Showing papers on "Alpha beta filter published in 1990"

Forecasting, Structural Time Series Models and the Kalman Filter

Abstract: List of figures Acknowledgement Preface Notation and conventions List of abbreviations 1. Introduction 2. Univariate time series models 3. State space models and the Kalman filter 4. Estimation, prediction and smoothing for univariate structural time series models 5. Testing and model selection 6. Extensions of the univariate model 7. Explanatory variables 8. Multivariate models 9. Continuous time Appendices Selected answers to exercises References Author index Subject index.

VSS observer for linear time varying system

Abstract: The problem of designing an observer for state estimation using variable structure system (VSS) theory is discussed. The theory and design principles for linear time-varying systems are presented. The observer is constructed by introducing a block-observable from which is similar to a lower triangular matrix. The convergence of the observer is guaranteed by a sliding mode with first-order filter. Simulation results show that the proposed observer is able to provide correct estimated values of the states. >

A Comparative Study of a Luenberger Observer and Adaptive Observer-Based Variable Structure Speed Control System Using a Self-Controlled

Abstract: Abstmct-This paper presents an analysis of the state observer-based robust speed control of a self-controlled synchronous motor (SCSM) . A variable structure control (VSC) technique is utilized to achieve robust ( parameter-insensitive) characteristics. The speed and acceleration signals required for the implementation of the variable structure speed control (VSSC) are dynamically estimated with state observers. Two kinds of observers-the Luenberger full-order observer and an adaptive observer- are explored in this paper. The results obtained illustrate that Luenberger observers do not estimate the system states accurately when the system parameters vary. This inaccuracy in the state estimation results in a deteriorated performance of the VSSC. Therefore, the possibility of using an adaptive state observer (ASO) is investigated. As expected, the AS0 estimates the system parameters and the system states simultaneously, thus making VSSC possible. The design methods and the simulation results presented demonstrate the potential of the proposed scheme.

Tracking targets using adaptive Kalman filtering

Abstract: A simple algorithm for estimating the unknown process noise variance of an otherwise known linear plant, using a Kalman filter is suggested. The process noise variance estimator is essentially dead beat, using the difference between the expected prediction error variance, computed in the Kalman filter, and the measured prediction error variance. The estimate is used to adapt the Kalman filter. The use of the adaptive filter is demonstrated in a simulated example in which a wildly maneuvering target is tracked. >

A comparative study of a Luenberger observer and adaptive observer-based variable structure speed control system using a self-controlled synchronous motor

Abstract: An analysis of the state-observer-based robust speed control of a self-controlled synchronous motor (SCSM) is presented. A variable-structure control technique is utilized to achieve robust (parameter-insensitive) characteristics. The speed and acceleration signals required for the implementation of the variable-structure speed control (VSSC) are dynamically estimated with state observers. Two kinds of observers-the Luenberger full-order observer and an adaptive observer-are explored. The results obtained illustrate that Luenberger observers do not estimate the system states accurately when the system parameters vary. This inaccuracy in the state estimation results in a deterioration of the VSSC performance. Therefore, the possibility of using an adaptive state observer (ASO) is investigated. It is shown that the ASO estimates the system parameters and the system states simultaneously, thus making VSSC possible. The design methods and simulation results are presented to demonstrate the potential of the scheme. >

Testing a decentralized filter for GPS/INS integration

Abstract: A decentralized Kalman filter strategy is presented and applied to GPS/INS (Global Positioning System/inertial navigation system) integration. Two Kalman filters are used. One is a local filter, processing GPS data and providing locally best estimates of position and velocity. The second is an INS filter which uses the results from the GPS filter as updates to the estimates obtained from the inertial data. Because of the high short-term accuracy of the inertial system, the position results from INS can be used for cycle slip detection and correction. The major advantages of this method are the flexible combination of GPS and INS and the simplicity of the implementation. Compared to centralized filtering, the decentralized filter gives globally the same optimal estimation accuracy as the centralized Kalman filter. The accuracy does not deteriorate when a suboptimal cascaded filter is used, which has some advantages in terms of computational efficiency. Extension of this method to more sensors is straightforward. Numerical results are used to illustrate the salient features of the method. >

Reconciling steady-state Kalman and alpha-beta filter design

Abstract: The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, alpha and beta . In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs. >

Real-time implementation of a narrow-band Kalman filter with a floating-point processor DSP32

Abstract: The author presents experimental results from two studies. First, a real-time narrowband Kalman filter is implemented with a floating-point digital processor DSP32. The real-time capability of this narrowband filter is investigated by varying parameters Q and R. The covariance matrices Q and R of the dynamic and measurement noise sequences are found to exhibit duality in the real-time tuning process and have a direct effect on system stability. If the value of Q used is smaller (with fixed R), the tracking time and the narrower tracking bandwidth of the filter will be longer. In addition, if the value of R used (with fixed Q) is smaller, the tracking time will be smaller, and the tracking bandwidth of the filter will be larger. The results are tabulated. Second, two optimal codes (in the sense of the execution speed), straight-line code and general matrix-based code, have been developed for implementing the narrowband Kalman filter. These two codes are compared in terms of program memory size, data memory size, and speed of execution. With the matrix-based code, the DSP32 performance is evaluated in terms of speed and memory size by varying the number of states of a Kalman filter. The results are also tabulated. >

A note on ship-motion prediction based on wave-excitation input estimation

Abstract: In order to predict the motion of a ship effectively, a new algorithm is developed in which the wave-excitation input information is extracted from the estimated ship-motion data, and a prediction is made by extrapolating the governing equation of the ship motion. Simulations performed with the algorithm and the conventional ship-motion prediction algorithm based on the standard Kalman filter are compared. >

Longitudinal Factor Score Estimation Using the Kalman Filter

Abstract: The advantages of the Kalman filter as a factor score estimator in the presence of longitudinal data are described. Because the Kalman filter presupposes the availability of a dynamic state space model, the state space model is reviewed first, and it is shown to be translatable into the LISREL model. Several extensions of the LISREL model specification are discussed in order to enhance the applicability of the Kalman filter for behavioral research data. The Kalman filter and its main properties are summarized. Relationships are shown between the Kalman filter and two wellknown cross-sectional factor score estimators: the regression estimator, and the Bartlett estimator. The indeterminacy problem of factor scores is also discussed in the context of Kalman filtering, and the differences are described between Kalman filtering on the basis of a zero-means and a structured-means LISREL model. By using a structured-means LISREL model, the Kalman filter is capable of estimating absolute latent developmental curves. An educational research example is presented. Index terms: factor score estimation, indeterminacy of factor scores, Kalman filter, LISREL

Mapping extended Kalman filters onto linear arrays

Abstract: Techniques for mapping extended Kalman filters onto linear arrays of programmable cells designed for real-time applications are described. First, a general method for mapping a standard (nonsquare root) Kalman filter, where the columns of the covariance matrix are updated in parallel, is introduced. Next, a general method for mapping a factorized (square root) filter, where fast Givens rotations are used to triangularize the prematrix and where rotations of the rows of the prematrix are performed in parallel, is introduced. These mappings are used to implement an extended Kalman filter commonly used in target tracking applications on the Warp computer. The Warp is a commercially available linear array of 10 or more programmable cells connected to an MC68020-based workstation. The Warp implementation of the standard Kalman filter running on 8 Warp cells achieves a measured speedup of 7 over the same filter running on a single cell. The Warp implementation of the factorized filter running on 10 Warp cells achieves a measured speedup of 2. >

A robust approach to reliable real-time Kalman filtering

Abstract: A complete approach to reliable, robust, and adaptive Kalman filtering is presented. It has applications in all types of navigation systems. The starting point is a measurement editing and filter divergence protection scheme based on measurement residuals and their expected statistics. Rather than simply increasing the white measurement noise variance, certain error sources which are known to be present can be included in the filter model via a Schmidt-Kalman filter, which allows certain states to be considered without being estimated. This type of filter configuration has many advantages over the usual Kalman filter such as larger region of convergence, smoother transitions between over-determined solutions, and more conservative modeling when certain states are frozen, such as during clock or altitude hold. Details are given on how this type of filter can be used with a factorized covariance. The same statistics used for filter integrity are also used to assess how well the filter is tuned to a particular dynamic environment. A reasonable adaptive process noise matrix scheme based on these statistics is presented. Specific examples of the application of these techniques in Global Positioning System receiver are given. >

An overview of decentralized Kalman filter techniques

Abstract: The federated Kalman filter, which combines data from multiple Kalman filters, is discussed. The federated filter can provide performance equal to that of a single Kalman filter that integrates all the independent sensor data in the system. The advantage is that a single filter is impractical with existing sensors. The federated filter is practical, but for true optimal performance it is necessary that all Kalman filters contain the same process model and make their covariance matrices available on the serial data bus. The federated filter can be reconfigured to provide a less optimal solution with a higher degree of fault tolerance. The application of the federated filter to combine data from two Kalman filters in a navigation system is simulated, and results are provided. >

Kalman filter-based optimizer and method and optimizing

Abstract: Making use of the conceptual and computational similarities between the Karmarkar method and the Kalman filter a controller system is capable of handling the observer function, the minimum time controller function and the minimum energy controller function. The system includes an element that has the computational structure of a Kalman filter. The inputs of this element are qualitatively controlled to deliver the desired results to the remaining computation elements. In a controller for an LP control task, the element develops the dual vector signal used in the affine scaling algorithm by applying information to it as if its task were to estimate the states of a system whose observable output is Dx(k) c, the input is O, the observation noise covariance matrix R is close to zero, the transition matrix is I and the matrix that describes the relationship between the measurable parameters and the observable output is AT Dx(k). Different controls applied to the Kalman filter structure element (and to the other elements of the system) yield control signals for QP control tasks.

Efficient estimators for an HF radio link

Abstract: A technique for the estimation of the sampled impulse response of an HF radio link was developed several years ago and was shown by computer simulation tests to have a substantial potential advantage in performance over more conventional systems A number of further developments have led to new channel estimators In some of these, a Kalman filter is incorporated into the system in such a way that the filter operates on only a few variable quantities and is therefore considerably less complex than a conventional Kalman filter Three different Kalman filters are studied, two of these being designed for a channel varying linearly (at a constant rate) with time, and the third being a conventional Kalman filter that is designed for a time-invariant or very slowly time-varying channel All of these employ an exponential window and therefore operate with a fading memory A description is given of the various estimators, the results of a series of computer simulation tests are presented, and the accuracies of the channel estimates given by the different systems are compared >

Estimating short-period dynamics using an extended Kalman filter. [for aircraft controllability]

Abstract: An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.

Observer design for discrete systems with unknown exogenous inputs

Abstract: A design procedure is developed for determining optimal discrete observers for estimating system states and unknown exogenous system inputs. This procedure is based on augmenting a standard system observer with an input model. The augmented model is then transformed into the discrete z-domain to determine relevant input/output transfer function matrices. The transfer function matrices are used to develop transfer function relationships between unknown exogenous inputs and the observer estimate of these inputs. It is shown that the optimal observer gains can be determined by implementing the observer as a Fisher filter. An example of the procedure is demonstrated with a third-order point-mass tracking filter. >

State space models and the Kalman filter

Abstract: The state space form is an enormously powerful tool which opens the way to handling a wide range of time series models. Once a model has been put in state space form, the Kalman filter may be applied and this in turn leads to algorithms for prediction and smoothing. The state space form is described in the first section of this chapter, while the second section develops the Kalman filter. Prediction and smoothing are described in sections 3.5 and 3.6 respectively. The Kalman filter also opens the way to the maximum likelihood estimation of the unknown parameters in a model. This is done via the prediction error decomposition and a full account can be found in section 3.4. The present chapter can be read independently of the rest of the book, and taken as a guide to the uses of the state space models in areas outside engineering. On the other hand, those interested primarily in the practical aspects of structural time series modelling will be reassured to know that they do not have to master all the technical details of the Kalman filter set out here. The most important parts of the chapter with which to become familiar are sections 3.1 and 3.5, the earlier parts of sections 3.2, 3.4 and 3.6, and, for those interested in non-linear models, sub-section 3.7.1. The reader will also benefit by at least skimming through the remaining sections, since there is some reference back to the various algorithms in later chapters and it is useful to have some idea of what these algorithms do and how they fit into the overall picture.

Estimating short-period dynamics using an extended Kalman filter

Abstract: An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.

Parallel Kalman filtering on the Connection Machine

Abstract: A parallel algorithm for square-root Kalman filtering has been developed and implemented on the Connection Machine (CM). Performance measurements show that the CM filter runs in time linear in the state vector size. This represents a great improvement over serial implementations, which run in cubic time. A specific multiple-target-tracking application in which several targets are to be tracked simultaneously, each requiring one or more filters, is considered. A parallel algorithm that, for fixed-size filters, runs in constant time, independently of the number of filters simultaneously processed, has been developed. >

Fast stable Kalman filter algorithms utilising the square root

Abstract: Consideration is given to Kalman filtering algorithms from the viewpoint of fast and stable implementation. A number of authors have reformulated certain signal processing and linear algebra algorithms to be square-root-free in an effort to simplify parallel implementation. Following these derivations a number of Kalman filter algorithms and parallel array architectures have been realized that also avoid square-root computations. It is shown that, contrary to the motivation for realizing these algorithms, the standard algorithms (utilizing square roots) can be implemented more quickly than the square-root-free versions. Furthermore, the square-root-free versions suffer from overflow/underflow and in some cases are numerically unstable. >

Lyapunov-based nonlinear observer, design for stochastic systems

Abstract: An observer design methodology which is applicable to more general nonlinear stochastic system models is given. The method relies not on the optimization theory but on Lyapunov-type stochastic stability results which can guarantee a mean square exponential rate of convergence for the estimation error. It is proved that discrete- and continuous-time state estimation is possible using the method. An example is given to illustrate the performance of this observer relative to some of the most commonly used filters in this field. >

Noise Adaptation and Correlated Maneuver Gating of an Extended Kalman Filter

Abstract: : Extended Kalman filtering is used to provide estimates of the position and velocity of a target based upon observations of the target's bearing and range. Non-stationary noise is shown to degrade the performance of the filter and cause filter divergence. By estimating the noise power from the variance of the filter's residual we adapt the filter to compensate for varying noise power. This thesis also introduces the method of correlated maneuver gating to adapt the Kalman filter to target dynamics. By spatially and temporally correlating the Mahalanobis Distance of the residual, the Kalman filter's performance is increased while tracking tangentially accelerating targets. Monte Carlo simulations are run for three different sets of target dynamics: stationary, moving linearly, and accelerating tangentially. Results for the simulation show significant performance advantages of using correlated maneuver gating in conjunction with noise adaptation. These results should generalize to other applications of the extended Kalman filter whose state and observation spaces enjoy a one-to-one mapping.

Multiple target tracking using an extended Kalman filter

Abstract: The paper centers on the continued development of the symmetric measurement equation (SME)filter developed by Kamen' for track maintenance in multiple target tracking. In this approach there is noneed to correctly associate measurements and targets before target state estimation can take place. Rather the data association problem is embedded in the process of target state estimation. The "first order" version of the SME filter is an extended Kalman filter (EKF), and thus the computational requirementsfor filter implementation are comparable to that for a standard Kalman filter. In addition, in contrast toprobabilistic data association filters, the estimator does not rely on the computation of probabilities forcorrect measurement/target associations. The SME filter is based on a standard state model for the targetstate trajectories. However, in contrast to existing approaches, the measurements are defmed in terms of nonlinear symmetric functionals of the target positions, except for one of the measurements which is

Derivation of a Leading Index for the United States Using Kalman Filters

Abstract: The purpose of this paper is to construct a leading index for the United States by deriving a set of weights based on Kalman filters. The weights have certain optimality properties and are related to the existing weighting methods of A. F. Burns and W. C. Mitchell (1946), S. H. Hymans (1973), and A. J. Auerbach (1982). The Kalman filter leading index is compared with the CIBCR leading composite index and an index suggested by Auerbach by subjecting all indexes to a number of tests. The results of the tests are mixed, but suggest that the use of Kalman filters as a way of constructing leading indexes is encouraging. Copyright 1990 by MIT Press.