Showing papers on "Alpha beta filter published in 1971"

On-line identification of linear dynamic systems with applications to Kalman filtering

Abstract: Kalman gave a set of recursive equations for estimating the state of a linear dynamic system. However, the Kalman filter requires a knowledge of all the system and noise parameters. Here it is assumed that all these parameters are unknown and therefore must be identified before use in the Kalman filter. A correlation technique which identifies a system in its canonical form is presented. The estimates are shown to be asymptotically normal, unbiased, and consistent. The scheme is capable of being implemented on-line and can be used in conjunction with the Kalman filter. A technique for more efficient estimation by using higher order correlations is also given. A recursive technique is given to determine the order of the system when the dimension of the system is unknown. The results are first derived for stationary processes and are then extended to nonstationary processes which are stationary in the q th increment. An application of the results to a practical problem is presented.

A comparison of several nonlinear filters for reentry vehicle tracking

Abstract: This paper compares the performance of several non-linear filters for the real-time estimation of the trajectory of a reentry vehicle from its radar observations. In particular, it examines the effect of using two different coordinate systems on the relative accuracy of an extended Kalman filter. Other filters considered are iterative-sequential filters, single-stage iteration filters, and second-order filters. It is shown that a range-direction-cosine extended Kalman filter that uses the measurement coordinate system has less bias and less rms error than a Cartesian extended Kalman filter that uses the Cartesian coordinate system. This is due to the fact that the observations are linear in the range-direction-cosine coordinate system, but nonlinear in the Cartesian coordinate system. It is further shown that the performance of the Cartesian iterative-sequential filter that successively relinearizes the observations around their latest estimates and that of a range-direction-cosine extended Kalman filter are equivalent to first order. The use of a single-stage iteration to reduce the dynamic nonlinearity improves the accuracy of all the filters, but the improvement is very small, indicating that the dynamic nonlinearity is less significant than the measurement nonlinearity in reentry vehicle tracking under the assumed data rates and measurement accuracies. The comparison amongst the nonlinear filters is carried out using ten sets of observations on two typical trajectories. The performance of the filters is judged by their capability to eliminate the initial bias in the position and velocity estimates.

Real-Time Tracking Filter Evaluation and Selection for Tactical Applications

Abstract: Five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications. A rationale for selecting among these filters, which include a Kalman filter, a simplified Kalman filter, an ?-s filter, a Wiener filter, and a two-point extrapolator, is illustrated by two examples taken from the authors' recent experience.

Computational requirements for a discrete Kalman filter

Abstract: How practical is a Kalman filter? One answer to this question is provided by the computational requirements for the filter. Computational requirements-computational time per cycle (iteration) and required storage-determine minimum sampling rates and computer memory size. These requirements are provided in this paper as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then to use sequential processing than to process them together via simultaneous processing.

The Kalman Filter for the Equalization of a Digital Communications Channel

Abstract: Consideration is given to the use of the discrete Kalman filter as an equalizer for digital binary transmission in the presence of noise and intersymbol interference. When the channel is modeled as an n -tap transversal filter, the Kalman filter assumes a similar form with "feed forward and feedback." It is shown how the Kalman filter can be used to estimate both the tap weights and the binary signal. Computer results on a fixed 6-tap channel show that use of the 6-tap Kalman filter yields a considerably smaller error probability than when a conventional transversal equalizer with 15 taps is used. Limited computer studies on the same channel, assumed to be initially unknown, suggest that the Kalman filter is capable of converging rapidly in the adaptive mode. Though these results are very encouraging, much work remains in the study and optimization of performance in the adaptive mode.

Two-level form of the Kalman filter

Abstract: Sequential estimation of the states of several high-order interconnected systems may be prohibitive on computer time and storage if the problem is formulated as for a single system. Therefore, multilevel systems theory has been applied to derive a coordination algorithm, with one-step convergence, for a number of subsystem Kalman estimators. The procedure may be computationally attractive for sparsely coupled subsystems with few stochastic inputs.

Linear minimum-variance estimation and control in systems with state-dependent noise

Abstract: A recursive, minimum-variance linear filter and controller is derived for systems in which white state-dependent noise appears in the system dynamics and measurements. The filter without control is a generalization of the Kalman filter and possesses many of its desirable properties. First, the discrete form of the filter is derived. By taking a formal limit, a continuous filter with convergence in distribution to an Ito representation is obtained. The concept of a perfect controller is given, showing the formal duality of the filter and controller with the stochastic controller derived by Wonham. Finally, some of the properties of the filter-controller system are illustrated through the use of a scalar example. It is shown that a filter-controller designed by neglecting the state-dependent noise can destabilize a dynamically stable system.

A Comparison of the Extended Kalman Filter and Weighted Least Squares in Early-Orbit Determination

Abstract: : The problem of estimating the orbit parameters from early-orbit observations of an earth satellite is used to compare the accuracy and application of the extended Kalman filter and the classifical filtering method of weighted least squares. To obtain an absolute comparison, a treu two-body, drag-free Keplerian orbit is simulated, observations are computed and contaminated with noise, and the orbit parameters estimated by each filter are compared. The accuracy of the two filters was compared using the same set of observations to determine the effect of observation truncation and initial conditions on the results. Based on this study it was concluded that the weighted least squares filter and the extended Kalman filter yield about the same accuracy in the early-orbit determination problem.

Stability of a discrete closed-loop system which includes a Kalman filter†

Abstract: This paper describes a method of determining the stability at the sampling instants, of a discrete closed-loop system which includes a Kalman filter. This is done by determining the z-plane poles of a special augmented transition matrix. While this result stems from stochastic optimal control work, the method applies to any, not just optimal, values of the feedback matrix, M, and filter feedforward matrix K. It is still applicable when the filter model and the plant are dissimilar in coefficient values and order.

Comments on "A note on the nature of optimality in the discrete Kalman filter"

Abstract: The optimality property for the discrete Kalman filter derived in a recent correspondence is shown to follow from a more fundamental property.