Showing papers on "Alpha beta filter published in 2013"
TL;DR: In this article, three model-based state observer designs including Luenberger observer, Extended Kalman Filter (EKF), and Sigma Point Kalman filter (SPKF) are carried out and studied.
213 citations
TL;DR: This paper proposes a terminal sliding-mode (TSM) observer for estimating the immeasurable mechanical parameters of permanent-magnet synchronous motors (PMSMs) used for complex mechanical systems and shows the effectiveness of the proposed method.
Abstract: This paper proposes a terminal sliding-mode (TSM) observer for estimating the immeasurable mechanical parameters of permanent-magnet synchronous motors (PMSMs) used for complex mechanical systems. The observer can track the system states in finite time with high steady-state precision. A TSM control strategy is designed to guarantee the global finite-time stability of the observer and, meanwhile, to estimate the mechanical parameters of the PMSM. A novel second-order sliding-mode algorithm is designed to soften the switching control signal of the observer. The effect of the equivalent low-pass filter can be properly controlled in the algorithm based on requirements. The smooth signal of the TSM observer is directly used for the parameter estimation. The experimental results in a practical CNC machine tool are provided to demonstrate the effectiveness of the proposed method.
206 citations
TL;DR: Testing results suggest that the proposed indoor tracking and navigation system based on measurements of received signal strength in wireless local area network (WLAN) is used to guide visually impaired subjects to their desired destinations.
Abstract: An indoor tracking and navigation system based on measurements of received signal strength (RSS) in wireless local area network (WLAN) is proposed. In the system, the location determination problem is solved by first applying a proximity constraint to limit the distance between a coarse estimate of the current position and a previous estimate. Then, a Compressive Sensing-based (CS--based) positioning scheme, proposed in our previous work , , is applied to obtain a refined position estimate. The refined estimate is used with a map-adaptive Kalman filter, which assumes a linear motion between intersections on a map that describes the user's path, to obtain a more robust position estimate. Experimental results with the system that is implemented on a PDA with limited resources (HP iPAQ hx2750 PDA) show that the proposed tracking system outperforms the widely used traditional positioning and tracking systems. Meanwhile, the tracking system leads to 12.6 percent reduction in the mean position error compared to the CS-based stationary positioning system when three APs are used. A navigation module that is integrated with the tracking system provides users with instructions to guide them to predefined destinations. Thirty visually impaired subjects from the Canadian National Institute for the Blind (CNIB) were invited to further evaluate the performance of the navigation system. Testing results suggest that the proposed system can be used to guide visually impaired subjects to their desired destinations.
176 citations
26 May 2013
TL;DR: Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.
Abstract: We consider the filtering problem in linear state space models with heavy tailed process and measurement noise. Our work is based on Student's t distribution, for which we give a number of useful results. The derived filtering algorithm is a generalization of the ubiquitous Kalman filter, and reduces to it as special case. Both Kalman filter and the new algorithm are compared on a challenging tracking example where a maneuvering target is observed in clutter.
176 citations
TL;DR: The distributed weighted robust Kalman filter developed in this paper has stronger fault-tolerance ability and is derived for uncertain systems with multiple sensors.
160 citations
TL;DR: In this article, the authors examine the relationship between MI(xed) Da(ta) S(ampling) (MIDAS) regressions and the Kalman filter when forecasting with mixed frequency data.
Abstract: We examine the relationship between Mi(xed) Da(ta) S(ampling) (MIDAS) regressions and the Kalman filter when forecasting with mixed frequency data. In general, state space models involve a system of equations, whereas MIDAS regressions involve a single equation. As a consequence, MIDAS regressions might be less efficient, but could also be less prone to parameter estimation error and/or specification errors. We examine how MIDAS regressions and Kalman filters match up under ideal circumstances, that is in population, and in cases where all the stochastic processes—low and high frequency—are correctly specified. We characterize cases where the MIDAS regression exactly replicates the steady state Kalman filter weights. We compare MIDAS and Kalman filter forecasts in population where the state space model is misspecified. We also compare MIDAS and Kalman filter forecasts in small samples. The paper concludes with an empirical application. Overall we find that the MIDAS and Kalman filter methods give similar ...
155 citations
TL;DR: In this article, a hybrid Kalman filter is used for the low-low frequency component to capture the near-linear relationship between the input load component and the output measurement, while neural networks trained by unscented Kalman filters are used for low-high and high frequency components to capture their nonlinear relationships.
Abstract: Very short-term load forecasting predicts the loads in electric power system one hour into the future in 5-min steps in a moving window manner. To quantify forecasting accuracy in real-time, the prediction interval estimates should also be produced online. Effective predictions with good prediction intervals are important for resource dispatch and area generation control, and help power market participants make prudent decisions. We previously presented a two level wavelet neural network method based on back propagation without estimating prediction intervals. This paper extends the previous work by using hybrid Kalman filters to produce forecasting with prediction interval estimates online. Based on data analysis, a neural network trained by an extended Kalman filter is used for the low-low frequency component to capture the near-linear relationship between the input load component and the output measurement, while neural networks trained by unscented Kalman filters are used for low-high and high frequency components to capture their nonlinear relationships. The overall variance estimate is then derived and evaluated for prediction interval estimation. Testing results demonstrate the effectiveness of hybrid Kalman filters for capturing different features of load components, and the accuracy of the overall variance estimate derived based on a data set from ISO New England.
128 citations
TL;DR: A novel model is developed to describe possible random delays and losses of measurements transmitted from a sensor to a filter by a group of Bernoulli distributed random variables and the optimal filter is given by Kalman filter when packets are time-stamped.
Abstract: A novel model is developed to describe possible random delays and losses of measurements transmitted from a sensor to a filter by a group of Bernoulli distributed random variables. Based on the new developed model, an optimal linear filter dependent on the probabilities is presented in the linear minimum variance sense by the innovation analysis approach when packets are not time-stamped. The solution to the optimal linear filter is given in terms of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state filter is given. At last, the optimal filter is given by Kalman filter when packets are time-stamped.
125 citations
TL;DR: A new state estimation algorithm called the square root cubature information filter (SRCIF) for nonlinear systems, first derived from an extended information filter and a recently developed cubature Kalman filter.
Abstract: Nonlinear state estimation plays a major role in many real-life applications. Recently, some sigma-point filters, such as the unscented Kalman filter, the particle filter, or the cubature Kalman filter have been proposed as promising substitutes for the conventional extended Kalman filter. For multisensor fusion, the information form of the Kalman filter is preferred over standard covariance filters due to its simpler measurement update stage. This paper presents a new state estimation algorithm called the square root cubature information filter (SRCIF) for nonlinear systems. The cubature information filter is first derived from an extended information filter and a recently developed cubature Kalman filter. For numerical accuracy, its square root version is then developed. Unlike the extended Kalman or extended information filters, the proposed filter does not require the evaluation of Jacobians during state estimation. The proposed approach is further extended for use in multisensor state estimation. The efficacy of the SRCIF is demonstrated by a simulation example of a permanent magnet synchronous motor.
116 citations
TL;DR: An efficient nonlinear filtering algorithm called the Gaussian-sum cubature Kalman filter (GSCKF) for the bearings-only tracking problem is presented and demonstrates comparable performance to the particle filter (PF) with significantly reduced computational cost.
Abstract: Herein is presented an efficient nonlinear filtering algorithm called the Gaussian-sum cubature Kalman filter (GSCKF) for the bearings-only tracking problem. It is developed based on the recently proposed cubature Kalman filter and is built within a Gaussian-sum framework. The new algorithm consists of a splitting and merging procedure when a high degree of nonlinearity is detected. Simulation results show that the proposed algorithm demonstrates comparable performance to the particle filter (PF) with significantly reduced computational cost.
110 citations
TL;DR: It will be shown that the proposed approach does provide a smaller order of disturbance observer than that of conventional approaches, while maintaining satisfactory performances.
TL;DR: A backstepping-based technique is proposed for the design of the output injection weights by making use of the (extended) linearization of the semilinear observer error system with respect to the observer state.
Abstract: The design of an extended Luenberger observer is considered to solve the state observation problem for semilinear distributed-parameter systems. For this, a backstepping-based technique is proposed for the design of the output injection weights by making use of the (extended) linearization of the semilinear observer error system with respect to the observer state. Stability of both the linearized and the semilinear observer error dynamics is analyzed theoretically. Moreover, an efficient sample-and-hold implementation is considered to improve the computational efficiency of the observer design. Simulation examples are provided for a bistable semilinear partial differential equation and the simplified model of a bioreactor with Monod kinetics.
TL;DR: The aim of the technical note is to propose a new local filter that utilises stochastic integration methods providing the asymptotically exact integral evaluation with computational complexity similar to the traditional filters.
Abstract: The technical note deals with state estimation of nonlinear stochastic dynamic systems. Traditional filters providing local estimates of the state, such as the extended Kalman filter, unscented Kalman filter, or the cubature Kalman filter, are based on computationally efficient but approximate integral evaluations. On the other hand, the Monte Carlo based Kalman filter takes an advantage of asymptotically exact integral evaluations but at the expense of substantial computational demands. The aim of the technical note is to propose a new local filter that utilises stochastic integration methods providing the asymptotically exact integral evaluation with computational complexity similar to the traditional filters. The technical note will demonstrate that the unscented and cubature Kalman filters are special cases of the proposed stochastic integration filter. The proposed filter is illustrated by a numerical example.
TL;DR: This work derives a different form of the Kalman filter by considering, at each iteration, a block of time samples instead of one time sample as it is the case in the conventional approach.
Abstract: The Kalman filter is a very interesting signal processing tool, which is widely used in many practical applications. In this paper, we study the Kalman filter in the context of echo cancellation. The contribution of this work is threefold. First, we derive a different form of the Kalman filter by considering, at each iteration, a block of time samples instead of one time sample as it is the case in the conventional approach. Second, we show how this general Kalman filter (GKF) is connected with some of the most popular adaptive filters for echo cancellation, i.e., the normalized least-mean-square (NLMS) algorithm, the affine projection algorithm (APA) and its proportionate version (PAPA). Third, a simplified Kalman filter is developed in order to reduce the computational load of the GKF; this algorithm behaves like a variable step-size adaptive filter. Simulation results indicate the good performance of the proposed algorithms, which can be attractive choices for echo cancellation.
TL;DR: In an effort to assess the performance of newer estimation algorithms, many prior publications have presented comparative studies where the Extended Kalman Filter (EKF) failed.
Abstract: In an effort to assess the performance of newer estimation algorithms, many prior publications have presented comparative studies where the Extended Kalman Filter (EKF) failed. This is because the ...
TL;DR: This work proposes an adaptive scheme, based on lifting Mehra's idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases results in a natural additive inflation that improves state estimation.
Abstract: A necessary ingredient of an ensemble Kalman filter (EnKF) is covariance inflation, used to control filter divergence and compensate for model error There is an on-going search for inflation tunings that can be learned adaptively Early in the development of Kalman filtering, Mehra (1970, 1972) enabled adaptivity in the context of linear dynamics with white noise model errors by showing how to estimate the model error and observation covariances We propose an adaptive scheme, based on lifting Mehra’s idea to the non-linear case, that recovers the model error and observation noise covariances in simple cases, and in more complicated cases, results in a natural additive inflation that improves state estimation It can be incorporated into nonlinear filters such as the extended Kalman filter (EKF), the EnKF and their localised versions We test the adaptive EnKF on a 40-dimensional Lorenz96 model and show the significant improvements in state estimation that are possible We also discuss the extent to which such an adaptive filter can compensate for model error, and demonstrate the use of localisation to reduce ensemble sizes for large problems Keywords: ensemble Kalman filter, data assimilation, non-linear dynamics, covariance inflation, adaptive filtering (Published: 2 July 2013) Citation: Tellus A 2013, 65 , 20331, http://dxdoiorg/103402/tellusav65i020331
Proceedings Article•
09 Sep 2013TL;DR: A new filter called Discrete Extended Kalman Filter on Lie Groups (D-LG-EKF) is proposed, which assumes that the posterior distribution of the state is a concentrated Gaussian distribution on Lie groups.
Abstract: In this paper, we generalize the Discrete Extended Kalman Filter (D-EKF) to the case where the state and the observations evolve on Lie group manifolds. We propose a new filter called Discrete Extended Kalman Filter on Lie Groups (D-LG-EKF). It assumes that the posterior distribution of the state is a concentrated Gaussian distribution on Lie groups. Our formalism yields closed-form equations for both nonlinear discrete propagation and update of the distribution parameters based on the likelihood. We also show that the D-LG-EKF reduces to the traditional D-EKF if the state evolves on an Euclidean space. Our approach leads to a systematic methodology for the design of filters, which is illustrated by the application to a camera pose estimation problem. Results show that the D-LG-EKF outperforms both a constrained D-EKF and a D-EKF applied on the Lie algebra of the Lie group.
TL;DR: A new control scheme based on the Kalman filter and the linear quadratic regulator (LQR) is proposed to improve the performance of power quality conditioning devices.
Abstract: A new control scheme based on the Kalman filter and the linear quadratic regulator (LQR) is proposed to improve the performance of power quality conditioning devices. Grid perturbations such as load variations, frequency deviation, voltage distortion, line impedance, unbalance, and measurement noise are taken into account. A new model of the plant is developed that allows the use of the LQR controller with a better performance. This new controller structure is feasible thanks to an algorithm based on the Kalman filter (KF), which estimates the state space variables at the point of common coupling, used in the proposed control system. This algorithm is also responsible for generating the references for the controller. The proposed control system was implemented using a digital signal controller. Extensive tests and experimental results are presented in order to verify the performance of the proposal.
TL;DR: This paper reviews Bayesian filters that possess the aforementioned properties, and focuses on parametric methods, among which there are three types of filters: filters based on analytical approximations (extended Kalman filter, iterated extended Kalman filters, and Gauss-Hermite filter), and filtersbased on the Gaussian sum approximation (Gaussian sum filter).
Abstract: Nonlinear stochastic dynamical systems are commonly used to model physical processes. For linear and Gaussian systems, the Kalman filter is optimal in minimum mean squared error sense. However, for nonlinear or non-Gaussian systems, the estimation of states or parameters is a challenging problem. Furthermore, it is often required to process data online. Therefore, apart from being accurate, the feasible estimation algorithm also needs to be fast. In this paper, we review Bayesian filters that possess the aforementioned properties. Each filter is presented in an easy way to implement algorithmic form. We focus on parametric methods, among which we distinguish three types of filters: filters based on analytical approximations (extended Kalman filter, iterated extended Kalman filter), filters based on statistical approximations (unscented Kalman filter, central difference filter, Gauss-Hermite filter), and filters based on the Gaussian sum approximation (Gaussian sum filter). We discuss each of these filters, and compare them with illustrative examples.
TL;DR: An adaptive observer form is derived which can be utilized in designing the reduced order state observer and results are given to exhibit the effectiveness of proposed synthesis approaches in dealing with the practical systems.
17 Jun 2013
TL;DR: A filtering algorithm for angular quantities in nonlinear systems that is based on circular statistics and switches between three different representations of probability distributions on the circle, the wrapped normal, the von Mises, and a Dirac mixture density is presented.
Abstract: Estimation of circular quantities is a widespread problem that occurs in many tracking and control applications. Commonly used approaches such as the Kalman filter, the extended Kalman filter (EKF), and the unscented Kalman filter (UKF) do not take periodicity explicitly into account, which can result in low estimation accuracy. We present a filtering algorithm for angular quantities in nonlinear systems that is based on circular statistics. The new filter switches between three different representations of probability distributions on the circle, the wrapped normal, the von Mises, and a Dirac mixture density. It can be seen as a systematic generalization of the UKF to circular statistics. We evaluate the proposed filter in simulations and show its superiority to conventional approaches.
TL;DR: In this paper, a discrete-time robust nonlinear filtering algorithm is proposed to deal with the contami-nated Gaussian noise in the measurement, which is based on a robust modification of the derivative-free Kalman filter.
TL;DR: The Kalman smoother is derived in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother, and lower and upper bounds for their estimation error covariances are derived.
TL;DR: The concept of SVSF chattering is introduced and explained, and is used to determine the presence of modeling uncertainties and to create combined filtering strategies in an effort to improve the overall accuracy and stability of the estimates.
TL;DR: Using a normal form characterizing the class of nonlinear uniformly observable single output nonlinear systems, it is shown that a particular stationary solution of a continuous discrete time Lyapunov equation can be used to design a constant high gain observer.
Abstract: This work considers the problem of observer design for continuous-time systems with sampled output measurements (continuous-discrete time systems). In classical literature and in many applications, the continuous-discrete time extended Kalman filter (EKF) is used in order to tackle this problem. In this work, using a normal form characterizing the class of nonlinear uniformly observable single output nonlinear systems, it is shown that a particular stationary solution of a continuous discrete time Lyapunov equation can be used in order to design a constant high gain observer. Explicit conditions are given to ensure global convergence of the observer. Finally, an illustration of this result is given using an example of a biological process.
15 Sep 2013
TL;DR: In this paper, a state-space current control method for active damping of the resonance frequency of the LCL filter and setting the dominant dynamics of the converter current through the direct pole placement is presented.
Abstract: This paper presents a state-space current control method for active damping of the resonance frequency of the LCL filter and setting the dominant dynamics of the converter current through the direct pole placement. A state observer is used, whereupon additional sensors are not needed compared to the conventional L filter design. The relationship between the system delay and instability caused by the resonance phenomenon is considered. Nyquist diagrams are used to examine the parameter sensitivity of the proposed method, and the method is validated with simulations and experiments.
TL;DR: In this paper, the unscented Kalman filter was used to capture nonlinearities in fixed income pricing and compared with the particle filter for fixed income fixed-income pricing.
Abstract: The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed income applications. We investigate if the unscented Kalman filter should be used to capture nonlinearities, and compare the performance of the Kalman filter to that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also performs well when compared to the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may prove to be a good approach for variety of problems in fixed income pricing.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2322760
TL;DR: A new systematic approach to state of charge (SoC) observer design for battery cells is presented, based on a purely data driven model and a nonlinear observer constructed from it, and the use of a fuzzy observer is beneficial in combination with LMNs.
TL;DR: The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.
Abstract: This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992, ‘Design of Observers for Linear Systems with Unknown Inputs’, IEEE Transactions on Automatic Control, 37, 871–875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.
TL;DR: In this paper, a Luenberger-type PDE-ODE cascaded observer is derived to estimate the state variables of the system and an observer-based output feedback stabilizing controller is developed.
Abstract: This paper addresses the problems of observer design and output feedback stabilization for a class of nonlinear multivariable systems, where the nonlinear system dynamics are described by ordinary differential equations (ODEs), and the sensor dynamics are governed by diffusion partial differential equations (PDEs). Based on the Luenberger observer theory, a Luenberger-type PDE-ODE cascaded observer is derived to estimate the state variables of the system. Then, an observer-based output feedback stabilizing controller is developed. The exponential stability of both the observer error system and closed-loop control system is proven via the Lyapunov direct method. Finally, numerical examples are provided to illustrate the effectiveness of the proposed design methods.