Improved Transients in Multiple Frequencies Estimation via Dynamic Regressor Extension and Mixing

A problem of performance enhancement for multiple frequencies estimation is studied. First, we consider a basic gradient-based estimation approach with global exponential convergence. Next, we apply dynamic regressor extension and mixing technique to improve transient performance of the basic approach and ensure non-strict monotonicity of estimation errors. Simulation results illustrate benefits of the proposed solution.Comment: This paper is submitted for the ALCOSP 2016 conferenc

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

A parallel prefiltering approach for the identification of a biased sinusoidal signal: theory and experiments

The problem of estimating the amplitude, frequency, and phase of an unknown sinusoidal signal from a noisy-biased measurement is addressed in this paper by a family of parallel prefiltering schemes. The proposed methodology consists in using a pair of linear filters of specified order to generate a suitable number of auxiliary signals that are used to estimate\u2014in an adaptive way\u2014the frequency, the amplitude, and the phase of the sinusoid. Increasing the order of the prefilters improves the noise immunity of the estimator, at the cost of an increase of the computational complexity. Among the whole family of estimators realizable by varying the order of the filters, the simple parallel prefilters of orders 2 C 2 and 3 C 3 are discussed in detail, being the most attractive from the implementability point of view. The behavior of the two algorithms with respect to bounded external disturbances is characterized by input-to-state stability arguments. Finally, the effectiveness of the proposed technique is shown both by comparative numerical simulations and by a real experiment addressing the estimation of the frequency of the electrical mains from a noisy voltage measurement

Globally stable tracking and estimation for single-phase electrical signals with DC-offset rejection

This work introduces a new algorithm, named Global Quadrature PLL (GQPLL) for tracking a sinusoidal signal and for estimating its frequency and amplitude. The proposed technique derives from the well-known PLL architecture based on Quadrature Signal Generation, that is widely used for tracking the fundamental of single-phase electrical signals. The proposed algorithm improves the existing quadrature-PLL solutions from two different perspectives. First, the cancellation of the DC-bias is embedded by construction. Moreover, a Lyapunov-based stability analysis guarantees the global convergence of the estimates for arbitrarily large adaptation gains, enabling fast adaptation transients. Simulations show that the proposed algorithm is able to deal with sudden variations of the fundamental frequency and of the DC-bias magnitude

An Adaptive Observer-based Robust Estimator of Multi-sinusoidal Signals

This paper presents an adaptive observer-based robust estimation methodology of the amplitudes, frequencies and phases of biased multi-sinusoidal signals in presence of bounded perturbations on the measurement. The parameters of the sinusoidal components are estimated on-line and the update laws are individually controlled by an excitation-based switching logic enabling the update of a parameter only when the measured signal is sufficiently informative. This way doing, the algorithm is able to tackle the problem of over-parametrization (i.e., when the internal model accounts for a number of sinusoids that is larger than the true spectral content) or temporarily fading sinusoidal components. The stability analysis proves the existence of a tuning parameter set for which the estimator\u2019s dynamics are input-to-state stable with respect to bounded measurement disturbances. The performance of the proposed estimation approach is evaluated and compared with other existing tools by extensive simulation trials and real-time experiments

A Review of the Frequency Estimation and Tracking Problems

This report presents a concise review of some frequency estimation and frequency tracking problems. In particular, the report focusses on aspects of these problems which have been addressed by members of the Frequency Tracking and Estimation project of the Centre for Robust and Adaptive Systems. The report is divided into four parts: problem specification and discussion, associated problems, frequency estimation algorithms and frequency tracking algorithms. Part I begins with a definition of the various frequency estimation and tracking problems. Practical examples of where each problem may arise are given. A comparison is made between the frequency estimation and tracking problems. In Part II, block frequency estimation algorithms, fast block frequency estimation algorithms and notch filtering techniques for frequency estimation are dealt with. Frequency tracking algorithms are examined in Part III. Part IV of this report examines various problems associated with frequency estimation. Associated problems include Cramer-Rao lower bounds, theoretical algorithm performance, frequency resolution, use of the analytic signal and model order selection

Adaptive rejection of finite band disturbances - theory and applications

Le chapitre présente les techniques de rejection adpative de perturbation inconnue mais de bande finie. Plusieurs exemples sont mentionnés et l'application au rejet adaptatifs de perturbation inconnues sur une suspension active est décrite en détailThe techniques for adaptive rejection of unknown finite band disturbances are reviewed. Several applications are mentionned and the application to the adaptive rejection of unknown disturbances on an active suspension is presented in detail

Calculation of the Performance of Communication Systems from Measured Oscillator Phase Noise

Oscillator phase noise (PN) is one of the major problems that affect the performance of communication systems. In this paper, a direct connection between oscillator measurements, in terms of measured single-side band PN spectrum, and the optimal communication system performance, in terms of the resulting error vector magnitude (EVM) due to PN, is mathematically derived and analyzed. First, a statistical model of the PN, considering the effect of white and colored noise sources, is derived. Then, we utilize this model to derive the modified Bayesian Cramer-Rao bound on PN estimation, and use it to find an EVM bound for the system performance. Based on our analysis, it is found that the influence from different noise regions strongly depends on the communication bandwidth, i.e., the symbol rate. For high symbol rate communication systems, cumulative PN that appears near carrier is of relatively low importance compared to the white PN far from carrier. Our results also show that 1/f^3 noise is more predictable compared to 1/f^2 noise and in a fair comparison it affects the performance less.Comment: Accepted in IEEE Transactions on Circuits and Systems-I: Regular Paper

A space communications study Final report, 15 Sep. 1966 - 15 Sep. 1967

Investigation of signal to noise ratios and signal transmission efficiency for space communication system