Cooperative Robust Estimation with Local Performance Guarantees

The paper considers the problem of cooperative estimation for a linear uncertain plant observed by a network of communicating sensors. We take a novel approach by treating the filtering problem from the view point of local sensors while the network interconnections are accounted for via an uncertain signals modelling of estimation performance of other nodes. That is, the information communicated between the nodes is treated as the true plant information subject to perturbations, and each node is endowed with certain believes about these perturbations during the filter design. The proposed distributed filter achieves a suboptimal $H_\infty$ consensus performance. Furthermore, local performance of each estimator is also assessed given additional constraints on the performance of the other nodes. These conditions are shown to be useful in tuning the desired estimation performance of the sensor network.Comment: 2016 American Control Conference, Boston, 201

Feature extraction using extrema sampling of discrete derivatives for spike sorting in implantable upper-limb neural prostheses

Next generation neural interfaces for upper-limb (and other) prostheses aim to develop implantable interfaces for one or more nerves, each interface having many neural signal channels that work reliably in the stump without harming the nerves. To achieve real-time multi-channel processing it is important to integrate spike sorting on-chip to overcome limitations in transmission bandwidth. This requires computationally efficient algorithms for feature extraction and clustering suitable for low-power hardware implementation. This paper describes a new feature extraction method for real-time spike sorting based on extrema analysis (namely positive peaks and negative peaks) of spike shapes and their discrete derivatives at different frequency bands. Employing simulation across different datasets, the accuracy and computational complexity of the proposed method are assessed and compared with other methods. The average classification accuracy of the proposed method in conjunction with online sorting (O-Sort) is 91.6%, outperforming all the other methods tested with the O-Sort clustering algorithm. The proposed method offers a better tradeoff between classification error and computational complexity, making it a particularly strong choice for on-chip spike sorting

Orthogonality preserving property for pairs of operators on Hilbert C∗C^*-modules

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner product structure of a Hilbert $C^*$-module is determined essentially by the module structure and by the orthogonality structure, pairs of linear and local orthogonality-preserving mappings are investigated, not a priori bounded. The intuition is that most often $C^*$-linearity and boundedness can be derived from the settings under consideration. In particular, we obtain that if $\mathscr{A}$ is a $C^{*}$-algebra and $T, S:\mathscr{E}\longrightarrow \mathscr{F}$ are two bounded ${\mathscr A}$-linear mappings between full Hilbert $\mathscr{A}$-modules, then $\langle x, y\rangle = 0$ implies $\langle T(x), S(y)\rangle = 0$ for all $x, y\in \mathscr{E}$ if and only if there exists an element $\gamma$ of the center $Z(M({\mathscr A}))$ of the multiplier algebra $M({\mathscr A})$ of ${\mathscr A}$ such that $\langle T(x), S(y)\rangle = \gamma \langle x, y\rangle$ for all $x, y\in \mathscr{E}$. In particular, for adjointable operators $S$ we have $T=(S^*)^{-1}$, and any bounded invertible module operator $T$ may appear. Varying the conditions on the mappings $T$ and $S$ we obtain further affirmative results for local operators and for pairs of a bounded and of an unbounded module operator with bounded inverse, among others. Also, unbounded operators with disjoint ranges are considered. The proving techniques give new insights.Comment: 23 pages, In this last revision several new examples are added and some minor changes appeared in the text. To appear in Aequat. Mat

Nonlinear Attitude Filtering: A Comparison Study

This paper contains a concise comparison of a number of nonlinear attitude filtering methods that have attracted attention in the robotics and aviation literature. With the help of previously published surveys and comparison studies, the vast literature on the subject is narrowed down to a small pool of competitive attitude filters. Amongst these filters is a second-order optimal minimum-energy filter recently proposed by the authors. Easily comparable discretized unit quaternion implementations of the selected filters are provided. We conduct a simulation study and compare the transient behaviour and asymptotic convergence of these filters in two scenarios with different initialization and measurement errors inspired by applications in unmanned aerial robotics and space flight. The second-order optimal minimum-energy filter is shown to have the best performance of all filters, including the industry standard multiplicative extended Kalman filter (MEKF)

Analytic height correlation function of rough surfaces derived from light scattering

We derive an analytic expression for the height correlation function of a rough surface based on the inverse wave scattering method of Kirchhoff theory. The expression directly relates the height correlation function to diffuse scattered intensity along a linear path at fixed polar angle. We test the solution by measuring the angular distribution of light scattered from rough silicon surfaces, and comparing extracted height correlation functions to those derived from atomic force microscopy (AFM). The results agree closely with AFM over a wider range of roughness parameters than previous formulations of the inverse scattering problem, while relying less on large-angle scatter data. Our expression thus provides an accurate analytical equation for the height correlation function of a wide range of surfaces based on measurements using a simple, fast experimental procedure.Comment: 6 pages, 5 figures, 1 tabl