Showing papers on "Invariant extended Kalman filter published in 2002"

Kalman filtering with state equality constraints

Abstract: Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem.

A novel Kalman filter for frequency estimation of distorted signals in power systems

Abstract: A simple and novel approach in the design of an extended Kalman filter (EKF) for the measurement of power system frequency has been presented in this paper. The design principles and the validity of the model have been outlined. The performance of this filter has been compared with some of the existing methods for estimating the frequency of a signal under noisy conditions. The feasibility of the proposed filter has been tested in the laboratory under worst-case measurement and network conditions, which might occur in a typical power system. Also, the proof of the stability for the proposed filter has been discussed for a single sinusoid. It has been found that the proposed algorithm is suitable for real-time applications especially when the frequency changes are abrupt and the signal is corrupted with noise and other disturbances due to harmonics.

Tracking a ballistic target: comparison of several nonlinear filters

Abstract: This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.

Direct Kalman filtering approach for GPS/INS integration

Abstract: We present a novel Kalman filtering approach for GPS/INS integration. In the approach, GPS and INS nonlinearities are preprocessed prior to a Kalman filter. The GPS preprocessed data are taken as measurement input, while the INS preprocessed data are taken as additional information for the state prediction of the Kalman filter. The advantage of this approach, over the well-studied (extended) Kalman filtering approaches is that a simple and linear Kalman filter can be implemented to achieve significant computation saving with very competitive performance figures.

Adaptive Kalman Filtering for Low Cost INS/GPS

Abstract: GPS and low cost INS sensors are widely used for positioning and attitude determination applications. Low cost inertial sen- sors exhibit large errors which are compensated using position and velocity updates from GPS. Combining both sensors using a Kalman filter provides high accuracy real time navigation. The Kalman filter relies on the definition of the correct mea- surement and process noise matrices which are generally de- fined 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 fil- tering techniques. These are artificially scaling the predicted Kalman filter covariance, the Adaptive Kalman Filter and Mul- tiple Model Adaptive Estimation. The algorithms are tested with the IESSG's 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.

Extended Kalman filter tuning in sensorless PMSM drives

Abstract: The use of an extended Kalman filter (EKF) as nonlinear speed and position observer for permanent magnet synchronous motor (PMSM) drives is a mature research topic. Notwithstanding, the shift from research prototype to a market-ready product still calls for a solution of 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 normalisation of the EKF algorithm representation. Successful experimental results are included in the paper.

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

Abstract: We present a robust recursive Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has a one-step predictor-corrector structure and minimizes an upper bound of 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 with conventional Kalman filtering techniques.

Extended Kalman Filter Methods for Tracking Weak GPS Signals

Abstract: A combined phase-locked loop/delay-locked loop has been developed for tracking weak GPS C/A signals. This work enables the use of the weak side-lobe signals that are available at geosynchronous altitudes. The tracking algorithm is an extended Kalman filter (EKF) that estimates code phase, carrier phase, Doppler shift, rate of change of Doppler shift, carrier amplitude and data bit sign. It forms a likelihood function that depends on the errors between accumulations and their predicted values. It recursively minimizes this likelihood function in order to track the signal. It deals with data bit uncertainty using a Bayesian analysis that determines a posteriori probabilities for each bit sign. A second filter is used to initialize the EKF. This batch filter starts with coarse carrier frequency and code phase estimates and refines them using maximum likelihood techniques while estimating the carrier phase and the first PRN code period of a navigation data bit. The resulting system can acquire and maintain lock on a signal as weak as 15 dB Hz if the receiver clock is an ovenized crystal oscillator and if the line-of-sight acceleration variations are as mild as those seen by a geostationary user vehicle.

Near-Well Reservoir Monitoring Through Ensemble Kalman Filter

Abstract: In the management of reservoirs it is an important issue to utilize the available data in order to make accurate forecasts. In this paper a novel approach for frequent updating of the near-well reservoir model as new measurements becomes available is presented. The main focus of this approach is to have an updated model usable for forecasting. These forecasts should have initial values that are consistent with recent measurements. The novel approach is based on utilizing a Kalman filter technique. The idea behind the Kalman filter is to incorporate the information from the measurements into the current estimate of the state of the model, taking into account the uncertainty that belongs both to the state of the model and the measurements. The uncertainty of the model is updated simultaneously with the model itself. A benefit of this approach compared to usual history matching is that the initial values for the forecasts will be in better agreement with the current measurements. Originally, the Kalman filter had shortcomings for large, non-linear models. During the last decade, however, Kalman filter techniques has been further developed, and applied successfully for such models within oceanographic and hydrodynamic application. This work is based on use of the ensemble Kalman filter. The ensemble Kalman filter is easy to impl ement, and have some good properties for non-linear problems. Here, we demonstrate the use of this technique within nearwell reservoir monitoring, focusing on its performance in forecasting the future production.

Comparison of EKF, pseudomeasurement, and particle filters for a bearing-only target tracking problem

Abstract: In this paper we consider a nonlinear bearing-only target tracking problem using three different methods and compare their performances. The study is motivated by a ground surveillance problem where a target is tracked from an airborne sensor at an approximately known altitude using depression angle observations. Two nonlinear suboptimal estimators, namely, the extended Kalman Filter (EKF) and the pseudomeasurement tracking filter are applied in a 2-D bearing-only tracking scenario. The EKF is based on the linearization of the nonlinearities in the dynamic and/or the measurement equations. The pseudomeasurement tracking filter manipulates the original nonlinear measurement algebraically to obtain the linear-like structures measurement. Finally, the particle filter, which is a Monte Carlo integration based optimal nonlinear filter and has been presented in the literature as a better alternative to linearization via EKF, is used on the same problem. The performances of these three different techniques in terms of accuracy and computational load are presented in this paper. The results demonstrate the limitations of these algorithms on this deceptively simple tracking problem.

Parameter Estimation of Nonlinear Stochastic Differential Equations: Simulated Maximum Likelihood versus Extended Kalman Filter and Itô-Taylor Expansion

Abstract: This article compares several estimation methods for nonlinear stochastic differential equations with discrete time measurements. The likelihood function is computed by Monte Carlo simulations of the transition probability (simulated maximum likelihood SML) using kernel density estimators and functional integrals and by using the extended Kalman filter (EKF and second-order nonlinear filter SNF). The relation with a local linearization method is discussed. A simulation study for a diffusion process in a double well potential (Ginzburg–Landau equation) shows that, for large sampling intervals, the SML methods lead to better estimation results than the likelihood approach via EKF and SNF. A second study using a nonlinear diffusion coefficient (generalized Cox–Ingersoll–Ross model) demonstrates that the EKF type estimators may serve as efficient alternatives to simple maximum quasilikelihood approaches and Monte Carlo methods.

Automated Tuning of an Extended Kalman Filter Using the Downhill Simplex Algorithm

Abstract: A method of tuning a Kalman filter by means of the downhill simplex numerical optimization algorithm is presented. The problem is defined by a brief description of the Kalman filter and the extended Kalman filter and the sensitivity of filter performance to process noise and measurement noise covariance matrices Q and R. The filter tuning problem for a system processing simulated data is then formulated as a numerical optimization problem by defining a performance index based on state estimate errors. The resulting performance index is then minimized using the downhill simplex algorithm. The technique is then applied to three numerical examples of increasing complexity to demonstrate its practical utility.

Combining geostatistics and Kalman filtering for data assimilation in an estuarine system

Abstract: Data assimilation (DA) has been applied in an estuarine system in order to implement operational analysis in the management of a coastal zone. The dynamical evolution of the estuarine variables and corresponding observations are modelled with a nonlinear state-space model. Two DA methods are used for controlling the evolution of the model state by integrating information from observations. These are the reduced rank square root (RRSQRT) Kalman filter, which is a suboptimal implementation of the extended Kalman filter, and the ensemble Kalman filter which allows for nonlinear evolution of error statistics while still applying a linear equation in the analysis. First, these methods are applied and examined with a simple 1D ecological model. Then the RRSQRT Kalman filter is applied to the 3D hydrodynamics of the Odra lagoon using the model TRIM3D and water elevation measurements from fixed pile stations. Geostatistical modelling ideas are discussed in the application of these algorithms. (Some figures in this article are in colour only in the electronic version)

Modeling and prediction of environmental data in space and time using Kalman filtering

Abstract: The Kalman filter is used in this paper as a framework for space time data analysis. Using Kalman filtering it is possible to include physically based simulation models into the data analysis procedure. Attention is concentrated on the development of fast filter algorithms to make Kalman filtering feasible for high dimensional space time models. The ensemble Kalman filter and the reduced rank square root filter algorithm are briefly summarized. A new algorithm, the partially orthogonal ensemble Kalman filter is introduced too. We will illustrate the performance of the Kalman filter algorithms with a real life air pollution problem. Here ozone concentrations in a part of North West Europe are estimated and predicted.

Stability and performance of switching Kalman filters

Abstract: This paper considers the state estimation problem for switched affine systems. A switching Kalman filter is proposed and its performance analysed. It is proved that this filter leads to an optimal and stable estimation for all switching sequences of the system. In contrast to this, a switching stationary filter may cause an infinitely growing estimation error, which is demonstrated by an example.

Adaptive Kalman filter method for accurate estimation of forward path geometry of an automobile

Abstract: The present invention provides a method and apparatus for estimation of vehicle forward path geometry utilizing an adaptive Kalman filter bank and a two-clothoid road model. The invention provides that each of a plurality of Kalman filters, utilizing the latest available measurement vector Y k at time k, estimates the state vector X k and error covariance matrix P k . The outputs of filter 504 a , 504 b , and 504 c denoted as as X k j and P k j , are provided to a plurality of weighting elements, which calculate weight factors, W k j 506 a , 506 b , and 506 c for each filter. The weight factor of each filter is the probability that the upcoming road geometry matches the road model hypothesized in the filter. After being assigned a weighted value, the weighted value road models are fused in a fusion element 508 , and a weighted output road geometry model is provided.

Visual Vehicle Tracking Using An Improved EKF

Abstract: In this paper, a dynamic model of car motion is proposed in which the turn of the steering wheel and the distance between the front and rear wheel are taken into account. Extended Kalman Filter (EKF) is widely used in visual tracking systems. However, because there is no direct link between the behaviour of the driver who controls the motion of the car and the assumed dynamic model, the traditional EKF does not perform well when the car carries out a complicated manoeuvre. In order to reduce the sensitivity of the filter to the model uncertainty, we use a modified EKF by adding a new objective function. Experimental results show that the performance of our approach is much better than the traditional EKF and its recent variant.

Application of Kalman filters with a loop delay in synchronization

Abstract: Discrete-time Kalman filters under a loop-delay constraint suffer performance loss and cease to be optimal. In this letter, modified Kalman filters are proposed to compensate for loop delay. The proposed filter performance is similar to a Kalman predictor. The results are applied to synchronizer loop-filter, design. Closed form expressions for both the update gain and the performance values are derived for first- and second-order disturbance models.

Kalman filtering of dgps positions for a parallel tracking application

Abstract: A Kalman filter was developed to improve the DGPS position estimates for a parallel tracking application. Applying Kalman filtering to raw DGPS measurement data effectively removes the DGPS noise and reduces the root–mean–squared (RMS) positioning error. In our study, the maximum cross–tracking error (XTE) was reduced from 9.83 m to 2.76 m by Kalman filtering. The Kalman filter also reduced the root–mean–squared XTE from 0.58 m to 0.56 m. In the direction of travel, the Kalman filter had much smaller positioning error than the mean filter; the RMS positioning errors in the direction of travel were 1.35 m for the mean filter and 0.26 m for the Kalman filter. The GPS bias error was the major source of the cross–tracking error. Further study is recommended to estimate and reduce the GPS bias error for parallel tracking applications.

Adaptive Classification by Variational Kalman Filtering

Abstract: We propose in this paper a probabilistic approach for adaptive inference of generalized nonlinear classification that combines the computational advantage of a parametric solution with the flexibility of sequential sampling techniques. We regard the parameters of the classifier as latent states in a first order Markov process and propose an algorithm which can be regarded as variational generalization of standard Kalman filtering. The variational Kalman filter is based on two novel lower bounds that enable us to use a non-degenerate distribution over the adaptation rate. An extensive empirical evaluation demonstrates that the proposed method is capable of infering competitive classifiers both in stationary and non-stationary environments. Although we focus on classification, the algorithm is easily extended to other generalized nonlinear models.

Investigation of automatic path tracking using an extended Kalman filter

Abstract: This paper proposes a lane marker recognition method that uses the steering angle in addition to image information. A Kalman filter was reconfigured regarding the yaw motion and lateral motion of lane markers, previously treated as a stochastic process, as the states of a vehicle model driven on the basis of the steering angle. Driving tests conducted with an actual vehicle verified that this method provides good tracking at the time of steering input and avoids misrecognition of lane marker candidate points in inclement weather.

Identification of Hammerstein/Wiener nonlinear systems with extended Kalman filters

Abstract: The extended Kalman filter (EKF) is considered for parameter identification of Hammerstein/Wiener nonlinear systems. The EKFs for parameter identification of both combined Hammerstein/Wiener as well as for pure Hammerstein and pure Wiener models are formulated. In order to enable efficient estimation of unknown nonlinearities linear parametrizations with linear static mappings and basis function expansions are proposed and the EKFs for these cases are established. The efficiency and performance of the approach is demonstrated by means of a computer simulation of a Hammerstein and a Wiener model.

An iterated-extended Kalman filter algorithm for tracking surface and sub-surface targets

Abstract: Coastal System Station has developed, implemented and tested an algorithm for tracking surface and sub-surface targets. The algorithm accepts various combinations of range, elevation, bearing, speed and Doppler measurements. At a minimum, the tracker requires bearing and elevation measurements; additional measurements will improve filter performance but are not required. The tracker consists of an iterated-extended Kalman filter with measurement/track matching logic. Special attention has been given to deriving good initial estimates of target position, initial estimates of the error covariance matrix, and correcting filter divergence with a line search. The improved initial error covariance estimate reduces filter transients and improves filter accuracy. Filter stability problems uncovered during testing were also corrected by adding measurement de-weighting to spurious elevation and bearing measurements. Problems associated with missing range measurements have been solved by implementing a multi-depth mode Kalman filter which allows the Kalman filter to determine a unique x, y, z position solution for target track given only elevation and bearing angle measurements. The multi-depth mode works by creating a family of filters for each target; each filter in the family restricts the target's tracked depth to within prescribed limits. The measurement/track matching logic computes the normalized residual error inner product test statistic. This test statistic has a chi-squared distribution and is used to statistically compare new measurements to all existing target tracks. The tracking algorithm has been tested with several at-sea data sets consisting of elevation and bearing measurements only. In most cases, the algorithm successfully localizes the target positions to within the prescribed angular (elevation and bearing) errors.