Piotr Kaczmarek

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.

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.

Generalized adaptive notch filters

The problem of identification/tracking of quasi-periodically varying systems is considered. This problem is a generalization, to the system case, of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise. The proposed solution is based on the exponentially weighted basis function (EWBF) approach. First, the global EWBF algorithm is derived and its decomposed, parallel-form and cascade-form variants, are described. Then the frequency-adaptive versions of both schemes are obtained using the recursive prediction error method. In the (special) signal processing case the paper offers new attractive solutions to the problem of adaptive notch filtering.

Estimation and tracking of complex-valued quasi-periodically varying systems

The problem of identification/tracking of quasi-periodically varying complex systems is considered. This problem is a generalization, to the system case, of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise. The proposed solution is based on the exponentially weighted basis function (EWBF) approach. First, the basic EWBF algorithm is derived. Then its frequency-decoupled, parallel-form and cascade-form variants, with highly modular structure and reduced computational requirements, are described. Finally, the frequency-adaptive versions of all schemes are obtained using the recursive prediction error method.

Generalized adaptive notch and comb filters for identification of quasi-periodically varying systems

The problem of identification/tracking of quasi-periodically varying real-valued systems is considered. This problem is a generalization, to the system case, of a classical signal processing task of either elimination or extraction of nonstationary sinusoidal signals buried in noise. The solution is based on the exponentially weighted basis function (EWBF) approach. The proposed algorithms are capable of tracking slow changes in system frequencies, which means that not only the expansion coefficients in the basis function description of the analyzed system but also the basis functions themselves are adjusted in an adaptive manner. First, assuming that the system frequencies are known and constant, the running basis and fixed basis variants of the EWBF algorithm are derived, and their relationship to the classical notch filter with constrained poles and zeros is established. Next, the frequency-adaptive versions of both algorithms are obtained using the gradient search and recursive prediction error principles, respectively. Finally, the interrelated frequencies case is analyzed and two additional parameter tracking algorithms (generalized adaptive comb filters) are derived.

Central heating temperature control algorithm for systems with condensing boilers

The problem of control of a central heating system in a small residence is considered. It is assumed that the system is based on a condensing boiler. Since the boiler efficiency depends on a returning water temperature, the proposed control goal is to provide proper air temperature in the residence as well as the lowest possible water temperature. The proposed algorithm is applied to two buildings. Both of them have the same heating energy requirements, but the heat capacity of their walls differs. The presented simulation study shows reduction of energy consumption compared to that yielded by the traditional control algorithms.

Compensation of an Estimation Delay in Self-Optimizing Adaptive Notch Filters

It is shown that estimation accuracy of adaptive notch filters (ANFs) can be increased by combining two techniques that were previously used separately: automatic gain adjustment and frequency debiasing. To achieve this goal one has to solve a nontrivial problem of determining estimation delay introduced by a variable-gain ANF filter.

Generalized adaptive notch filters - does gradient smoothing technique help?

Generalized adaptive notch filters (GANF) are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered extension, to the system case, of classical adaptive notch filters. We analyze the enhanced GANF algorithm, proposed in the literature, which incorporates gradient smoothing. We show, both analytically and by means of computer simulation, that gradient smoothing does not improve tracking performance of generalized adaptive notch filters.