Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

A novel ensemble method for retrieving properties of warm cloud in 3-D using ground-based scanning radar and zenith radiances

We present a novel method for retrieving high-resolution, three-dimensional (3-D) nonprecipitating cloud fields in both overcast and broken-cloud situations. The method uses scanning cloud radar and multiwavelength zenith radiances to obtain gridded 3-D liquid water content (LWC) and effective radius (re) and 2-D column mean droplet number concentration (Nd). By using an adaption of the ensemble Kalman filter, radiances are used to constrain the optical properties of the clouds using a forward model that employs full 3-D radiative transfer while also providing full error statistics given the uncertainty in the observations. To evaluate the new method, we first perform retrievals using synthetic measurements from a challenging cumulus cloud field produced by a large-eddy simulation snapshot. Uncertainty due to measurement error in overhead clouds is estimated at 20% in LWC and 6% in re, but the true error can be greater due to uncertainties in the assumed droplet size distribution and radiative transfer. Over the entire domain, LWC and re are retrieved with average error 0.05–0.08 g m-3 and ~2 μm, respectively, depending on the number of radiance channels used. The method is then evaluated using real data from the Atmospheric Radiation Measurement program Mobile Facility at the Azores. Two case studies are considered, one stratocumulus and one cumulus. Where available, the liquid water path retrieved directly above the observation site was found to be in good agreement with independent values obtained from microwave radiometer measurements, with an error of 20 g m-2.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

A Floating-point Extended Kalman Filter Implementation for Autonomous Mobile Robots

Localization and Mapping are two of the most important capabilities for autonomous mobile robots and have been receiving considerable attention from the scientific computing community over the last 10 years. One of the most efficient methods to address these problems is based on the use of the Extended Kalman Filter (EKF). The EKF simultaneously estimates a model of the environment (map) and the position of the robot based on odometric and exteroceptive sensor information. As this algorithm demands a considerable amount of computation, it is usually executed on high end PCs coupled to the robot. In this work we present an FPGA-based architecture for the EKF algorithm that is capable of processing two-dimensional maps containing up to 1.8 k features at real time (14 Hz), a three-fold improvement over a Pentium M 1.6 GHz, and a 13-fold improvement over an ARM920T 200 MHz. The proposed architecture also consumes only 1.3% of the Pentium and 12.3% of the ARM energy per feature.

Localization of a mobile robot based on odometry and natural landmarks using extended kalman filter

SANTANA, André M.; SOUZA, Anderson A. S.; BRITTO, Ricardo S.; ALSINA, Pablo J.; MEDEIROS, Adelardo A. D. Localization of a mobile robot based on odometry and natural landmarks using extended Kalman Filter. In: INTERNATIONAL CONFERENCE ON INFORMATICS IN CONTROL, AUTOMATION AND ROBOTICS, 5., 2008, Funchal, Portugal. Proceedings... Funchal, Portugal: ICINCO, 2008.

A Discussion Related to Orbit Determination Using Nonlinear Sigma Point Kalman Filter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Unscented Kalman Filter Applied to the Spacecraft Attitude Estimation with Euler Angles

The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite (China Brazil Earth Resources Satellite). The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.

Comparative analysis of synchronization algorithms based on PLL, RDFT and Kalman Filter

This paper discusses the main characteristics and presents a comparative analysis of three synchronization algorithms based respectively, on a Phase-Locked Loop, a Kalman Filter and a Discrete Fourier Transform. It will be described the single and three-phase models of the first two methods and the single-phase model of the third one. Details on how to modify the filtering properties or dynamic response of each algorithm will be discussed in terms of their design parameters. In order to compare the different algorithms, these parameters will be set for maximum filter capability. Then, the dynamic response, during input amplitude and frequency deviations will be observed, as well as during the initialization procedure. So, advantages and disadvantages of all considered algorithms will be discussed. ©2007 IEEE.

Trade-growth relationship in Cuba: estimation using the Kalman filter

Includes bibliography

Kalman Filter approaches on crane swing

The purpose of this study is to explore a Kalman Filter approach to estimating swing of crane-suspended loads. Measuring real-time swing is needed to implement swing damping control strategies where crane joints are used to remove energy from a swinging load. The typical solution to measuring swing uses an inertial sensor attached to the hook block. Measured hook block twist is used to resolve the other two sensed body rates into tangential and radial swing. Uncertainty in the twist measurement leads to inaccurate tangential and radial swing calculations and ineffective swing damping. A typical mitigation approach is to bandpass the inertial sensor readings to remove low frequency drift and high frequency noise. The center frequency of the bandpass filter is usually designed to track the load length and the pass band width set to trade off performance with damping loop gain. The Kalman Filter approach developed here allows all swing motions (radial, tangential and twist) to be measured without the use of a bandpass filter. This provides an alternate solution for swing damping control implementation. After developing a Kalman Filter solution for a two-dimensional swing scenario, the three-dimensional system is considered where simplifying assumptions, suggested by the two-dimensional study, are exploited. One of the interesting aspects of the three-dimensional study is the hook block twist model. Unlike the mass-independence of a pendulum's natural frequency, the twist natural frequency depends both on the pendulum length and the load’s mass distribution. The linear Kalman Filter is applied to experimental data demonstrating the ability to extract the individual swing components for complex motions. It should be noted that the three-dimensional simplifying assumptions preclude the ability to measure two "secondary" hook block rotations. The ability to segregate these motions from the primary swing degrees of freedom was illustrated in the two-dimensional study and could be included into the three-dimensional solution if they were found to be important for a particular application.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

Methodology for adapting the parameters of a fuzzy system using the extended Kalman filter

When we try to analyze and to control a system whose model was obtained only based on input/output data, accuracy is essential in the model. On the other hand, to make the procedure practical, the modeling stage must be computationally efficient. In this regard, this paper presents the application of extended Kalman filter for the parametric adaptation of a fuzzy model

Application of the Extended Kalman filter to fuzzy modeling: Algorithms and practical implementation

Modeling phase is fundamental both in the analysis process of a dynamic system and the design of a control system. If this phase is in-line is even more critical and the only information of the system comes from input/output data. Some adaptation algorithms for fuzzy system based on extended Kalman filter are presented in this paper, which allows obtaining accurate models without renounce the computational efficiency that characterizes the Kalman filter, and allows its implementation in-line with the process

Improved Animal Tracking Algorithm using Distributed Kalman Filter-based Algortihms

Animal tracking has been addressed by different initiatives over the last two decades. Most of them rely on satellite connectivity on every single node and lack of energy-saving strategies. This paper presents several new contributions on the tracking of dynamic heterogeneous asynchronous networks (primary nodes with GPS and secondary nodes with a kinetic generator) motivated by the animal tracking paradigm with random transmissions. A simple approach based on connectivity and coverage intersection is compared with more sophisticated algorithms based on ad-hoc implementations of distributed Kalman-based filters that integrate measurement information using Consensus principles in order to provide enhanced accuracy. Several simulations varying the coverage range, the random behavior of the kinetic generator (modeled as a Poisson Process) and the periodic activation of GPS are included. In addition, this study is enhanced with HW developments and implementations on commercial off-the-shelf equipment which show the feasibility for performing these proposals on real hardware.