Disclosed herein are systems and methods for calculating angular acceleration based on inertial data using two or more inertial measurement units (IMUs). The calculated angular acceleration may be used to estimate a position of a wearable head device comprising the IMUs. Virtual content may be presented based on the position of the wearable head device. In some embodiments, a first IMU and a second IMU share a coincident measurement axis.

The invention is a method for estimating and updating the bias of a sensor. After an initialization phase, the method includes the following steps: acquiring a signal (s.sub.k) at a measurement time (t.sub.k), there corresponding to each measurement time a bias (m.sub.k) determined in a preceding iteration or during the initialization and a dispersion threshold (v.sub.th,k) determined in a preceding iteration or during the initialization; associating an analysis time period (t.sub.k) with the measurement time (t.sub.k), and calculating a dispersion indicator (v.sub.k) representing a dispersion of the signals acquired over the analysis time period; comparing the dispersion indicator thus calculated with the dispersion threshold (v.sub.th,k) used in the first step; depending on the comparison, either keeping the bias at an unchanged value or updating the bias; subtracting the bias (m.sub.k) resulting from the preceding step from the signal (s.sub.k) acquired at the measurement time; and incrementing the measurement time (t.sub.k) and reiterating the steps listed above.
When the bias is updated, the dispersion threshold is also updated depending on the dispersion indicator (v.sub.k) calculated at the measurement time.

The invention is a method for estimating and updating the bias of a sensor. After an initialization phase, the method includes the following steps: acquiring a signal (s.sub.k) at a measurement time (t.sub.k), there corresponding to each measurement time a bias (m.sub.k) determined in a preceding iteration or during the initialization and a dispersion threshold (v.sub.th,k) determined in a preceding iteration or during the initialization; associating an analysis time period (t.sub.k) with the measurement time (t.sub.k), and calculating a dispersion indicator (v.sub.k) representing a dispersion of the signals acquired over the analysis time period; comparing the dispersion indicator thus calculated with the dispersion threshold (v.sub.th,k) used in the first step; depending on the comparison, either keeping the bias at an unchanged value or updating the bias; subtracting the bias (m.sub.k) resulting from the preceding step from the signal (s.sub.k) acquired at the measurement time; and incrementing the measurement time (t.sub.k) and reiterating the steps listed above.
When the bias is updated, the dispersion threshold is also updated depending on the dispersion indicator (v.sub.k) calculated at the measurement time.

A jack leveling apparatus utilizes a Hall effect sensor to determine a rate of movement of the jack leveling apparatus. The rate of movement is correlated to loading or unloading of the jack level device. When a load is applied to the jack level, the rate of movement will slow while alternatively, if a load is removed, the rate of movement will increase. Utilizing these values, the controller may also determine the position of the leg of the jack level device.

A method of recognizing obstacles on operation of a vibratory pile driver of a work machine includes monitoring an acceleration signal of the vibratory pile driver during operation of the vibratory pile operator and analyzing the acceleration signal to determine the presence of an obstacle. The acceleration signal may be monitored over a time period which is determined based on an excitation frequency of the vibratory pile driver. The analysis may include comparing negative and positive half-waves of the acceleration signal. Responsive to the analysis indicating an obstacle, a system operator may be alerted, and/or operation of the vibratory pile driver may be adjusted via controller intervention.

A method of recognizing obstacles on operation of a vibratory pile driver of a work machine includes monitoring an acceleration signal of the vibratory pile driver during operation of the vibratory pile operator and analyzing the acceleration signal to determine the presence of an obstacle. The acceleration signal may be monitored over a time period which is determined based on an excitation frequency of the vibratory pile driver. The analysis may include comparing negative and positive half-waves of the acceleration signal. Responsive to the analysis indicating an obstacle, a system operator may be alerted, and/or operation of the vibratory pile driver may be adjusted via controller intervention.

A real acceleration computing unit 3 calculates the real acceleration Gw in the direction of travel of a vehicle by acquiring the velocity V a wheel speed sensor 12 installed in the vehicle detects. A road surface gradient computing unit 5 calculates the inclination of a road surface (road surface gradient 1) from the real acceleration Gw and the accelerations Gx and Gz in the back and forth and up and down directions of the vehicle an acceleration sensor 11 installed in the vehicle detects. A pitching angle computing unit 6 calculates the inclination of the vehicle with respect to the road surface (pitching angle 2) from the real acceleration Gw and the accelerations Gx and Gz.

A real acceleration computing unit 3 calculates the real acceleration Gw in the direction of travel of a vehicle by acquiring the velocity V a wheel speed sensor 12 installed in the vehicle detects. A road surface gradient computing unit 5 calculates the inclination of a road surface (road surface gradient 1) from the real acceleration Gw and the accelerations Gx and Gz in the back and forth and up and down directions of the vehicle an acceleration sensor 11 installed in the vehicle detects. A pitching angle computing unit 6 calculates the inclination of the vehicle with respect to the road surface (pitching angle 2) from the real acceleration Gw and the accelerations Gx and Gz.

A device includes two electrically isolated metalized posts attached in close proximity to each other on a bendable substrate. When the bendable substrate bends concavely with respect to the surface onto which the posts are mounted, the distance between the tops of the two posts decreases. At a fixed bending curvature, the two posts will meet and complete an electrical circuit. The posts comprise a flexible material so that the meeting of the posts has minimal effect on the spring constant or damping coefficient of the harmonic oscillation.

A device includes two electrically isolated metalized posts attached in close proximity to each other on a bendable substrate. When the bendable substrate bends concavely with respect to the surface onto which the posts are mounted, the distance between the tops of the two posts decreases. At a fixed bending curvature, the two posts will meet and complete an electrical circuit. The posts comprise a flexible material so that the meeting of the posts has minimal effect on the spring constant or damping coefficient of the harmonic oscillation.