Showing papers on "Kalman filter published in 1995"

An Introduction to the Kalman Filter

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

An Introduction to the Kalman Filter

Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

The simulation smoother for time series models

Abstract: SUMMARY Recently suggested procedures for simulating from the posterior density of states given a Gaussian state space time series are refined and extended. We introduce and study the simulation smoother, which draws from the multivariate posterior distribution of the disturbances of the model, so avoiding the degeneracies inherent in state samplers. The technique is important in Gibbs sampling with non-Gaussian time series models, and for performing Bayesian analysis of Gaussian time series.

Nonlinear state and tire force estimation for advanced vehicle control

Abstract: Vehicle motion and tire force histories are estimated from an incomplete, noise-corrupted measurement set using an extended Kalman filter. A nine degree-of-freedom vehicle model and an analytic tire force model are used to simulate true vehicle motion, and a five degree-of-freedom vehicle model is used in the estimator. The filtered histories of forces and motion can be used to construct tire force models through off-line analysis, and both tire force estimates and state estimates are available for real time control. No prior knowledge of tire force characteristics or external factors that affect vehicle motion is required for the nonlinear estimation procedure. Simulation of a simple slip control braking system using slip and slip angle estimates for feedback demonstrates the effectiveness of the extended Kalman filter in providing adequate state estimates for advanced control of ground vehicles. >

An approximate Kaiman filter for ocean data assimilation: An example with an idealized Gulf Stream model

Abstract: A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximation of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

Bearings-only tracking using a set of range-parameterised extended Kalman filters

Abstract: Bearings-only tracking using the extended Kalman filter (EKF) configured in Cartesian and modified polar coordinate systems is reviewed. A new tracking approach is proposed which consists of a set of weighted EKFs each with a different initial range estimate and this is referred to as the range-parameterised (RP) tracker. This new approach overcomes the problems exhibited with existing EKF trackers when the bearing rate is very high or near zero. In addition, it allows a more natural implementation for the prior knowledge of-the target velocity, which can allow the range to be inferred even before the first observer manoeuvre. Results are presented for a typical tracking scenario, involving a manoeuvring observer and a constant velocity target. The results show that the RP tracker gives stable, consistent and unbiased estimates in all the cases considered, whereas the same is not true for the Cartesian and modified polar EKF trackers. Although only constant velocity target trajectories have been considered in this paper, the RP tracker provides a natural framework for consideration of manoeuvring targets. The extension to include manoeuvring targets is currently under investigation.< >

System and method of multi-sensor fusion of physiological measurements

Abstract: A system and method for fusing independent measures of the physiological parameter uses a Kalman filter for each possible combination of sensor measurements. The Kalman filter utilize probability density functions of a nominal error contamination model and a prediction error model as well as past estimates of the physiological parameter to produce the Kalman filter outputs. A confidence calculator uses Bayesian statistical analysis to determine a confidence level for each of the Kalman filter outputs, and selects a fused estimate for the physiological parameter based on the confidence level. The fused estimate and the confidence level are used to dynamically update the nominal error contamination model and prediction error model to create an adaptive measurement system. The confidence calculator also takes into account the probability of artifactual error contamination in any or all of the sensor measurements. The system assumes a worst case analysis of the artifactual error contamination, thus producing a robust model able to adapt to any probability density function of the artifactual error and a priori probability of artifact.

A frequency-domain analysis of head-motion prediction

Abstract: The use of prediction to eliminate or reduce the effects of system delays in Head-Mounted Display systems has been the subject of several recent papers. A variety of methods have been proposed but almost all the analysis has been empirical, making comparisons of results difficult and providing little direction to the designer of new systems. In this paper, we characterize the performance of two classes of head-motion predictors by analyzing them in the frequency domain. The first predictor is a polynomial extrapolation and the other is based on the Kalman filter. Our analysis shows that even with perfect, noise-free inputs, the error in predicted position grows rapidly with increasing prediction intervals and input signal frequencies. Given the spectra of the original head motion, this analysis estimates the spectra of the predicted motion, quantifying a predictor's performance on different systems and applications. Acceleration sensors are shown to be more useful to a predictor than velocity sensors. The methods described will enable designers to determine maximum acceptable system delay based on maximum tolerable error and the characteristics of user motions in the application. CR

Performance enhancement of a multiple model adaptive estimator

Abstract: We describe performance improvement techniques for a multiple model adaptive estimator (MMAE) used to detect and identify control surface and sensor failures on an unmanned flight vehicle. Initially failure identification was accomplished within 4 s of onset, but by removing the "/spl beta/ dominance" effects, bounding the hypothesis conditional probabilities, retuning the Kalman filters, increasing the penalty for measurement residuals, decreasing the probability smoothing, and increasing residual propagation, the identification time was reduced to 2 s. >

Performance analysis of general tracking algorithms

Abstract: A general family of tracking algorithms for linear regression models is studied. It includes the familiar least mean square gradient approach, recursive least squares, and Kalman filter based estimators. The exact expressions for the quality of the obtained estimates are complicated. Approximate, and easy-to-use, expressions for the covariance matrix of the parameter tracking error are developed. These are applicable over the whole time interval, including the transient, and the approximation error can be explicitly calculated. >

Estimation of absolute vehicle speed using fuzzy logic rule-based Kalman filter

Abstract: Accurate knowledge on the absolute or true speed of a vehicle, if and when available, can be used to enhance advanced vehicle dynamics control systems such as anti-lock brake systems (ABS) and auto-traction systems (ATS) control schemes. Current conventional method uses wheel speed measurements to estimate the speed of the vehicle. As a result, indication of the vehicle speed becomes erroneous and, thus, unreliable when large slips occur between the wheels and terrain. This paper describes a fuzzy rule-based Kalman filtering technique which employs an additional accelerometer to complement the wheel-based speed sensor, and produce an accurate estimation of the true speed of a vehicle. We use the Kalman filters to deal with the noise and uncertainties in the speed and acceleration models, and fuzzy logic to tune the covariances and reset the initialization of the filter according to slip conditions detected and measurement-estimation condition. Experiments were conducted using an actual vehicle to verify the proposed strategy.

Real-time estimation and tracking of optical flow vectors for obstacle detection

Abstract: Optical flow contains information about the motion of a camera relative to its environment and about the three-dimensional structure of the imaged scene. In this contribution we use that information to detect obstacles in front of a moving vehicle. Since the detection is based on motion no a-priori knowledge about obstacle shape is required. Optical flow vectors are estimated from spatio-temporal derivatives of the gray value function which are computed at video frame rate by the custom-designed hardware MiniVISTA. To eliminate outliers and to speed up obstacle detection by data reduction the estimated vectors are clustered before they are passed to the obstacle test. The purpose of the obstacle test is to separate moving objects from the stationary environment and to separate elevated objects from the ground plane. In continuation of our previous work, obstacle detection is regarded as a state estimation problem. This enables us to enlarge the motion stereo basis by applying a Kalman filter to track optical flow vectors over subsequent image frames. Experimental results obtained from image sequences recorded with our experimental vehicle are presented.

Conditions for stability of the extended Kalman filter and their application to the frequency tracking problem

Abstract: The error dynamics of the extended Kalman filter (EKF), employed as an observer for a general nonlinear, stochastic discrete time system, are analyzed. Sufficient conditions for the boundedness of the errors of the EKF are determined. An expression for the bound on the errors is given in terms of the size of the nonlinearities of the system and the error covariance matrices used in the design of the EKF. The results are applied to the design of a stable EKF frequency tracker for a signal with time-varying frequency.

Kalman filtering with unknown inputs via optimal state estimation of singular systems

Abstract: A new method for designing a Kalman filter for linear discrete-time systems with unkown inputs is presented. The algorithm recently developed for stochastic singular systems is applied to obtain a linear estimation of the state and unkown inputs. The necessary and sufficient conditions for the existence and stability of the filter are derived and proved. An illustrative example is included.

H/sub /spl infin// nonlinear filtering of discrete-time processes

Abstract: This correspondence investigates the problem of H/sub /spl infin// estimation of a discrete-time nonlinear process. An estimator, which may be nonlinear, is introduced so that an H/sub /spl infin//-norm-like of what we call a generalized estimation error is guaranteed to be bounded by a prescribed level. Conditions for the existence of such an estimator, and formulae for its derivation, are obtained utilizing a discrete-time analog of the Hamilton-Jacobi inequality. An approximate filter based on linearization is developed. This filter relates to the extended Kalman filter in the same way that the linear H/sub /spl infin// filter relates to the Kalman filter. >

Adaptive interacting multiple model algorithm for tracking a manoeuvring target

Abstract: The paper describes an adaptive interacting multiple-model algorithm (AIMM) for use in manoeuvring target tracking. The algorithm does not need predefined models. A two-stage Kalman estimator is used to estimate the acceleration of the target. This acceleration value is then fed to the subfilters in an interacting multiple-model (IMM) algorithm, where the subfilters have different acceleration parameters. Results compare the performance of the AIMM algorithm with the IMM algorithm, using simulations of different manoeuvring-target scenarios. Also considered are the relative computational requirements, and the ease with which the algorithms can be implemented on parallel machines.

Method and system for resolving double difference GPS carrier phase integer ambiguity utilizing decentralized kalman filters

Abstract: A method and system for accurately determining the position coordinates of a mobile GPS receiver by resolving the double difference GPS carrier phase integer ambiguity. A reference station is provided at precisely known coordinates and carrier phase data and pseudoranges for each received GPS satellite are calculated at both the reference station and the mobile GPS receiver. A communications link couples carrier phase data, pseudorange data and the known reference station position from the reference station to the mobile GPS receiver. A first Kalman filter within the mobile GPS receiver operates on GPS satellite ephemeris parameters and the calculated pseudoranges to obtain an error state vector for position and time. The GPS satellite ephemeris parameters and calculated carrier phase data are then applied to a second Kalman filter to obtain a predicted vector of velocity and clock rate error. Line of sight range and range rates are then estimated utilizing the outputs of both Kalman filters and utilized, together with double difference phase measurements, to resolve the double difference carrier wave integer ambiguity providing an accurate set of coordinates for the mobile GPS receiver.

Maximum-likelihood estimation of a class of chaotic signals

Abstract: The chaotic sequences corresponding to tent map dynamics are potentially attractive in a range of engineering applications. Optimal estimation algorithms for signal filtering, prediction, and smoothing in the presence of white Gaussian noise are derived for this class of sequences based on the method of maximum likelihood. The resulting algorithms are highly nonlinear but have convenient recursive implementations that are efficient both in terms of computation and storage. Performance evaluations are also included and compared with the associated Cramer-Rao bounds. >

New square-root algorithms for Kalman filtering

Abstract: Presents some new square-root algorithms that allow more reliable computation of the state estimates, using, as far as possible, quantities obtained via orthogonal operations. New algorithms are given for covariance quantities and information quantities, and a new combined algorithm is also presented. >

On-line sensing system of dynamic ship’s attitude by use of servo-type accelerometers

Abstract: For an accurate automatic measurement of ship’s attitude the paper proposes an intelligent on-line sensing system which uses four servo-type accelerometers and one servo-type inclinometer appropriately located on the ship. Through an adequate location of the accelerometers, the heaving, rolling, and pitching signals of the ship are separated from each other with adequate linear combinations of the four sensors’ outputs. Furthermore, the inclinometer is utilized to extract a bias signal of the pitching. By introducing linear dynamic models and linear observation equations on the three signals, their on-line measurement is reduced to the state estimation of the linear dynamic systems. A bank of Kalman filters are used to execute the on-line state estimation and to overcome changes in parameters in the dynamic models with time.

The use of artificial neural networks for the intelligent optimal control of surface ships

Abstract: Many conventional ship autopilots use proportional integral and derivative (PID) control algorithms to guide a ship on a fixed heading (course-keeping) or a new heading (course-changing). Such systems usually have a gyrocompass as a single sensory input. Modern sea going vessels have a range of navigation aids most of which may be interconnected to form integrated systems. It is possible to employ the navigational data to provide best estimates of state vectors (Kalman filter) and optimal guidance strategies. Such techniques require powerful computing facilities, particularly if the dynamic characteristics of the vessel are changing, as may be the case in a maneuvering situation or changes in forward speed. This paper investigates the possibility of training a neural network to behave in the same manner as an optimal ship guidance system, the objective being to provide a system that can adapt its parameters so that it provides optimal performance over a range of conditions, without incurring a large computational penalty. A series of simulation studies have been undertaken to compare the performance of a trained neural network with that of the original optimal guidance system over a range of forward speeds. It is demonstrated that a single network has comparable performance to a set of optimal guidance control laws, each computed for different forward speeds. >

An interacting multiple model approach for target tracking with glint noise

Abstract: The application of the interacting multiple model (IMM) estimation approach to the problem of target tracking when the measurements are perturbed by glint noise is considered. The IMM is a very effective approach when the system has discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties. It is shown that this method performs better than the "score function" method. It is also shown that the IMM method performs robustly when the exact prior information of the glint noise is not available. >

Mobile vehicle navigation in unknown environments: a multiple hypothesis approach

Abstract: The paper describes an algorithm for sensor-based map building and navigation for an autonomous mobile vehicle. The algorithm is based on the use of an extended Kalman filter to obtain estimates of the location and identity of geometric features in an unknown environment. A multitarget tracking methodology is applied to the evaluation of multiple hypotheses about the locations of geometric features in the environment. The algorithm does not require any a priori information about the environment. It is capable of initiating new geometric features and identifying the type of a geometric feature from the given set of geometric features, utilising the data provided by a set of sonar sensors. The algorithm is also capable of deleting geometric features from the map of the environment when they are no longer detected by the sensors. The implementation of the algorithm is discussed, and results using real sonar data are presented.

Nonlinear system identification using neural state space models, applicable to robust control design

Abstract: Prediction error learning algorithms for neural state space models are developed, both for the deterministic case and the stochastic case with measurement and process noise. For the stochastic case, a predictor with direct parametrization of the Kalman gain by a neural net architecture is proposed. Expressions for the gradients are derived by applying Narendra's sensitivity model approach. Finally a linear fractional transformation representation is given for neural state space models, which makes it possible to use these models, obtained from input/output measurements on a plant, in a standard robust performance control scheme.

Maneuvering target tracking using adaptive turn rate models in the interacting multiple model algorithm

Abstract: This paper presents an interacting multiple model algorithm (IMM) utilizing adaptive turn rate models to track a maneuvering target. The turning rate is calculated at each time step from the velocity and acceleration estimates of the center filter as the magnitude of the acceleration divided by the speed of the target. The comparison of the tracking performance of the proposed algorithm is made with that of an IMM algorithm, utilizing a straight line motion model in conjunction with a single turn rate model which uses an estimate of the turn rate and also to that of an IMM algorithm utilizing three constant turn rate models.

An assessment of fuzzy logic vessel path control

Abstract: A fuzzy logic controller for ship path control in restricted waters is developed and evaluated. The controller uses inputs of heading, yaw rate, and lateral offset from the nominal track to produce a commanded rudder angle. Input variable fuzzification, fuzzy associative memory rules, and output set defuzzification are described. Two maneuvering situations are evaluated: track keeping along a specified path where linearized regulator control is valid; and larger maneuvers onto a specified path where nonlinear modeling and control are required. For the track keeping assessment, the controller is benchmarked against a conventional linear quadratic Gaussian (LQG) optimal controller and Kalman filter control system. The Kalman filter is used to produce the input state variable estimates for the fuzzy controller as well. An initial startup transient and regulator control performance with an external hydrodynamic disturbance are evaluated using linear model simulations of a crude oil tanker. A fully nonlinear maneuvering model for a smaller product tanker is used to assess the larger maneuvers. The fuzzy controller exhibits promising performance and application flexibility.