Marc Reinhardt

The Hypothesizing Distributed Kalman Filter

This paper deals with distributed information processing in sensor networks. We propose the Hypothesizing Distributed Kalman Filter that incorporates an assumption of the global measurement model into the distributed estimation process. The procedure is based on the Distributed Kalman Filter and inherits its optimality when the assumption about the global measurement uncertainty is met. Recursive formulas for local processing as well as for fusion are derived. We show that the proposed algorithm yields the same results, no matter whether the measurements are processed locally or globally, even when the process noise is not negligible. For further processing of the estimates, a consistent bound for the error covariance matrix is derived. All derivations and explanations are illustrated by means of a new classification scheme for estimation processes.

Minimum Covariance Bounds for the Fusion under Unknown Correlations

One of the key challenges in distributed linear estimation is the systematic fusion of estimates. While the fusion gains that minimize the mean squared error of the fused estimate for known correlations have been established, no analogous statement could be obtained so far for unknown correlations. In this contribution, we derive the gains that minimize the bound on the true covariance of the fused estimate and prove that Covariance Intersection (CI) is the optimal bounding algorithm for two estimates under completely unknown correlations. When combining three or more variables, the CI equations are not necessarily optimal, as shown by a counterexample.

Decentralized data fusion with inverse covariance intersection

In distributed and decentralized state estimation systems, fusion methods are employed to systematically combine multiple estimates of the state into a single, more accurate estimate. An often encountered problem in the fusion process relates to unknown common information that is shared by the estimates to be fused and is responsible for correlations. If the correlation structure is unknown to the fusion method, conservative strategies are typically pursued. As such, the parameterization introduced by the ellipsoidal intersection method has been a novel approach to describe unknown correlations, though suitable values for these parameters with proven consistency have not been identified yet. In this article, an extension of ellipsoidal intersection is proposed that guarantees consistent fusion results in the presence of unknown common information. The bound used by the novel approach corresponds to computing an outer ellipsoidal bound on the intersection of inverse covariance ellipsoids. As a major advantage of this inverse covariance intersection method, fusion results prove to be more accurate than those provided by the well-known covariance intersection method.

Generalized covariance intersection based on noise decomposition

In linear decentralized estimation, several nodes concurrently aim to estimate the state of a common phenomenon by means of local measurements and data exchanges. In this contribution, an efficient algorithm for consistent estimation of linear systems in sensor networks is derived. The main theorems generalize Covariance Intersection by means of an explicit consideration of individual noise terms. We apply the results to linear decentralized estimation and obtain covariance bounds with a scalable precision between the exact covariances and the bounds provided by Covariance Intersection.

Reconstruction of joint covariances in networked linear systems

We propose a sample representation of estimation errors that is utilized to reconstruct the joint covariance in distributed estimation systems. The key idea is to sample uncorrelated and fully correlated noise according to different techniques at local estimators without knowledge about the processing of other nodes in the network. In this way, the correlation between estimates is inherently linked to the representation of the corresponding sample sets. We discuss the noise processing, derive key attributes, and evaluate the precision of the covariance estimates.

Optimal Sequence-Based Control and Estimation of Networked Linear Systems

Abstract In this paper, a unified approach to sequence-based control and estimation of linear networked systems with multiple sensors is proposed. Time delays and data losses in the controller-actuator link are compensated by sending sequences of control inputs. The sequence-based design paradigm is further extended to the sensor-controller connections without increasing the load of the network. In this context, we present a recursive solution based on the Hypothesizing Distributed Kalman Filter (HKF) that is included in the overall sequence-based controller design. Zusammenfassung Vorgestellt wird ein einheitlicher Ansatz zur sequenzbasierten Regelung digital vernetzter, linearer Systeme mit mehreren Sensoren. Übertragungsverzögerungen und Datenverluste zwischen Regler und Aktor werden durch das Senden ganzer Regelungssequenzen kompensiert. Weiterhin wird die sequenzbasierte Regelungsphilosophie auf den Datenkanal zwischen Sensoren und Regler übertragen, ohne dabei die Netzwerklast zu erhöhen. Hierzu wird eine Erweiterung des sogenannten Hypothesizing Distributed Kalman Filter (HKF) vorgestellt und in den übergeordneten sequenzbasierten Regelungsentwurf integriert.

Decentralized control based on globally optimal estimation

A new method for globally optimal estimation in decentralized sensor-networks is applied to the decentralized control problem. The resulting approach is proven to be optimal when the nodes have access to all information in the network. More precisely, we utilize an algorithm for optimal distributed estimation in order to obtain local estimates whose combination yields the globally optimal estimate. When the interconnectivity is high, the local estimates are almost optimal, which motivates the application of the principle of separation. Thus, we optimize the controller and finally obtain a flexible algorithm, whose quality is evaluated in different scenarios. In applications where the strong requirements on a perfect communication cannot be guaranteed, we derive quality bounds by help of a detailed evaluation of the algorithm. When information is regularly exchanged, it is demonstrated that the algorithm performs almost optimally and therefore, offers system designers a flexible and easy to implement approach. The field of applications lies within the area of strongly networked systems, in particular, when communication disturbances cannot be foreseen or when the network structure is too complicated to apply optimized regulators.