Showing papers on "Alpha beta filter published in 1983"

Canonical form observer design for non-linear time-variable systems

Abstract: An observer of canonical (phase-variable) form for non-linear time-variable systems is introduced. The development of this non-linear time-variable form requires regularity of the non-linear time-variable- observability matrix of the system. From the relationships derived during the development, it follows that a non-linear time-variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non-linearities about the reconstructed state trajectories is permissible. This is an assumption similar to that of the extended Kalman filter based on a linearization about the current estimate.

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.

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.

The application of Kalman filtering estimation techniques in power station control systems

Abstract: This paper describes the application of Kalman filter estimation techniques to an operational 500 MW oil-fired boiler/turbine unit. In common with most physical processes, the plant contains nonlinearities, unknown or poorly defined variables, and bias disturbances. These problems are overcome by the use of bias states which are appended to the system state equations.

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

On the design of discrete-time optimal dynamic controllers using the partial state observer

Abstract: This paper considers the problem of designing optimal dynamic controllers, based on a partial state observer, for discrete-time linear time-invariant systems with inaccessible state. It is assumed that the initial system state is an unknown random vector with known mean and covariance. The performance index is taken to be the expectation, with respect to the initial state, of the standard quadratic one for the discrete-time regulator. Necessary and sufficient conditions for optimality are derived, provided that the subspace which ensures the existence of a partial state observer, is given. A design algorithm is also obtained which can be directly solved for the parameters of the optimal observer and requires the solution of a matrix Riccati equation of the observer order. As in the continuous-time case, the separation property in the restricted sense is seen to hold. Finally an example is presented to illustrate the procedure.

Observers for a class of 2-D filters

Abstract: In this paper, a 2-D observer is proposed for 2-D systems of the Fornasini-Marchesini type. Conditions are given for the existence of the proposed observer where both the case of known and unknown boundary conditions are considered. Design equations are developed for calculation of the observer matrices. Conditions are also given for being able to choose the form of the observer in the simple form for 2-D systems proposed by Attasi. Finally, it is shown how the proposed observer can be used in a feedback scheme to stabilize a 2-D filter having a state-space model of the Attasi type.

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.

Real-Time Implementation Of Systolic Kalman Filters

Abstract: This paper describes a systolic signal processor architecture which is well suited for digital filtering, target tracking, image processing and signal processing. The architecture is based on apping the widely-used Kalman filter equations onto a linearly connected systolic array. A detailed analysis of finite wordlength effects, roundoff-error propagation, stability and estimation sensitivity is presented for the systolic Kalman filter architecture.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

An Optically Implemented Multiple-Stage Kalman Filter Algorithm

Abstract: A working paper is presented on the mathematical development and analysis of an optically implemented multiple-stage Kalman filter algorithm which uses two previously developed estimation models (linear first-order Gauss-Markov and constant turn-rate) for high energy laser pointing and tracking. An overview of the estimation models reveals model equivalence in mid- to long-range tracking applications and superiority of the constant turn-rate model (at the expense of a much higher computational burden) for both short-range and evasive target tracking. Real world constraints are to be forcibly imposed on the optical filter by limiting the choice of all system components to off-the-shelf units whose performance criteria are well characterized. Derivation of the filter architecture subject to the real world constraints shows the pielined iterative systolic array architecture to be significantly superior. Filter development based on this architecture is expected to generate a MTF which yields superior performance of the optical filter over its electronic counterpart based both on the output statistics produced and system throughput capability Additional analyses of filter performance reveal potential filter enhancement with the incorporation of range and relative velocity data obtained through use of a laser doppler velocimeter and an optical heterodyne detector. Current and planned future research efforts are also presented.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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.

State observer for quadratic systems

Abstract: This paper considers a minimal order state observer for a quadratic system. The given observer is an extension of one for a bilinear system. Sufficient conditions are given for the existence of the state observer and design procedure is presented.

Reduced-order observers for linear multivariable systems with disturbance and tracking signal accommodation

Abstract: As observer poles influence the dynamics of the feedback loop, observer reduction to the smallest order necessary is of practical interest. Using a unified approach to plant, disturbance and tracking process observation, several stages of obsorver-order reduction are discussed and a new, minimal order observer design is presented.

Duality of the discrete-time optimal filter and regulator problems

Abstract: The duality exhibited between the discrete-time Kalman-Bucy filter with correlated process and measurement noise and the discrete-time optimal regulator is investigated.

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.