Showing papers on "Kalman filter published in 1980"

Remarks on "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems"

Abstract: Some remarks are made on a paper dealing with convergence analysis of the extended Kalman filter as a parameter estimator for linear systems. In particular, some interesting differences in the convergence properties of a predictive and a filtering procedure are illustrated.

Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty

Abstract: The optimal control of watershed systems requires accurate real-time short-term forecasts of river flows. For the first time, this paper formulates a large, nonlinear conceptual model (the National Weather Service catchment model) in a mode amenable to analysis of uncertainty and the utilization of real-time information (measurements, forecasts, guesses) to update system states and improve streamflow predictions. The proposed methodology is based on the state space formulation of the equations describing the hydrologic model and the assumption of sources of uncertainty in the data and in the model structure. The first two moments of random variables are estimated in a computationally efficient way using on-line linear estimation techniques. Linearization of functional relationships is performed with the uncommon but powerful multiple-input describing function technique for the most strongly nonlinear responses and Taylor expansion for the rest. The linear feedback rule developed is based on the Kalman filter.

A Dynamic Positioning System Based on Kalman Filtering and Optimal Control

Abstract: This paper describes a computer-based, dynamic positioning system for floating vessels. The system is based on a detailed mathematical model of vessel motion in response to forces from thrusters, wind, waves and water current. The system uses a Kalman filter for optimal estimation of vessel motions and environmental forces from wind, waves and current. The control system is based on feedback from the motion varibles where the oscillatory, wave-induced component is removed by the estimator. Feedback from the water current estimate provides the integral action of the system, and feed forward from the wind force estimates are implemented. Simulation results and recordings from actual operation of the system indicate an excellent system performance.

Studies in the synthesis of control structures for chemical processes: Part III: Optimal selection of secondary measurements within the framework of state estimation in the presence of persistent unknown disturbances

Abstract: When primary control objectives cannot be measured directly, secondary measurements have to be selected and used in conjunction with estimators to infer the value of the unmeasurable variables. Unmeasured process disturbances (state excitation noise) are assumed to be of major importance, dominating the errors caused by measurement noise. Since the white noise assumption is generally insufficient for the persistent disturbances commonly occuring in the Chemical Engineering, environment, a nonstationary noise model has been employed, and is shown to yield superior estimations under these circumstances. New necessary and sufficient conditions have been developed for the observability of the dynamic system augmented to include the noise model. A variety of new measurement selection criteria is presented here, with the goal of minimizing estimation error. One class of criteria aims at minimizing the transient estimation error when a static estimator is used. The other class minimizes the measurement error caused by the unobservable subspace. The design of state reconstruction procedures (which are able to handle persistent unmeasured process disturbances) is explained in a stochastic and a deterministic framework. Finally, the synthesis of reduced order control schemes is discussed. The power of the selection criteria and the superiority of a Kalman filter design employing a nonstationary noise model is demonstrated in many examples.

Dynamic positioning of floating vessles based on Kalman filtering and optimal control

Abstract: This paper describes computer-based, dynamic positioning system for floating vessels. The system is based on a detailed mathematical model of vessel motion in response to forces from thrusters, wind, waves and water current. The system uses a Kalman filter for optimal estimation of vessel motions and environmental forces from wind, waves and current. The control system is based on feedback from the motion variables where the oscillatory, wave-induced component is removed by the estimator. Feedback from the water current estimate provides the integral action of the system and feed forward from the wind force estimates are implemented. Simulation results and recordings from actual operation of the system indicate an excellent system performance. Reference is given to installations made on actual vessels.

Improved extended Kalman filter design for passive tracking

Abstract: Extended Kalman filters are here modified for coordinate estimation of a stationary object using bearing measurements taken from a moving platform. The modifications improve significantly the coordinate estimation on the initial period of data collection when otherwise the performance is far from optimal. The modifications are to the nonlinearities and could, in some instances, be implemented by the introduction of a time decreasing amplitude dither signal in the extended Kalman filter prior to the output nonlinearity. A bound on a Lyapunov function decay rate is also given which assists in the design of the modified nonlinearities and in the selection of an appropriate coordinate basis to be used in the extended Kalman filter.

Use of Kalman filtering techniques in dynamic ship-positioning systems

Abstract: The position-control systems for dynamically positioned vessels include wave filters to remove the wave motion signals. These ensure that the sytem only responds to low-frequency forces that would cause the vessel to move off-station. Several filters have been proposed and used in this role, and in the following discussion the Kalman filter is considered. The Kalman filter depends upon the model of the vessel, and the development of such a model is described. Simulation results are given to illustrate the performance of the filter and the performance of the combined Kalman filter and optimal state-feedfack control system.

Coping with singular transition matrices in estimation and control stability theory

Abstract: When stabilizing linear discrete-time finite dimensional systems in control and estimation either optimally or suboptimally, technical difficulties arise in the conventional stability theories for coping with state transition matrices which are permitted to be singular or with eigenvalues arbitrarily small. In overcoming these difficulties, earlier results for feedback stabilization of linear systems and for Kalman filters and regulators are generalized in this paper, with proofs being in fact more direct than those explored earlier.

Statistical analysis of a two-ellipsoid overlap test for real-time failure detection

Abstract: Real-time failure detection for systems having linear stochastic dynamical truth models has been posed in terms of two confidence region sheaths in [1]-[3]. One confidence region sheath is about the expected nominal no-failure trajectory; the other is about the Kalman estimate of the state(s) being monitored for failures. The implementation of a necessary and sufficient test of whether these two confidence regions of elliptical cross section are disjoint at any time instant is shown to result in a scalar test statistic that is compared to a prespecified decision threshold at each check-time in making failure/no-failure decisions. The motivating theoretical basis of the test statistic is briefly discussed, the implementation equations and theoretical milestones previously encountered in guaranteeing algorithm convergence and establishing convergence rate are Summarized, then the details are presented for: 1) the derivation and analytic evaluation of the expressions for the probabilities of false alarm and correct detection that serve as a basis for subsequent tradeoffs in setting the threshold level; and 2) the derivation of an expression for the decision threshold and a technique for its calculation from the covariance of the Kalman filter. The probability of correct detection is shown to be a monotonely increasing function of the underlying fundamental signal-to-noise ratio response of the Kalman filter estimate of the failure mode state to a particular magnitude of failure. Real data results are provided to illustrate application of this technique for the two-dimensional case to detect failures in an inertial navigation system having two-degree-of-freedom gyros. This is the application for which the technique was developed.

UDU/T/ covariance factorization for Kalman filtering

Abstract: There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

A new form of the extended Kalman filter for parameter estimation in linear systems with correlated noise

Abstract: A well-known method for estimation of parameters in linear systems with correlated noise is the extended Kalman filter where the unknown parameters are estimated as a part of an enlarged state vector. To avoid the computational burden in determining the state estimates when only the parameter estimates are required, a new simple form of the extended Kalman filter, where the state consists only of the parameters to be estimated, is proposed. The algorithm is based on the inclusion of the computed residuals in the observation matrix of a state representation of the system, an idea first introduced in the so-called extended least-squares or Panuska's method. Convergence properties of the proposed algorithm are studied, and the algorithm is shown to perform a gradient-based minimization of the maximum likelihood loss function. Some special cases of the algorithm are also discussed, and an extension to an estimator for randomly varying parameters is outlined.

Sensor Fault Detection in a System with Random Disturbances

Abstract: Sensor faults are detected in an operating automatic system by a simplified version of the dedicated observer scheme Control inputs are augmented by a random disturbance of moderate intensity The dedicated observer in this case is a Kalman filter, driven by a single sensor This filter provides estimates of the outputs from the other, nonredundant, sensors A logical combination of these functionally redundant signals with the actual sensor signals provides prompt detection of incipient faults on all instruments without false alarms The scheme is applied to a simulation of the lateral axis control system of a hydrofoil boat in which four sensors are to be covered by the fault detection scheme Tests indicate that the scheme is robust with respect to variations in the intensity of the random disturbance

Adaptive filtering through detection of isolated transient errors in rainfall‐runoff models

Abstract: Real-time river discharge forecasting models operate under widely different wet and dry regimes, producing sequences of highly nonstationary prediction residuals. Errors in the mean areal precipitation estimation are often magnified due to model approximations and nonlinear behavior and result in significant effective input errors which propagate as transient signals through the system. Normal operation of a feedback scheme based on the Kalman filter with stationary error statistics cannot account for such discrepancies leading to local divergence between expected and observed prediction residuals. An adaptive filtering methodology which explicitly accounts for transient errors in the prediction due to errors in the estimation of the effective rainfall is presented. The filter operates normally under the assumption of only stationary or slowly varying noise, while a generalized likelihood ratio test is used to detect the presence of transient errors. When such errors are detected, estimates of their timing and magnitude are obtained, and the forecasts are appropriately corrected. An illustrative example of the procedure operation is given.

An Adaptive Two-Dimensional Kalman Tracking Filter

Abstract: A continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets. The track residuals in each coordinate, which are a measure of track quality, are sensed, normalized to unity variance, and then filtered in a single-pole filter. The magnitude Z of the output of this single-pole filter, when it exceeds a threshold Z1 is used to vary the maneuver noise spectral density q in the Kalman filter model in a continuous manner. This has the effect of increasing the tracking filter gains and containing the bias developed by the tracker due to the maneuvering target. The probability of maintaining track, with reasonably sized target gates, is thus increased, The operational characteristic of q versus Z assures that the tracker gains do not change unless there is high confidence that a maneuver is in progress.

Estimation of Roadway Traffic Density on Freeways Using Presence Detector Data

Abstract: Existing methods of estimating section link density on freeways from data provided by electronic presence loop detectors typically require extensive knowledge or strong assumptions on prevailing flow conditions, such as homogeneity. Consequently, these methods are known to produce poor estimates in inhomogeneous conditions, or when a priori knowledge of traffic conditions is not available. In this paper, a new data processing approach is presented which estimates density well over a wide range of traffic conditions. It does this by detecting spatially inhomogeneous traffic conditions and compensating the density estimation algorithm appropriately. The data processing algorithm is computationally simple, is not flow-level dependent, does not require any a priori knowledge of traffic conditions on the road and is insensitive to the types of uncertainty found in detector data. The algorithm uses both flow and occupancy data from adjacent detector stations to track the density on a link. A scalar Kalman filter formulation is used to provide the desired density estimate. The simplicity of the filter algorithm is achieved by using a scalar Generalized Likelihood Ratio GLR event detection algorithm to compensate the filter for spatially inhomogeneous conditions. Performance of the algorithm is demonstrated with a microscopic freeway simulation.

A direct approach to identify the noise covariances of Kalman filtering

Abstract: A new approach is presented for the estimation of the noise covariances associated with the linear discrete Kalman filter

Adaptive Filter Structures for Deconvolution of Seismic Signals

Abstract: The results of application of three different methods to the "adaptive deconvolution" of seismic data are reported here. These are based on the adaptive tapped delay line filter, the adaptive lattice filter and the adaptive Kalman-filter identifier. All the three methods are shown to be superior to the "fixed-structure" predictor. A comparison of the three methods shows that the adaptive lattice structure has faster convergence than the adaptive tapped delay line structure. The adaptive Kalman filter identifier is found to be better than both the others, although it is computationally more complex. The conclusions are based both on theoretical studies as well as on experiments with real seismic data.

Reduced-order optimal state estimator for linear systems with partially noise corrupted measurement

Abstract: The problem of reduced-order Optimal state estimation for linear systems with singular noise covariance matrix is studied. It is shown that the optimal estimator is somewhat different from the Kalman filter. The state estimator problem in the singular case can be cast as a constrained optimization problem. Solving this optimization problem yields the truly optimal estimator. The estimator derived here is of the form of the hybrid estimator of Fairman [7]. However, the derivations here are somewhat more direct.

Target vehicle tracking apparatus

Abstract: Vehicle tracking and position predicting apparatus includes an improved Kalman velocity filter feedback loop having a forward gain matrix for loop coordinate error factors and those of their derivatives; and position predicting computing apparatus in the loop feedback path between the system output and an input error node. Sensor reference target signals (e.g., range, bearing and elevation) are connected as inputs to the filter error node. In accordance with one aspect of the present invention, sensor coordinate reference errors from the input error node are converted to target reference coordinates. Pursuant to a further aspect of the present invention, the gain matrix is varied dependent upon sensor coordinate variables. Gain matrix variations are thus independent of geometry and sensor reference coordinates.

Kalman filter design for target tracking

Abstract: The problem of solving the matrix Riccati differential equation in the design of Kalman filters for the target tracking problem is considered. An algebraic transformation method is used to reduce the order of the Riccati differential equation and to obtain explicit expressions for the filter gains (in terms of the interceptor /target separation range) which results in a substantial reduction of the computer burden involved in estimating the target states. The applicability of the transform technique is demonstrated for the receiver thermal noise and the target glint noise cases.

Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain

Abstract: A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.

Multivariate Model Identification and Stochastic Control of a Chemical Reactor

Abstract: Multivariate time series and process identification methods are used to develop a dynamicstochastic model for a packed bed tubular reactor carrying out highly exothermic hydrogenolysis reactions. A canonical analysis procedure is used on the data collected from the reactor to first reduce the dimensionality of the identification and control problems. The identified transfer function-ARIMA model is transformed into a state space model form and used to develop a multivariable optimal stochastic controller for the reactor. The controlled variables are inferred production rates reconstructed from temperature and flow measurements. The parameters of the inferential equation are updated recursively using measurements of actual concentrations available periodically. The controller is implemented using a process minicomputer, and is shown to perform very well.

Determination of instrumentation errors from measured data using maximum likelihood method

Abstract: The maximum likelihood method is used for estimation of unknown initial conditions, constant bias and scale factor errors in measured flight data. The model for the system to be identified consists of the airplane six-degree-of-freedom kinematic equations, and the output equations specifying the measured variables. The estimation problem is formulated in a general way and then, for practical use, simplified by ignoring the effect of process noise. The algorithm developed is first applied to computer generated data having different levels of process noise for the demonstration of the robustness of the method. Then the real flight data are analyzed and the results compared with those obtained by the extended Kalman filter algorithm.

Comments on "Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control"

Abstract: The decentralized system in the above paper can be reduced to a simpler system, which achieves the same goal but with less computations. The new system is obtained by a straightforward decomposition of the Kalman filter.

Survey of radar data-processing techniques in air-traffic-control and surveillance systems

Abstract: The application of data-filtering techniques for air-traffic-control and surveillance systems is re-reviewed. Operational requirements of these systems are primarily described. They are typically composed of radars (mechanical scanning and phased array), data-processing devices (digital computers) and displays. The environment is determined by the number and characteristics of targets and by the density and characteristics of the unintentional (weather, etc.) and intentional interferences. The effect of the environment on the filtering techniques used is also considered. In the case of air traffic control, a(?, s) filtering algorithm, which is used for primary radars, secondary radars and d.a.b.s. (discrete address beacon systems) is described. Collision-avoidance techniques and their implementation are also mentioned. In the case of air defence and surveillance systems, the algorithms are more sophisticated because of unpredictable target motion, high acceleration and intentional interferences. The types of algorithms which may be employed are the Kalman filter (also with variable data rate for phased-array radar), adaptive filters for manoeuvring targets, filters for target tracking in clutter and jamming environment, a filter for tracking of targets formations and, finally, nonlinear filters using radial velocity information. Moreover, the above mentioned techniques affect fire-control and interceptor-guidance methods. The filtering methods are extended to the multiradar case. Some specific problems, which are herein emphasised, concern the ways of combining the information coming from the different radars, the measurement time alignment and co-ordinate conversion over large areas. The methods of filter implementation, being affected by the technology available, are also described. Finally, a comprehensive list of references, refering to the different topics, has been included.