Showing papers on "Invariant extended Kalman filter published in 1983"

Utilization of modified polar coordinates for bearings-only tracking

Abstract: Previous studies have shown that the Cartesian coordinate extended Kalman filter exhibits unstable behavior characteristics when utilized for bearings-only target motion analysis (TMA). In contrast, formulating the TMA estimation problem in modified polar (MP) coordinates leads to an extended Kalman filter which is both stable and asymptotically unbiased. Exact state equations for the MP filter are derived without imposing any restrictions on own-ship motion; thus, prediction accuracy inherent in the traditional Cartesian formulation is completely preserved. In addition, these equations reveal that MP coordinates are well-suited for bearings-only TMA because they automatically decouple observable and unobservable components of the estimated state vector. Such decoupling is shown to prevent covariance matrix ill-conditioning, which is the primary cause of filter instability. Further investigation also confirms that the MP state estimates are asymptotically unbiased. Realistic simulation data are presented to support these findings and to compare algorithm performance with respect to the Cramer-Rao lower bound (ideal) as well as the Cartesian and pseudolinear filters.

Nonlinear Kalman filtering techniques for terrain-aided navigation

Abstract: The application of nonlinear Kalman filtering techniques to the continuous updating of an inertial navigation system using individual radar terrain-clearance measurements has been investigated. During this investigation, three different approaches for handling the highly nonlinear terrain measurement function were developed and their performance was established. These were 1) a simple first-order extended Kalman filter using local derivatives of the terrain surface, 2) a modified stochastic linearization technique which adaptively fits a least squares plane to the terrain surface and treats the associated fit error as an additional noise source, 3) a parallel Kalman filter technique utilizing a bank of reduced-order filters that was especially important in applications with large initial position uncertainties. Theoretical and simulation results are presented.

Observability, Eigenvalues, and Kalman Filtering

Abstract: In higher order Kalman filtering applications the analyst often has very little insight into the nature of the observability of the system. For example, there are situations where the filter may be estimating certain linear combinations of state variables quite well, but this is not apparent from a glance at the error covariance matrix. It is shown here that the eigenvalues and eigenvectors of the error covariance matrix, when properly normalized, can provide useful information about the observability of the system.

Design and analysis of a dynamic positioning system based on Kalman filtering and optimal control

Abstract: -A novel adaptive filtering technique is described for a class of systems with unknown disturbances. The estimator includes both a self-tuning filter and a Kalman filter. The state estimates are employed in a closed-loop feedback control scheme wbich is designed via the usual linear quadratic approach. The approach was developed for application to the dynamic ship positioning control problem and has the advantage that existing nonadaptive Kalman filtering systems may be easily modified to include the self-tuning feature. work was supported b\\l GEC Electrical Projects Ltd., and the United Manuscript received April 21, 1982: revised September 27, 1982. This Kingdom Science and Engineering Research Council. P. T.-K. Fung \\vas with the Department of Electrical Engineering, University of Strathclyde, Glasgow, Scotland. He is now with the Space and Electronic Group, Spar Aerospace Ltd.. Weston. Ont.. Canada. vrrsity of Strathclyde. Glasgow, Scotland. M. J. Grimble is with the Department of Electrical Engineering, Uni

Dynamic ship positioning using a self-tuning Kalman filter

Abstract: A novel adaptive filtering technique is described for a class of systems with unknown disturbances. The estimator includes both a self-tuning filter and a Kalman filter. The state estimates are employed in a closed-loop feedback control scheme which is designed via the usual linear quadratic approach. The approach was developed for application to the dynamic ship positioning control problem and has the advantage that existing nonadaptive Kalman filtering systems may be easily modified to include the self-tuning feature.

Decoupled Kalman filters for phased array radar tracking

Abstract: Kalman filters have been used in numerous phased array radars to track satellites, reentry vehicles, and missiles. This paper considers the design of these filters to reduce computational requirements, ill-conditioning, and the effects of nonlinearities. Several special coordinate systems used to represent the Kalman filter error covariance matrix are described. These covariance coordinates facilitate the approximate decoupling required for practical filter design. A tutorial discussion and analysis of ill-conditioning in Kalman filters is used to motivate these design considerations. This analysis also explains several well-known phenomena reported in the literature. In addition, a discussion of nonlinearities and methods to mitigate their ill effects is included.

A stochastic analysis of a modified gain extended Kalman filter with applications to estimation with bearings only measurements

Abstract: A new globally convergent nonlinear observer called the modified gain extended Kalman observer (MGEKO) is developed for a special class of systems. The stochastic stability of this observer used as a filter (now called the MGEKF), is analyzed in the probabilistic Hilbert space L2. Sufficient conditions for the MGEKF to be asymptotically stable are established. Finally, the MGEKO and the MGEKF are applied to the three-dimensional bearing only measurement problem (BOMP) where the EKF often shows erratic behaviors.

Analytical Steady State Solution for a Kalman Tracking Filter

Abstract: Analytical expressions are given for the steady state solution to a Kalman tracking filter used in a track-while-scan radar system. The radar sensor measures range and range rate, and both these measurements are utilized in the filter. The solution for range measurements only is obtained as a special case. Graphs are also given which show how the solution depends on different parameters.

Application of multiple model estimation to a recursive terrain height correlation system

Abstract: This paper describes the results of an investigation of the performance capabilities of an extended Kalman filter (EKF)-based recursive terrain correlation system proposed for low-altitude helicopter navigation. The major disadvantage of this concept is its sensitivity to initial position error. One method for reducing this sensitivity, involves the use of multiple model estimation techniques. In the multiple model approach, a bank of identical EKF's, each of which is initialized at a different point in the a priori uncertainty basket, is employed to ensure that one filter is initialized near the true aircraft position. In this manner, the probability of filter convergence is increased substantially, leading to improved navigation performance.

An approach to robust Kalman filtering

Abstract: We consider the problem of robustifying the Kalman filter. First, we review some known approaches to the problem. Then we establish the equivalence between the Kalman filter and a particular least squares regression problem. We suggest that the regression problem be solved robustly. Some well known approaches for doing this are discussed. Finally, the possibility of gleaning more information from past data is discussed.

Kalman filter formulation of low-Level television image motion estimation

Abstract: The problem of television image motion estimation is formulated as an application of Kalman filter theory. The nonuniform image motion present in a television scene is represented as the state variable of a randomly driven difference equation. A new approach is then introduced for linearizing measurement equations that arise in low-level image velocity estimation. Kalman filter theory is applied to the problem of optimally solving the nonuniform motion estimation problem based upon the image motion model and the linearized measurement equations.

A Kalman Filter Approach to Precision GPS Geodesy

Abstract: The high stability of the GPS signals makes it possible to determine differential position over short baselines with an accuracy of the order of centimeters. This has been demonstrated using very long baseline interferometry (VLBI) methods of radio astronomy. This paper presents an alternative approach using Kalman filter methods. It is based on an adaptive filter concept developed by D. T. Magi11 in 1965. The scheme employs parallel Kalman filters with each filter being modeled for a different integer wavelength assumption. As the phase measurement sequence progresses, the adaptive scheme “learns” which Kalman filter corresponds to the correct hypothesis, and thus it both resolves the wavelength ambiguity and estimates differential position simultaneously. Simulated results are presented which indicate convergence in about 10 minutes of satellite observation time.

Speech parameter estimation by time-weighted-error Kalman filtering

Abstract: In this paper, we discuss a method of improving the parameter-tracking performance of the Kalman filter for modeling time-varying signals. The Kalman filter is an effective means of recursively estimating the coefficients of an AR (or ARMA) model; however, its effectiveness is diminished by the weight which the filter gives to the history of the signal. With a view toward improved modeling of speech signals, we examine the use of a time-weighted error criterion to remedy this situation.

Credibility theory and the Kalman filter

Abstract: Following Mehra (1975) we indicate how some of the well known credibility models may be formulated as Kalman filters. The formulation yields recursive premium forecasts including recursive predictions errors which are of importance to practitioners.

A new look at the Magill adaptive filter as a practical means of multiple hypothesis testing

Abstract: The Magill adaptive filter can be used to detect known signals in the presence of Gauss-Markov noise. In this application, the various hypotheses are accounted for outside the bank of Kalman filters, and thus all filters have the same gains and error covariances. This commonality makes it feasible to use the Magill scheme in large-scale multiple-hypothesis testing applications.

Application of Kalman filters to the regulation of dead time processes

Abstract: A single-input single-output control algorithm for a process with dead time and dead time uncertainty is described. The process dynamics consist of first-order mixing and pure delay with the pure delay being dominant. The process is disturbed at the upstream end by a disturbance sequence consisting of white noise passed through a first-order shaping filter. The process output is subject to white measurement noise. A discrete Kalman filter is used to produce state estimates for the disturbance mixing and dead time states which are updated from the process output residual error. In order to handle dead time uncertainty of up to a priori established limits, the residual error is passed through a dynamic dead band whose magnitude is a function of the dead time states of a separate process dynamic model driven by the process input. The dead band eliminates dead time error components from the residual. Control is achieved by state feedback from the upstream Kalman filter state estimate. The algorithm is in use on paper machine and bleach plant control applications and gives near minimum variance performance when properly tuned.

Analytical Results for a Kalman Tracker Using Position and Rate Measurements

Abstract: Analytical results are presented for determining the steady-state components of the gain and error covariance matrices of the two-state Kalman tracking filter with white noise maneuver capability.

Recursive self-tuning algorithm for adaptive Kalman filtering

Abstract: A new recursive algorithm for adaptive Kalman filtering is proposed The signal state-space model and its noise statistics are assumed to depend on an unknown parameter taking values in a subset [', '] of Rs The parameter is estimated recursively using the gradient of the innovation sequence of the Kalman filter The unknown parameter is replaced by its current estimate in the Kalman-filtering algorithm The asymptotic properties of the adaptive Kalman filter are discussed

Rotation Invariant Pattern Recognition

Abstract: This paper reports on recent progress on invariant pattern recognition. Circular harmonic component (CHC) matched filters allow pattern recognition that is invariant under translations and rotations of the objects, and does not require segmentation of the object from its background. Now that the problem of the proper center for expansion of the filter has been solved, it has become easier to use such filters. The performance of the filter may be improved without using multiple filters by using composite CHC filters. When both target discrimination and sidelobe reduction are required, a composite filter that is an average between two composite filters must be used. The use of other invariant features is discussed.

Tracking characteristics of the Kalman filter in a nonstationary environment for adaptive filter applications

Abstract: In this paper, the Kalman filter theory is used to develop an algorithm for updating the tap-weight vector of an adaptive tapped-delay line filter that operates in a nonstationary environment. The tracking behaviour of the algorithm is discussed in detail. Computer simulation experiments show that this algorithm, unlike the exponentially weighted recursive least-squares (deterministic) algorithm, is always stable. Simulation results are included in the paper to illustrate this phenomenon.

Observer Design for Linear System with unknown input

Abstract: The purpose of this project is to design an observer for linear system with unknown input, which can predict the state in the future time. In this specific design, the focused point is Kalman filter. During the first stage of design, the fundamental knowledge were presented, which are the bas ic information about state observer, the controller properties, including stability, controllability and observability, and the Kalman filter structure and algorithm. After adeq uate preparation for rudimentary knowledge, a practical model—'Position and velocity measurement based on kalman filter ' is constructed and achieved by programming based on Matlab. At first, with the aim of testing the normal operation of the Kalman filter itself, there is external input to the built system. Then, the unknown input is added to the w hole system.

State variable estimation using adaptive Kalman filter with robust smoothing

Abstract: The development of a conventional Kalman filter is based on full knowledge of system parameters, noise statistics and deterministic forcing functions. This work addresses the problem of known system parameters and unknown noise statistics and deterministic forcing functions. Two concepts are investigated: 1) adaptive weight functions for the Kalman filter gain and error covariance matrices, where these weights are functions of sample means and variances of the innovations sequence; and 2) robust smoothing of the estimated state variables. The concepts presented relative to this particular problem address the limited class of linear system dynamics with associated linear measurements. Nonlinear system dynamics with associated linear or nonlinear measurements, however, are not precluded. The concepts apply to those cases where the observations made by a sensor are the variables to be estimated. An application to a simple linear system is presented; however, primary application would be to the estimation of position, velocity and acceleration for a maneuvering body in three dimensional space based on observed data collected by a remote sensor tracking the maneuvering body. Estimates of the state variables using the adaptive process for the simple linear system during the periods when the system is not being forced are relatively close to those of the conventional Kalman filter for congruent periods, but there is some increase in mean square error because the adaptive estimator is no longer optimal. During periods when the system is being forced a vast improvement, as compared with those estimates of the conventional Kalman filter, is realized with the adaptive gain, covariance weight, and associated robust smoothing procedure. The estimates derived with the adaptive procedure during the periods of system forcing do, however, contain a considerable level of mean-square error. This seems to be a prevailing shortfall of adaptive estimation procedures. The tradeoff is knowledge of the deterministic forcing functions versus high mean-square estimate error in the absence of that knowledge.

Efficient square root algorithm for measurement update in Kalman filtering

Abstract: This paper introduces a new L-D measurement update algorithm. The new algorithm is superior to the conventional one when only part of the states are directly related to the measurements. As the number of these states decreases, the computational efficiency of the new algorithm improves. The new algorithm is developed and discussed and its computation load is analyzed in comparison with th£ conventional L-D algorithm. An example demonstrates its efficiency. This measurement update algorithm together with a recently introduced modified UD propagation algorithm render an overall efficient square root filtering scheme. Identical results are obtained when a U-D rather than the L-D algorithm is used.

A Modification of the Extended Kalman Filter Algorithm with Application in Hydrology

Abstract: In this paper we propose a method for the solution of a hydrological problem, which is equivalent to the problem of estimating the parameters of a linear parabolic differential equation. The same problem was formulated and solved in Bagchi et al. (1980), where the authors used an explicit discrete scheme and a usual extended Kalman filter /EKF/ method. In this paper we propose to use an implicit discrete scheme, which has better stability properties. As a result we have to modify the EKF algorithm for the case, when the state space equation is implicit.

Partitioned estimators based on the perturbed kalman filter equations

Abstract: In this paper, the generalized partitioned filter, predictor and smoother formulae for continuous time linear systems in which the partitioned initial states are mutually correlated are derived by using the perturbed Kalman filter equations. It is shown that the results obtained here are extensions of recent results ( Lainiotis 1971, Ljung and Kailath 1977) to more general cases, and that the works of Lainiotis and Andrisani II ( 1979) can be approached without using the partition theorem based on the Bayes estimation theory. Finally, the bias correcting estimators are briefly discussed in order to show the applicability of the formulae.

Hardware verification of distributed/adaptive control

Abstract: Adaptive control techniques are studied for their future application to the control of large space structures, where uncertain or changing parameters may destabilize standard control system designs. The approach used is to examine an extended Kalman filter estimator, in which the state vector is augmented with the unknown parameters. The associated Riccatti equation is linearized about the case of exact knowledge of the parameters. By assuming that parameter variations occur slowly, the filter complexity is reduced further yet. Simulations on a two degree-of-freedom oscillator demonstrate the parameter-tracking capability of the filter, and an implementation on the JPL Flexible Beam Facility using an incorrect model shows the adaptive filter/optimal control to be stable where a standard Kalman filter/optimal control design is unstable.