Nonlinear stochastic dynamical systems are commonly used to model physical processes. For linear and Gaussian systems, the Kalman filter is optimal in minimum mean squared error sense. However, for nonlinear or non-Gaussian systems, the estimation of states or parameters is a challenging problem. Furthermore, it is often required to process data online. Therefore, apart from being accurate, the feasible estimation algorithm also needs to be fast. In this paper, we review Bayesian filters that possess the aforementioned properties. Each filter is presented in an easy way to implement algorithmic form. We focus on parametric methods, among which we distinguish three types of filters: filters based on analytical approximations (extended Kalman filter, iterated extended Kalman filter), filters based on statistical approximations (unscented Kalman filter, central difference filter, Gauss-Hermite filter), and filters based on the Gaussian sum approximation (Gaussian sum filter). We discuss each of these filters, and compare them with illustrative examples.

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Objective The aim of this study was to compare handrim wheelchair propulsion technique between individuals with spinal cord injury with and without shoulder pain. Design A cross-sectional study including 38 experienced handrim wheelchair users with spinal cord injury was conducted. Participants were divided into the “shoulder pain” (n = 15) and “no-shoulder pain” (n = 23) groups using the Local Musculoskeletal Discomfort scale. Kinetic and spatiotemporal aspects of handrim wheelchair propulsion during submaximal exercise on a motor-driven treadmill were analyzed. Data were collected using a measurement wheel instrumented with three-dimensional force sensors. Results After correction for confounders (time since injury and body height), linear regression analyses showed that the pain group had a 0.30-sec (95% confidence interval, −0.5 to −0.1) shorter cycle time, 0.22-sec (95% confidence interval, −0.4 to −0.1) shorter recovery time, 15.6 degrees (95% confidence interval, −27.4 to −3.8) smaller contact angle, and 8% (95% confidence interval, −15 to 0) lower variability in work per push compared with the no-pain group. Other parameters did not differ between groups. Conclusions This study indicates that individuals with spinal cord injury who experience shoulder pain propel their handrim wheelchair kinematically differently from individuals with spinal cord injury without shoulder pain. This difference in propulsion technique might be a pain-avoiding mechanism aimed at decreasing shoulder range of motion.

For automation of managed pressure drilling (MPD) to succeed, the automation system needs access to accurate measurement data and the ability to translate this into a correct representation of reality in the well. However, inaccuracies due to calibration problems and errors or omissions in manually entered data may combine with spurious behavior in the control model to make the automation system unreliable. This study presents a novel control scheme for automated MPD that addresses the problem of model reliability by using multiple control models to provide optimal control moves, even with the failure of one or two models. This work simulates the ability to optimize MPD operations with realistic measurement signals using Model Predictive Control (MPC) with a range of model types. Further, it provides a robust automated MPD system to reduce interruptions to drilling operations. This work makes use of a high fidelity dynamic well bore model in addition to low order and empirical control models. The three controllers feed into a switch that selects the best available controller recommendation and allows for a seamless transition between controllers. The switch control scheme enables automated switching between the controllers in the event of one or two models failing and also allows for the tuning and troubleshooting of one model while the others continue to run, all without any interruption to the drilling process. One of the key innovations in the ensemble switch is the seamless transition between controllers. This is accomplished by using the current process manipulated variable values as initial values for the optimization routines in the model predictive controllers that are not actively used to control the well. The strategy is tested in common drilling situations. Two typical drilling scenarios are simulated: normal drilling operations and a pipe connection procedure. The validity of the novel control structure in each scenario is verified through simulated outliers, drift, and noise, as well as simulated controller failure and lack of optimal solution convergence. The controller is able to maintain bit pressure within +/− 1 bar of the 400 bar set point during normal drilling operations despite temporary signal loss and poor data quality. Also, the bit pressure is held within +/− 5 bar of the 340 bar set point during a pipe connection procedure with no bit pressure measurements available to the controller. The techniques presented here can be used for more robust and stable automated MPD. Moreover, multiple models provide benefits that are typically associated with improved reliability due to hardware and safety systems redundancy allowing drilling to continue with fewer interruptions.