A Bayesian Reflection on Surfaces

The topic of this paper is a novel Bayesian continuous-basis field representation and inference framework. Within this paper several problems are solved: The maximally informative inference of continuous-basis fields, that is where the basis for the field is itself a continuous object and not representable in a finite manner; the tradeoff between accuracy of representation in terms of information learned, and memory or storage capacity in bits; the approximation of probability distributions so that a maximal amount of information about the object being inferred is preserved; an information theoretic justification for multigrid methodology. The maximally informative field inference framework is described in full generality and denoted the Generalized Kalman Filter. The Generalized Kalman Filter allows the update of field knowledge from previous knowledge at any scale, and new data, to new knowledge at any other scale. An application example instance, the inference of continuous surfaces from measurements (for example, camera image data), is presented.Comment: 34 pages, 1 figure, abbreviated versions presented: Bayesian Statistics, Valencia, Spain, 1998; Maximum Entropy and Bayesian Methods, Garching, Germany, 199

Comparison of Five System Identification Algorithms for Rotorcraft Higher Harmonic Control

This report presents an analysis and performance comparison of five system identification algorithms. The methods are presented in the context of identifying a frequency-domain transfer matrix for the higher harmonic control (HHC) of helicopter vibration. The five system identification algorithms include three previously proposed methods: (1) the weighted-least- squares-error approach (in moving-block format), (2) the Kalman filter method, and (3) the least-mean-squares (LMS) filter method. In addition there are two new ones: (4) a generalized Kalman filter method and (5) a generalized LMS filter method. The generalized Kalman filter method and the generalized LMS filter method were derived as extensions of the classic methods to permit identification by using more than one measurement per identification cycle. Simulation results are presented for conditions ranging from the ideal case of a stationary transfer matrix and no measurement noise to the more complex cases involving both measurement noise and transfer-matrix variation. Both open-loop identification and closed- loop identification were simulated. Closed-loop mode identification was more challenging than open-loop identification because of the decreasing signal-to-noise ratio as the vibration became reduced. The closed-loop simulation considered both local-model identification, with measured vibration feedback and global-model identification with feedback of the identified uncontrolled vibration. The algorithms were evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and relative ease of implementation

Time resolved tracking of a sound scatterer in a turbulent flow: non-stationary signal analysis and applications

It is known that ultrasound techniques yield non-intrusive measurements of hydrodynamic flows. For example, the study of the echoes produced by a large number of particle insonified by pulsed wavetrains has led to a now standard velocimetry technique. In this paper, we propose to extend the method to the continuous tracking of one single particle embedded in a complex flow. This gives a Lagrangian measurement of the fluid motion, which is of importance in mixing and turbulence studies. The method relies on the ability to resolve in time the Doppler shift of the sound scattered by the continuously insonfied particle. For this signal processing problem two classes of approaches are used: time-frequency analysis and parametric high resolution methods. In the first class we consider the spectrogram and reassigned spectrogram, and we apply it to detect the motion of a small bead settling in a fluid at rest. In more non-stationary turbulent flows where methods in the second class are more robust, we have adapted an Approximated Maximum Likelihood technique coupled with a generalized Kalman filter.Comment: 16 pages 9 figure

Spatial modeling using graphical Markov models and wavelets

Graphical Markov models use graphs to represent possible dependencies among random variables. This class of models is extremely rich and includes inter alia causal Markov models and Markov random fields. In this dissertation, we develop a very efficient optimal-prediction algorithm for graphical Markov models. The algorithm is a generalization of the Kalman-filter algorithm for temporal processes, and it can in principle be applied to any Gaussian undirected graphical model and any Gaussian acyclic directed graphical model;We also propose a new class of multiscale models for stochastic processes in terms of scale-recursive dynamics defined on acyclic directed graphs. The models are an extension of multiscale tree-structured models. The optimal prediction can be obtained using the newly developed generalized Kalman-filter algorithm referred to above, and the parameters can be estimated by maximum likelihood via the EM algorithm. A subclass of these models are multiscale wavelet models, for which we show that the optimal predictors of hidden state variables can be obtained by a level-dependent (scale-dependent) wavelet shrinkage rule;In a series of papers, D. Donoho and I. Johnstone develop wavelet shrinkage methods to solve statistical problems. We propose a new rationale for wavelet shrinkage, based on the assumption that the underlying process can be decomposed into a large-scale deterministic trend plus a small-scale Gaussian process. Our approach has several advantages over current shrinkage methods. It takes the dependencies of empirical wavelet coefficients, both within scales and across scales, into account. Moreover, it does not rely on asymptotic properties for its justification so that it is also appropriate when the sample size is small;Finally, we introduce partially ordered Markov models, which are acyclic directed graphical models for spatial problems. The model can be regarded as a Markov random field with neighborhood structures derivable from an associated partially ordered set. We use a martingale approach to derive the asymptotic properties of maximum (composite) likelihood estimators for partially ordered Markov models. We prove that the maximum (composite) likelihood estimators are consistent, asymptotically normal, and also asymptotically efficient under checkable conditions

Measurement of Lagrangian velocity in fully developed turbulence

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particule at a turbulent Reynolds number $R_{\lambda} = 740$. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form $E^{L}(\omega) = u_{rms}^{2} T_{L} / (1 + (T_{L}\omega)^{2})$, in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.Comment: 4 pages, 5 figures. to appear in PR

BADANIA I MODELOWANIE LOKALNEGO SYSTEMU NAWIGACJI NAZIEMNEJ ROBOTA MOBILNEGO

The algorithm of complex information processing in the local navigation system of a terrestrial mobile robot and its physical model is developed. Experimental researches of this physical model have been carried out, as a result of which qualitative characteristics of the developed local navigation system have been determined. The trajectory of the object, based on the calculated navigation parameters, has a configuration identical to the actually passed route (adequate functioning of the system as a course indicator). The error in determining the coordinates of an offline object has value 0.012t2 (1.2 m per 10 s) when moving linearly and 0.022t2 (2.2 m per 10 s) when maneuvering. The orientation angles are worked out with precision (0.1÷0.3)о for roll and pitch angles and (2÷3)о for the angle of the course. Precise characteristics of the developed physical model LNS for determining orientation angles and motion parameters МR similar to the passport serial data SINS, and in some cases due to navigation features МR show even better accuracy.Opracowano algorytm złożonego przetwarzania informacji w lokalnym systemie nawigacji naziemnego mobilnego robota i jego modelu fizycznego. Przeprowadzono eksperymentalne badania tego modelu fizycznego, w wyniku których określono cechy jakościowe opracowanego lokalnego systemu nawigacji. Trajektoria obiektu, określona na podstawie obliczonych parametrów nawigacyjnych, ma konfigurację identyczną z rzeczywistą przebytą trasą (system działa poprawnie jako wskaźnik). Błąd w określaniu współrzędnych obiektu offline wynosi 0,012t2 (1,2 m w 10 s) podczas ruchu liniowego i 0,022t2 (2,2 m w 10 s) podczas manewrowania. Kąty orientacji są obliczane z dokładnością (0,1÷0,3)o dla kątów przechyłu i pochylenia oraz (2÷3)o dla kąta kursu. Dokładne cechy opracowanego modelu fizycznego systemu do określania kątów orientacji i parametrów ruchu robota mobilnego są podobne do danych paszportowych seryjnych BINS, a w niektórych przypadkach, ze względu na cechy nawigacji robotów mobilnych, wykazują jeszcze lepszą dokładność