Showing papers on "Kalman filter published in 1978"

An algorithm for tracking multiple targets

Abstract: An algorithm for tracking multiple targets in a cluttered environment is developed. The algorithm is capable of initiating tracks, accounting for false or missing reports, and processing sets of dependent reports. As each measurement is received, probabilities are calculated for the hypotheses that the measurement came from previously known targets in a target file, or from a new target, or that the measurement is false. Target states are estimated from each such data-association hypothesis, using a Kalman filter. As more measurements are received, the probabilities of joint hypotheses are calculated recursively using all available information such as density of unknown targets, density of false targets, probability of detection, and location uncertainty. This branching technique allows correlation of a measurement with its source based on subsequent, as well as previous, data. To keep the number of hypotheses reasonable, unlikely hypotheses are eliminated and hypotheses with similar target estimates are combined. To minimize computational requirements, the entire set of targets and measurements is divided into clusters that are solved independently. In an illustrative example of aircraft tracking, the algorithm successfully tracks targets over a wide range of conditions.

Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem

Abstract: A decentralized control problem involving K nodes is formulated At each node are sensors and controls. The object is to share the information of each sensor, processed with a local Kalman estimator, with all the other nodes so that the controllers can be computed using the best estimate of the state of the system given the information from all the sensors. The controls are determined so that the expected value of a quadratic performance index is minimized. The problem is formulated as a decentralized control problem without a central supervisor so that the system performance will degrade gracefully under structural perturbations. Therefore, the transmission of data is from each node to every other node; there are \sum\liminf{i-1}\limsup{k}(i-1) links connecting all nodes. It is shown that if the dimension of the controls at each node l is less than both the dimension of the data at node m and the dimension of the state, then a data vector with dimension of the control at l can be transmitted from m to l . compression of data transmission is done at the expense of propagating an additionaal data dependent vector at each node beyond the usual Kalman filter equations.

Application of Fast Kalman Estimation to Adaptive Equalization

Abstract: Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.

The Cramér-Rao estimation error lower bound computation for deterministic nonlinear systems

Abstract: For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramer-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.

Relationships between digital signal processing and control and estimation theory

Abstract: The purpose of this paper is to explore several current research directions in the fields of digital signal processing and modern control and estimation theory. We examine topics such as stability theory, linear prediction, and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing, in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the two disciplines.

A decentralized computational algorithm for the global Kalman filter

Abstract: In this paper a new decentralized computational structure is developed for Optimal state estimation in large scale linear interconnected dynamical systems. The new filter uses a hierarchical structure to perform successive orthogoilalizations on the measurement subspaces of each sub-system in order to provide the optimal estimate. This ensures substantial savings in computation time. In addition, since only low-order subsystem equations are manipulated at each stage, numerical inaccuracies are reduced, and the filter remains stable for even high-order systems. This is illustrated on a multimachine example of a system comprising eleven interconnected machines.

Linear system identification from non-stationary cross-sectional data

Abstract: The identification of time invariant linear stochastic systems from cross-sectional data on non-stationary system behavior is considered. A strong consistency and asymptotic normality result for maximum likelihood and prediction error estimates of the system parameters, system and measurement noise covariances and the initial state covariance is proven. A new identifiability property for the system model is defined and appears in the set of conditions for this result. The non-stationary stochastic realization (i.e., covariance factorization) theorem in [1] describes sufficient conditions for the identifiability property to hold. An application illustrating the use of a computer program implementing the identification method is presented.

Adaptive Tracking Filter for Maneuvering Targets

Abstract: A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.

Kalman Filter Divergence and Aircraft Motion Estimators

Abstract: Kalman filters designed for many aerospace systems turn out to be unsatisfactory. The estimate errors become large compared to the errors predicted by the theory ('divergence'). One of the principal causes of this failure is that the system model contains states or modes that are undisturbed by the modeled process noise, and are neutrally stable (NS). One cure for such problems is periodic restarting of a time-varying Kalman filter. Other cures include minimum variance observers with eigenvalue constraints, added noise, pole-shifting, and destabilization. Several examples are given, including effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several NS modes are undisturbed by wind gusts. An interpretation of these estimators as a 'strapdown IMU' without accelerometers, gimbaled gyros, or servos is given.

Recursive prediction error methods for adaptive estimation

Abstract: Convenient recursive prediction error algorithms for identification and adaptive state estimation are proposed, and the convergence of these algorithms to achieve off-line prediction error minimization solutions is studied. To set the recursive prediction error algorithms in another perspective, specializations are derived from significant simplifications to a class of extended Kalman filters. The latter are designed for linear state space models with the unknown parameters augmenting the state vector and in such a way as to yield good convergence properties. Also, specializations to approximate maximum likelihood recursions, Kalman filters with adaptive gains, and connections to the extended least squares algorithms are noted.

An Extended Kalman-Bucy Filter for Atmospheric Temperature Profile Retrieval with a Passive Microwave Sounder.

Abstract: An extended Kalman-Bucy filter has been implemented for atmospheric temperature profile retrievals from observations made using the Scanned Microwave Spectrometer (SCAMS) instrument carried on the Nimbus 6 satellite. This filter has the advantage that it requires neither stationary statistics in the underlying processes nor linear production of the observed variables from the variables to be estimated. This extended Kalman-Bucy filter has yielded significant performance improvement relative to multiple regression retrieval methods. A multi-spot extended Kalman-Bucy filter has also been developed in which the temperature profiles at a number of scan angles in a scanning instrument are retrieved simultaneously. These multi-spot retrievals are shown to outperform the single-spot Kalman retrievals.

Single-channel white-noise estimators for deconvolution

Abstract: The Wiener filtering approach to deconvolution is limited by certain modeling assumptions, which may not always be valid. We develop a Kalman filtering approach to deconvolution which permits more flexible modeling assumptions than the Wiener filtering approach. Our approach is applicable to time‐varying or time‐invariant wavelets as well as to nonstationary or stationary noise processes. We develop equations herein for minimum‐variance estimates of the reflection coefficient sequence, as well as error variances associated with these estimates. Our estimators are compared with an ad hoc “prediction error filter,” which has recently been reported on in the geophysics literature. We show that our estimators perform better than the prediction error filter. Simulation results are included, for both time‐invariant and time‐varying situations, which support our theoretical developments.

Principles and Simulation of JTIDS Relative Navigation

Abstract: The time-synchronous operation and high accuracy time-of arrival (TOA) measurement capability of Joint Tactical Information Distribution System (JTIDS) terminals makes possible a high performance relative nagivaton (RELNAV) function through addition of only software in the terminal's computer program. The principles of operation, the basic observation equations, and the system architecture for both absolute (geographic) and relative navigation are described. Sequential passive ranging by means of the TOA measurements, in conjunction with appropriate source selection logic and a recursive (e. g., Kalman) filter mechanization are employed to determine the user's position, velocity, and time bias. The filter algorithms and error sources, the software functional flow, and some simulation results are presented.

Steady state river quality modeling by sequential extended Kalman filters

Abstract: Sequential extended Kalman filters (EKF) are applied as a technique for steady state river water quality modeling. The approach was demonstrated by using water quality data collected over a 36.4-mi (58.6 km) stretch of the Jordan River, Utah. Each EKF was used to represent a river reach in which hydraulic and quality characteristics were judged fairly uniform. Mean and variance boundary conditions between successive filters were adjusted to represent the effects of point loads and tributaries discharging into the main river. Approximate minimum variance estimates of the system state (water quality parameters) and confidence intervals on these estimates were provided by combining two independent estimates of the system)state. The independent estimates were based on (1) predictions from an ‘internally meaningful’ model of the stream transport processes and biochemical transformations and (2) measurements of the water quality parameters. The estimates were combined by a weighting procedure based on uncertainties associated with each estimate. A smoothing algorithm was also applied in order that estimates from passes of the filter procedure in both the downstream and upstream directions could be combined. In this way, information contained in the measurements was used both upstream and downstream of the location of the measurement. The calibration capability of the filter procedure was demonstrated by simultaneous estimation of the state vector and one of the model coefficients. This capability was also used to estimate simultaneously the rate of lateral loading for one of the water quality parameters. Simultaneous estimation of coefficients of lateral loading was shown to increase the uncertainty associated with filter estimates because of the inclusion of uncertainty associated with these coefficients and lateral loading rates.

An analysis of the multiple model adaptive control algorithm. Ph.D. Thesis

Abstract: An analysis of the Multiple Model Adaptive Control algorithm is presented based on the analysis of a canonical problem simulations of which are similar to those obtained in applications. These results allow the prediction of stability and the characterization of the behaviors observed in the system.

Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors

Abstract: We are concerned with obtaining bounds on the performance of Kalman-type, linear, continuous-time filters susceptible to modeling errors. Limiting the discussion to stationary performance, we obtain bounds on the performance index, the mean square error of estimates for suboptimal and optimal (Kalman) filters. The bounds are expressed in terms of the model matrices and the range of errors of the matrices. The results are useful to a designer in comparing the performance of a suboptimal filter with that of the optimal filter when he has information on the range of modeling errors. The tightness of the bounds is shown by an application of the results in the estimation of the motion of an aircraft carrier at sea.

Bounds on estimation errors of discrete-time filters under modeling uncertainty

Abstract: The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a designer can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices are available.

The discrete Kalman filter applied to linear regression models: statistical considerations and an application

Abstract: In this paper we show how the Kalman filter, which is a recursive estimation procedure, can be applied to the standard linear regression model. The resulting “Kalman estimator” is compared with the classical least-squares estimator. The applicability and (dis)advantages of the filter are illustrated by means of a case study which consists of two parts. In the first part we apply the filter to a regression model with constant parameters and in the second part the filter is applied to a regression model with time-varying stochastic parameters. The prediction-powers of various “Kalman predictors” are compared with “least-squares predictors” by using Theil‘s prediction-error coefficient U.

Transfer-function solution of the Kalman-Bucy filtering problem

Abstract: A novel, transfer-function solution of the Kalman-Bucy time-invariant filtering problem is presented. It is assumed that both message model and noise intensities are time invariant and that the mixture of message and noise has been observed over an infinite interval. This transfer-function approach is based on matrix fractions and spectral factorization of polynomial matrices. It offers an interesting comparison of state-variable and trasnfer-function methods, provides a deep insight into the problem discussed and, what is most important, it is computationally attractive.

Estimation of steady-state Kalman filter gain

Abstract: An external description of multivariable linear stochastic systems gives a new estimation method of the steady, state Kalman filter gain for systems with unknown noise covariances.

Kalman Filter in Open Channel Flow Estimation

Abstract: In computing water surface profiles in open channels, uncertainties often arise in selection of resistance coefficients, such as Manning’s n. In this paper the Kalman filtering approach is developed to deal with such uncertainties. This approach combines a mathematical system model and an observation model. The former consists of (1)A stochastic nonlinear differential equation governing the steady one-dimensional open channel flow; and (2)one of three possible stochastic differential equations expressing Manning’s n (constant, function of the location of channel cross section, or function of both the location and the water depth). The observation model simply shows the observed water depth as the sum of “true water depth” and “error.” The estimation technique was tested for its accuracy in generating estimates of water depth and Manning’s n at several different schemes of sampling or measuring water depths. Results with Kalman filtering are compared with two paralle methods normally used today.

Relationship between Kalman and notch filters used in dynamic ship positioning systems

Abstract: In dynamic ship positioning systems notch filters have been used mainly to remove the unwanted wave motion signals. Recently, Kalman filters have been introduced for this purpose. It is demonstrated that for this application the stationary Kalman filter is approximated by a notch filter together with a low-pass filter in cascade.

Recent advances in EEG data processing.

Abstract: It is argued that the most interesting advances in EEG signal processing are with methods based on descriptive mathematical models of the process. Formulation of auto-regressive (AR) and mixed autoregressive and moving average (ARMA) models is reviewed for the scalar and the multidimensional cases and extensions to allow time-varying coefficients are pointed out. Data processing with parametric models, DPPM, involves parameter estimation and a large number of algorithms are available. Emphasis is put on those that are simple to apply and require a modest amount of computation. A recursive algorithm by Levinson, Robinson and Durbin is well suited for estimation of the coefficients in the AR model and for tests of model order. It is applicable to both the scalar and multidimensional cases. The ARMA model can be handled by approximation of an AR model or by nonlinear optimization. Recursive estimation with AR and ARMA models is reviewed and the connection with the Kalman filter pointed out. In this way processes with time-varying properties may be handled and a stationarity index is defined. The recursive algorithms can deal with AR or ARMA models in the same way. A reformulation of the algorithm to include sparsely updated parameter estimates significantly speeds up the calculations. It will allow several EEG channels to be handled simultaneously in real time on a modern minicomputer installation. DPPM has been particularly successful in the areas of spectral analysis and detection of short transients such as spikes and sharp waves. Recently some interesting attempts have been made to apply classification algorithms to estimated parameters. A brief review is made of the main results in these areas.

Stream Temperature Estimation Using Kalman Filter

Abstract: The system model used combines the deterministic sinusoidal model with a simple stochastic (first-order autoregressive) model of the residuals from the actual temperature of the temperature estimation given by the sinusoidal model. The estimation and forecasting technique was tested for its capability to generate daily streamflow temperature between several different measurement intervals. Results with Kalman filter are compared with those obtained in the four parallel models (the sinusoidal, the sinusoidal coupled with either the first-order or second-order autoregressive modeling of the random deviations, and the sinusoidal coupled with first-order autoregressive-moving average modeling of the random deviations). The mean-square deviation of estimated or predicted temperatures from the actually observed is used to measure the relative accuracy of the estimations by the five different techniques. The results show a definite advantage of using Kalman filter.

Performance Analysis of a Particularly Simple Kalman Filter

Abstract: Because of stringent storage restrictions, a very simple Kalman filter has been proposed for optimally aiding a strapdown inertial navigation system (INS) with data from a radiometric area correlator (RAC) onboard a weapon system currently under development. However, the adequacy of two decoupled three-state filters to meet performance specifications was subject to serious question. A set of covariance analyses has been conducted to determine estimation capabilities in a realistic environment generated by accurate *'truth models" of the error characteristics of two competing inertial systems (one using laser gyros and the other, conventional dry gyros) and the RAC system. Despite the simple form, the filters performed well enough to meet system specifications on navigation errors. Because of its extreme precision at low altitudes, the RAC was the dominant factor in attaining this accuracy, with the laser gyro INS providing somewhat better performance than the dry gyro system. Sensitivity analyses revealed that better RAC hardware or RAC error models in the filters would provide the most effective performance enhancement.