USING ROBOTIC MODELS TO IMPROVE ESTIMATES OF SENSOR ORIENTATION AND HUMAN MOVEMENT.

## Introduction

Inertial measurement units (IMUs) including accelerometers and gyroscopes are becoming very common and can be found in cell phones, fitness trackers, and other wearable devices. We demonstrate a system that can be used to estimate the distance traveled by a human while walking. We model the human leg as a two-link revolute robot. IMU sensors placed on the thigh and shin provide the required measurement inputs to an extended Kalman filter to estimate state parameters associated with forward motion and walking distance. Additionally, we show that angle estimates from acclerometers can be inaccurate for typical motions and present a method using the same robotic model to correct the accelerometer angle estimate and improve overall orientation estimates at rest and in motion using an extended Kalman filter (EKF).

## Walking Distance Estimate

The first part of our approach involved creating a model for the human leg. In taking a single step forward, the human leg is similar to a two-link robot manipulator with the hip

and knee as two joints. We assign three-dimensional Cartesian reference frames to each joint, as seen in the figure to the left. Frames F0, F1, and F2 are assigned to the hip, knee and foot, respectively. Frame F0 is oriented such that the x-axis is in the direction of motion, the y-axis is up, and the z-axis is out from the hip to the right. The subsequent frames are chosen as per Denavit-Hartenberg (D-H) convention.

We develop an extended Kalman filter to estimate the x and y displacement of F2 (the heel) relative to F0 (the hip) based on gyroscope data measured from two motion sensors placed on the thigh and shin. As the subject walks, we estimate the horizontal (x-axis) displacement of the foot as shown in the figure on the left. Based on the assumption that the person starts walking and stops with their heel in line with their hip, we accumulate all positive displacement to generate the plot on the right. This plot represents total distance walked. The distance estimate for straight line walking is greater than 97% accurate when compared to a Vicon motion capture system.

## Acceleration Correction for Improved Orientation Estimates

The EKF used in the walking distance estimate used the gyroscope only for the measurement. Gyroscopes suffer drift over time and therefore, the accuracy of the system could degrade. This is especially true when there is little to no motion. Accelerometers can be used to estimate orientation based the direction of the gravity vector; but when in motion, accelerometers also measure acceleration due to the motion. Because of the lack of accuracy during motion, the accelerometer angle estimate typically cannot be used for orientation estimates when sensors are in motion.

Our technique solves incoroprates the accelerometer into the the EKF by solving the motion based accelerometer issue in two ways. 1. When the sensor is in motion, we use the robot model to estimate the acceleration that will be caused by the motion of the sensor and subtract this from the accelerometer measurement. 2. We adjust the accelerometer parameter of the measurement noise covariance matrix based on the amount of motion sensed by the gyroscope. Combining these techniques improves the orientation estimate of the sensor. We see a RMSE of 0.0306 radians for this technique. The accelerometer only method, EKF with gyroscope, and EKF with gyroscope and unmodified acceleration have RMSE of 0.718 radians, 0.1011 radians, and 0.1873 radians respectively. The plots below show the results for each of these algorithms for sensor orientation estimation.

## Research Products

Bennett, T.; Jafari, R.; Gans, N., “An extended Kalman filter to estimate human gait parameters and walking distance,” American Control Conference (ACC), 2013 , vol., no., pp.752,757, 17-19 June 2013

Bennett, T.R.; Jafari, R.; Gans, N., “ Motion Based Acceleration Correction for Improved Sensor Orientation Estimates,” Wearable and Implantable Body Sensor Networks (BSN), 2014 11th International Conference on , vol., no., pp.109,114, 16-19 June 2014

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