Showing papers on "Invariant extended Kalman filter published in 2003"
TL;DR: In this paper, an unscented filter is used to estimate the attitude of a spacecraft in the presence of a gyro-based model for attitude propagation, and a multiplicative quaternion-error is derived from the local attitude error, which guarantees that quaternions normalization is maintained in the filter.
Abstract: A new spacecraft attitude estimation approach based on the unscented filter is derived. For nonlinear systems the unscented filter uses a carefully selected set of sample points to map the probability distribution more accurately than the linearization of the standard extended Kalman filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. The filter formulation is based on standard attitude-vector measurements using a gyro-based model for attitude propagation. The global attitude parameterization is given by a quaternion, whereas a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is derived from the local attitude error, which guarantees that quaternion normalization is maintained in the filter. Simulation results indicate that the unscented filter is more robust than the extended Kalman filter under realistic initial attitude-error conditions.
908 citations
TL;DR: In this paper, the authors consider various attitude error representations for the Multiplicative Extended Kalman Filter (MEFL) and its second-order extension, and compare them with a three-component representation for attitude errors.
Abstract: The quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation. The quaternion must obey a unit norm constraint, though, which has led to the development of an extended Kalman filter using a quaternion for the global attitude estimate and a three-component representation for attitude errors. We consider various attitude error representations for this Multiplicative Extended Kalman Filter and its second-order extension.
651 citations
10 Nov 2003
TL;DR: FastSLAM also substantially outperforms the EKF in environments with ambiguous data association, and it is shown how negative information can be incorporated into FastSLAM in order to improve the accuracy of the estimated map.
Abstract: The extended Kalman filter (EKF) has been the de facto approach to the Simultaneous Localization and Mapping (SLAM) problem for nearly fifteen years. However, the EKF has two serious deficiencies that prevent it from being applied to large, real-world environments: quadratic complexity and sensitivity to failures in data association. FastSLAM, an alternative approach based on the Rao-Blackwellized Particle Filter, has been shown to scale logarithmically with the number of landmarks in the map. This efficiency enables FastSLAM to be applied to environments far larger than could be handled by the EKF. In this paper, we show that FastSLAM also substantially outperforms the EKF in environments with ambiguous data association. The performance of the two algorithms is compared on a real-world data set with various levels of odometric noise. In addition, we show how negative information can be incorporated into FastSLAM in order to improve the accuracy of the estimated map.
495 citations
TL;DR: In this paper, the authors proposed a method based on the complete normalization of the extended Kalman filter (EKF) algorithm representation, which can put the EKF drive much closer to an off-the-shelf product.
Abstract: The use of an extended Kalman filter (EKF) as a nonlinear speed and position observer for permanent-magnet synchronous motor drives is a mature research topic. Notwithstanding, the shift from research prototype to a market-ready product still calls for a solution to some implementation pitfalls. The major and still unsolved topic is the choice of the EKF covariance matrices. This paper replaces the usual trial-and-error method with a straightforward matrices choice. These matrices, possibly combined with a novel self-tuning procedure, should put the EKF drive much closer to an off-the-shelf product. The proposed method is based on the complete normalization of the EKF algorithm representation. Successful experimental results are included in the paper.
491 citations
09 Jul 2003
TL;DR: Numerical results show that the proposed methodology to estimate n, based on an extended Kalman filter coupled with a change detection mechanism, shows both high accuracy as well as prompt reactivity to changes in the network occupancy status.
Abstract: Throughput performance of the IEEE 802.11 distributed coordination function (DCF) is very sensitive to the number n of competing stations. The contribute of this paper is threefold. First, we show that n can be expressed as function of the collision probability encountered on the channel; hence, it can be estimated based on run-time measurements. Second, we show that the estimation of n, based on exponential smoothing of the measured collision probability (specifically, an ARMA filter), results to be a biased estimation, with poor performance in terms of accuracy/tracking trade-offs. Third, we propose a methodology to estimate n, based on an extended Kalman filter coupled with a change detection mechanism. This approach shows both high accuracy as well as prompt reactivity to changes in the network occupancy status. Numerical results show that, although devised in the assumption of saturated terminals, our proposed approach results effective also in non-saturated conditions, and specifically in tracking the average number of competing terminals.
490 citations
04 Jun 2003
TL;DR: An empirical study comparing the performance of unscented and extended Kalman filtering for improving human head and hand tracking, represented with quaternions, which are critical for correct viewing perspectives in virtual reality.
Abstract: The unscented Kalman filter is a superior alternative to the extended Kalman filter for a variety of estimation and control problems. However, its effectiveness for improving human motion tracking for virtual reality applications in the presence of noisy data has been unexplored. In this paper, we present an empirical study comparing the performance of unscented and extended Kalman filtering for improving human head and hand tracking. Specifically, we examine human head and hand orientation motion signals, represented with quaternions, which are critical for correct viewing perspectives in virtual reality. Our experimental results and analysis indicate that unscented Kalman filtering performs equivalently with extended Kalman filtering. However, the additional computational overhead of the unscented Kalman filter and quasi-linear nature of the quaternion dynamics lead to the conclusion that the extended Kalman filter is a better choice for estimating quaternion motion in virtual reality applications.
340 citations
TL;DR: In this paper, the authors examined the use of three adaptive filtering techniques, i.e., adaptive Kalman filter covariance, multiple model adaptive estimation and adaptive estimation, to test the dynamic alignment of the inertial sensor errors.
Abstract: GPS and low-cost INS sensors are widely used for positioning and attitude determination applications. Low-cost inertial sensors exhibit large errors that can be compensated using position and velocity updates from GPS. Combining both sensors using a Kalman filter provides high-accuracy, real-time navigation. A conventional Kalman filter relies on the correct definition of the measurement and process noise matrices, which are generally defined a priori and remain fixed throughout the processing run. Adaptive Kalman filtering techniques use the residual sequences to adapt the stochastic properties of the filter on line to correspond to the temporal dependence of the errors involved. This paper examines the use of three adaptive filtering techniques. These are artificially scaling the predicted Kalman filter covariance, the Adaptive Kalman Filter and Multiple Model Adaptive Estimation. The algorithms are tested with the GPS and inertial data simulation software. A trajectory taken from a real marine trial is used to test the dynamic alignment of the inertial sensor errors. Results show that on line estimation of the stochastic properties of the inertial system can significantly improve the speed of the dynamic alignment and potentially improve the overall navigation accuracy and integrity.
231 citations
08 Jul 2003
TL;DR: In this article, an Unscented Kalman filter was proposed for real-time estimation of a rigid body orientation from measurements of acceleration, angular velocity and magnetic field strength.
Abstract: This paper describes a Kalman filter for the real-time estimation of a rigid body orientation from mea- surements of acceleration, angular velocity and magnetic field strength. A quaternion representation of the orienta- tion is computationally effective and avoids problems with singularities. The nonlinear relationship between estimated Orientation and expected measurement prevent the usage of a classical Kalman filter: This problem is solved by an Un- scented Kalman filter which allows nonlinear process and measurement models and is more accurate and less costly than the common Extended Kalman filter: Several exten- sions to the original Unscented Kalman filter are necessary to treat the inherent properties of unit quaternions. Results with simulated and measured data are discussed.
223 citations
22 May 2003
TL;DR: Novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing are presented, which are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.
Abstract: We present novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing. These algorithms, when compared against Kalman and extended Kalman filter-based predictors with derivative free measurement models, run approximately 135 times faster with equivalent prediction performance and simpler implementations. This paper describes these algorithms in detail along with the Kalman and extended Kalman Filter predictors tested against. In addition, we describe the details of a predictor experiment and present empirical results supporting the validity of our claims that these predictors are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.
176 citations
TL;DR: Performance comparisons show that the KPF is an improvement over Condensation, while the UPF has a much higher computational cost for equal tracking error.
158 citations
10 Nov 2003
TL;DR: This paper extends the sparse extended information filter to handle data association problems and report real-world results, obtained with an outdoor vehicle, that performs favorably when compared to the extended Kalman filter solution from which it is derived.
Abstract: In [Thrun, S., et al., 2001], we proposed the sparse extended information filter for efficiently solving the simultaneous localization and mapping (SLAM) problem. In this paper, we extend this algorithm to handle data association problems and report real-world results, obtained with an outdoor vehicle. We find that our approach performs favorably when compared to the extended Kalman filter solution from which it is derived.
TL;DR: In this paper, a performance comparison between a Kalman filter and the interacting multiple model (IMM) estimator is carried out for single-target tracking, and it is shown that above a certain maneuvering index an IMM estimator was preferred over a KF to track the target motion.
Abstract: In this paper, a performance comparison between a Kalman filter and the interacting multiple model (IMM) estimator is carried out for single-target tracking. In a number of target tracking problems of various sizes, ranging from single-target tracking to tracking of about a thousand aircraft for air traffic control, it has been shown that the IMM estimator performs significantly better than a Kalman filter. In spite of these studies and many others, the condition under which an IMM estimator is desirable over a single model Kalman filter versus an IMM estimator are quantified here in terms of the target maneuvering index, which is a function of target motion uncertainty, measurement uncertainty, and sensor revisit interval. Using simulation studies, it is shown that above a certain maneuvering index an IMM estimator is preferred over a Kalman filter to track the target motion. These limits should serve as a guideline in choosing the more versatile, but somewhat costlier, IMM estimator over a simpler Kalman filter.
TL;DR: Under the approximation of uncorrelatedness among the local models, the global filter is shown to be minimum variance and the proposed state estimator is demonstrated on a vehicle tracking problem and a backing up truck–trailer example.
21 May 2003
TL;DR: In this article, the authors adopted a one-dimensional vertical motion model with unknown ballistic coefficient, derived and analyzed the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compared the error performance of three nonlinear filters against the theoretical CRLBs.
Abstract: Tracking of a ballistic re-entry object from radar observations is a highly complex problem in nonlinear filtering. The paper adopts a one-dimensional vertical motion model with unknown ballistic coefficient, derives and analyses the posterior Cramer-Rao lower bounds (CRLBs) for this problem, and compares the error performance of three nonlinear filters against the theoretical CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Taking into account the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.
03 Dec 2003
TL;DR: The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.
Abstract: This paper presents an improved Kalman filter for real-time tracking of human body motions. An earlier version of the filter was presented at IROS 2001. Since then, the filter has been substantially improved. Real-time tracking of rigid body orientation is accomplished using the MARG (magnetic, angular rate, and gravity) sensors. A MARG sensor measures the three-dimensional local magnetic field, three-dimensional angular rate, and three-dimensional acceleration. A Kalman filter is designed to process measurements provided by the MARG sensors, and to produce real-time orientation represented in quaternions. There are many design decisions as related to choice of state vectors, output equations, process model, etc. The filter design presented in this paper utilizes the Gauss-Newton method for parameter optimization in conjunction with Kalman filtering. The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.
TL;DR: In this paper, an extension of the sequential importance sampling filter (SIR) is proposed to estimate the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF.
Abstract: . The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly non-Gaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.
TL;DR: In this article, the extended Kalman filter converges locally for a broad class of nonlinear systems if the initial estimation error of the filter is not too large, and the error goes to zero exponentially as time goes to infinity.
Abstract: We demonstrate that the extended Kalman filter converges locally for a broad class of nonlinear systems If the initial estimation error of the filter is not too large then the error goes to zero exponentially as time goes to infinity To demonstrate this, we require that the system be C 2 and uniformly observable with bounded second partial derivatives
13 Jul 2003
TL;DR: In this article, the authors explored the practical application of the Kalman filter to the analysis of harmonic levels in power systems and investigated the merits and limitations of different possible implementations and the effect of fundamental frequency variation.
Abstract: This paper explores the practical application of the Kalman filter to the analysis of harmonic levels in power systems. The merits and limitations of different possible implementations are investigated and the effect of fundamental frequency variation is examined. The tuning of the Kalman filter for desired dynamic response is discussed and an adaptive tuning algorithm derived for the improved convergence of nonlinear models. The effectiveness of the resulting schemes are tested under a variety of typical power system operating conditions.
TL;DR: In this article, the GPS composite clock is implemented using the Kalman filter for the estimation of the difference between two clocks, and it is shown that the non-observability of the clock time readings is controlled by the so-called "transparent variations" that do not interfere with the estimation algorithm.
Abstract: The Kalman filter is a very useful tool of estimation theory, successfully adopted in a wide variety of problems. As a recursive and optimal estimation technique, the Kalman filter seems to be the correct tool also for building precise timescales, and various attempts have been made in the past giving rise, for example, to the TA(NIST) timescale. Despite the promising expectations, a completely satisfactory implementation has never been found, due to the intrinsic non-observability of the clock time readings, which makes the clock estimation problem underdetermined. However, the case of the Kalman filter applied to the estimation of the difference between two clocks is different. In this case the problem is observable and the Kalman filter has proved to be a powerful tool. A new proposal with interesting results, concerning the definition of an independent timescale, came with the GPS composite clock, which is based on the Kalman filter and has been in use since 1990 in the GPS system. In the composite clock the indefinite growth of the covariance matrix due to the non-observability is controlled by the so-called `transparent variations'—squeezing operations on the covariance matrix that do not interfere with the estimation algorithm. A useful quantity, the implicit ensemble mean, is defined and the `corrected clocks' (physical clocks minus their predicted bias) are shown to be observable with respect to this quantity. We have implemented the full composite clock and we discuss some of its advantages and criticalities. More recently, the Kalman filter is generating new interest, and a few groups are proposing new implementations. This paper gives an overview of what has been done and of what is currently under investigation, pointing out the peculiar advantages and the open questions in the application of this attractive technique to the generation of a timescale.
09 Dec 2003
TL;DR: The recently developed fuzzy logic-based adaptive Kalman filter (FL-AKF) is used to build adaptive centralized, decentralized, and federated Kalman filters for adaptive multisensor data fusion (AMSDF).
Abstract: In this work the recently developed fuzzy logic-based adaptive Kalman filter (FL-AKF) is used to build adaptive centralized, decentralized, and federated Kalman filters for adaptive multisensor data fusion (AMSDF). The adaptation carried out is in the sense of adaptively adjusting the measurement noise covariance matrix of each local FL-AKF to fit the actual statistics of the noise profiles present in the incoming measured data. A fuzzy inference system (FIS) based on a covariance-matching technique is used as the adaptation mechanism. The effectiveness and accuracy of the proposed AMSDF approaches is demonstrated in a simulated example.
08 Jul 2003
TL;DR: In this paper, an alternative linearization of range rate that is not a function of the position elements is derived, which can improve a tracking system's velocity estimates without risk to its position estimates.
Abstract: Radar range rate measurements are not always used in target tracking filters because they are highly nonlinear in Cartesian space. A linear approxi- mation of range rate composed of its partial derivatives with respect to the track state vector is sometimes used in the measurement equation of an Extended Kalman filter. Unfortunately, this naive linearization can de- grade the filter's position estimates. The origins of this phenomenon are investigated and found to lie in the functional relationship induced by the linearization between the position elements of the track state vec- tor and the range rate innovation. An alternative lin- earization of range rate that is not a function of the position elements is derived. It is shown that the new linearization improves position estimate for some tra- jectories. An ordinary Kalman filter's gains are com- pared to those of the usual and alternative extended Kalman filters analytically and via simulation. The results show that the alternative linearization leads to a filter having the same position gains as an ordinary Kalman filter, and an additional gain on the track's radial velocity. This new extended Kalman filter can improve a tracking system's velocity estimates without risk to its position estimates.
TL;DR: In this paper, a new method to assimilate data into a model and estimate the state of a nonlinear dynamical system is suggested. And the performance of this new method of state estimation is compared with that of the extended Kalman filter, largely owing to it taking into account the nonlinearity of the system.
TL;DR: In this article, a study of three timescales formed from a Kalman filter operating on a model of a clock ensemble is presented, and an optimality property is proved for the reduced Kalman scale.
Abstract: This is a study of three timescales formed from a Kalman filter operating on a model of a clock ensemble. The raw Kalman scale is unstable at short averaging times. The Kalman-plus-weights and reduced Kalman scales are stable at all averaging times. An optimality property is proved for the reduced Kalman scale.
08 Jul 2003
TL;DR: In this article, Rao-Blackwellisation is used to calculate tractable integrations in the unscented Kalman filter, which leads to a re-duction in the quasi-Monte Carlo variance, and a decrease in the computational complexity by considering a common tracking problem.
Abstract: The Unscented Kalman Filter oflers sign$- cant improvements in the estimation of non-linear discrete- time models in comparison to the Extended Kalman Fil- ter 1121. In this paper we use a technique introduced by Casella and Robert (2), known as Rao-Blackwellisation, to calculate the tractable integrations that are found in the Unscented Kalman Filter: We show that this leads to a re- duction in the quasi-Monte Carlo variance, and a decrease in the computational complexity by considering a common tracking problem.
Patent•
08 Jan 2003TL;DR: In this paper, a navigation system includes a Kalman filter to compensate for bias errors in inertial sensing elements, and an observed pitch, roll or heading change is input to the filter either from an aiding source or when the system is in a known condition.
Abstract: A navigation system includes a Kalman filter to compensate for bias errors in inertial sensing elements. An observed pitch, roll or heading change is input to the Kalman filter either from an aiding source or when the navigation system is in a known condition. The Kalman filter generates a correction signal that is provided to the navigation computation system.
TL;DR: In this article, a modification of the standard Kalman filter was devised to take advantage of phase measurements differenced over time, where the phase measurement difference is a measure of the difference in position in the line-of-sight direction to the satellite, so it can act as a relative position constraint of the current position with respect to the previous one.
Abstract: Motivated by a requirement to provide real-time meter-level positioning of a NASCAR racing car, a modification of the standard Kalman filter was devised. This paper describes an approach that incorporates previous as well as current position states in a Kalman filter to take advantage of phase measurements differenced over time. In this formulation, the phase measurement difference is a measure of the difference in position in the line-of-sight direction to the satellite, so it can act as a relative position constraint of the current position with respect to the previous one. The formulation of the delta-phase observation equation is described, as well as the modifications made to the Kalman filter to incorporate it. An example used to illustrate the effectiveness of the delta-phase measurements in controlling position error growth is included. Test results in various urban environments are presented.
TL;DR: A nonlinear filter for estimating constant parameters in dynamic systems is presented to illustrate one application of the proposed GTSEKF, which is shown to be equivalent to the EKF with a decoupled computing structure.
Abstract: A general two-stage extended Kalman filter (GTSEKF), which extends the linear general two-stage Kalman filter to nonlinear systems, is further proposed. A new nonlinear two-stage transformation is introduced to facilitate achieving this extension. As in the linear one, the GTSEKF is derived mainly by applying the nonlinear two-stage transformation to the well-known extended Kalman filter (EKF), and is shown to be equivalent to the EKF with a decoupled computing structure. A nonlinear filter for estimating constant parameters in dynamic systems is presented to illustrate one application of the proposed GTSEKF. A literature example is also given to demonstrate the correctness and usefulness of the proposed results.
TL;DR: In this article, a new sequential filtering algorithm that incorporates the radial velocity measurement into a Kalman filter, in the presence of correlated range and radii measurement errors, is presented, and an analysis concerning its asymptotic behavior on the basis of analysis of its stochastic controllability and observability.
Abstract: A new sequential filtering algorithm that incorporates the radial velocity measurement into a Kalman filter, in the presence of correlated range and radial velocity measurement errors, is presented. An analysis is given concerning its asymptotic behavior on the basis of analysis of its stochastic controllability and observability. The simulation results verify the analysis and show that the new algorithm is superior to the conventional extended Kalman filter (EKF) and close to an ideal filter.
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TL;DR: In this paper, the authors present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance, and mention the fundamental case of Gaussian noises where they obtain the well-known Kalman Filter.
Abstract: In this article we present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance. We shall first mention the fundamental case of Gaussian noises where we obtain the well-known Kalman Filter.
Because of common nonlinearities, we will be discussing the Extended Kalman Filter.
01 Sep 2003
TL;DR: In this paper, a neural extended Kalman filter was used to improve motion model prediction during maneuvers, which can be used to reduce the noise of a high process noise model to hold a target through a maneuver with poor velocity and acceleration estimates.
Abstract: A neural extended Kalman filter algorithm was embedded in an interacting multiple model architecture for target tracking. The neural extended Kalman filter algorithm is used to improve motion model prediction during maneuvers. With a better target motion mode, noise reduction can be achieved through a maneuver. Unlike the interacting multiple model architecture which, uses a high process noise model to hold a target through a maneuver with poor velocity and acceleration estimates, a neural extended Kalman filter is used to predict the correct velocity and acceleration states of a target through a maneuver. The neural extended Kalman filter estimates the weights of a neural network, which in turn is used to modify the state estimate predictions of the filter as measurements are processed. The neural network training is performed on-line as data is processed. In this paper, the results of a neural extended Kalman filter embedded in an interacting multiple model tracking architecture will be shown using a high fidelity model of a phased array radar. Six different targets of varying maneuverability will be tracked. The phased array radar is controlled via Level 4 Data Fusion feedback to the Level 0 radar process. Highly maneuvering threats are a major concern for the Navy and DoD and this technology will help address this issue.