Dirk Tenne

The higher order unscented filter

This article proposes a technique for the selection of the /spl sigma/-set for a probability distribution approximation filter, i.e., the unscented filter. The /spl sigma/-set is selected so as to capture the higher order input statistics. The Taylor series expansion is used to illustrate that the 3/sup rd/ order and higher statistics of the nonlinear transformation can be reproduced while the unscented filter captures the statistics up to the 3/sup rd/ order only. Two benchmark problems are used to corroborate the proposed solution.

Characterizing performance of /spl alpha/-/spl beta/-/spl gamma/ filters

The /spl alpha/-/spl beta/-/spl gamma/ filter, a sampled data target tracker which can asymptotically track a constant acceleration target, is discussed in detail. The /spl alpha/,/spl beta/,/spl gamma/ parameters are studied to characterize the stability of the filter and its performance viz its transient behavior. A closed-form equation for the mean square response of the system to white noise is derived. In addition, performance measures to gauge the transient response and the steady state tracking error are derived. The closed-form equations for the noise ratio and the transient and steady state error are exploited to optimally select the /spl alpha/, /spl beta/, /spl gamma/ parameters. The resulting solutions are shown to reduce to some results presented in the literature for the /spl alpha/-/spl beta/ filter.

Efficient minimax control design for prescribed parameter uncertainty

The purview of this paper is the design of a controller that includes knowledge of parametric uncertainties and their distributions. The parameter distributions are approximated by a finite set of points that are calculated by the unscented transformation. This set of points is used to design robust controllers that minimize the worst performance of the plant over the domain of uncertainty. The proposed technique is illustrated on two benchmark problems. The first relates to the design of prefilters for a spring‐mass‐dashpot system and the second is the feedback control of a hovering helicopter. Numerical simulations are used to illustrate the proximity of the resulting controller to the minimax controller.

Circular prediction algorithms-hybrid filters

The focus of the paper is on the development of a geometric algorithm as an alternative to the coordinated turn procedures. The fact that the trajectories of maneuvering targets are always smooth has been exploited to derive an algorithm, which constrains the predicted position of the target to lie on a circle formed by prior measurements. This filter is then used in conjunction with an /spl alpha/-/spl beta/ filter to arrive at a series of filters, which are tested on benchmark trajectories. The performances show promising results for the proposed filters.

ROBUST FEED-FORWARD/FEEDBACK DESIGN FOR TAPE TRANSPORT

The purview of this paper is the design of controller which include knowledge of parametric uncertainties and their distributions. The parameter distributions are approximated by a nite set of points which are calculated by the unscented transformation. This set of points is used to design robust controllers which minimize the worst performance of the plant over the domain of uncertainty. The proposed technique is illustrated on a tape transport system. Two approaches to arrive at robust prelters and feedback controllers are proposed. The rst, which involves sequential design of the feedback and prelter and the second, which simultaneously arrives at optimal parameters of the feedback gain matrix and the time-delay prelter. Numerical results illustrate desirable response over the operating region of the system.

Tracking for maneuvering target trajectories via the 3D circular filter

A circular prediction algorithm is proposed, which integrates the measured data into the filter and constrains the prediction to lie on a smooth curve modeled by an arc of a circle. The circular prediction is entirely defined in relation to three measurements in three-dimensional space. It is therefore not necessary to calculate the center and the radius of the circle. To obtain the statistics of the circular prediction, the unscented transformation has been utilized. The proposed hybrid filter combines the circular prediction and a constant velocity prediction by utilizing the covariance intersection (CI). This combined prediction can be updated with the subsequent measurement using a linear estimator. The proposed technique is compared with standard filters and the interacting multiple model (IMM) approach on a benchmark trajectory which includes coordinated turns and straight line maneuvers.

Optimal design of /spl alpha/-/spl beta/-/spl gamma/(/spl gamma/) filters

Optimal sets of the smoothing parameter (/spl alpha/, /spl beta/ and /spl gamma/) are derived for a sampled data target tracker. A constrained parameter optimization problem is formulated for specific trajectories of the target, which includes the noise in the measurement, the steady state error and the transient response of the filter. This work considers two classes of target trajectories, circular and straight line maneuvers. Closed form expressions for the steady state error and the sum of the square of the errors capturing the transient behavior are derived for a straight line trajectory where the target moves with constant acceleration and a circular trajectory with the target moving at constant speed. The constrained optimization includes, besides the maneuver errors, a metric of noise capacity strength, expressed by the mean square response of the filter to white noise. An optimal selection of /spl alpha/, /spl beta/ and /spl gamma/ parameters is provided for various penalties on the noise filtering.