Step length estimation with wearable sensors using a switched-gain nonlinear observer

This paper focuses on step length estimation using inertial measurement sensors. Accurate step length estimation has a number of useful health applications, including its use in characterizing the postural instability of Parkinson's disease patients. Three different sensor configurations are studied using sensors on the shank and/or thigh of a human subject. The estimation problem has several challenges due to unknown measurement bias, misalignment of the sensors on the body and the desire to use a minimum number of sensors. A nonlinear estimation problem is formulated that aims to estimate shank angle, thigh angle, bias parameters of the inertial sensors and step lengths. A nonlinear observer is designed using Lyapunov analysis and requires solving an LMI to find a stabilizing observer gain. It turns out that global stability over the entire operating region can only be obtained by using switched gains, one gain for each piecewise monotonic region of the nonlinear output function. Experimental results are presented on the performance of the nonlinear observer and compared with gold standard reference measurements from an infrared camera capture system. An innovative technique that utilizes three sensors is shown to provide a step length accuracy nearly equal to that of the four-sensor configuration.