Showing papers on "Invariant extended Kalman filter published in 1999"

Adaptive Kalman Filtering for INS/GPS

Abstract: After reviewing the two main approaches of adaptive Kalman filtering, namely, innovation-based adaptive estimation (IAE) and multiple-model-based adaptive estimation (MMAE), the detailed development of an innovation-based adaptive Kalman filter for an integrated inertial navigation system/global positioning system (INS/GPS) is given. The developed adaptive Kalman filter is based on the maximum likelihood criterion for the proper choice of the filter weight and hence the filter gain factors. Results from two kinematic field tests in which the INS/GPS was compared to highly precise reference data are presented. Results show that the adaptive Kalman filter outperforms the conventional Kalman filter by tuning either the system noise variance–covariance (V–C) matrix `Q' or the update measurement noise V–C matrix `R' or both of them.

Stochastic stability of the discrete-time extended Kalman filter

Abstract: The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.

Robust extended Kalman filtering

Abstract: Linearization errors inherent in the specification of an extended Kalman filter (EKF) can severely degrade its performance. This correspondence presents a new approach to the robust design of a discrete-time EKF by application of the robust linear design methods based on the H/sub /spl infin// norm minimization criterion. The results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications.

Development and experimental validation of an adaptive extended Kalman filter for the localization of mobile robots

Abstract: A basic requirement for an autonomous mobile robot is its capability to elaborate the sensor measures to localize itself with respect to a coordinate system. To this purpose, the data provided by odometric and sonar sensors are here fused together by means of an extended Kalman filter. The performance of the filter is improved by an online adjustment of the input and measurement noise covariances obtained by a suitably defined estimation algorithm.

Frequency estimation of distorted power system signals using extended complex Kalman filter

Abstract: The paper proposes an extended complex Kalman filter and employs it for the estimation of power system frequency in the presence of random noise and distortions. From the discrete values of the 3-phase voltage signals of a power system, a complex voltage vector is formed using the well known /spl alpha//spl beta/-transform. A nonlinear state space formulation is then obtained for this complex signal and an extended Kalman filtering approach is used to compute the true state of the model iteratively with significant noise and harmonic distortions. As the frequency is modeled as a state, the estimation of the state vector yields the unknown power system frequency. Several computer simulations test results are presented in the paper to highlight the usefulness of this approach in estimating near nominal and off-nominal power system frequencies.

The extended Kalman filter as an exponential observer for nonlinear systems

Abstract: We analyze the behavior of the extended Kalman filter as a state estimator for nonlinear deterministic systems. Using the direct method of Lyapunov, we prove that under certain conditions, the extended Kalman filter is an exponential observer, i.e., the dynamics of the estimation error is exponentially stable. Furthermore, we discuss a generalization of the Kalman filter with exponential data weighting to nonlinear systems.

Dual Estimation and the Unscented Transformation

Abstract: Dual estimation refers to the problem of simultaneously estimating the state of a dynamic system and the model which gives rise to the dynamics. Algorithms include expectation-maximization (EM), dual Kalman filtering, and joint Kalman methods. These methods have recently been explored in the context of nonlinear modeling, where a neural network is used as the functional form of the unknown model. Typically, an extended Kalman filter (EKF) or smoother is used for the part of the algorithm that estimates the clean state given the current estimated model. An EKF may also be used to estimate the weights of the network. This paper points out the flaws in using the EKF, and proposes an improvement based on a new approach called the unscented transformation (UT) [3]. A substantial performance gain is achieved with the same order of computational complexity as that of the standard EKF. The approach is illustrated on several dual estimation methods.

A receding horizon Kalman FIR filter for discrete time-invariant systems

Abstract: A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples.

Optimal solution of the two-stage Kalman estimator

Abstract: The two-stage Kalman estimator was originally proposed to reduce the computational complexity of the augmented state Kalman filter. It was also applied to the tracking of maneuvering targets by treating the target acceleration as a bias term. Except in certain restrictive conditions, the conventional two-stage estimators are suboptimal in the sense that they are not equivalent to the augmented state filter. In this paper, the authors propose a new two-stage Kalman estimator, i.e., new structure, which is an extension of Friedland's estimator and is optimal in general conditions. In addition, we provide some analytic results to demonstrate the computational advantages of two-stage estimators over augmented ones.

Vehicle Dynamics Estimation Using Kalman Filters

Abstract: This paper deals with the application of stochastic state estimators in vehicle dynamics control. It is often unrealistic to assume that all vehicle states and the disturbances acting on it can be measured. System states that cannot be measured directly, can be estimated by a Kalman Filter. The idea of the Kalman filter is to implement a model of the real system in an on-board computer in parallel with the system itself. This paper will give 3 examples of this principle applied to automotive systems.

Circumventing dynamic modeling: evaluation of the error-state Kalman filter applied to mobile robot localization

Abstract: The mobile robot localization problem is treated as a two-stage iterative estimation process. The attitude is estimated first and is then available for position estimation. The indirect (error state) form of the Kalman filter is developed for attitude estimation when applying gyro modeling. The main benefit of this choice is that combined dynamic modeling of the mobile robot and its interaction with the environment is avoided. The filter optimally combines the attitude rate information from the gyro and the absolute orientation measurements. The proposed implementation is independent of the structure of the vehicle or the morphology of the ground. The method can easily be transferred to another mobile platform provided it carries an equivalent set of sensors. The 2D case is studied in detail first. Results of extending the approach to the 3D case are presented. In both cases the results demonstrate the efficacy of the proposed method.

On phase-locked loops and Kalman filters

Abstract: Driessen (1994) and Christiansen (1994) independently showed that for a specific dynamic model, the proportional-integral phase-locked loop (PLL) has the same structure as the Kalman filter. In this paper, closed-form expressions of the corresponding Kalman gain values are derived both in acquisition and tracking modes of the PLL.

Tracking through singularities and discontinuities by random sampling

Abstract: Some issues in markerless tracking of human body motion are addressed. Extended Kalman filters have commonly been applied to kinematic variables, to combine predictions consistent with plausible motion, with the incoming stream of visual measurements. Kalman filtering is applicable only when the underlying distribution is approximately Gaussian. Often this assumption proves remarkably robust. There are two pervasive circumstances under which the Gaussianity assumption can break down. The first is kinematic singularity and the second is at joint endstops. Failure of Kalman filtering under these circumstances is illustrated. The non-Gaussian nature of the distributions is demonstrated experimentally by means of Monte Carlo simulation. Random simulation (particle filtering or Condensation) proves to provide a robust alternative algorithm for tracking that can also deal with these difficult conditions.

Comparison of extended and ensemble Kalman filters for data assimilation in coastal area modelling

Abstract: Data assimilation in a two-dimensional hydrodynamic model for bays, estuaries and coastal areas is considered. Two different methods based on the Kalman filter scheme are presented. These include (1) an extended Kalman filter in which the error covariance matrix is approximated by a matrix of reduced rank using a square root factorisation (RRSQRT KF), and (2) an ensemble Kalman filter (EnKF) based on a Monte Carlo simulation approach for propagation of errors. The filtering problem is formulated by utilising a general description of the model noise process related to errors in the model forcing, i.e. open boundary conditions and meteorological forcing. The performance of the two Kalman filters is evaluated using a twin experiment based on a hypothetical bay region. For both filters, the error covariance approximation sufficiently resolves the error propagation in the model at a computational load that is significantly smaller than required by the full Kalman filter algorithm. Furthermore, the Kalman filters are shown to be very robust with respect to defining the errors. Even in the case of a severely biased model error, the filters are able to efficiently correct the model. In general, the use of coloured model noise provides a numerically more efficient algorithm as well as a better performance of the filter. The error covariance approximation in the RRSQRT KF is shown to be more efficient than the error representation in the EnKF. For strongly non-linear dynamics, however, the EnKF is preferable. Copyright © 1999 John Wiley & Sons, Ltd.

Peak-seeking control with application to formation flight

Abstract: A new controller is proposed for linear systems with unknown optimal operating points. It is assumed that the desired operating point represents the maximum of a function of the states of the system. The controller uses a modified Kalman filter to estimate the derivatives of this function, and the controller drives the system to the optimum. The controller is derived in the context of the formation flight of aircraft for drag reduction, and a simulation is used to provide preliminary results.

On the Kalman filtering method in neural network training and pruning

Abstract: In the use of the extended Kalman filter approach in training and pruning a feedforward neural network, one usually encounters the problems of how to set the initial condition and how to use the result obtained to prune a neural network. In this paper, some cues on the setting of the initial condition are presented with a simple example illustrated. Then based on three assumptions: 1) the size of training set is large enough; 2) the training is able to converge; and 3) the trained network model is close to the actual one, an elegant equation linking the error sensitivity measure (the saliency) and the result obtained via an extended Kalman filter is devised. The validity of the devised equation is then testified by a simulated example.

A receding horizon Kalman FIR filter for linear continuous-time systems

Abstract: A receding horizon Kalman finite-impulse response (FIR) filter is suggested for continuous-time systems, combining the Kalman filter with the receding horizon strategy. In the suggested filter, the horizon initial state is assumed to be unknown. It can always be obtained irrespective of unknown information on the horizon initial state. The filter may be the first stochastic FIR form for continuous-time systems that may have many good inherent properties. The suggested filter can be represented in an iterative form and also in a standard FIR form. The suggested filter turns out to be a remarkable deadbeat observer. The validity of the suggested filter is illustrated by numerical examples.

Design of Kalman filters for mobile robots; evaluation of the kinematic and odometric approach

Abstract: Kalman filters have for a long time been widely used on mobile robots as a location estimator. Many different Kalman filter designs have been proposed, using models of various complexity. In this paper, two different design methods are evaluated and compared. Focus is put on the common setup where the mobile robot is equipped with a dual encoder system supported by some additional absolute measurements. A common filter type for this setup is the odometric filter, where readings from the odometry system on the robot are used together with the geometry of the robot movement as a model of the robot. If additional kinematic assumptions are made, for instance regarding the velocity of the robot, an augmented model can be used instead. This kinematic filter has some advantages when used intelligently, and it is shown how this type of filter can be used to suppress noise on encoder readings and velocity estimates. The Kalman filter normally consists of a time update followed by one or more data updates. However, it is shown that when using the kinematic filter, the encoder measurements should be fused prior to the time update for better performance.

A Kalman filter approach to direct depth estimation incorporating surface structure

Abstract: The problem of depth-from-motion using a monocular image sequence is considered A pixel-based model is developed for direct depth estimation within a Kalman filtering framework A method is proposed for incorporating local surface structure into the Kalman filter Experimental results are provided to illustrate the effect of structural information on depth estimation

Comparison of SDINS in-flight alignment using equivalent error models

Abstract: The psi-angle model and the equivalent tilt (ET) model have been widely used for in-flight alignment (IFA) to align and to calibrate a strapdown inertial navigation system (SDINS) on a moving base. However, these models are not effective for a system with large attitude errors because the neglected error terms in the models degrade the performance of a designed filter. In this paper, with an odometer as an external aid, a velocity-aided SDINS is designed for IFA. Equivalent error models applicable to IFA with large attitude errors are derived in terms of rotation vector error and additive and multiplicative quaternion errors. It is found that error models in terms of additive quaternion error (AQE) become linear. Thus the proposed error models reduce unmodeled error terms for a linear filter. From a number of van tests, it is shown that the proposed error models effectively improve the performance of IFA.

Finite horizon robust Kalman filter design

Abstract: In this paper, we study the problem of finite horizon Kalman filtering for systems involving a norm-bounded uncertain block. A new technique is presented for robust Kalman filter design. This technique involves using multiple scaling parameters which can be optimized by solving a semidefinite program. The use of optimized scaling parameters leads to an improved design. Also proposed is a recursive design method which can be applied to real-time applications.

Synchronization through extended Kalman filtering

Abstract: We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an extended Kalman filter that is driven by a noisy drive signal from the transmitter. Extensive computer simulations show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to secure communication is also given.

Kalman Filters : A Tutorial

Abstract: A Kalman filter is a stochastic, recursive estimator, which estimates the state of a system based on the knowledge of the system input, the measurement of the system output, and a model of the relation between input and output. The Kalman filter equations are well known, but often little effort is spent to explain or understand how the Kalman filter really works, and what its assets and limitations are. This paper introduces the Kalman filter in a very intuitive way, and looks at its properties: what information can be extracted from it, and what are its limitations. This intuitive understanding should help to develop successful practical applications. The paper also points at further reading.

An interlaced extended Kalman filter

Abstract: An estimation algorithm for a class of discrete time nonlinear systems is proposed. The system structure we deal with is partitionable into in subsystems, each affine w.r.t. the corresponding part of the state vector. The algorithm consists of a bank of m interlaced Kalman filters, and each of them estimates a part of the state, considering the remaining parts as known time-varying parameters whose values are evaluated by the other filters at the previous step. The procedure neglects the subsystem coupling terms in the covariance matrix of the state estimation error and counteracts the errors so introduced by suitably "increasing" the noise covariance matrices. Comparisons through numerical simulations with the extended Kalman filter and its modified versions proposed in the literature illustrate the good trade-off provided by the algorithm between the reduction of the computational load and the estimation accuracy.

Robust adaptive Kalman filters for linear time-varying systems with stochastic parametric uncertainties

Abstract: We present an adaptive robust Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has the one-step predictor-corrector structure and minimizes the mean square estimation error at each step, with the minimization reduced to a convex optimization problem based on linear matrix inequalities. The algorithm is shown to converge when the system is mean square stable and the state-space matrices are time-invariant. A numerical example, consisting of equalizer design for a communication channel, demonstrates that our algorithm offers considerable improvement in performance when compared to standard Kalman filtering techniques.