Robust finite-horizon Kalman filtering for uncertain discrete-time systems

In this note, we propose a design for a robust finite-horizon Kalman filtering for discrete-time systems suffering from uncertainties in the modeling parameters and uncertainties in the observations process (missing measurements). The system parameter uncertainties are expected in the state, output and white noise covariance matrices. We find the upper-bound on the estimation error covariance and we minimize the proposed upper-bound.

Multi-target tracking via space transformations using a single frequency continuous wave radar

This paper investigates the location and velocity estimation problem involving multiple targets using the phase difference and frequency shift of the returned Doppler modulated signal. The minimal receiver configuration that addresses the data association and missing information problem is presented for the case of linear arrays. Non-linearly modeled Doppler radar measurements are used to obtain an accurate estimate of the target dynamics progressively in a linear framework utilizing a recently developed robust state estimation approach.

Localization and tracking of agents for close range applications

This research investigates the state estimation problem in close-range involving multiple targets using Doppler Radar. As the main theme is based on measurements with linear sensor arrays, optimal sensor arrangements are studied for two most popular measurement technologies: Angle-of-Arrival and range based localization systems.

Improved robust Kalman filtering for uncertain systems with missing measurements

In this paper, a novel robust finite-horizon Kalman filter is developed for discrete linear time-varying systems with missing measurements and normbounded parameter uncertainties. The missing measurements are modelled by a Bernoulli distributed sequence and the system parameter uncertainties are in the state and output matrices. A two stage recursive structure is considered for the Kalman filter and its parameters are determined guaranteeing that the covariances of the state estimation errorsare not more than the known upper bound. Finally, simulation results are presented to illustrate the outperformance of the proposed robust estimator compared with the previous results in the literature.

A method for stereo-vision based tracking for robotic applications

Vision based tracking of an object using the ideas of perspective projection inherently consists of nonlinearly modelled measurements although the underlying dynamic system that encompasses the object and the vision sensors can be linear. Based on a necessary stereo vision setting, we introduce an appropriate measurement conversion techniques which subsequently facilitate using a linear filter. Linear filter together with the aforementioned measurement conversion approach conforms a robust linear filter that is based on the set values state estimation ideas; a particularly rich area in the robust control literature. We provide a rigorously theoretical analysis to ensure bounded state estimation errors formulated in terms of an ellipsoidal set in which the actual state is guaranteed to be included to an arbitrary high probability. Using computer simulations as well as a practical implementation consisting of a robotic manipulator, we demonstrate our linear robust filter significantly outperforms the traditionally used extended Kalman filter under this stereo vision scenario. © 2008 IEEE.

Functional observer design with application to pre-compensated multi-variable systems

Partial state estimation of dynamical systems provides significant advantages in practical applications. Likewise, pre-compensator design for multi variable systems invokes considerable increase in the order of the original system. Hence, applying functional observer to pre-compensated systems can result in lower computational costs and more practicability in some applications such as fault diagnosis and output feedback control of these systems. In this note, functional observer design is investigated for pre-compensated systems. A lower order pre-compensator is designed based on a H2 norm optimization that is designed as the solution of a set of linear matrix inequalities (LMIs). Next, a minimum order functional observer is designed for the pre-compensated system. An LTI model of an irreversible chemical reactor is used to demonstrate our design algorithm, and to highlight the benefits of the proposed schemes.

Driver behaviour prediction for motion simulators using changepoint segmentation

Driving phenomenon is a repetitive process, that permits sequential learning under identifying the proper change periods. Sequential filtering is widely used for tracking and prediction of state dynamics. However, it suffers at abrupt changes, which cause sudden incremental prediction error. We provide a sequential filtering approach using online Bayesian detection of change points to decrease prediction error generally, and specifically at abrupt changes. The approach learns from optimally detected segments for identifying driving behaviour. Change points detection is done by the Pruned Exact Linear Time algorithm. Computational cost of our approach is bounded by the cost of the implemented sequential filter. This computational performance is suitable to the online nature of motion simulator's delay reduction. The approach was tested on a simulated driving scenario using Vortex by CM Labs. The state dimensions are simulated 2D space coordinates, and velocity. Particle filter was used for online sequential filtering. Prediction results show that change-point detection improves the quality of state estimation compared to traditional sequential filters, and is more suitable for predicting behavioural activities.

Um algoritmo para estimação de estado em alimentadores de distribuição de energia elétrica com base no método da soma de potências

Most algorithms for state estimation based on the classical model are just adequate for use in transmission networks. Few algorithms were developed specifically for distribution systems, probably because of the little amount of data available in real time. Most overhead feeders possess just current and voltage measurements at the middle voltage bus-bar at the substation. In this way, classical algorithms are of difficult implementation, even considering off-line acquired data as pseudo-measurements. However, the necessity of automating the operation of distribution networks, mainly in regard to the selectivity of protection systems, as well to implement possibilities of load transfer maneuvers, is changing the network planning policy. In this way, some equipments incorporating telemetry and command modules have been installed in order to improve operational features, and so increasing the amount of measurement data available in real-time in the System Operation Center (SOC). This encourages the development of a state estimator model, involving real-time information and pseudo-measurements of loads, that are built from typical power factors and utilization factors (demand factors) of distribution transformers. This work reports about the development of a new state estimation method, specific for radial distribution systems. The main algorithm of the method is based on the power summation load flow. The estimation is carried out piecewise, section by section of the feeder, going from the substation to the terminal nodes. For each section, a measurement model is built, resulting in a nonlinear overdetermined equations set, whose solution is achieved by the Gaussian normal equation. The estimated variables of a section are used as pseudo-measurements for the next section. In general, a measurement set for a generic section consists of pseudo-measurements of power flows and nodal voltages obtained from the previous section or measurements in real-time, if they exist -, besides pseudomeasurements of injected powers for the power summations, whose functions are the load flow equations, assuming that the network can be represented by its single-phase equivalent. The great advantage of the algorithm is its simplicity and low computational effort. Moreover, the algorithm is very efficient, in regard to the accuracy of the estimated values. Besides the power summation state estimator, this work shows how other algorithms could be adapted to provide state estimation of middle voltage substations and networks, namely Schweppes method and an algorithm based on current proportionality, that is usually adopted for network planning tasks. Both estimators were implemented not only as alternatives for the proposed method, but also looking for getting results that give support for its validation. Once in most cases no power measurement is performed at beginning of the feeder and this is required for implementing the power summation estimations method, a new algorithm for estimating the network variables at the middle voltage bus-bar was also developed

Line based camera calibration in machine vision dynamic applications

The problem of dynamic camera calibration considering moving objects in close range environments using straight lines as references is addressed. A mathematical model for the correspondence of a straight line in the object and image spaces is discussed. This model is based on the equivalence between the vector normal to the interpretation plane in the image space and the vector normal to the rotated interpretation plane in the object space. In order to solve the dynamic camera calibration, Kalman Filtering is applied; an iterative process based on the recursive property of the Kalman Filter is defined, using the sequentially estimated camera orientation parameters to feedback the feature extraction process in the image. For the dynamic case, e.g. an image sequence of a moving object, a state prediction and a covariance matrix for the next instant is obtained using the available estimates and the system model. Filtered state estimates can be computed from these predicted estimates using the Kalman Filtering approach and based on the system model parameters with good quality, for each instant of an image sequence. The proposed approach was tested with simulated and real data. Experiments with real data were carried out in a controlled environment, considering a sequence of images of a moving cube in a linear trajectory over a flat surface.

Analise de desempenho de observadores de estado robustos na localizacao de falhas

The state observers can reconstruct and monitor unmeasurable states. A new concept of fault detection and isolation using state observers is presented. The method selects the parameters from components that may fail during the process and constructs optimized robust observers. To isolate component failures via robust observation, a bank of detection observers is organized, in which each observer is only sensitive to one specified component failure while robust to all other component failures. This paper analyzes the performance of transient and steady-state behavior of the state observer.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Observer-based control design for switched affine systems and applications to DC-DC converters

This paper deals with the problem of establishing a state estimator for switched affine systems. For that matter, a modification on the Luenberger observer is proposed, the switched Luenberger observer, whose idea is to design one output gain matrix for each mode of the original system. The efficiency of the proposed method relies on a simplification on estimation error which is proved always valid, guaranteeing the estimation error to asymptotically converge to zero, for any initial state and switching law. Next, a dynamic output-dependent switching law is formulated. Then, design methodologies using linear matrix inequalities are proposed, which, to the authors's knowledge, have not yet been applied to this problem. Finally, observers for DC-DC converters are designed and simulated as application examples. © 2013 Brazilian Society for Automatics - SBA.

Desenvolvimento de um estimador de estado para sistemas de distribuição de energia elétrica desbalanceados

Pós-graduação em Engenharia Elétrica - FEIS

Desenvolvimento de um sistema de gerenciamento de energia (EMS - Energy Management System) para a rede elétrica inteligente (Smart Grid)

Pós-graduação em Engenharia Elétrica - FEIS

Study of the effect of biodiesel fuel on passive oxidation in a catalyzed particulate filter

A 2007 Cummins ISL 8.9L direct-injection common rail diesel engine rated at 272 kW (365 hp) and 317 kW (425 hp) was used to load the filter to 2.2 g/L and passively oxidize particulate matter (PM) within an aftertreatment system consisting of a diesel oxidation catalyst (DOC) and catalyzed particulate filter (CPF). The tests conducted with the engine rated at 365 hp used a 2007 DOC and CPF. The tests conducted with the engine rated at 425 hp used a 2010 DOC and 2007 CPF. Understanding the passive NO2 oxidation kinetics of PM within the CPF allows for reducing the frequency of active regenerations (hydrocarbon injection) and the associated fuel penalties. Modeling the passive oxidation of accumulated PM in the CPF will lead to creating accurate state estimation strategies. The MTU 1-D CPF model will be used to simulate data collected from this study to examine differences in the PM oxidation kinetics when soy methyl ester (SME) biodiesel is used as the source of fuel for the engine, and when the engine is operated at a higher power rating. A test procedure developed by Hutton et al. [1, 2] was modified to improve the ability to model the experimental data and provide additional insight into passively oxidized PM in a partially regenerated CPF. A test procedure was developed to allow PM oxidation rates by NO2 to be determined from engine test cell data. An experimental matrix consisting of CPF inlet temperatures from 250 to 450 °C with varying NOX/PM from 25 to 583and NO2/PM ratios from 5 to 240 was used. SME biodiesel was volumetrically blended with ULSD in 10% (B10) and 20% (B20) portions. This blended fuel was then used to evaluate the effect of biodiesel on passive oxidation rates. Four tests were performed with B10 and four tests with B20. Gathering data to determine the effect of fuel type (ULSD and biodiesel blends) on PM oxidation is the primary goal. The engine used for this testing was then configured to a higher power rating and one of the tests planned was performed. Additional testing is scheduled to take place with ULSD fuel to determine the affect the engine rating has on the PM oxidation. The experimental reaction rates during passive oxidation varied based upon the average CPF temperature, NO2 concentrations, and the NOX/PM ratios for each engine rating and with all fuels. The data analysis requires a high fidelity model that includes NO2 and thermal oxidation mechanisms and back diffusion to determine the details of the PM oxidation process.