Benjamin Noack

• Professor
• Professor at Otto-von-Guericke University Magdeburg

In the era of burgeoning high-dimensional data, particularly in fields likemedicine, where data collection is increasing, the need for effective feature selectionin machine learning is paramount. Feature selection helps mitigate challengessuch as noise and irrelevant information, leading to a deeper understanding ofresults and improved predictive c...

Over the past two and a half decades, covariance intersection (CI) has provided a means for robust estimation in scenarios where the uncertainty information is incomplete. Estimation in distributed and decentralized data fusion (DDF) settings is typically characterized by having nonzero cross-correlations between the estimates to be merged. Mean-...

This work introduces a flexible and versatile method for the data-efficient yet conservative transmission of covariance matrices, where a matrix element is only transmitted if a triggering condition is satisfied for the element. Here, triggering conditions can be parametrized on a per-element basis, applied simultaneously to yield combined triggeri...

Distributed state estimation and localisation methods have become increasingly popular with the rise of ubiquitous computing, and have led naturally to an increased concern regarding data and estimation privacy. Traditional distributed sensor navigation methods typically involve the leakage of sensor or navigator information by communicating measur...

A key challenge in Bayesian decentralized data fusion is the `rumor propagation' or `double counting' phenomenon, where previously sent data circulates back to its sender. It is often addressed by approximate methods like covariance intersection (CI) which takes a weighted average of the estimates to compute the bound. The problem is that this boun...

Ensembles of convolutional neural networks have shown remarkable results in learning discriminative semantic features for image classification tasks. However, the models in the ensemble often concentrate on similar regions in images. This work proposes a novel method that forces a set of base models to learn different features for a classification...

In this paper, environmental monitoring by mobile robots is considered where expensive or time-consuming sampling has to be carried out in order to obtain a metamodel of the phenomenon investigated. Due to limited resources, often not only a limited number of samples can be taken, but also the cost and time of the traveled distance between the samp...

Convolutional neural networks have shown remarkable ability to learn discriminative semantic features in image recognition tasks. Though, for classification they often concentrate on specific regions in images. This work proposes a novel method that combines variant rich base models to concentrate on different important image regions for classifica...

State estimation via public channels requires additional planning with regards to state privacy and information leakage of involved parties. In some scenarios, it is desirable to allow partial leakage of state information, thus distinguishing between privileged and unprivileged estimators and their capabilities. Existing methods that make this dist...

Information fusion in networked systems poses challenges with respect to both theory and implementation. Limited available bandwidth can become a bottleneck when high-dimensional estimates and associated error covariance matrices need to be transmitted. Compression of estimates and covariance matrices can endanger desirable properties like unbiased...

We present a novel Riemannian approach for planar pose graph optimization problems. By formulating the cost function based on the Riemannian metric on the manifold of dual quaternions representing planar motions, the nonlinear structure of the SE(2) group is inherently considered. To solve the on-manifold least squares problem, a Riemannian Gauss-N...

The exploitation of dependencies between state estimates from distributed trackers plays a vital role in so-called track-to-track fusion and has been extensively studied for state estimates with the same state space. In contrast, dependencies are often neglected when considering heterogeneous state estimates referring to different state spaces, sin...

Networks consisting of several spatially distributed sensor nodes are useful in many applications. While distributed processing of information can be more robust and flexible than centralized filtering, it requires careful consideration of dependencies between local state estimates. This paper proposes an algorithm to keep track of dependencies in...

Fast covariance intersection is a widespread technique for state estimate fusion in sensor networks when cross-correlations are not known and fast computations are desired. The common requirement of sending estimates from one party to another during fusion forfeits local privacy. Current secure fusion algorithms rely on encryption schemes that do n...

Optical belt sorters are a versatile means to sort bulk materials. In previous work, we presented a novel design of an optical belt sorter, which includes an area scan camera instead of a line scan camera. Line scan cameras, which are well-established in optical belt sorting, only allow for a single observation of each particle. Using multitarget t...

Sensor-based sorting is a well-established single particle separation technology. It has found wide application as a quality assurance and control approach in food processing, mining, and recycling. In order to assure high sorting quality, a high degree of control of the motion of individual particles contained in the material stream is required. S...

Sensor-based sorting is a machine vision application that has found industrial application in various fields. An accept-or-reject task is executed by separating a material stream into two fractions. Current systems use line-scanning sensors, which is convenient as the material is perceived during transportation. However, line-scanning sensors yield...

We present a novel Riemannian approach for planar pose graph optimization problems. By formulating the cost function based on the Riemannian metric on the manifold of dual quaternions representing planar motions, the nonlinear structure of the SE(2) group is inherently considered. To solve the on-manifold least squares problem, a Riemannian Gauss–...

Event-based communication and state estimation offer the potential to improve resource utilization in networked sensor and control systems significantly. Sensor nodes can trigger transmissions when data are deemed useful for the remote estimation units. To improve the estimation performance, the remote estimator can exploit the implicit information...

The exploitation of dependencies between state estimates from distributed trackers plays a vital role in so-called track-to-track fusion and has been extensively studied for state estimates with the same state space. In contrast, dependencies are often neglected when considering heterogeneous state estimates referring to different state spaces, sin...

We present a novel Riemannian approach for planar pose graph optimization problems. By formulating the cost function based on the Riemannian metric on the manifold of dual quaternions representing planar motions, the nonlinear structure of the SE(2) group is inherently considered. To solve the on-manifold least squares problem, a Riemannian Gauss-N...

Decentralized data fusion is a challenging task even for linear estimation problems. Nonlinear estimation renders data fusion even more difficult as dependencies among the nonlinear estimates require complicated parameterizations. It is nearly impossible to reconstruct or keep track of dependencies. Therefore, conservative approaches have become a...

We propose a geometry-driven deterministic sampling method for Bingham distributions in arbitrary dimensions. With flexibly adjustable sampling sizes, the novel scheme can generate equally weighted samples that satisfy requirements of the unscented transform and approximate higher-order shape information of the Bingham distribution. By leveraging r...

Sensor networks allow robust and precise estimation by fusing estimates from several distributed sensor nodes. Because of the often limited communication resources, a trade-off between the amount of information communicated and the quality of the fusion result has to be made. On the one hand, obtaining the optimal fusion result often needs an infea...

Distributing workload between sensor nodes is a practical solution to monitor large-scale phenomena. In doing so, the system can be split into smaller subsystems that can be estimated and controlled more easily. While current state-of-the-art fusion methods for distributed estimation assume the fusion of estimates referring to the full dimension of...

With modern communication technology, sensors, estimators, and controllers can be pushed apart to distribute intelligence over wide distances. Instead of congesting channels by periodic data transmissions, smart sensors can decide on their own whether data are worth transmitting. This paper studies event-based transmissions from sensor to estimator...

Using a network of spatially distributed sensors to track a moving object can be a challenging task. In applications with limited communication between sensor nodes and packet loss, it may be impossible to process measurements from these distributed sensor nodes in a central unit. Therefore, it is often necessary to use only the locally available m...

In this paper, we propose the Progressive Bingham Filter (PBF), a novel stochastic filtering algorithm for nonlinear spatial orientation estimation. As an extension of the orientation filter previously proposed only for the identity measurement model based on the Bingham distribution, our method is able to handle arbitrary measurement models. Inste...

State-of-the-art optical sorting systems suffer from delays between the particle detection and separation stage, during which the material movement is not accounted for. Commonly line scan cameras, using simple assumptions to predict the future particle movement, are employed. In this study, a novel prediction approach is presented, where an area s...

Transformation of a random variable is a common need in a design of many algorithms in signal processing, automatic control, and fault detection. Typically, the design is tied to an assumption on a probability density function of the random variable, often in the form of the Gaussian distribution. The assumption may be, however, difficult to be met...

In this article, we are concerned with state estimation in Networked Control Systems where both control inputs and measurements are transmitted over networks which are lossy and introduce random transmission delays. We focus on the case where acknowledgment packets transmitted by the actuator upon reception of applicable control inputs are also sub...

In this paper, we consider Networked Control Systems where the transmission of sensor data is restricted in terms of a fixed communication budget due to the limited capacity of the underlying network. Therefore, the remote estimator cannot be supplied with measurements every time step, which impacts the accuracy of the estimates and consequently th...

For multisensor data fusion, distributed state estimation techniques that enable a local processing of sensor data are the means of choice in order to minimize storage and communication costs. In particular, a distributed implementation of the optimal Kalman filter has recently been developed. A significant disadvantage of this algorithm is that th...

Automated optical sorting systems are important devices in the growing field of bulk solids handling. The initial sorter calibration and the precise optical sorting of many materials is still very time consuming and difficult. A numerical model of an automated optical belt sorter is presented in this study. The sorter and particle interaction is de...

Utilizing parallel algorithms is an established way of increasing performance in systems that are bound to real-time restrictions. Sensor-based sorting is a machine vision application for which firm real-time requirements need to be respected in order to reliably remove potentially harmful entities from a material feed. Recently, employing a predic...

Optical belt sorters can be used to sort a large variety of bulk materials. By the use of sophisticated algorithms , the performance of the complex machinery can be further improved. Recently, we have proposed an extension to industrial optical belt sorters that involves tracking the individual particles on the belt using an area scan camera. If th...

In this paper, we consider state estimation in Networked Control Systems where both control inputs and measurements are transmitted via networks which are lossy and introduce random transmission delays. In contrast to the common notion of TCP-like communication, where successful transmissions are acknowledged instantaneously and without losses, we...

Decentralized data fusion is a challenging task. Either it is too difficult to maintain and track the information required to perform fusion optimally, or too much information is discarded to obtain informative fusion results. A well-known solution is Covariance Intersection, which may provide too conservative fusion results. A less conservative al...

Event-based sampling of sensor signals has become a mature alternative to time-periodic sampling completed with solutions for event-based estimation and control. Among those solutions there is a class of estimators exploiting the fact that an event was not triggered. Not receiving a new measurement is then interpreted as a sensor signal that has no...

State-of-the-art optical belt sorters commonly employ line scan cameras and use simple assumptions to predict each particle's movement, which is required for the separation process. Previously, we have equipped an experimental optical belt sorter with an area scan camera and were able to show that tracking the particles of the bulk material results...

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 correlatio...

Sensor-based sorting provides state-of-the-art solutions for sorting of cohesive, granular materials. Systems are tailored to a task at hand, for instance by means of sensors and implementation of data analysis. Conventional systems utilize scanning sensors which do not allow for extraction of motionrelated information of objects contained in a mat...

Sensor-based sorting provides state-of-the-art solutions for sorting cohesive, granular materials. Typically, involved sensors, illumination, implementation of data analysis and other components are designed and chosen according to the sorting task at hand. A common property of conventional systems is the utilization of scanning sensors. However, t...

State-of-the-art sensor-based sorting systems provide solutions to sort various products according to quality aspects. Such systems face the challenge of an existing delay between perception and separation of the material. To reliably predict an object's position when reaching the separation stage, information regarding its movement needs to be der...

In this paper, we propose an algorithm for tracking mobile devices (such as smartphones, tablets, or smartglasses) in a known environment for augmented reality applications. For this purpose, we interpret the environment as an extended object with a known shape, and design likelihoods for different types of image features, using association models...

Multitarget tracking problems arise in many real-world applications. The performance of the utilized algorithm strongly depends both on how the data association problem is handled and on the suitability of the motion models employed. Especially the motion models can be hard to validate. Previously, we have proposed to use multitarget tracking to im...

In this paper, we present a novel approach to optimally fuse estimates in distributed state estimation for linear and nonlinear systems. An optimal fusion requires the knowledge of the correct correlations between locally obtained estimates. The naive and intractable way of calculating the correct correlations would be to exchange information about...

Optical sorters are important devices in the processing and handling of the globally growing material streams. The precise optical sorting of many bulk solids is still difficult due to the great technical effort necessary for transport and flow control. In this study, particle separation with an automated optical belt sorter is modeled numerically....

Visual properties are powerful features to reliably classify bulk materials, thereby allowing to detect defect or low quality particles. Optical belt sorters are an established technology to sort based on these properties, but they suffer from delays between the simultaneous classification and localization step and the subsequent separation step. T...

Optical belt sorters are a versatile, state-of-the-art technology to sort bulk materials that are hard to sort based on only nonvisual properties. In this paper, we propose an extension to current optical belt sorters that involves replacing the line camera with an area camera to observe a wider field of view, allowing us to observe each particle o...

In many dynamic systems, the evolution of the state is subject to specific constraints. In general, constraints cannot easily be integrated into the prediction-correction structure of the Kalman filter algorithm. Linear equality constraints are an exception to this rule and have been widely used and studied as they allow for simple closed-form expr...

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 min...

A common approach to attack the simultaneous localization and mapping problem (SLAM) is to consider factor-graph formulations of the underlying filtering and estimation setup. While Kalman filter-based methods provide an estimate for the current pose of a robot and all landmark positions, graph-based approaches take not only the current pose into a...

Distributed Kalman filtering aims at optimizing an estimate at a fusion center based on information that is gathered in a sensor network. Recently, an exact solution based on local estimation tracks has been proposed and an extension to cope with packet losses has been derived. In this contribution, we generalize both algorithms to packet delays. T...

The problem of fusing state estimates is encountered in many network-based multi-sensor applications. The majority of distributed state estimation algorithms are designed to provide multiple estimates on the same state, and track-to-track fusion then refers to the task of combining these estimates. While linear fusion only requires the joint cross-...

The Covariance Intersection algorithm linearly combines estimates when the cross-correlations between their errors are unknown. It provides a fused estimate and an upper bound of the corresponding mean square error matrix. The weights of the linear combination are designed in order to minimise the upper bound. This paper analyses the optimal weight...

To reduce the amount of data transfer in networked systems measurements are usually taken only when an event occurs rather than periodically in time. However, a fundamental assessment on the response of estimation algorithms receiving event sampled measurements is not available. This research presents such an analysis when new measurements are samp...

Distributed implementations of state estimation algorithms generally have in common that each node in a networked system computes an estimate on the entire global state. Accordingly, each node has to store and compute an estimate of the same state vector irrespective of whether its sensors can only observe a small part of it. In particular, the tas...

In this paper, a sample representation of the estimation error is utilized to reconstruct the joint covariance matrix in a distributed estimation system. 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. This w...

State estimation techniques for centralized, distributed, and decentralized systems are studied. An easy-to-implement state estimation concept is introduced that generalizes and combines basic principles of Kalman filter theory and ellipsoidal calculus. By means of this method, stochastic and set-membership uncertainties can be taken into considera...

State fusion is a method for merging multiple estimates of the same state into a single fused estimate. Dealing with multiple estimates is one of the main concerns in distributed state estimation, where an estimated value of the desired state vector is computed in each node of a networked system. Most solutions for distributed state estimation curr...

The federated Kalman filter embodies an efficient and easy-to-implement solution for linear distributed estimation problems. Data from independent sensors can be processed locally and in parallel on different nodes without running the risk of erroneously ignoring possible dependencies. The underlying idea is to counteract the common process noise i...

For systems suffering from different types of uncertainties, finding criteria for validating measurements can be challenging. In this paper, we regard both stochastic Gaussian noise with full or imprecise knowledge about correlations and unknown but bounded errors. The validation problems arising in the individual and combined cases are illustrated...

In this paper, linear distributed estimation is revisited on the basis of the hypothesizing distributed Kalman filter and equations for a flexible application of the algorithm are derived. We propose a new approximation for the mean-squared-error matrix and present techniques for automatically improving the hypothesis about the global measurement m...

To reduce the amount of data transfer in networked systems, measurements are usually taken only when an event occurs rather than periodically in time. However, this complicates estimation problems considerably as it is not guaranteed that new sensor data will be sampled. Therefore, an existing state estimator is extended so to cope with event-based...