Mapping prior information onto LMI eigenvalue-regions for discrete-time subspace identification

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding LMI regions. In this paper, first we argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constraint the possible locations of the eigenvalues of the discrete-time model. Then, we show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.Comment: Under revie

A low-cost wireless system of inertial sensors to postural analysis during human movement

The dynamics of the human body has generated considerable recent research interest among scientist devoted to reducing the number of injuries and for performance improvement. In these studies, the investigation is usually addressed by means of commercial devices based on video recordings. However, these systems based on video recordings are usually expensive and require suitable laboratories for their use, which makes it unfeasible to collect data for activities outside controlled environments. In this work, we have shown that it is possible to present similar results with a much lower sampling rate, focusing on the evaluation of minimum and maximum values of the gait. As a result, it has been possible to develop a wearable, compact, portable, low-cost, wireless and embedded system to simultaneously analyze the three-dimensional angular position in eight points. This technology can be used in many sorts of environments. It is also possible to access information in real time with reliable and accurate measurements by means of simple modelling for the use of fusion techniques implemented in the microcontroller. Tests were conducted to evaluate the metrological characteristics of the system using the Complementary Filter (CF) and the Kalman Filter (KF). An algorithm of evolutionary strategies tuned both filters, providing errors of less than 5% for static situations in the measurement of the angular position over the entire system utilization range. Our results have been compared with the commercial system Qualisys Motion-Capture. The statistical method elaborated by Bland and Altman has been used. We have found our method yields a motion analyses in good agreement with results using post-processed video