Showing papers on "Kalman filter published in 1992"

introduction to random signals and applied kalman filtering

Abstract: Probability and Random Variables Mathematical Description of Random Signals Response of Linear Systems to Random Inputs Wiener Filtering The Discrete Kalman Filter Applications and Additional Topics on Discrete Kalman Filtering The Continuous Kalman Filter Discrete Smoothing and Prediction Linearization and Additional Topics on Applied Kalman Filtering The Global Positioning System: A Case Study.

A hybrid neural network‐first principles approach to process modeling

Abstract: A hybrid neural network-first principles modeling scheme is developed and used to model a fedbatch bioreactor. The hybrid model combines a partial first principles model, which incorporates the available prior knowledge about the process being modeled, with a neural network which serves as an estimator of unmeasuredprocess parameters that are difficult to model from first principles. This hybrid model has better properties than standard “black-box” neural network models in that it is able to interpolate and extrapolate much more accurately, is easier to analyze and interpret, and requires significantly fewer training examples. Two alternative state and parameter estimation strategies, extended Kalman filtering and NLP optimization, are also considered. When no a priori known model of the unobserved process parameters is available, the hybrid network model gives better estimates of the parameters, when compared to these methods. By providing a model of these unmeasured parameters, the hybrid network can also make predictions and hence can be used for process optimization. These results apply both when full and partial state measurements are available, but in the latter case a state reconstruction method must be used for the first principles component of the hybrid model.

Data fusion in robotics and machine intelligence

Abstract: Data fusion and sensor integration - state-of-the-art 1990s, R.C. Luo and M.G. Gay multi-source spatial fusion using Bayesian reasoning, A. Elfes multi-sensor strategies using Dempster/Shafer belief accumulation, S.A. Hutchinson and A.C. Kak data fusion techniques using robust statistics, R. McKendall and M. Mintz recursive fusion operators - desirable properties and illustrations, Y. Chen and R.L. Kashyap distributed data fusion using Kalman filtering - a robotics application, C. Brown, et al kinematic and satistical models for data fusion using Kalman filtering, T.J. Broida and S.S. Blackman least-squares fusion of multi-sensory data, R.O. Eason and R.C. Gonzalez fusion of multi-dimensional data using regularization, M.A. Abidi geometric fusion - minimizing uncertainty ellipsoid volumes, Y. Nakamura combination of fuzzy information in the framework of possibility theory, D. Dubois and H. Prade data fusion - a neural networks implementation, T.L. Huntsberger.

Dynamic map building for an autonomous mobile robot

Abstract: This article presents an algorithm for autonomous map building and maintenance for a mobile robot. We believe that mobile robot navigation can be treated as a problem of tracking ge ometric features that occur naturally in the environment. We represent each feature in the map by a location estimate (the feature state vector) and two distinct measures of uncertainty: a covariance matrix to represent uncertainty in feature loca tion, and a credibility measure to represent our belief in the validity of the feature. During each position update cycle, pre dicted measurements are generated for each geometric feature in the map and compared with actual sensor observations. Suc cessful matches cause a feature's credibility to be increased. Unpredicted observations are used to initialize new geometric features, while unobserved predictions result in a geometric feature's credibility being decreased. We describe experimental results obtained with the algorithm that demonstrate successful map building using real son...

Forecasting, Structural Time Series and the Kalman Filter

Abstract: (1992). Forecasting, Structural Time Series and the Kalman Filter. Technometrics: Vol. 34, No. 4, pp. 496-497.

Using the Extended Kalman Filter with a Multilayer Quasi-Geostrophic Ocean Model

Abstract: The formulation of the extended Kalman filter for a multilayer nonlinear quasi-geostrophic ocean circulation model is discussed. The nonlinearity in the ocean model leads to an approximative equation for error covariance propagation, where the transition matrix is dependent on the state trajectory. This nonlinearity complicates the dynamics of the error covariance propagation, and effects which are nonexistent in linear systems contribute significantly. The transition matrix can be split into two parts, where one part results in pure evolution of error covariances in the model velocity field, and the other part contains a statistical correction term caused by the nonlinearity in the model. This correction term leads to a linear unbounded instability, which is caused by the statistical linearization of the nonlinear error propagation equation. Different ways of handling this instability are discussed. Further, nonlinear small-scale instabilities also develop, since energy is accumulated at wavelengths 2Δx, owing to the numerical discretization. These small-scale oscillations are removed with a Shapiro filter, and the effect they have on the error covariance propagation is discussed. Some data assimilation experiments are performed using the full extended Kalman filter, to examine the properties of the filter. An experiment where only the first part of the transition matrix is used to propagate the error covariances is also performed. This simplified experiment actually performs better than the full extended Kalman filter because the unbounded instability associated with the statistical correction term is avoided.

Position estimation for a mobile robot using vision and odometry

Abstract: The authors describe a method for locating a mobile robot moving in a known environment. This technique combines position estimation from odometry with observations of the environment from a mobile camera. Fixed objects in the world provide landmarks which are listed in a database. The system calculates the angle to each landmark and then orients the camera. An extended Kalman filter is used to correct the error between the observed and estimated angle to each landmark. Results from experiments in a real environment are presented. >

A fast new algorithm for training feedforward neural networks

Abstract: A fast algorithm is presented for training multilayer perceptrons as an alternative to the backpropagation algorithm. The number of iterations required by the new algorithm to converge is less than 20% of what is required by the backpropagation algorithm. Also, it is less affected by the choice of initial weights and setup parameters. The algorithm uses a modified form of the backpropagation algorithm to minimize the mean-squared error between the desired and actual outputs with respect to the inputs to the nonlinearities. This is in contrast to the standard algorithm which minimizes the mean-squared error with respect to the weights. Error signals, generated by the modified backpropagation algorithm, are used to estimate the inputs to the nonlinearities, which along with the input vectors to the respective nodes, are used to produce an updated set of weights through a system of linear equations at each node. These systems of linear equations are solved using a Kalman filter at each layer. >

Kalman filtering and Riccati equations for descriptor systems

Abstract: A general formulation of a discrete-time filtering problem for descriptor systems is considered. It is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems. Using a dual approach to estimation, the authors derive a so-called 3-block form for the optimal filter and a corresponding 3-block Riccati equation for a general class of time-varying descriptor models which need not represent a well-posed system in that the dynamics may be either over or under constrained. Specializing in the time-invariant case, they examine the asymptotic properties of the 3-block filter, and in particular analyze in detail the resulting 3-block algebraic Riccati equation. The noncausal nature of discrete-time descriptor dynamics implies that future dynamics may provide some information about the present state. A modified form for the descriptor Kalman filter that takes this information into account is presented. >

Fast vision-guided mobile robot navigation using model-based reasoning and prediction of uncertainties

Abstract: The model-based vision system described in this paper allows a mobile robot to navigate indoors at an average speed of 8 to 10 m/min using ordinary laboratory computing hardware of approximately 16 MIPS power. The navigation capabilities of the robot are not impaired by the presence of stationary or moving obstacles. The vision system maintains a model of uncertainty and keeps track of the growth of uncertainty as the robot travels toward the goal position. The estimates of uncertainty are then used to predict bounds on the locations and orientations of landmarks expected to be seen in a monocular image. This greatly reduces the search for establishing correspondence between the features visible in the image and the landmarks. Given a sequence of image features and a sequence of landmarks derived from a geometric model of the environment, a special aspect of our vision system is the sequential reduction in the uncertainty as each image feature is matched successfully with a landmark, allowing subsequent features to be matched more easily; this is a natural by-product of the manner in which we use Kalman filter-based updating.

Motion and Structure from Image Sequences

Abstract: Estimating motion and structure of the scene from image sequences is a very important and active research area in computer vision. The results of research have applications in vision-guided navigation, robot vision, 3-D object recognition and manipulation etc. Many theoretical results and new techniques developed may also apply to the related problems of other fields. Computing the image displacement field, or matching two images is one of the difficult problems in motion analysis. A computational approach to image matching has been developed that uses multiple attributes associated with images to yield a generally overdetermined system of matching constraints, taking into account possible structural discontinuities and occlusions. From the computed image displacement field, the next step is to compute the motion parameters and the structure of the scene. A two-step approach is introduced to solve the nonlinear optimization problem reliably and efficiently. The uniqueness of solution, robustness of the solution in the presence of noise, estimation of errors, dependency of the reliability of solution on motion, scene, and the parameters of image sensors have been investigated. It is analyzed that a batch processing technique (Levenberg-Marquardt nonlinear least-squares method) generally performs better than a sequential processing technique (iterated extended Kalman filtering) for nonlinear problems. For those problems where estimates are needed before all the data are acquired, a recursive batch processing technique has been developed to improve performance and computational efficiency. The performance of the motion estimation algorithm has essentially reached the Cramer-Rao bound. The algorithm has been applied to real world scenes with depth discontinuities and occlusions to compute motion parameters, dense depth maps and occlusion maps, from two images taken at different unknown positions and orientations relative to the scene. The standard discrepancy between the projection of the inferred 3-D scene and the actually observed projection is as small as one half of a pixel. Other problems investigated include: (1) motion and structure from point correspondences for planar scenes. (2) motion and structure from line correspondences. (3) dynamic motion estimation and prediction from long image sequences.

Optimal estimation of position and heading for mobile robots using ultrasonic beacons and dead-reckoning

Abstract: An active beacon localization system that estimates position and heading for a mobile robot is described. An iterated extended Kalman filter was applied to the beacon and dead-reckoning data to estimate optimal values of position and heading, given a model for the localizer and robot motion. The author describes the implementation and experimental results of the localization system. Position and heading angle updates were calculated in real time every 150 ms with a measured standard deviation of path error of 40 mm in a 12 m/sup 2/ workspace. >

Posterior Mode Estimation by Extended Kalman Filtering for Multivariate Dynamic Generalized Linear Models

Abstract: A family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family. Besides common conditionally Gaussian models, this article deals with univariate models for counted and binary data and, as the most interesting multivariate case, models for nonstationary multicategorical time series. For univariate responses, a related yet different class of models has been introduced in a Bayesian setting by West, Harrison and Migon. Assuming conjugate prior-posterior distributions for the natural parameter of the exponential family, they derive an approximate filter for estimation of time-varying states or parameters. However, their method raises some problems; in particular, in extending it to the multivariate case. A different approach to filtering and smoothing is chosen in this article. To avoid a full Bayesian analysis based on numerical integration, which becomes computationally critical for higher...

Unified approach to inertial navigation system error modeling

Abstract: Several inertial navigation system error models have been developed and used in the literature. Most of the models are ad hoc models which were needed to solve certain particular problems and were developed for that purpose only. Consequently, the relationship, correspondence, and equivalence between the various models is not evident. This paper presents a new methodology for developing inertial navigation systems error models which also puts all of the known models in the same framework and shows the equivalence between them. The new methodology is based on several choices the developer has to make which uniquely define the error model. This new approach enables the development of all existing models in a unified way, hence the equivalence and correspondence between them is obvious. Moreover, any new model which is of interest can be developed using the methodology presented in this work. In fact, any new model which will ever be developed for the class of systems considered here will fit into the framework described in this paper.

Speed sensorless vector control of an induction motor using an extended Kalman filter

Abstract: The vector control of an induction motor by speed estimation using an extended Kalman filter (EKF) is described. The rotor speed is regarded as a parameter, and the composite state is composed of the original state and the rotor speed. The EKF is employed to identify the speed of an induction motor and rotor magnetic flux based on the measured quantities such as stator currents and DC link voltage. The estimated speed is used for vector control and overall speed control. The current control is performed in the synchronous rotating reference frame, and the estimated speed information is used for reference frame transformation of the current controller. Computer simulation of the speed control has been carried out to confirm the usefulness of the speed estimation algorithm. The error between the real speed and the estimated speed is within a few RPM even in the low speed range of about 20 RPM. >

Bearings-only and Doppler-bearing tracking using instrumental variables

Abstract: In bearings-only tracking (BOT) or Doppler and bearing tracking (DBT), both common passive sonar problems, the measurement equations are nonlinear. To apply the Kalman filter, it is necessary either to linearize the equations or to embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence, while the latter produces biased estimates. A formulation of BOT and DBT which has a constant state vector and simplifies the tracking problem to one of constant parameter estimation is given. The solution is by the instrumental variable method. The instrumental variables are obtained from predictions based on past measurements and are therefore independent of the present noisy measurements. The result is a recursive unbiased estimator. The theoretical developments are verified by simulation, which also shows that the formulation leads to near optimal estimators whose errors are close to the Cramer-Rao lower bound (CRLB). >

Method and apparatus for maximum likelihood estimation direct integer search in differential carrier phase attitude determination systems

Abstract: A method for comparing the relative phase of carrier signals received from GPS satellites to determine the roll, pitch and azimuth attitude of ships, aircraft, land vehicles, or survey instruments, accomplishes a maximum likelihood estimation (MLE) optimum solution over the full range of integers and vehicle attitudes. The problem is formulated as an MLE optimization, where vehicle attitude and integers are regarded as parameters to be adjusted to maximize probability of first-difference carrier phase measurements that are actually generated by hardware. Formulation results in weighted-fit error W as the objective criterion to minimize. A Kalman filter is introduced, having same objective criterion. Minimizing computation in Kalman filter leads to a decision tree for the integers. Two ways are shown to prune decision tree. The first is to exclude impossible combinations, such as those that produce an antenna upside down. The second is to generate a lower bound for W at each branch of the tree. A running sum is kept at each stage moving down the tree. When that sum exceeds a reasonableness bound or the current best W found elsewhere in the search, it is guaranteed that all subsequent integer combinations further down the current branch will produce a larger W and the remainder of the current branch can be cut off, speeding up the search.

Training recurrent networks using the extended Kalman filter

Abstract: The author describes some relationships between the extended Kalman filter (EKF) as applied to recurrent net learning and some simpler techniques that are more widely used. In particular, making certain simplifications to the EKF gives rise to an algorithm essentially identical to the real-time recurrent learning (RTRL) algorithm. Since the EKF involves adjusting unit activity in the network, it also provides a principled generalization of the teacher forcing technique. Preliminary simulation experiments on simple finite-state Boolean tasks indicated that the EKF can provide substantial speed-up in number of time steps required for training on such problems when compared with simpler online gradient algorithms. The computational requirements of the EKF are steep, but scale with network size at the same rate as RTRL. >

Comparative analysis of backpropagation and the extended Kalman filter for training multilayer perceptrons

Abstract: The relationship between backpropagation and extended Kalman filtering for training multilayer perceptrons is examined. These two techniques are compared theoretically and empirically using sensor imagery. Backpropagation is a technique from neural networks for assigning weights in a multilayer perceptron. An extended Kalman filter can also be used for this purpose. A brief review of the multilayer perceptron and these two training methods is provided. Then, it is shown that backpropagation is a degenerate form of the extended Kalman filter. The training rules are compared in two examples: an image classification problem using laser radar Doppler imagery and a target detection problem using absolute range images. In both examples, the backpropagation training algorithm is shown to be three orders of magnitude less costly than the extended Kalman filter algorithm in terms of a number of floating-point operations. >

Optimal stochastic estimation with exponential cost criteria

Abstract: The expected value of the exponential of a weighted quadratic sum of the squares of the estimation error is minimized with respect to the state estimate subject to a Gauss-Markov system. The state estimates are assumed to be a function of the measurement history up to the stage time of the state vector. The estimator which optimizes this exponential cost criterion is linear but is not a conditional mean estimator such as the Kalman filter. This shows that the implications of Sherman's theorem are restricted to functions of the estimates which have access to the same measurement history such as in smoothing problems. In the solution process the expectation operation is replaced by an extremization operation allowing the formulation of a deterministic discrete time game. The saddle point estimator resulting from this game is the same as that obtained from the solution of an associated disturbance attenuation problem. This optimal stochastic estimator which generalizes the Kalman filter can feature the estimation error of certain states over others by the choice of the quadratic weighting matrices in the cost criterion. Correlation between the measurement and process noises is included. >

Constraining Kalman Filter and Smoothing Estimates to Satisfy Time-Varying Restrictions

Abstract: It sometimes happens that the unobservable state vector of a linear dynamic model expressed in the state space is subject to known restrictions. Incorporation of this information into the Kalman filter procedure will increase the efficiency of estimation. It is shown that a simple augmentation of the measurement equation constrains the estimated state vector to obey the restrictions. The method applies whether the restrictions are time-invariant, time-varying, linear, or nonlinear. Copyright 1992 by MIT Press.

Dynamic factor analysis of nonstationary multivariate time series

Abstract: A dynamic factor model is proposed for the analysis of multivariate nonstationary time series in the time domain The nonstationarity in the series is represented by a linear time dependent mean function This mild form of nonstationarity is often relevant in analyzing socio-economic time series met in practice Through the use of an extended version of Molenaar's stationary dynamic factor analysis method, the effect of nonstationarity on the latent factor series is incorporated in the dynamic nonstationary factor model (DNFM) It is shown that the estimation of the unknown parameters in this model can be easily carried out by reformulating the DNFM as a covariance structure model and adopting the ML algorithm proposed by Joreskog Furthermore, an empirical example is given to demonstrate the usefulness of the proposed DNFM and the analysis

3D relative position and orientation estimation using Kalman filter for robot control

Abstract: A vision-based position sensing system which provides three-dimensional relative position and orientation (pose) of an arbitrary moving object with respect to a camera for a real-time tracking control is studied. Kalman filtering was applied to vision measurements for the implicit solution of the photogrametric equations and to provide significant temporal filtering of the resulting motion parameters resulting in optimal pose estimation. Both computer simulation and real-time experimental results are presented to verify the effectiveness of the Kalman filter approach with large vision measurement noise. >

Integrated enroute and approach guidance system for aircraft

Abstract: Data from long range aids such as the global positioning system (GPS) and an inertial navigation system (INS) and short range aids such as a microwave londing system (MLS) are used to smoothly and automatically transition an aircraft from the long range aids to the short range aids. During cruise a Kalman filter (70) combines data from the global positioning system and the inertial navigation system to provide accurate enroute information. When the aircraft arrives in the vicinity of the airport and begins to acquire (70) data from the microwave landing system, the Kalman filter (70) is calibrated with the MLS data to permit precision landing with GPS/INS data alone in case the MLS system subsequently fails. In addition, navigation information begins to be derived from a weighted sum of the GPS/INS and MLS data, the weighting being determined by distance from the airport. In a first region farthest from the airport, the GPS/INS data is given a 1.0 weighting factor; and in a second region nearest the airport, the MLS data is given a 1.0 weighting factor. In a third region intermediate the first and second regions, the GPS/INS data and MLS data are proportionately and complementarily weighted as a function of the distance from the airport. If the MLS system fails, the weighting system (76, 78, 80) is disabled (84) and navigation data is again derived from the GPS/INS combination. In addition, the data from both systems are monitored (74), and a cockpit alarm is sounded if the data diverged beyond a specific amount. The Kalman filter (70) supplies a weighting system comprising two weighting devices (76, 78), one (76) of which weights the MLS data, and the other (78) the GPS/INS combination data. The outputs of these devices (76, 78) are summed (80) and supplied to one terminal of a switch (84) for selecting between the weighting system (76, 78, 80) and the Kalman filter (70).

A Kalman filter approach to catch-at-length analysis

Abstract: A state-space representation of a length-structured population under commercial harvest is described and a Kalman filter is used to develop the conditional likelihood equation needed for estimating the underlying system parameters. The state of the system is characterized using conventional fisheries theory with commercial harvest representing the observations taken on the population. The conditional likelihood framework embedded in the Kalman filter facilitates the incorporation of both system stochasticity as well as observation error in the development of the overall likelihood equation. Within this framework a maximum likelihood approach is used to estimate population parameters while taking into account both sources of error.

Exact score for time series models in state space form

Abstract: The full-text of this article is not currently available in ORA. Citation: Koopman, S. J. & Shephard, N. (1992). 'Exact score for time series models in state space form', Biometrika, 79(40, 823-826. [Available at http://biomet.oxfordjournals.org/].