Unbiased FIR filter

loCalizaCión y orientaCión de equipos móviles usando Color juan sEbastián botEro valEncia 1 Edilson dElgado trEjos 2 Uno de los mayores problemas en el desarrollo de interfaces móviles autónomas está ligado al desarrollo del sistema de localización. Es fundamental que se conozca la posición del móvil para cerrar el lazo de control sobre la estrategia que se use en la planeación de trayectorias. En este trabajo se presenta un algoritmo que individualiza dos conjuntos de Robots Móviles además de orientar y localizar cada móvil en el plano. Con este fin, se propone el uso de técnicas de segmentación por umbralización binaria en conjunto con operaciones lógicas. El sistema está compuesto por una cámara digital periférica que observa la totalidad del plano y un conjunto de Móviles que son controlados por un sistema maestro. Los móviles en su construcción física sólo cuentan con dos posibles direcciones de desplazamiento y rotación sobre su eje. A partir del estudio, se obtiene un algoritmo que identifica por equipos dos conjuntos de móviles y obtiene la posición y orientación individual. El sistema es complementado con una estrategia de predicción que detecta una posible colisión. Finalmente, se obtiene un sistema que identifica de forma cartesiana dos conjuntos de Robots Móviles y coordina su desplazamiento.

“Theory of Conservation of Optima and Complexity” by Oscar Riveros just dropped — and it’s one of the cleanest, most rigorous pieces I’ve seen in years on the geometric approach to combinatorial optimization and P vs NP.
In 21 pages it does something genuinely new: it isolates five precise layers that any geometric representation must satisfy to legitimately claim it turns an NP-complete problem into a polynomial-time solvable one:

explicit binary encoding
exact representation (with linear cost lifting)
correct optimal support
strong exactness (polynomial extractor from continuous optimum to combinatorial solution)
uniform polynomial fidelity + controlled representational growth

It proves the key theorems (exact conservation of arg min, linear criterion for cost lifting, affine equivalence transport, and a fully typed complexity transfer theorem) and then delivers the first honest sufficient scheme for turning “my new polytope solves STSP ⇒ P = NP” into an actual theorem instead of hand-wavy intuition.
No hype. Just a crystal-clear formal contract that every future extended-formulation or pedigree-polytope paper will now have to meet.
If you work on polyhedral combinatorics, TSP, or the geometric side of complexity, this is required reading. It doesn’t solve P vs NP — but it finally tells us exactly what would constitute a valid solution.

En este artículo se describe un método para estimar la posición y orientación de un robot móvil en un entorno de trabajo ligeramente cambiante, según el procedimiento de celdillas de probabilidad. Se vale de la información obtenida por los sistemas sensoriales sonar y láser en la construcción de mapas de entorno y utiliza el Filtro de Kalman Extendido en la integración multisensorial. Palabras clave: Robot móvil, integración sensorial, estimación de posición, Filtro Extendido de Kalman. El campo de la robótica móvil se esta convirtiendo en uno de los más interesantes en los últimos tiempos. El desarrollo de la técnica evoluciona rápidamente a lo cual contribuye quizá su aplicación a un nuevo ámbito diferente del industrial, el doméstico, que si bien se encuentra en su fase inicial presenta buenas perspectivas. La mayoría de las alternativas propuestas hasta hace poco tiempo tenían como principal característica la rigidez. Tradicionalmente la robótica móvil ha sido tratada como automática, lejos de la visión autónoma. Los sistemas se programaban para realizar siempre las mismas labores en circunstancias perfectamente definidas a priori, así por ejemplo, los vehículos iban automáticamente de un punto a otro por una trayectoria fijada con anterioridad, de la cual no podían o debían desviarse porque estaban preparados sólo para operar en esas situaciones. De acuerdo a esto, se desarrollaron metodologías y algoritmos concretos que fallaban en cuanto se presentara un evento desconocido. Actualmente las tendencias son diferentes, los sistemas son autónomos, están proyectados para actuar en circunstancias diferentes de lo normal, incluso se investigan modelos de aprendizaje cada vez más sofisticados que permitan operar con el menor número de datos conocidos a priori. Para obtener información del entorno los robots se valen de los sensores. Estos proporcionan un sistema de aprendizaje del estado del mundo con posibilidades de actualización

In this paper we deal with an optimal filtering problem for uncertain discrete-time systems. Parametric uncertainties of the underlying model are assumed to be norm bounded. We propose an approach based on regularization and penalty function to solve this problem. The optimal robust filter with the respective recursive Riccati equation is written through unified frameworks defined in terms of matrix blocks. These frameworks do not depend on any auxiliary parameters to be tuned. Simulation results show the effectiveness of the robust filter proposed.

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.

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 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.

Las señales de ruido pueden afectar en forma muy negativa a los sistemas de control automático. La aplicación de los filtros de Kalman en estos casos constituye una alternativa capaz de producir notables mejoras en su desempeño. En el presente artículo, se desarrolla un ejemplo de aplicación del filtro de Kalman en tiempo continuo al caso del péndulo invertido accionado por un servomotor DC, el cual ha sido simulado mediante Matlab. Palabras claves: Filtro de Kalman, espacio de estados, simulación en MATLAB, señales aleatorias.

Resumen En el presente trabajo, se introducen las técnicas de kernel ACP (KACP) y conglomeramiento espectral con algunos ejemplos ilustrativos. Se pretende estudiar los efectos de aplicar ACP como preproceso sobre las observaciones que se desean agrupar, para lo cual se hacen experimentos con datos reales. Entre las tareas adicionales que requieren estos procedimientos está la sintonización de parámetros (ajuste de valores); el alineamiento del kernel se presenta como alternativa de solución. La técnica de alineamiento del kernel presenta buenos resultados al contrastar las curvas de alineamiento con los índices de Rand obtenidos para los datos evaluados. Finalmente, el estudio muestra que el éxito de ACP depende del problema y que no se tiene un criterio general para decidir.

En este artículo se describe un método para estimar la posición y orientación de un robot móvil en un entorno de trabajo ligeramente cambiante, según el procedimiento de celdillas de probabilidad. Se vale de la información obtenida por los sistemas sensoriales sonar y láser en la construcción de mapas de entorno y utiliza el Filtro de Kalman Extendido en la integración multisensorial. Palabras clave: Robot móvil, integración sensorial, estimación de posición, Filtro Extendido de Kalman.

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.

This study presents a methodology to perform the robust identification of a gantry crane control system. The robust modeling was performed by three sequential Kalman filters, where two of them are the dual Kalman filter for estimating the parameter and state system, and third filter is the robust statistic Kalman filter. The obtained results show that the robust statistic Kalman filter presents responses smoother for the position and the velocity of the gantry crane, compared with the standard identification strategies.

Facial features play a important role in developmen t of systems on computer vision for different applications such as: the huma n-computer interactive, facial expressions automatic recognition also identify fat igue in car drivers, within these systems, facial features tracking is a signif icant stages that need to be developed, Therefore, this paper focuses on review the different techniques for facial features tracking, such as model-free method s (Kalman filter, particle Filter, among other).

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

Rony), por esas intensas jornadas de fútbol y estudio, por los grandes momentos de risas y alegrías. Mención especial para Benjamín Olivares, con quien realicé el Magíster y he trabajado codo a codo por más de 2 años, gracias por tu amistad, apoyo, complicidad y por hacer más fácil y alegre el día a día en la universidad. Como no agradecerles a la Sra. Eliana y a su hija Renée por su diaria alegría, preocupación y gran disposición a ayudar, por sus conversaciones, todo fue más fácil y ameno gracias a ustedes. Finalmente, me gustaría agradecerles a quienes trabajaron conmigo: Hugo y Richi; al Profesor Jorge Silva por compartir su gran conocimiento y su particular simpatía; y al Profesor Marcos Orchard, por guiar este proyecto, por su vocación a la academia, por sus conocimientos, por su inmensa disposición a ayudar y a escuchar a sus alumnos, por su grandiosa calidad humana.

Digital signal processing is most widely used to process the signal. In digital signal processing filters are used to remove some unwanted constituents from aspired signal. Windowing is a scheme of finite impulse response filters. Present paper proposes a new versatile window function. It has two variable parameters first one is window span N and another changeable parameter is r. when the value of variable parameter r increases width of major lobe of window also increases with better side lobe reduction and vice versa. Gaussian window and Kaiser window are the well-known variable windows. This paper shows that the proposed window has more desirable results in comparison of Gaussian and Kaiser window with low power loss and better side lobe reduction. To achieve minimum power loss peak side lobe level should have to minimum. Proposed window has low peak side lobe level (-17.681dB) in comparison of Gaussian (-11.836dB) and Kaiser window (-6.9704dB). Proposed work shows that the propo...

For linear discrete state-space models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, a.k.a. the Kalman filter (KF). Interestingly, the linear minimum variance distortionless response (LMVDR) filter, when it exists, shares exactly the same recursion as the KF, except for the initialization. If LMVDR estimators are suboptimal in mean-squared error sense, they do not depend on the prior knowledge on the initial state. Thus, the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. In this perspective, we establish the general conditions under which existence of the LMVDRF is guaranteed. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. Indeed, the LMVDR fixed-point smoother can be used to compute recursively the solution of a generalization of the deterministic least-squares problem.

For linear discrete state-space models, under certain conditions, the linear least-mean-squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter. The purpose of this paper is to show that the linear minimum variance distortionless response (MVDR) filter shares exactly the same recursion, except for the initialization which is based on a weighted least-squares estimator. If the MVDR filter is suboptimal in mean-squared error sense, it is an infinite impulse response distortionless filter (a deconvolver) which does not depend on the prior knowledge (first-and second-order statistics) on the initial state. In other words, the MVDR filter can be pre-computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state.

El equipo TeamChaos ha participado en laś ultimas ediciones de la RoboCup en la categoría de robots con 4 patas. Varios de los subsistemas del software que controla los cuatro robots del equipo utilizan la lógica borrosa. En concreto en este artículo describimos el sistema de auto-localización de los robots que se basa en una mezcla de un sistema basado en una rejilla uniforme borrosa y una población de tamaño variable de filtros extendidos de Kalman.

El presente trabajo trata sobre la aplicación de los filtros de Kalman en los sistemas de navegación autónoma. En este contexto, los sistemas de navegación autónoma dependen de una variedad de sensores para recopilar información sobre el entorno y tomar decisiones en consecuencia. Sin embargo, la información que se recopila de estos sensores suele estar contaminada por ruido, errores y otros tipos de incertidumbre. Por lo tanto, se utilizan filtros de Kalman para mejorar la precisión de la información. El artículo explica cómo funciona el filtro de Kalman y cómo se aplica en los sistemas de navegación autónoma. Además, se mencionan algunas de las aplicaciones del filtro de Kalman en los sistemas de navegación autónoma, como la estimación de la posición, la velocidad y la orientación del vehículo, así como la fusión de datos de sensores para mejorar la precisión de la estimación del estado del vehículo. En general, el artículo destaca la importancia del filtro de Kalman en los sistem...

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. ...

Reducción de interferencia de línea de potencia en señales Reducción de interferencia de línea de potencia en señales electrocardiográficas mediante el filtro dual de Kalman electrocardiográficas mediante el filtro dual de Kalman Reduction of power line interference in electrocardiographic signals by dual Kalman filtering

Passive Ultra High Frequency Radio Identification (UHF RFID) systems used in metal objects exhibit challenges due to generation of Foucault currents and multiple reflections, creating reading problems and detection errors. One of these problems is unwanted RFID tag reads i.e., tags unintentionally detected by the reader. The paper presents one algorithm for reduction of such unwanted tag reads using normalized read rate and range of RFID tags. The algorithm was designed using extensive data from measurements of an actual RFID system with tags located over metal objects. Results show that the algorithm detects 96% of unwanted tag reads.

Hybrid Inertial Microwave Reflectometry (HIMR) is one of the most promising technologies for achieving the elusive, ultimate goal of wireless localization, i.e. motion-capture grade position tracking at long-range distances. In this paper, we introduce and analyze Kalman filter-based real-time position estimators for HIMR systems. Results from measured data show that the new approach results in a 5 mm RMS tracking error at a range of several meters-a 25% improvement with enhanced robustness over existing position estimators. Moreover, this performance level is shown to be achievable using only RF signals, without inertial data, thereby potentially simplifying RFID-based motion capture system design in many cases. The technique is scalable to ranges of tens-and hundreds-of-meters.

This document introduce a Rice mobile channel model suitable for the study of parameters of interest that modifies the accuracy in the estimation of the Time Of Arrival (TOA) for the signal emitted from a mobile station, operating in a DS-SS. This work shows the receiver performance in terms of the available number of channel estimates, the number of sensors in the antenna array and the type of signal source when sampling rate is higher than the chip rate. Received signal is modeled from time-space stochastic distributions and the cases of partially coherent distributed sources as well as fully coherent distributed sources and fully incoherent distributed sources are considered.

This article explain the development of a prototype for tracking system, which is made for low cost, and for closed environments such as offices and rooms with low density of obstacles. The position is obtained from pseudo-ranges, which are calculated from the time taken by the ultrasound signal to travel from a known-point to the receiver. This process is repeated continuously until the receiver has received three pseudoranges, then the process of estimation starts based on the trilateration algorithm. [1]

Wireless sensor networks (WSNs) are often characterized by random and asymmetric packet losses due to the wireless medium, leading to network topologies that can be modeled as random, time-varying and directed graphs. Most of existing works related to graph filtering in the context of WSNs assume that the probability of delivering an information from one node to a neighbor node is the same as in the reverse direction. This assumption is not realistic due to the typical link asymmetry in WSNs caused by interferences and background noise. In this work, we analyze the problem of applying stochastic graph filtering over random time-varying asymmetric network topologies. We show that it is possible to perform stochastic graph filtering under asymmetric links with node-variant graph filters, while optimizing a trade-off between the expected error (bias) and the variance of the error, with respect to performing graph filtering over a fixed static topology given by a certain connectivity radius of the nodes.

For linear discrete state-space models, under certain conditions, the linear least-mean-squares filter estimate has a convenient recursive predictor/corrector format, aka the Kalman filter. The purpose of this paper is to show that the linear minimum variance distortionless response (MVDR) filter shares exactly the same recursion, except for the initialization which is based on a weighted least-squares estimator. If the MVDR filter is sub-optimal in mean-squared error sense, it is an infinite impulse response distortionless filter (a deconvolver) which does not depend on the prior knowledge (first and second order statistics) on the initial state. In other words, the MVDR filter can be pre-computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state.

For linear discrete state-space models, under certain conditions, the linear least mean squares (LLMS) filter estimate has a recursive format, a.k.a. the Kalman filter (KF). Interestingly, the linear minimum variance distortionless response (LMVDR) filter, when it exists, shares exactly the same recursion as the KF, except for the initialization. If LMVDR estimators are suboptimal in mean-squared error sense, they do not depend on the prior knowledge on the initial state. Thus, the LMVDR estimators may outperform the usual LLMS estimators in case of misspecification of the prior knowledge on the initial state. In this perspective, we establish the general conditions under which existence of the LMVDRF is guaranteed. An immediate benefit is the introduction of LMVDR fixed-point and fixed-lag smoothers (and possibly other smoothers or predictors), which has not been possible so far. Indeed, the LMVDR fixed-point smoother can be used to compute recursively the solution of a generalization of the deterministic least-squares problem.