Maciej Niedzwiecki

Adaptive scheme for elimination of broadband noise and impulsive disturbances from AR and ARMA signals

The problem of elimination of measurement noise and impulsive disturbances from autoregressive and autoregressive moving average signals is considered. It is shown that the task of simultaneous detection/tracking/restoration can be stated as a nonlinear filtering problem and solved using the theory of extended Kalman filter. Numerical tests carried out for real audio signals corrupted by both real and artificially generated disturbances confirm very good properties of the proposed algorithm.

Tracking analysis of a generalized adaptive notch filter

The paper presents results of local performance analysis of a generalized adaptive notch filter (GANF). GANFs are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique. Even though restricted to a single-frequency case, the presented analysis provides valuable insights into the tracking mechanisms of GANF, including the associated speed/accuracy tradeoffs, the achievable performance bounds, and tracking limitations. In addition, it allows one to formulate some useful rules of thumb for choosing design parameters.

Recursive functional series modeling estimators for identification of time-varying plants-more bad news than good?

The properties of a class of recursive estimators-the exponentially weighted functional series modeling estimators-are discussed. These estimators can be used, e.g. in adaptive prediction or control applications. It is argued that there exists a relationship between the amount of information about time-varying system parameters, which is available a priori, and the robustness of the identification algorithm based on such prior knowledge. The more specialized the estimation algorithm is, the less reliable it might be under nonstandard conditions. This is the reason why simple algorithms such as exponentially weighted least squares have to be recommended as if no information about the system nonstationarity is available in advance. >

Identification of quasi-periodically varying systems using the combined nonparametric/parametric approach

The problem of identification of quasi-periodically varying finite impulse response systems is considered. Neither the number of system frequency modes nor the initial frequency values are assumed to be known a priori. The proposed solution is a blend of the parametric (model based) and nonparametric (discrete Fourier transform based) approach to system identification. It is shown that the results of nonparametric analysis can be used to identify the number of frequency modes and to determine initial conditions needed to smoothly start (or restart) the model-based tracking algorithm. Such a combined nonparametric/parametric approach allows one to preserve advantages of both frameworks, leading to an estimation procedure which guarantees global frequency search, high-frequency resolution, fast initial convergence, and good steady-state tracking capabilities.

A New Approach to Active Noise and Vibration Control—Part II: The Unknown Frequency Case

This paper presents a new approach to rejection of complex-valued sinusoidal disturbances acting at the output of a discrete-time stable linear plant with unknown dynamics. It is assumed that the frequency of the sinusoidal disturbance is known, and that the output signal is contaminated with wideband measurement noise. The disturbance rejection control rule is first derived and analyzed for a nominal plant model, different from the true model. Then a special adaptation mechanism is added, which is capable of compensating modeling biases (errors in both magnitude and phase) so that, under Gaussian assumptions, the closed-loop system can converge in mean to the optimal solution.

Identification of time-varying systems using combined parameter estimation and filtering

The problem of tracking time-varying parameters of a linear stochastic system is considered, and an identification method based on parameter estimation and filtering is described. The proposed algorithm combines the standard weighted least squares (WLS) identification with low-pass filtering of parameter estimates. It is shown that the parameter tracking properties of the combined estimation-filtering method are exactly the same as the tracking capabilities of the WLS estimator characterized by the appropriately defined weighting sequence and can be analyzed in terms of the associated frequency characteristics. The main advantage of the method is that it allows for efficient implementation of banks of adaptive filters characterized by different memory lengths without compromising the good tracking capabilities of WLS estimators. Additionally, it provides the designer with much greater flexibility in shaping the window. >

Application of particle filtering in navigation system for blind

The navigation system for the blind, equipped with the GPS receiver, digital map and dead-reckoning sensors, is described. The problem of estimation of the pedestrian position, based on information from different sources, is solved using the approach known as particle filtering. The particle clustering and convex region mapping techniques are used to guarantee that at all times the position estimates are feasible, i.e. that they comply with the constraints imposed by the digital map of the traversed area.

Multiple-model approach to finite memory adaptive filtering

The multiple-model technique is proposed for the purpose of finite memory adaptive filtering of nonstationary signals. Its most important feature is the parallel structure of computation: not one but several identification algorithms characterized by different memory-controlling parameters are run in parallel and combined appropriately. The results substantially improve the robustness of the adaptive scheme to the experimenters choice of design parameters such as forgetting factors, adaptation gains, and model orders. The author suggests a technique which allows for a rational decision to be made when several competitive adaptive filters work simultaneously. The results obtained can also be used for the purpose of model order determination, and their close correspondence to Rissanens predictive least squares principle and Akaikes concept of model likelihoods is noted. >

On tracking characteristics of weighted least squares estimators applied to nonstationary system identification

The parameter-tracking abilities of weighted-least-squares (WLS) estimators are characterized in terms of a suitably defined variability matrix and associated frequency characteristics. Using these concepts, the conflict arising between the estimation variance and estimation bandwidth is easily explained and quantified. >

Fast recursive basis function estimators for identification of time-varying processes

When system parameters vary rapidly with time, the weighted least squares filters are not capable of following the changes satisfactorily; some more elaborate estimation schemes, based on the method of basis functions, have to be used instead. The basis function estimators have increased tracking capabilities but are computationally very demanding. The paper introduces a new class of adaptive filters, based on the concept of postfiltering, which have improved parameter tracking capabilities that are typical of the basis function algorithms but, at the same time, have pretty low computational requirements, which is typical of the weighted least squares algorithms.