Showing papers on "Alpha beta filter published in 1989"

Robustification of Kalman Filter Models

Abstract: Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme outlying observations are encountered, and we point out that this can be achieved by assuming a multivariate distribution with Student-t marginals. To achieve fully robust results of the kind desired, it becomes necessary to forsake an exact distribution-theory approach and adopt an approximation method involving “poly-t” distributions. A recursive mechanism for implementing the multivariate-t—based Kalman filter is described, its properties are discussed, and the procedure is illustrated by an example.

Robust control system design with a proportional integral observer

Abstract: A design method for a robust controller including a new type of observer called the proportional integral observer (PI observer) is proposed. The new observer differs from the conventional one by an integration path which provides additional degrees of freedom. This freedom can be used to make the observer-based controller design less sensitive to parameter variation of the system. It is shown that some of the difficulties that may arise in the exclusive pursuit of a design for the conventional observer-based controller from the point of view of system robustness are resolved in a straightforward manner using the PI observer. A systematic robustness recovery procedure is described for the PI observer-based controller design which asymptotically achieves the same loop transfer functions as the full-state feedback control implementation. A design example is included and the effectiveness of our method is illustrated by simulation results.

Training feed-forward networks with the extended Kalman algorithm

Abstract: It is shown that training feed-forward nets can be viewed as a system identification problem for a nonlinear dynamic system. For linear dynamic systems, the Kalman filter is known to produce an optimal estimator. Extended versions of the Kalman algorithm can be used to train feed-forward networks. The performance of the Kalman algorithm is examined using artificially constructed examples with two inputs, and it is found that the algorithm typically converges in a few iterations. Backpropagation is used on the same examples, and the Kalman algorithm invariably converges in fewer iterations. For the XOR problem, backpropagation fails to converge on any of the cases considered, whereas the Kalman algorithm is able to find solutions with the same network configurations. >

Use of asymptotic observers having-high-gains in the state and parameter estimation

Abstract: The estimation of the unknown parameters of a nonlinear system is reduced to the estimation of its state variables by a state-space immersion. The Luenberger observer is used in the state estimation of the extended nonlinear system. The use of high gains in the cancellation of nonlinearities in order to simplify the observer design is studied. The high gain induces a time-scale separation between the nonlinear system and the observer, and therefore the singular perturbation theory can be used in the stability analysis of the error dynamics. In particular, it is shown that the error dynamics reaches stable equilibrium very fast, ensuring that the slow dynamics of the observer is just that of the given nonlinear system. >

Application of extended Luenberger observer for flux and rotor time-constant estimation in induction motor drives

Abstract: The synthesis method of an extended state observer for a nonlinear dynamical system is described. A presented observer enables the observation of system state vector and the identification of system parameter simultaneously. This method was adapted to the designing of the extended state and parameter observer for the induction motor. Generally, the proposed observer belongs to the class of time-varying reduced-order estimators. An analysis of the dynamical properties of each observeris presented. It is discovered that this kind of observer enables observation of the rotor flux and the identification of the rotor time-constant simultaneously, in synchronous or asynchronous operation, which greatly improves the computational facility and flexibility in the the microprocessor realisation of such a system.

Optimal observer motion for localization with bearing measurements

Abstract: System observability in nonlinear estimation problems is a significant factor governing solution behavior. This paper addresses the effects of observer motion on estimation accuracy for bearings-only localization. The role of the observer is to create a target/observer geometry that maximizes system observability, thereby minimizing the region of uncertainty. Two approaches are presented for deriving optimal observer paths. The first approach generates optimal observer motion numerically via the determinant of the Fisher Information Matrix, while the second involves the application of control theory to an alternative criterion. In addition, optimal fixed aspect angles are similarly determined for deviated pursuit curves. The error ellipses associated with the trajectories are compared and analyzed. It is shown that observer motion involves a trade-off between increasing bearing-rate and decreasing range. Particular characteristics of an observer path and its effect on estimation accuracy depend on the scenario initially encountered.

An observer for time lag systems

Abstract: A full state vector observer is derived for a class of linear differential state delayed control systems. The approach dualizes a feedback stabilization theory based on the reducing transformation technique. A major feature of the approach is that the observer, or the combined controller/observer, can be designed by well-known finite-dimensional state vector methods once the set of unstable and poorly damped modes of the system has been determined. >

Robust adaptive Kalman filtering with unknown inputs

Abstract: A method is proposed to adapt the Kalman filter to the changes in the input forcing functions and the noise statistics. The resulting procedure is stable in the sense that the duration of divergences caused by external disturbances are finite and short and, also, the procedure is robust with respect to impulsive noise (outlier). The input forcing functions are estimated by a running window curve-fitting algorithm, which concurrently provides estimates of the measurement noise covariance matrix and the time instant of any significant change in the input forcing functions. In addition, an independent technique for estimating the process noise covariance matrix is suggested which establishes a negative feedback in the overall adaptive Kalman filter. This procedure is based on the residual characteristics of the standard optimum Kalman filter and a stochastic approximation method. The performance of the proposed method is demonstrated by simulations and compared to the conventional sequential adaptive Kalman filter algorithm. >

Application of an extended Kalman filter to parameter identification of an induction motor

Abstract: An extended Kalman filter is used to identify the parameters of an induction motor using measurements of the stator voltages, currents, and rotor speed. A model of the induction motor in the state space and the Kalman filter algorithm are shown. This filter is applied to the parameter identification of an inverter-fed induction motor. A simple and practical method of setting the covariance matrices of the noises, which are important in the Kalman filter algorithm, is proposed. The starting values of the state and parameter vectors as well as the covariance matrix of the estimation error are then shown, and, finally, the results of parameter identification are shown. The results demonstrate that the filter is capable of identifying the parameters. >

Estimating Dynamic Models Using Kalman Filtering

Abstract: The Kalman filter is useful to estimate dynamic models via maximum likelihood. To do this the model must be set up in state space form. This article shows how various models of interest can be set up in that form. Models considered are Auto Regressive-Moving Average (ARMA) models with measurement error and dynamic factor models. The filter is used to estimate models of presidential approval. A test of rational expectations in approval shows the hypothesis not to hold. The filter is also used to deal with missing approval data and to study whether interpolation of missing data is an adequate technique. Finally, a dynamic factor analysis of government entrepreneurial activity is performed. Appendices go through the mathematical details of the filter and show how to implement it in the computer language GAUSS.

Observer-based Control of Uncertain Linear Systems: Recovering State Feedback Robustness Under Matching Condition

Abstract: In this paper we study the problem of observer design for a class of state-feedback controllers that includes high-gain linear control, continuous approximations of min-max control and continuous approximations of variable structure control. Assuming that the state-feedback controller robustly stabilizes the system in the presence of matched parametric uncertainties, we are to design the observer such that the observer-based control recovers the stability robustness of the state-feedback-control. We will show that it is possible to design such an observer, if the nominal, system is left-invertible and minimum-phase.

On the properties of reduced order Kalman filters

Abstract: Several known results are unified by considering properties of reduced-order Kalman filters. For the case in which the number of noise sources equals the number of observations, it is shown that the reduced-order Kalman filter achieves zero steady-state variance of the estimation error if and only if the plant has no transmission zeros in the right-half plane, since these would be among the poles of the Kalman filter. The reduced-order Kalman filter cannot achieve zero variance of the estimation error if the number of independent noise sources exceeds the number of observations. It is also shown that the reduced-order Kalman filter achieves the generalized Doyle-Stein condition for robustness when the noise sources are colocated with the control inputs. When there are more observations than noise sources, additional noise sources can be postulated to improve the observer frequency response without diminishing robustness. >

The Discrete Kalman Filter

Abstract: In Chapter 6, we discussed the problem of making recursive estimates of a random vector X. The problem was static in the sense that every measurement was used to update or improve the estimate of the same random vector X. We now consider the case where the random vector changes in time, between measurements, according to a specified statistical dynamic.

Application Of The Extended Kalman Filter To Parameter And State Estimation Of Induction Motors

Abstract: This paper deals with the estimation of the state variables and the identification of some parameters of the model of an induction motor. A general algorithm, based on the Extended Kalman Filter te...

Improved understanding of the loss-of-symmetry phenomenon in the conventional Kalman filter

Abstract: An unclear treatment is corrected of the conventional Kalman filter implementation as presented by M. H. Verhaegen and P. van Dooren (1986). It shows that the habitual implementation of the Kalman filter makes it extremely sensitive to the so-called loss-of-symmetry phenomenon. Furthermore, it is also demonstrated that an exact implementation of the conventional Kalman filter removes this sensitivity. >

Design of observers

Abstract: This chapter shows that an estimate of the states x can be obtained using an asymptotic observer whenever the system is observable. We also showed that an observer of order (n-m) is adequate to estimate all the states. We also defined a minimal order observer to estimate linear functions of states. When only a single (scalar) linear function of states is desired, an observer of order (r-1), where r is the observability index of the system, is possible.

Fast Mapping Of A Kalman Filter On Warp

Abstract: A parallel algorithm for solving an n-state Kalman filter on an (n+2)-cell linear array is described. The algorithm is the basis for the mapping of a 9-state target tracking filter on the Warp computer. The Warp implementation is written in a high-level language and achieves a measured speedup of almost 300 over the same filter running on a Sun workstation.

Design of single-functional observers for linear time-varying multivariable systems

Abstract: A method is presented for the design of an observer capable of reconstructing a single linear functional of the states of a linear time-varying system. The method is based on a canonical transformation of uniformly observable time-varying multi-variable system. It is shown that this canonical form, along with certain pre-specified structures of observer coefficient matrices, leads to a systematic and straightforward procedure for designing a functional observer of minimal order.

New Kalman filter algorithms based on orthogonal transformations for serial and vector computers

Abstract: A new numerically stable Kalman filter algorithm based on a special Givens transformation is developed theoretically. The advantage of the new Kalman filter algorithm vs. conventional formulations is examined for the support of inertial navigation systems (simulation data). The conventional Kalman-Bucy filter, the Bierman formulation and the new Kalman filter algorithms are implemented on IBM 4381 and 3090 computers and vector processors CRAY-1S and CRAY-X-MP. A comparison of CPU-times of the algorithms on the different computers is shown.

Effects of modeling errors on the stability and innovations moments of kalman filters

Abstract: The effects of modeling errors on the performance of Kalman filters are classified and analyzed for the scalar time-invariant continuous-time case. Sufficient conditions for filter divergence are presented showing that process instability and unbounded deterministic control inputs usually cause the filter to go unstable if the dynamic parameters are incorrect. For stable processes and bounded control inputs errors in the dynamic parameters normally cause the filter innovations process to cease being zero mean. Errors in the noise covariances normally have no effect on the filter stability or the innovations mean, but such errors have impact on the innovations "whiteness" and covariance. The paper results may be applied for development of practical guidelines for Failure Detection and Diagnosis problems in dynamic systems.

Estimation of atmospheric and transponder survey errors with a navigation Kalman filter

Abstract: The Completely Integrated Reference Instrumentation System (CIRIS) is an aircraft inertial navigation system (INS) aided with range and range-rate measurements from precisely surveyed ground transponders. The full-ordered Kalman filter 'truth' model for this system is developed with the goal of increasing the error-estimation accuracy of the CIRIS Kalman filter. The authors present the basic structure of the 127-state 'truth' model Kalman filter. The random bias shaping filter model for the transponder positioon survey-errors and the first order Markov shaping filter model for the atmospheric propagation delays are developed. The full-ordered Kalman filter based on the CIRIS 'truth' model is used to process empirical data from a CIRIS flight. The time histories of selected correlated measurement errors' means, covariances, and range residuals are plotted and analyzed with respect to the filter's estimate of position and velocity errors, as well as the aircraft trajectory. The initial conclusions drawn from these data are presented. >

A 2-D adaptive diagonal block Kalman filter for nonsymmetric half plane image models

Abstract: A 2-D diagonal block recursive representation for 2-D autoregressive (AR) image models with nonsymmetric half-plane (NSHP) regions of support that does not have noncausality problems is introduced. The relevant 2-D block Kalman filter equations are used to obtain suboptimal block filtered estimates for the blurred and noisy image. A recursive parameter identification scheme can be used online to update the model parameters at each processing window suggested. Simulation results are presented. >