This paper formulates the attitude filtering problem as a nonlinear stochastic filter problem evolved directly on the Special Orthogonal Group SO (3). One of the traditional potential functions for nonlinear deterministic complimentary filters is studied and examined against angular velocity measurements corrupted with noise. This work demonstrates that the careful selection of the attitude potential function allows to attenuate the noise associated with the angular velocity measurements and results into superior convergence properties of estimator and correction factor. The problem is formulated as a stochastic problem through mapping SO (3) to Rodriguez vector parameterization. Two nonlinear stochastic complimentary filters are developed on SO (3). The first stochastic filter is driven in the sense of Ito and the second one considers Stratonovich. The two proposed filters guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood of the origin. Simulation results are presented to illustrate the effectiveness of the proposed filters considering high level of uncertainties in angular velocity as well as body-frame vector measurements.

We employed a novel action potential detection and classification technique to study the relationship between the recruitment of sympathetic action potentials (i.e., neurons) and the size of integrated sympathetic bursts in human muscle sympathetic nerve activity (MSNA). Multifiber postganglionic sympathetic nerve activity from the common fibular nerve was collected using microneurography in 10 healthy subjects at rest and during activation of sympathetic outflow using lower body negative pressure (LBNP). Burst occurrence increased with LBNP. Integrated burst strength (size) varied from 0.22 ± 0.07 V at rest to 0.28 ± 0.09 V during LBNP. Sympathetic burst size (i.e., peak height) was directly related to the number of action potentials within a sympathetic burst both at baseline (r = 0.75 ± 0.13; P < 0.001) and LBNP (r = 0.75 ± 0.12; P < 0.001). Also, the amplitude of detected action potentials within sympathetic bursts was directly related to the increased burst size at both baseline (r = 0.59 ± 0.16; P < 0.001) and LBNP (r = 0.61 ± 0.12; P < 0.001). In addition, the number of detected action potentials and the number of distinct action potential clusters within a given sympathetic burst were correlated at baseline (r = 0.7 ± 0.1; P < 0.001) and during LBNP (r = 0.74 ± 0.03; P < 0.001). Furthermore, action potential latency (i.e., an inverse index of neural conduction velocity) was decreased as a function of action potential size at baseline and LBNP. LBNP did not change the number of action potentials and unique clusters per sympathetic burst. It was concluded that there exists a hierarchical pattern of recruitment of additional faster conducting neurons of larger amplitude as the sympathetic bursts become stronger (i.e., larger amplitude bursts). This fundamental pattern was evident at rest and was not altered by the level of baroreceptor unloading applied in this study.

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This paper proposes two novel nonlinear attitude filters evolved directly on the Special Orthogonal Group SO (3) able to ensure prescribed measures of transient and steadystate performance. The tracking performance of the normalized Euclidean distance of attitude error is trapped to initially start within a large set and converge systematically and asymptotically to the origin from almost any initial condition. The convergence rate is guaranteed to be less than the prescribed value and the steady-state error does not exceed a predefined small value. The first filter uses a set of vectorial measurements with the need for attitude reconstruction. The second filter does not require attitude reconstruction and instead uses only a rate gyroscope measurement and two or more vectorial measurements. These filters provide good attitude estimates with superior convergence properties and can be applied to measurements obtained from low cost inertial measurement units (IMUs). Simulation results illustrate the robustness and effectiveness of the proposed attitude filters with guaranteed performance considering high level of uncertainty in angular velocity along with body-frame vector measurements.