Iterated Extended Kalman Filter Research Articles

정밀 행성 착륙을 위한 지형 보조 관성 항법 연구

본 논문에서는 정밀 행성 착륙을 위해 광학센서와 관성항법시스템을 이용한 지형보조 관성항법 시스템을 구현하였다. 또한 측정된 지형 데이터와 사전에 탑재한 지형 데이터간의 특징점 추출, 매칭, 추적의 영상 처리 과정을 수행하였고 이를 통해 특징점의 좌표를 추출할 수 있다. 반복 확장칼만필터를 이용한 항법 시스템은 기존 관성 항법 장치의 항법 오차 누적을 보상하여 보다 정밀한 항법 정보를 제공한다. 이는 향후 착륙선의 유도 및 제어 법칙과 결합하여 정밀 행성 착륙을 위한 시스템 구현에 적용이 가능하다. This study investigates Terrain Aided Inertial Navigation(TAIN) which consists of Inertial Navigation System (INS) with the optical sensor for precise planetary landing. Image processing is conducted to extract the feature points between measured terrain data and on-board implemented terrain information. The navigation algorithm with Iterated Extended Kalman Filter(IEKF) can compensate for the navigation error, and provide precise navigation information compared to single INS. Simulation results are used to demonstrate the feasibility of integration to accomplish precise planetary landing. The proposed navigation approach can be implemented to the whole system coupled with guidance and control laws.

Predictive Iterated Kalman Filter for INS/GPS Integration and Its Application to SAR Motion Compensation

This paper deals with the problem of state estimation for the integration of an inertial navigation system (INS) and Global Positioning System (GPS). For a nonlinear system that has the model error and white Gaussian noise, a predictive filter (PF) is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) is proposed and is called predictive iterated Kalman filter (PIKF). The basic idea of the PIKF is to compensate the state estimate by the estimated model error. An INS/GPS integration system is implemented using the PIKF and applied to synthetic aperture radar (SAR) motion compensation. Through flight tests, it is shown that the PIKF has an obvious accuracy advantage over the IEKF and unscented Kalman filter (UKF) in velocity.

Passive location of the nonlinear systems with fuzzy uncertainty

With the merits such as hiding receiving, easy-deploying and high security, passive location has attracted more and more attention and plays an important role in fields as diverse as navigation, location, and tracking, etc. However, the current filters models for passive location methods are most under the framework of the probability theory, thus they can not estimate the state in some passive location with fuzzy uncertainty accurately. Although the fuzzy extended Kalman filter (FEKF) can deal with the fuzzy uncertainty, it unavoidably introduces truncation error. In this paper, based on the FEKF and the iterated extended Kalman filter (IEKF) principle, a new fuzzy passive location model is built, and moreover, an iterated fuzzy extended Kalman filter (IFEKF) is proposed for estimating the target state. Compared to the FEKF and the IEKF, the proposed algorithm can not only reduce the truncation error, but also deal with fuzzy uncertainty. Moreover, it is proved that the IFEKF update is an application of the Gauss–Newton method. Then, a fuzzy passive location algorithm is proposed. Simulation results demonstrate that the proposed approach has better estimation precision than the traditional fuzzy extended Kalman filter.

Joint State and Parameter Estimation For Biochemical Dynamic Pathways With Iterative Extended Kalman Filter: Comparison With Dual State and Parameter Estimation

A biochemical dynamic pathway is usually modeled as a nonlinear system described by a set of nonlinear ODEs. In most cases, only partial states can be measured. Moreover, the system parameters, reaction rates, may be unknown or poorly known. Therefore, it is of significance to estimate the states and parameters, for analyzing the biochemical dynamic pathway. Due to the limitation of some traditional parameter estimation approaches, it is natural to choose sequential methods such as extended Kalman filter to do the parameter estimation for biochemical dynamic pathways. In this paper, dual/joint state and parameter estimation with iterative extended Kalman filter (EKF) are investigated to obtain state and parameter estimates for a biochemical pathway simultaneously. The simulated results between two methods are compared to show the validity of parameter estimation for a biochemical dynamic pathway. It has shown that, for the nonlinear biochemical system, the joint state and parameter estimation with EKF, can give desirable convergence and estimation performance.

An approach to aid INS using time-differenced GPS carrier phase (TDCP) measurements

This paper presents a simple and effective approach that incorporates single-frequency, L1 time-differenced GPS carrier phase (TDCP) measurements without the need of ambiguity resolution techniques and the complexity to accommodate the delayed-state terms. Static trial results are included to illustrate the stochastic characteristics and effectiveness of the TDCP measurements in controlling position error growth. The formulation of the TDCP observation model is also described in a 17-state tightly-coupled GPS/INS iterative, extended Kalman filter (IEKF) approach. Preliminary land vehicle trial results are also presented to illustrate the effectiveness of the TDCP which provides sub-meter positional accuracies when operating for more than 10 min.

A New Version of Unscented Kalman Filter

Abstract — This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results. Keywords — Extended Kalman Filter, Iterated EKF, Nonlinear state estimator, Unscented Kalman Filter.I. I NTRODUCTION CCURATE estimation of state variables of systems is important for fault detection and control applications. However, estimation in nonlinear systems is not easy to deal with. The optimal (Bayesian) solution to the problem requires propagation of description of full probability density function (pdf) [1]. This solution is general and includes factors such as multimodality, asymmetries, and discontinuities. However, since the form of pdf is not restricted, it cannot, in general, be represented using finite number of parameters. Therefore, any practical estimator must use an approximation of some kinds. Many different types of approximations have been developed; unfortunately, most are either computationally unmanageable or require special assumptions about the form of the process and observation models that cannot be satisfied in practice. For these and other reasons, the KF remains the most widely used estimation algorithm. The most common application of the KF to nonlinear systems is in the form of extended KF (EKF) [2, 3]. EKF was first used by Wu et al. to find the 3D location. Exploiting the assumption that all transformations are quasi-linear, the EKF simply linearizes all nonlinear transformations and substitutes Jacobian matrices for the linear transformations in the KF equations. In addition, EKF is very convenient and fast for real-time processing and quite straightforward to implement if a priori information of the measurement and process noise covariance matrices are available. Linearization in EKF

Sigma point Kalman filter for bearing only tracking

Relative merits of sigma point Kalman filters (SPKF), also known as unscented Kalman filters (UKF) vis-à-vis extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) for a bearing-only target-tracking problem using rms error and robustness with respect to outlier initial conditions are explored. After establishing that the rms error performance obtainable by SPKF/UKF and IEKF for this fairly severe non-linear system is similar to those obtainable from other competing techniques, the relative robustness of IEKF, SPKF/UKF and EKF with respect to large initial condition uncertainty (a common occurrence for this class of tracking problems) is investigated. Using several versions of SPKF/UKF, it is shown that SPKF is about 20 times more robust compared to EKF. It is illustrated that the additional design freedom available with a scaled version of SPKF/UKF may be utilised for further improvement of the robustness. The main contribution of this paper is quantification of relative robustness of these non-linear filters. A simplified criterion is suggested and used for quantifying track loss and the relative occurrence of such track loss in batch Monte Carlo simulation has been used as a measure of (lack of) robustness. As the SPKF/UKF does not introduce substantial computational burden, when compared to EKF, it is argued that SPKF/UKF algorithm may become a strong candidate for on-board implementation.

Mobile robot localization using a non-linear evolutionary filter

This article describes a localization system for autonomous mobile robot navigation in an indoor semi-structured environment. A peripheral ring of 24 ultrasonic sensors and a camera with a motorized zoom on a pan-tilt platform are used to obtain the information required for the localization process. A non-linear filter based on a genetic algorithm as an emerging optimization method to search for optimal positions is presented. The proposed algorithm is based upon an iterative extended Kalman filter (EKF), which utilizes matches between observed geometric beacons and a generic map of beacon locations and the detection of artificial landmarks, to correct the position and orientation of the vehicle. No exhaustive map of the environment is provided to the mobile robot. It must work with a generic description of the kinds of entities in the environment. The resulting self-localization module has been integrated successfully in a more complex navigation system based on a reactive architecture. Various experimental results show the effectiveness of the presented algorithm, including a comparison with the EKF method.

A regularization approach to continuous learning with an application to financial derivatives pricing

We consider the training of neural networks in cases where the nonlinear relationship of interest gradually changes over time. One possibility to deal with this problem is by regularization where a variation penalty is added to the usual mean squared error criterion. To learn the regularized network weights we suggest the Iterative Extended Kalman Filter (IEKF) as a learning rule, which may be derived from a Bayesian perspective on the regularization problem. A primary application of our algorithm is in financial derivatives pricing, where neural networks may be used to model the dependency of the derivatives’ price on one or several underlying assets. After giving a brief introduction to the problem of derivatives pricing we present experiments with German stock index options data showing that a regularized neural network trained with the IEKF outperforms several benchmark models and alternative learning procedures. In particular, the performance may be greatly improved using a newly designed neural network architecture that accounts for no-arbitrage pricing restrictions.

A Genetic Algorithm for Mobile Robot Localization Using Ultrasonic Sensors

This paper describes an ultrasonic sensor localization system for autonomous mobile robot navigation in an indoor semi-structured environment. The proposed algorithm is based upon an iterative extended Kalman filter, which utilizes matches between observed geometric beacons and an a priori map of beacon locations, to correct the position and orientation of the vehicle. We present a non-linear filter based on a genetic algorithm as an emerging optimization method to search for optimal positions. Experiments demonstrate its effectiveness in real world applications.

Tracking Persons in Monocular Image Sequences

Quantitative geometric descriptions of the movements of persons are obtained by fitting the projection of a three-dimensional person model to consecutive frames of an image sequence. The kinematic of the person model is given by a homogeneous transformation tree and its body parts are modeled by right-elliptical cones. The values of a varying number of degrees of freedom (DOFs; body joints, position, and orientation of the person relative to the camera) can be determined according to the application and the kind of image sequence. The determination of the DOFs is understood as an estimation problem which is solved by an iterated extended Kalman filter (IEKF). For this purpose, the person model is augmented by a simple motion model of constant velocity for all DOFs which is used in the prediction step of the IEKF. In the update step, both region and edge information are used. Various experiments demonstrate the efficiency of our approach.

Experiments on estimating egomotion and structure parameters using long monocular image sequences

This paper presents a simple but robust model based approach to estimating the kinematics of a moving camera and the structure of the objects in a stationary environment using long, noisy, monocular image sequences. Both batch and recursive algorithms are presented and the problem due to occlusion is addressed. The approach is based on representing the constant translational velocity and constant angular velocity of the camera motion using nine rectilinear motion parameters, which are 3-D vectors of the position of the rotation center, linear and angular velocities. The structure parameters are 3-D coordinates of the salient feature points in the inertial coordinate system. Due to redundancies in parameterization, the total number of independent parameters to be estimated is 3M+7, whereM is the number of feature points. The image plane coordinates of these feature points in each frame are first detected and matched over the frames. These noisy image coordinates serve as the input to our algorithms. Due to the nonlinear nature of perspective projection, a nonlinear least squares method is formulated for the batch algorithm, and a conjugate gradient method is then applied to find the solution. A recursive method using an Iterated Extended Kalman Filter (IEKF) for incremental estimation of motion and structure is also presented. Since the plant model is simple in our formulation, closed form solutions for the state and covariance transition equations are easily derived. Experimental results for simulated imagery as well as several real image sequences are included.

Study on a modified algorithm—iterative Kalman filter and its application in enzymic kinetics

A modified algorithm, the iterative Kalman filter, for the analysis of enzymic kinetic data was investigated and successfully applied to the determination of urea in human blood by a urease catalytic reaction. This reaction was monitored with a novel sensor, the surface acoustic wave enzyme sensor system recently proposed by our laboratory. The results were compared with those provided by a calibration graph and classical colorimetry methods. In contrast to these conventional methods, the iterative extended-Kalman filter is shown to be an excellent data analysis method for enzyme kinetic analysis. The urease kinetic parameters were also estimated according to the iterative Kalman filtering results.

Multivariable Iterative Extended Kalman Filter Based Adaptive Control: Case Study of Solid Substrate Fermentation

In solid substrate fermentation (SSF), the on-line measurements of the states of the fermentation like biomass content, dry matter content, and moisture content are not possible. Also, the control of the temperature and the moisture content is critical for optimization of the process. A multivariable adaptive control structure along with state estimation using an iterative extended Kalman filter (IEKF) is proposed for the control. The IEKF uses the measurements of total wet weight and CO 2 evolution rate to estimate the states. An autoregressive with exogenous input (ARX) model is used as a model of the process relating controlled variables with manipulated variables (dry air flow rate and the water replenishment rate) and forms the basis for the determination of future control input

Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration. >

Recursive 3-D motion estimation from a monocular image sequence

Consideration is given to the design and application of a recursive algorithm to a sequence of images of a moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth in the sense that it can be modeled by retaining an arbitrary number of terms in the appropriate Taylor series expansions. Translational motion involves a standard rectilinear model, while rotational motion is described with quaternions. Neglected terms of the Taylor series are modeled as process noise. A state-space model is constructed, incorporating both kinematic and structural states, and recursive techniques are used to estimate the state vector as a function of time. A set of object match points is assumed to be available. The problem is formulated as a parameter estimation and tracking problem which can use an arbitrarily large number of images in a sequence. The recursive estimation is done using an iterated extended Kalman filter (IEKF), initialized with the output of a batch algorithm run on the first few frames. Approximate Cramer-Rao lower bounds on the error covariance of the batch estimate are used as the initial state estimate error covariance of the IEKF. The performance of the recursive estimator is illustrated using both real and synthetic image sequences. >

Passive Position Location Estimation Using the Extended Kalman Filter

Several papers have been published recently using the method ofleast squares for passive position location estimation. While the Kalman filter is mentioned as an alternative approach in most ofthese papers, none of the papers actually compare the performanceof the Kalman filter with the method of least squares. In this paper,the performances of the extended Kalman filter and the iteratedextended Kalman filter are compared with the method of leastsquares. Monte Carlo results are given showing how the a prioricovariance matrix influences the accuracy of the extended Kalmanfilter.

Aquifer Parameter Estimation Using Kalman Filters

An iterated extended Kalman filter (IEKF) has been used for the estimation of aquifer parameters in the presence of uncertainties in the system and noise in the measurements. The technique is sequential and each additional observation reduces the error covariance of the parameter estimates. The method is computationally efficient and gives the confidence limits of the parameter estimates. Only a few observations are sufficient to provide a reasonable estimate of the aquifer parameters. Actual aquifer test data for confined nonleaky and leaky aquifers have been analyzed and the results compared with those obtained using the known technique. The IEKF method gives less residual square error and eliminates the subjectivity involved in the conventional curve matching techniques.