Dietrich Fränken

Improved fast covariance intersection for distributed data fusion

Among the possible approaches to tackling the problem of data incest in distributed data fusion networks, covariance intersection is a candidate that yields consistent estimates independent of network structure and any possible cross-correlation between local estimates. The corresponding weighting coefficients are usually chosen with the aim for a minimum trace or determinant of the resulting error variance matrix. A fast non-iterative algorithm exists that, to a certain extent, approximately solves this nonlinear optimization problem with extremely reduced numerical implementation effort. Yet, the obtained weighting coefficients do not depend on the relative orientation of the estimation error variance matrices which may lead to a degraded performance in certain applications. Hence, an improved fast covariance intersection algorithm is developed that comes with a slightly increased implementation effort while yielding significantly better estimation results in some cases and comparable results in all other ones. Simulation results confirm the postulated performance improvement.

Generation of wave digital structures for networks containing multiport elements

Most standard wave digital filters are derived from passive reference circuits, where only parallel and serial connections between one-port elements occur. In this paper, a framework for the automated generation of the wave digital structures is presented, where the reference circuit is assumed to comprise arbitrary connection types. It is shown how the representation of the underlying graph by its so-called SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with networks containing certain multiport elements. We propose two different novel approaches to finding a valid tree representation from a given reference circuit. The first approach relies on the usage of apt replacement graphs for the multiport elements. The second one is based on searches for circles on suitably constructed graph representations and generates wave digital structures with minimum implementation effort even in presence of nonreciprocal elements. In both approaches, standard separation algorithms with known efficient implementations can be applied.

Consistent unbiased linear filtering with polar measurements

The problem of tracking objects moving in Cartesian space with sensors delivering polar measurements has been under investigation of several researchers for quite some time now. Different proposals for using measurement conversion techniques in combination with a linear Kalman filter have been made in order to reduce the range bias that shows up in the filter estimates when a Cartesian pseudo-measurement is created from the polar measurements by applying the respective conversion formulae in combination with a corresponding linearized form of the measurement error covariance matrix. It turns out that the actual behavior of these different approaches strongly depends on the specific situation under consideration where observed effects range from a truly (approximate) suppression of conversion bias up to an even increased bias. In this paper, a systematic approach to analyzing the bias effects of measurement conversion in certain typical tracking situations is presented. Starting from this approach, a new measurement conversion technique is proposed that yields consistent unbiased estimates in these cases.

Passive parametric modeling of dynamic loudspeakers

In this paper, an electrical circuit is proposed which is suitable for a parametric modeling of electrodynamic transducers, e.g., dynamic loudspeakers. Since the system modeled is known to be passive, the preservation of this property is a key issue of the approach presented here. This is of special importance when nonlinear effects are taken into account, as passivity always ensures different kinds of stability. The only nonlinear elements occurring in the circuit model are ideal transformers, the turns ratios of which are not constant but depend, in particular, on some signal quantity. As a consequence, the circuit can be digitally simulated by applying principles known from the theory of wave digital filters.

Observer-based feedback linearization of dynamic loudspeakers with Ac amplifiers

For a reduction of nonlinear distortion produced by a dynamic loudspeaker, there exists a variety of approaches, one of them using the known principle of exact input-output linearization. In combination with a discrete state-space observer, this approach can successfully be applied as long as the amplifier driving the loudspeaker is dc-coupled. This paper discusses how ac amplifiers can be used in this context. It will be shown that an exact linearization is in general not possible with ac amplifiers due to insufficient stability of the feedback system. Two approaches will be presented that abandon the pursuit of an exact linearization in favor of stability and yield satisfactory results when implemented on a floating-point digital signal processor.

Some Results on Linear Unbiased Filtering with Polar Measurements

The problem of tracking objects moving in Cartesian space with sensors delivering polar measurements has been under investigation of several researchers for quite some time now. Different proposals for using measurement conversion techniques in combination with a linear Kalman filter have been made. As one possible altennative approach, an (appnoximate) best linear unbiased estimator (BLUE) has been proposed. In this paper, some of these approaches are reinvestigated by means of a common representation form for all covered techniques (that is, including the BLUE filter) that helps analyzing and understanding the general behavior of these estimators. Some notewonthy results are presented. It will be argued that the BLUE filten in its original form may be prone to yielding indefinite estimation error variance matrices and that later variants of this filter do not exhibit this behavior. A new initialization method for these filters will be derived.

Numerical stability properties of passive Runge-Kutta methods

Recently, network-theoretical considerations of numerical integration methods have led to so-called passive Runge-Kutta methods. In this paper, it is shown that these numerical integration methods exhibit a variety of numerical stability properties. For an intuitive understanding, the methods as well as the stability properties and criteria are formulated by means of Kirchhoff networks and the corresponding transfer matrices.

Generation of wave digital structures for connection networks containing ideal transformers

Most standard wave digital filters are derived from passive reference circuits where only parallel and series connections between two-terminal elements occur. In this paper, a framework for the automated generation of wave digital structures is presented where the reference circuit is assumed to comprise arbitrary connection types. It is shown how the representation of the underlying graph by its SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with additional ideal transformers. To this end, suitable replacement graphs are derived such that networks with multi-terminal elements can also be treated with standard separation algorithms.

Improving wave digital simulation by extrapolation techniques

Summary Wave digital simulation principles are known to exhibit excellent numerical stability properties due to their inherent passivity. Yet, the achievable accuracy may not suffice in all applications. In this paper, it will be discussed how extrapolation techniques known from numerical mathematics can be merged with the wave digital concept. The proposed techniquecan be applied to both ordinary and partial differential equations. Astwo examples will show, high numerical accuracy can be obtained this way withoutsacrifycing passivity and the advantageous properties induced by the latter.

Wave digital simulation of electrical networks containing nonlinear dynamical elements-a new approach

Wave digital filter principles are known to be applicable to the numerical solution of many kinds of differential equations. But, when applied to an electrical network containing nonlinear dynamical elements, the resulting algorithm often includes implicit equations. In this paper, a new approach is presented which leaves the underlying wave digital structure unchanged but avoids the task of finding exact solutions to the implicit equations involved.