Yuriy S. Shmaliy | Universidad de Guanajuato (original) (raw)

Papers by Yuriy S. Shmaliy

Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples c... more Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided.

It is proved that the iterative computation form for the mean square error (MSE) matrix of the ba... more It is proved that the iterative computation form for the mean square error (MSE) matrix of the batch unbiased finite impulse response (UFIR) filter exactly equals to that of the iterative UFIR filter form, unlike what was previously thought. Based on the iterative MSE matrix form, we suggest two strategies for defining the optimal horizon length for the UFIR filter. The results are verified using the two-state polynomial and harmonic models. Index Terms—Unbiased FIR filter, mean square error, iterative algorithm, optimal horizon, state-space.

—Smart sensors are often designed to operate under harsh industrial conditions with incomplete in... more —Smart sensors are often designed to operate under harsh industrial conditions with incomplete information about noise and missing data. Therefore, signal processing algorithms are required to be unbiased, robust, predictive, and desirably blind. In this paper, we propose a novel blind iterative unbiased finite impulse response (UFIR) filtering algorithm, which fits these requirements as a more robust alternative to the Kalman filter (KF). The trade-off in robustness between the UFIR filter and KF is learned analytically. The predictive UFIR algorithm is developed to operate in control loops under temporary missing data. Experimental verification is given for carbon monoxide concentration and temperature measurements required to monitor urban and industrial environments. High accuracy and precision of the predictive UFIR estimator are demonstrated in a short time and on a long baseline.

—Industrial wireless sensor networks (WSNs) often operate under harsh conditions that requires ro... more —Industrial wireless sensor networks (WSNs) often operate under harsh conditions that requires robustness from an estimator of a measured quantity. We propose a novel distributed unbiased finite impulse response (UFIR) filter called micro-UFIR filter that, unlike the micro Kalman filter (micro-KF), is robust against modeling errors in uncertain noise environments. The micro-UFIR filter is derived based on average consensus on measurements and, unlike the micro-KF, requires only one consensus filter. Better robustness of the micro-UFIR filter is shown analytically and confirmed by simulations of a WSN and a vehicle travelling along a circular trajectory under unpredictable impacts, impulsive noise, and errors in the noise statistics.

—We analyze and approximate the jitter distribution function in the breakpoints of the measured g... more —We analyze and approximate the jitter distribution function in the breakpoints of the measured genome copy number alterations (CNAs). The CNAs measured using the high resolution technologies of hybridization are contaminated with an intensive noise that may cause uncertainty in the detected breakpoints and segments. We show that jitter is fundamentally inherent to the simulate CNAs and that the jitter probability represented with the discrete skew Laplace distribution is not accurate when the signal-to-noise ratio (SNR) is small. To approximate the jitter distribution with highest accuracy, we modify the skew Laplace distribution to have the SNR function dependent on the discrete departure from the breakpoint. We propose several approximating functions and test them by experimental data.

—Robustness is required from an estimator to provide better performance if a wireless sensor netw... more —Robustness is required from an estimator to provide better performance if a wireless sensor network (WSN) operates under harsh conditions with incomplete information about noise. This paper shows that robustness of the WSN can be improved by using the distributed unbiased finite impulse response (UFIR) filter rather than the traditional distributed Kalman filter (KF), both based on the average consensus. Unlike the KF, the UFIR filter completely ignores the noise statistics and initial values which are typically not well known. As an example, we consider a vehicle travelling along a circular trajectory under unpredictable impacts and errors in the noise statistics. A case of impulsive noise generated by manufacturing process is also considered.

Chromosomal structural changes in human body known as copy number alterations (CNAs) are often as... more Chromosomal structural changes in human body known as copy number alterations (CNAs) are often associated with disease such as cancer. Therefore, accurate estimation of the CNAs using high resolution technologies is on a front line of bioinformatics and engineering. Since the Laplace distribution recently justified to represent jitter in the CNA breakpoints is not sufficiently accurate to estimate small changes, we propose a more accurate approximation based on the modified Bessel function of the second kind and zeroth order. We develop the relevant confidence masks to bound the CNA estimates for the given probability. The masks are applied to test the estimates obtained using the profile copy number of single nucleotide polymorphism (SNP) array data. We also show how to improve the estimates for the required confidence probability by removing some unlikely existing breakpoints.

—Industrial processes are often organized using mechanical systems with multiple degrees-of-freed... more —Industrial processes are often organized using mechanical systems with multiple degrees-of-freedom (DOF). For real-time operation of such systems in noise environments, fast, optimal and robust estimators are required. In this paper, information gathering about multi-DOF system states is provided using the optimal finite impulse response (OFIR) filter. To use this filter in real time, a fast iterative algorithm is developed with a pseudo code available for immediate use. Although the iterative algorithm utilizes Kalman recursions, it is more robust against uncertainties and model errors owing to the transversal structure. We use this algorithm to estimate state in the 1-DOF torsion system and 3-DOF helicopter system.

Measurements are often provided in the presence of noise and uncertainties that require optimal f... more Measurements are often provided in the presence of noise and uncertainties that require optimal filters to estimate processes with highest accuracy. The ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm presented in this paper is more robust in real world than the Kalman filter. It completely ignores the noise statistics and initial values while demonstrating better accuracy under the mis-modeling and temporary uncertainties and lower sensitivity to errors in the noise statistics.

—The general unbiased FIR (UFIR) filter proposed in this paper has important structural advantage... more —The general unbiased FIR (UFIR) filter proposed in this paper has important structural advantages against its basic predecessor: it can be applied to systems with or without the control input. We derive this filter in a batch form and then design its fast iterative Kalman-like algorithm using recursions. The iterative UFIR algorithm proposed is applied to the three-state polynomial model which is basic in clock synchronization. We test it by the Global Positioning System-based frequency steering of an oven controlled crystal oscillator. Better robustness and higher accuracy of the UFIR filter against the Kalman filter are shown experimentally.

Measurements are often provided in the presence of noise and uncertainties that require optimal f... more Measurements are often provided in the presence of noise and uncertainties that require optimal filters to estimate processes with highest accuracy. The ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm presented in this paper is more robust in real world than the Kalman filter. It completely ignores the noise statistics and initial values while demonstrating better accuracy under the mismodeling and temporary uncertainties and lower sensitivity to errors in the noise statistics.

In this survey, the authors examine the trade-off between the unbiased, optimal, and in-between s... more In this survey, the authors examine the trade-off between the unbiased, optimal, and in-between solutions in finite impulse response (FIR) filtering. Specifically, they refer to linear discrete real-time invariant state-space models with zero mean noise sources having arbitrary covariances (not obligatorily delta shaped) and distributions (not obligatorily Gaussian). They systematically analyse the following batch filtering algorithms: unbiased FIR (UFIR) subject to the unbiasedness condition, optimal FIR (OFIR) which minimises the mean square error (MSE), OFIR with embedded unbiasedness (EU) which minimises the MSE subject to the unbiasedness constraint, and optimal UFIR (OUFIR) which minimises the MSE in the UFIR estimate. Based on extensive investigations of the polynomial and harmonic models, the authors show that the OFIR-EU and OUFIR filters have higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.

We analyze the code reading error probability (EP) in the radio frequency identification surface ... more We analyze the code reading error probability (EP) in the radio frequency identification surface acoustic wave (SAW) tags with pulse position coding (PPC) and peak-pulse detection. EP is found in a most general form assuming M groups of codes with N slots each and allowing individual signal-to-noise ratios (SNRs) in each slot. The basic case of zero signal in all Off-pulses and equal signals in all On-pulses is investigated in detail. We show that if a SAW-tag with PPC is designed such that the spurious responses are ...

IET Signal Processing, 2012

Continuous-Time Systems, 2007

18th European Frequency and Time Forum (EFTF 2004), 2004

Abstract Passive wireless surface acoustic wave (SAW) sensors are used to measure temperature, pr... more Abstract Passive wireless surface acoustic wave (SAW) sensors are used to measure temperature, pressure and torque, identify the railway vehicle at high speed, etc. with a resolution of about 1%. Most frequently, the information bearer in such sensors is a time delay of the SAW estimated at the receiver. The basic principle utilized in such a technique combines advantages of the precise piezoelectric sensors, high SAW sensitivity to the environment, passive (without a power supplied) operation, and wireless communication ...

2013 10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 2013

Measurements are often provided in the presence of noise and uncertainties that require optimal f... more Measurements are often provided in the presence of noise and uncertainties that require optimal filters to estimate processes with highest accuracy. The ultimate iterative unbiased finite impulse response (UFIR) filtering algorithm presented in this paper is more robust in real world than the Kalman filter. It completely ignores the noise statistics and initial values while demonstrating better accuracy under the mismodeling and temporary uncertainties and lower sensitivity to errors in the noise statistics.

IET Signal Processing, 2012

Continuous-Time Systems, 2007

18th European Frequency and Time Forum (EFTF 2004), 2004

2013 10th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 2013

Chromosomal structural changes in human body known as copy number alteration (CNA) are often asso... more Chromosomal structural changes in human body known as copy number alteration (CNA) are often associated with diseases, such as various forms of cancer. Therefore, accurate estimation of breakpoints of the CNAs is important to understand the genetic basis of many diseases. The high‐resolution comparative genomic hybridization (HRCGH) and single‐nucleotide polymorphism (SNP) technologies enable cost‐efficient
and high‐throughput CNA detection. However, probing provided using these profiles gives data highly contaminated by intensive Gaussian noise having white properties. We observe the probabilistic properties of CNA in HR‐CGH and SNP measurements and show that jitter in the breakpoints can statistically be described with either the discrete skew Laplace distribution when the segmental signal‐to‐noise ratio (SNR) exceeds unity or modified Bessel function‐based approximation when SNR is <1. Based upon these approaches, the confidence masks can be developed and used to enhance the estimates of the CNAs for the given confidence probability by removing some unlikely existing breakpoints.

This book is a collective work made ba various authors well-recognised owing to their appreciable... more This book is a collective work made ba various authors well-recognised owing to their appreciable contributions to the theory and applications of probability. Both mathematical and engineering aspects of probability outline its framework. Readers can find here several timely topics such as risk theory and applications, Laplace distributions which describe the heavy-tailed noise, Poisson sums having applications in business and engineering, Markov chains investigations and approximations, Berstein-Hoeffding-type exponential inequalities useful for proving limiting theorems, Bayesian computational methods, as well as a modern view on sampling and reconstruction of Gaussian and non-Gaussian random processes.

This book addresses novel results in thye field of optimal finite impulse response (FIR) estimati... more This book addresses novel results in thye field of optimal finite impulse response (FIR) estimation and steering of the local clock time errors using the Global Positioning System (GPS) timing signals. The studies are motivated by permanently increased demands for accuracy of the local timescales in different areas of applications of wire and wireless digital systems. The main limitations of accuracy here are the GPS time uncertainty caused by different satellites in a view and the sawtooth noise induced by the commercially available GPS timing receivers owing to the principle of the one pulse per second (1PPS) signal formation. Due to the GPS time uncertainty, flicker components of the clock noise, and non Gaussian sawtooth noise, the standard Kalman algorithms may become unstable and noisy, even when the sawtooth correction is applied. We show that an efficient way of providing stable and accurate filtering, smoothing, prediction, and steering of the local clock errors is to use the optimal FIR structures, which are inherently bounded input/bounded output (BIBO) stable and more robust against temporary uncertainties and round-off errors. Moreover, unbiased polynomial FIR solutions having strong engineering features become actually optimal by large averaging horizons typically used in timekeeping. Such solutions are found and investigated in detail theoretically and for real measurements. Based upon, it is stated that optimal (unbiased) FIR estimators are likely the best candidates to use in the modern filtering, prediction, and synchronisations algorithms intended for the estimation and steering of local clocks.

Continuous-Time Systems is a description of linear, nonlinear, time-invariant, and time-varying e... more Continuous-Time Systems is a description of linear, nonlinear, time-invariant, and time-varying electronic continuous-time systems. As an assemblage of physical or mathematical components organized and interacting to convert an input signal (also called excitation signal or driving force) to an output signal (also called response signal), an electronic system can be described using different methods offered by the modern systems theory. To make possible for readers to understand systems, the book systematically covers major foundations of the systems theory. First, the quantitative and qualitative methods of systems description are presented along with the stability analysis. The representation of linear time-invariant systems in the time domain is provided using the convolution, ordinarily differential equations (ODEs), and state space. In the frequency domain, these systems are analyzed using the Fourier and Laplace transforms. The linear time-varying systems are represented using the general convolution, ODEs, and state space. The nonlinear time-invariant systems are described employing the Taylor and Volterra series expansions, ODEs, state space, and approximate methods such as averaging, equivalent linearization, and describing function. Finally, the representation of nonlinear time-varying systems is given using the Taylor and Volterra series, ODEs, modulation functions method, and state space modelling. Review of matrix theory and other useful generalizations are postponed to Appendices.

This book offers an extended description of continuous-time signals related to signals and system... more This book offers an extended description of continuous-time signals related to signals and systems. As a time-varying process of any physical state of any object, which serves for representation, detection, and transmission of messages, a modern electrical signal possesses, in applications, many specific properties. The text covers principle foundations of signals theory. Presenting bandlimited and analytic signals, the book reviews the methods of their description, transformation (by Hilbert transform), and sampling.

Espacios cerrados de navegacion con rejillas de informacion utilizando etiquetas RFID vislumbra... more Espacios cerrados de navegacion con rejillas de informacion utilizando etiquetas RFID vislumbran un futuro prometedor para aplicaciones industriales y otras necesidades de ingeniera; la razon es simple: cada etiqueta puede proporcionar informacion acerca del entorno local en 2D o 3D. Sin embargo para obtener su maximo rendimiento se requiere una alta precision del vehculo movil que se desplaza por la rejilla; ya que los errores que se produzcan durante el trayecto pueden generar fallas no deseadas o inclusive colisiones fatales. Por ello se propone un nuevo tipo de ltro denominado Filtro Extendido de Respuesta Finita al Impulso sin Desplazamiento (EFIR) que se caracteriza por ser insesgado y su condicion de extendido se deriva de que es aplicado a un proceso no lineal; este tipo de ltro es recursivo presentando la forma del ltro de Kalman que ha sido ampliamente utilizado en ingeniera. Este trabajo de investigacion presenta a traves de una basta gama de simulaciones el comportamiento del ltro EFIR y se compara con el ltro extendido de Kalman (EKF) el cual se ha empleado en la ultima decada en aplicaciones con etiquetas RFID y autolocalizacion de robots moviles; se demuestra como los errores en las matrices de covarianza de ruido pueden provocar divergencia en el ltro EKF; mientras que el ltro EFIR permanece estable convirtiendolo en un ltro con mayor robustez y un fuerte candidato en distintas aplicaciones de ltrado digital.

Esta investigación plantea el uso de un novedoso algoritmo de suavizado de tiempo variante FB y U... more Esta investigación plantea el uso de un novedoso algoritmo de suavizado de tiempo variante FB y UFIR (Unbiased Finite Impulse Response, respuesta finita al impulso sin bies) para utilizarlo en el ´area de genética. El suavizador FB UFIR une ventajas de estructuras lineales robustas y de algunas no lineales, además propone la solución para preservar los cambios sin jitter, provee una eficiente eliminación de ruido y tiene suficiente robustez contra el ruido heavy-tailed; en el Capitulo II se muestra la estructura del algoritmo. A continuación se da una introducción del objetivo del suavizador en el área mencionada, así como la razones de su aplicación.

—Wireless sensor networks (WSNs) often operate under harsh conditions requiring robustness from t... more —Wireless sensor networks (WSNs) often operate under harsh conditions requiring robustness from the estimator. This paper develops a distributed unbiased finite impulse response (UFIR) filter based on average consensus as a more robust alternative to the Kalman filter (KF). Unlike the distributed KF, the distributed UFIR filter typically requires only one consensus filter and completely ignores the noise statistics and initial values. As an example, we consider a vehicle travelling along a circular trajectory under unpredictable impacts and errors in the noise statistics. Better performance of the UFIR filter is demonstrated under diverse operation conditions.

Efficient iterative extended finite impulse response (EFIR) filtering algorithms are developed fo... more Efficient iterative extended finite impulse response (EFIR) filtering algorithms are developed for nonlinear discrete-time state-space estimation. An advantage of the EFIR approach is that the noise statistics are not required on a horizon of N opt points and zero mean noise is allowed to have any distribution and covariance. The EFIR algorithm is developed for nonlinear estimation over sensor networks that implies time-varying matrix structures. A modified EFIR algorithm employs the nonlinear-to-linear observation conversion. Applications are given to robot indoor self-localization over radio frequency identification tag grid excess channels.

The copy number variations (CNVs) are a form of structural genetic changes which are recognized t... more The copy number variations (CNVs) are a form of structural genetic changes which are recognized to have an importance for diagnosing human disease. Therefore, accurate estimation of the CNVs using high resolution technologies has been under peer attention in both research and clinical applications during last decades. We propose a more accurate approximation for jitter distribution in the CNVs breakpoints based on the modified Bessel function of the second kind and zeroth order. We show that the modified distribution allows improving the estimates of the CNVs when the segmental signal-to-noise ratio is small and extremely small.

Accuracy of mobile objects self-localization in radio frequency identification (RFID) tag network... more Accuracy of mobile objects self-localization in radio frequency identification (RFID) tag networks depends on many environmental and design factors. This paper analyzes effect of such factors on estimates of the mobile object location. As an estimator, we use the extended finite impulse response (EFIR) filter. It is shown that accuracy of self-localization in the ultra high frequency (UHF) RFID tag networks can be increased by the factor of several times if to optimize design of the tag and network environment and obtain the optimal angle of arrival and viewing angle. Many other factors are also considered.

In this paper, we give an analysis of the embedded unbiasedness (EU) on optimal finite impulse re... more In this paper, we give an analysis of the embedded unbiasedness (EU) on optimal finite impulse response (OFIR) estimates. By minimizing the mean square error (MSE) constrained by the unbiasedness condition, a new OFIR-EU filter is derived. We show that the OFIR-EU filter does not require the initial conditions, and occupies an intermediate place between the UFIR and OFIR filters. It is also shown that the MSEs of the OFIR-EU and OFIR filters diminish with the estimation horizon. A numerical example has demonstrated that the OFIR-UE filter has better robustness against temporary model uncertainties than the OFIR and Kalman filters.

In this paper, we propose a new nonlinear filtering algorithm that can provide more accurate and ... more In this paper, we propose a new nonlinear filtering algorithm that can provide more accurate and reliable localization compared with the pure particle filtering (PF). In the proposed algorithm, failures of the PF are detected, and the failed PF is recovered using a finite impulse response (FIR) filter. The resulting filter is called the combined particle/FIR filter (CPFF). We demonstrate the performance of the CPFF by the indoor human localiza-tion. Key–Words: Localization, particle filter, finite impulse response (FIR) filter, combined particle/FIR filter.

Fast optimal estimates are often required in control and signal processing. In this paper, we dis... more Fast optimal estimates are often required in control and signal processing. In this paper, we discuss an approach to optimal finite impulse response (OFIR) filtering for discrete time-variant systems using finite measurements. The mean square error is minimized to obtain the batch OFIR algorithm which requires measurements on an a finite horizon of N points. Fast iterative algorithm is found using recursions. It is shown that each recursion has a predictor/corrector Kalman filter (KF)-like format with special initial conditions. In this sense, the KF is considered as a special case of the proposed iterative OFIR filtering algorithm when N approaches infinity for known initial conditions. It has been confirmed by simulation that the iterative form of the OFIR filter operates much faster than the batch form.