A kepstrum approach to filtering, smoothing and prediction

The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

Adaptive Filtering for Large Space Structures: A Closed-Form Solution

In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system

Bayesian Inference on Dynamic Models with Latent Factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.Bayesian Dynamic Models, Simulation Based Inference, Particle Filters, Latent Factors, Business Cycle

Two-dimensional recursive parameter identification for adaptive Kalman filtering

Includes bibliographical references (page 1081).This paper is concerned with the development of a 2-D adaptive Kalman filtering by recursive adjustment of the parameters of an autoregressive (AR) image model with non symmetric half-plane (NSHP) region of support. The image and degradation models are formulated in a 2-D state-space model, for which the relevant 2-D Kalman filtering equations are given. The recursive parameter identification is achieved using the extension of the stochastic Newton approach to the 2-D case. This process can be implemented on-line to estimate the image model parameters based upon the local statistics in every processing window. Simulation results for removing an additive noise from a degraded image are also presented

Time-Varying Modeling of Glottal Source and Vocal Tract and Sequential Bayesian Estimation of Model Parameters for Speech Synthesis

abstract: Speech is generated by articulators acting on a phonatory source. Identification of this phonatory source and articulatory geometry are individually challenging and ill-posed problems, called speech separation and articulatory inversion, respectively. There exists a trade-off between decomposition and recovered articulatory geometry due to multiple possible mappings between an articulatory configuration and the speech produced. However, if measurements are obtained only from a microphone sensor, they lack any invasive insight and add additional challenge to an already difficult problem. A joint non-invasive estimation strategy that couples articulatory and phonatory knowledge would lead to better articulatory speech synthesis. In this thesis, a joint estimation strategy for speech separation and articulatory geometry recovery is studied. Unlike previous periodic/aperiodic decomposition methods that use stationary speech models within a frame, the proposed model presents a non-stationary speech decomposition method. A parametric glottal source model and an articulatory vocal tract response are represented in a dynamic state space formulation. The unknown parameters of the speech generation components are estimated using sequential Monte Carlo methods under some specific assumptions. The proposed approach is compared with other glottal inverse filtering methods, including iterative adaptive inverse filtering, state-space inverse filtering, and the quasi-closed phase method.Dissertation/ThesisMasters Thesis Electrical Engineering 201

Structured matrices and fast RLS adaptive filtering

We present a new approach to the discrete-time Chandrasekhar recursions and some generalizations thereof. We extend the recursions to a class of structured time-variant state-space models, and discuss connections with the (generalized) Schur algorithm. We also apply the extended recursions to the adaptive filtering problem and give a transparent derivation of fast recursive least-squares algorithms

Distributed Target Tracking and Synchronization in Wireless Sensor Networks

Wireless sensor networks provide useful information for various applications but pose challenges in scalable information processing and network maintenance. This dissertation focuses on statistical methods for distributed information fusion and sensor synchronization for target tracking in wireless sensor networks. We perform target tracking using particle filtering. For scalability, we extend centralized particle filtering to distributed particle filtering via distributed fusion of local estimates provided by individual sensors. We derive a distributed fusion rule from Bayes\u27 theorem and implement it via average consensus. We approximate each local estimate as a Gaussian mixture and develop a sampling-based approach to the nonlinear fusion of Gaussian mixtures. By using the sampling-based approach in the fusion of Gaussian mixtures, we do not require each Gaussian mixture to have a uniform number of mixture components, and thus give each sensor the flexibility to adaptively learn a Gaussian mixture model with the optimal number of mixture components, based on its local information. Given such flexibility, we develop an adaptive method for Gaussian mixture fitting through a combination of hierarchical clustering and the expectation-maximization algorithm. Using numerical examples, we show that the proposed distributed particle filtering algorithm improves the accuracy and communication efficiency of distributed target tracking, and that the proposed adaptive Gaussian mixture learning method improves the accuracy and computational efficiency of distributed target tracking. We also consider the synchronization problem of a wireless sensor network. When sensors in a network are not synchronized, we model their relative clock offsets as unknown parameters in a state-space model that connects sensor observations to target state transition. We formulate the synchronization problem as a joint state and parameter estimation problem and solve it via the expectation-maximization algorithm to find the maximum likelihood solution for the unknown parameters, without knowledge of the target states. We also study the performance of the expectation-maximization algorithm under the Monte Carlo approximations used by particle filtering in target tracking. Numerical examples show that the proposed synchronization method converges to the ground truth, and that sensor synchronization significantly improves the accuracy of target tracking

Quantum feedback and adaptive measurements

Summary form only given. Although real-time feedback of measured signals is an essential component of sensing and control in classical settings, models for quantum feedback that are rigorous yet useful have only become possible since the advent of measurement-based quantum trajectory theory. The quantum feedback scenario introduces new concerns of coherence and measurement backaction, but recent work has shown that these can be treated properly in a formal integration of quantum trajectory theory with standard state-space formulations of filtering and control theory. Pioneering studies by H. M. Wiseman have shown that such models can be used to design and to analyze realistic schemes for adaptive homodyne measurement and for feedback control of atomic motion. Much of the ongoing research in our group focuses on the experimental implementation of such schemes. For a broad range of quantum feedback scenarios, certain recurring technical issues arise out of the need to perform complex, high-bandwidth processing of measured signals. We are developing a "rapid-prototyping" approach to refining signal processing and feedback algorithms via quantum trajectory simulation on a PC, followed by translation of the algorithms into hardware Description language (HDL)