based environmental filtering. In the second study I tested for evidence of environmental filtering and niche differentiation based on trait dispersion patterns, with or without accounting for intraspecific trait variation. The tests provided evidence of strong trait-based environmental filtering and weak niche differentiation, and these patterns were strengthened by the inclusion of intraspecific trait variation, demonstrating its importance for community assembly. In the third study I examined the contributions of intraspecific variation and species turnover to community trait responses to environmental gradients across a 1200-km latitudinal extent in the eastern United States. Community trait shifts in response to broad-scale climatic variation were driven primarily by species turnover, but intraspecific variation contributed strongly to trait shifts along edaphic gradients and at fine spatial scales. Finally I investigated the role of intraspecific variation in community trait responses to experimental nutrient enrichment in old-field communities and the influence of community functional diversity and dispersal in mediating these responses. After three years, community functional responses were driven almost entirely by intraspecific trait shifts, which were strongest in communities with high initial intraspecific variation for some traits. Taken together, my results suggest that intraspecific trait variation plays a strong role in the assembly of old-field plant communities and shed light on the circumstances in which intraspecific variation is likely to be important for plant community ecology in general

A study of manual control methodology with annotated bibliography

Manual control methodology - study with annotated bibliograph