Unbiased FIR filtering

The contribution of this work is the creation and development of a novel procedure for signals estimation, procedure LDM-G. The procedure will be developed with details and will consist of algorithms implementation for signals estimation via wavelet transform, applying the minimum description length principle for simultaneous and automatic selection of wavelet base and threshold value. By means of simulations, the implemented procedure was compared with techniques of universal threshold and Stein's SURE, where the effectiveness of the elaborated procedure was verified by means of the estimation of mean square error.

In this paper, we study stability and roust stability of the zero solution of discrete-time switched systems with delays. And we give sufficient conditions which guarantee that the zero solution of discrete-time switched systems with delays is asymptotically stable and robustly stable. Numerical simulations are also given to illustrate the results.

Zhibo Wen received his master degree in electrical engineering and information technology from the Technische Universität München, Germany, with the rating passed high distinction. He has received the "Leo-Brandt-Preis -DGON Master of Navigation" from the German Institute of Navigation for his master thesis on estimation of code and phase bias in satellite navigation. During his master studies, he has received a DAAD scholarship and an MAN scholarship for his excellent grades. He is currently a PhD candidate at the Institute for Communications and Navigation, Technische Universität München, working on precise point positioning. Patrick Henkel studied electrical engineering and information technology at the

This paper presents a noise covariance estimation method for dynamical models with rectangular noise gain matrices. A novel receding horizon least squares criterion to achieve high estimation accuracy and stability under environmental uncertainties and experimental errors is proposed. The solution to the optimization problem for the proposed criterion gives equations for a novel covariance estimator. The estimator uses a set of recent information with appropriately chosen horizon conditions. Of special interest is a constant rectangular noise gain matrices for which the key theoretical results are obtained. They include derivation of a recursive form for the receding horizon covariance estimator and iteration procedure for selection of the best horizon length. Efficiency of the covariance estimator is demonstrated through its implementation and performance on dynamical systems with an arbitrary number of process and measurement noises.

Recibido el 8 de marzo de 2011; aceptado el 10 de agosto de 2011 En este artículo se hace una descripción del proceso de identificación considerado como un filtro digital adaptivo en el que es necesario contar con: la función de transición estimada, el error de identificación y la función de ganancia. Lo que genera un problema con respecto a la evolución del sistema de referencia por el tiempo de procesamiento del filtrado al requerir cumplir con sus operaciones dentro del mismo intervalo de tiempo. En términos generales, la calidad de su respuesta se ve afectada por el parámetro usado en la función de transición estimada al intervenir éste de manera indirecta en las demás operaciones del filtrado. Esto dio origen a probar dos estimadores, el primero expresado de manera recursiva y el segundo seleccionando la ganancia dentro de una base de conocimiento de acuerdo con la l ógica difusa. Los resultados muestran que ambos estimadores dentro del identificador cuentan con buena convergencia con diferencias de error mínimas que permiten su aproximación a las condiciones estocásticas del modelo en el tiempo para k muestreos, utilizando al MatLab R como software de simulación. Descriptores: Modelación y simulación computacional; algoritmos para la aproximación de funcionales; procesos estocásticos; lógica difusa; inteligencia artificial. This paper describes the identification process as an adaptive digital filter using the estimated transition matrix, identification error and gain functions. One problem that the filter has is the time process, affecting the quality response and agreeing with the estimated transition function, which is a condition to be accomplished with respect to the reference time evolution system. Thus, the time process required must be met in all operations within the same time interval. Generally, the identifier filter answer is affected by the parameter used in the estimated transition function indirectly used in the other filter operations. In this case, seeking a better time estimation response two estimators were considered: the first expressed in a recursive form and the second, selected within the knowledge base gain used in accordance to fuzzy logic. The results show the convergence observed in the error differences and their approximations to the stochastic time model conditions with k samples, using, MatLab R as a simulation software.

The Kalman filter is a widely employed algorithm for state estimation and sensor fusion in various fields. However, its performance can degrade in the presence of modeling errors and uncertainties in the system dynamics. To enhance the robustness and accuracy of the Kalman filter, the concept of a Fading-Memory Kalman Filter (FMKF) has been introduced. The FMKF incorporates a fading-memory mechanism that effectively mitigates the impact of modeling errors and reduces permanent estimation errors. By assigning time-varying weights to past measurements and predictions, the FMKF adaptively adjusts its influence on the current state estimation. This mechanism allows the FMKF to better accommodate dynamic system behavior and parameter changes. In this paper, the effectiveness of the FMKF is evaluated by comparing it with the standard Kalman filter. The performance of both filters is assessed in scenarios where modeling errors are present, and parameter variations occur. The results demonstrate that the FMKF outperforms the standard Kalman filter by providing more accurate and robust state estimates, even in the presence of modeling errors. The FMKF's ability to adaptively update the weights based on the relevance of past information allows it to effectively handle dynamic system behavior and changing parameters.

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.

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 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.

In this paper, the optimal finite impulse response (OFIR) with embedded unbiasedness (EU) filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint for discrete time-invariant state-space models. Unlike the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. With a two-state harmonic model, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.

This paper discusses two algorithms of extended unbiased FIR (EFIR) filtering of nonlinear discrete-time state-space models used in tracking and state estimation. The basic algorithm employs the extended nonlinear state and observation equations. The modified algorithm utilizes the nonlinear-tolinear conversion of the observation equation which is provided using a batch EFIR filter having small memory. Unlike the extended Kalman filter (EKF), both EFIR algorithms ignore the noise statistics and demonstrate better robustness against temporary model uncertainties. These algorithms require an optimal horizon in order to minimize the mean square error. Applications are given for robot indoor selflocalization utilizing radio frequency identification tags.

Managers ar9 often required to make key program decisions based on the performance of some elements of a large system. This paper is intended to assist the manager in this important task in so far as it relates to the proper use of precise and accurate clocks. An intuitive approach will be used to show how a clock's stability is measured, why it is measured the way it is, and why it is described the way it is. 4n intuitive explanation of the meaning of time domain and frequency domain measures as well as why they are used will also be given.

Recent decades have celebrated a growing interest to wireless sensor networks (WSNs), both in theory and applications. Organized to have a large number of nodes, the WSN allows for redundant measurements that makes the distributed optimal estimation an adequate sensor fusion technique. The estimators developed for WSNs should ensure the consensus in the network while respecting restrictions imposed by the battery life, real-time estimation, and low computing burden. In this work, we develop the unbiased finite impulse response (UFIR) filtering technique to operate under consensus on the estimates in the distributed WSN. Properly tuned on optimal horizons, the distributed UFIR filter with consensus on estimates reduces the mean square error (MSE) as compared to the centralized UFIR. It also demonstrates higher robustness against model errors while respecting the restrictions of the WSN.

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.

It is often desirable to find the underlying trends in time series data. This is a well known signal processing problem that has many applications in areas such as financial data analysis, climatology, biological and medical sciences. Mean filtering finds a piece-wise constant trend in the data while trend filtering finds a piece-wise linear trend. When the signal is noisy, the main difficulty is finding the changing points in the data that mark the transition points when the mean or the trend changes. Previously proposed methods based on 1 filtering suffer from the occurrence of false changing points in the estimate. This is known as the staircase effect. The main contribution in this paper is incorporating a technique to remove these false changing points to a fast mean filtering algorithm, referred to as the taut-string method, resulting in an efficient procedure with accurate change point detection and thus the removal of the staircase effect. Index Terms 1 mean filtering, taut-string algorithm, staircase effect. I. INTRODUCTION Finding the underlying linear trends in time series data is a common signal processing problem that arises in many applications in areas such as financial time series analysis [1], in biological and medical sciences [2] and climatology [3] to list a few. This is a difficult estimation problem when noise and imperfections are present in the signal measurements. The main challenge in mean and trend filtering is to find the so-called changing points in the trend. These are the

Heart diseases are one of most frequent causes of death in the modern world. Therefore, the ECG signal features have been under peer review for decades to improve medical diagnostics. In this paper, we provide smoothing of the atrial premature complex (APC) of the electrocardiogram (ECG) signal using unbiased finite impulse response (UFIR) smoothing filtering. We investigate the P-wave distribution using the Rice law and determine the probabilistic confidence interval based on a database associated with normal heartbeats. It is shown that the abnormality in the APC is related to the P-wave morphology. Different filtering techniques employing predictive and smoothing filtering are applied to APC data and compared experimentally. It is demonstrated that UFIR smoothing provides better performance among others. We finally show that the P-wave confidence interval defined for the Rice distribution can be used to provide an automatic diagnosis with a given probability.

Unbiased estimation is an efficient alternative to optimal estimation when the noise statistics are not fully known and/or the model undergoes temporary uncertainties. In this paper, we investigate the effect of embedded unbiasedness (EU) on optimal finite impulse response (OFIR) filtering estimates of linear discrete time-invariant statespace models. A new OFIR-EU filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint. We show that the OFIR-UE filter is equivalent to the minimum variance unbiased FIR (UFIR) filter. Unlike the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. Contrary to the UFIR filter which MSE is minimized by the optimal horizon of N opt points, the MSEs in the OFIR-EU and OFIR filters diminish with N and these filters are thus full-horizon. Based upon several examples, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters.

Abstract: In this paper, we investigate one of the possibilities to adapt an unbiased moving average (MA) filter (finite impulse response [FIR] filter) to the slope of time error function. The linear regression coefficient is used as a statistical estimator of sample slope. We evaluate the error of the slope estimate and present two options for the adapting coefficient determination. To examine them, we generate the time error noisy signal with linear trend and estimate it with a simple MA, the optimally unbiased MA, and the two adapted filters. ...

Las técnicas de reducción de ruido son ampliamente utilizadas en la grabación de audio, la edición de imágenes y en el procesamiento de señales industriales. La idea es reconstruir los datos originales a partir de la señal ruidosa suprimiendo toda, o casi toda, la distorsión generada por el ruido inherente a los procesos físicos. En el presente trabajo se realiza una comparación de diferentes métodos de supresión de ruido que se basan en la selección adaptativa del umbral. Estas técnicas han sido usadas extensivamente en el procesamiento de imágenes pero el objetivo de este trabajo es evaluar su rendimiento en la reducción de ruido de señales industriales. En particular se analiza el comportamiento de los métodos Bayes Shrink, Normal Shrink, Modified Shrink y Neight Shrink para la reducción de ruido gaussiano en estas señales. A tales efectos se utilizó un conjunto de señales patrón, que incluye a las señales propuestas por Donoho y otras mediciones representativas obtenidas de procesos reales en las plantas de Níquel cubanas. Las pruebas realizadas revelan que el algoritmo Neigh Shrink es el que mejor se comporta en los datos analizados.