Low-Cost Numerical Method for Solving a Coefficient Inverse Problem for the Wave Equation in Three-Dimensional Space

2018 ◽  
Vol 58 (4) ◽  
pp. 548-561 ◽  
Author(s):  
A. B. Bakushinskii ◽  
A. S. Leonov
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Numerical Method ◽  
Dimensional Space ◽  
Low Cost ◽  
Three Dimensional ◽  
Coefficient Inverse Problem ◽  
Three Dimensional Space

scholarly journals Design and Implementation of a 3-Dimensional Attitudes Estimator Device using Low Cost Accelerometer & Gyroscope with Microcontroller IDE

2020 ◽  
Vol 12 (2) ◽  
pp. 151-161
Author(s):  
M. RAJA ◽  
Ugur GUVEN ◽  
Kartikay SINGH
Keyword(s):  
Dimensional Space ◽  
Low Cost ◽  
Three Dimensional ◽  
3 Dimensional ◽  
Aerospace Applications ◽  
Vector Quantity ◽  
Measurement Units ◽  
Fixed Axis ◽  
The Stability ◽  
Three Dimensional Space

Navigation and guidance systems for most automobile as well as aerospace applications require a coupled chip setup known as Inertial Measurement Units (IMU) which, depending on the degree of freedoms, contains a Gyroscope (for maintaining orientation and angular velocity), Accelerometers (to determine acceleration in the respective direction) and a Magnetometer (to determine the respective magnetic fields). In the three-dimensional space, any required rotation analysis is limited to the coordinate systems and all subtended angles in either direction must be defined by a fixed axis to effectively estimate the stability and to define all the attitude estimates needed to compile different rotations and orientations. The Quaternions are mathematical notations used for defining rotations and orientation in three-dimensional space. The simplest terms Quaternions are impossible to visualize in a three-dimensional space; the first three terms will be identical to the coordinate system, but through Quaternions another vector quantity is added into the equations, which may in fact underline how we can account for all rotational quantities. The fundamental analysis of these components different applications for various fields is proposed.

scholarly journals A New Perspective on Low-Cost MEMS-Based AHRS Determination

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1383
Author(s):  
Neda Navidi ◽  
Rene Landry
Keyword(s):  
Reference System ◽  
Dimensional Space ◽  
Low Cost ◽  
Three Dimensional ◽  
Navigation Systems ◽  
Adaptive Kalman Filter ◽  
Initial Attitude ◽  
New Perspective ◽  
And Control ◽  
Three Dimensional Space

Attitude and heading reference system (AHRS) is the term used to describe a rigid body’s angular orientation in three-dimensional space. This paper describes an AHRS determination and control system developed for navigation systems by integrating gyroscopes, accelerometers, and magnetometers signals from low-cost MEMS-based sensors in a complementary adaptive Kalman filter. AHRS estimation based on the iterative Kalman filtering process is required to be initialized first. A new method for AHRS initialization is proposed to improve the accuracy of the initial attitude estimates. Attitude estimates derived from the initialization and iterative adaptive filtering processes are compared with the orientation obtained from a high-end reference system. The improvement in the accuracy of the initial orientation as significant as 45% is obtained from the proposed method as compared with other selected techniques. Additionally, the computational process is reduced by 96%.

scholarly journals Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure

2019 ◽  
pp. 12-17
Author(s):  
I. M. Bodnarchuk
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Mild Solution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Absolute Value ◽  
Stochastic Measure ◽  
The Cauchy Problem ◽  
Three Dimensional Space ◽  
General Stochastic

We study the Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.

scholarly journals TIMESTAMP OFFSET DETERMINATION BETWEEN AN ACTUATED LASER SCANNER AND ITS CORRESPONDING MOTOR

2017 ◽  
Vol IV-1/W1 ◽  
pp. 99-106 ◽  
Author(s):  
R. Voges ◽  
C. S. Wieghardt ◽  
B. Wagner
Keyword(s):  
Data Acquisition ◽  
Point Cloud ◽  
Dimensional Space ◽  
Low Cost ◽  
Three Dimensional ◽  
Laser Scanner ◽  
3D Data ◽  
Laser Scanners ◽  
Slam Algorithm ◽  
Three Dimensional Space

Motor actuated 2D laser scanners are key sensors for many robotics applications that need wide ranging but low cost 3D data. There exist many approaches on how to build a 3D laser scanner using this technique, but they often lack proper synchronization for the timestamps of the actuator and the laser scanner. However, to transform the measurement points into three-dimensional space an appropriate synchronization is mandatory. Thus, we propose two different approaches to accomplish the goal of calculating timestamp offsets between laser scanner and motor prior to and after data acquisition. Both approaches use parts of a SLAM algorithm but apply different criteria to find an appropriate solution. While the approach for offset calculation prior to data acquisition exploits the fact that the SLAM algorithm should not register motion for a stationary system, the approach for offset calculation after data acquisition evaluates the perceived clarity of a point cloud created by the SLAM algorithm. Our experiments show that both approaches yield the same results although operating independently on different data, which demonstrates that the results reflect reality with a high probability. Furthermore, our experiments exhibit the significance of a proper synchronization between laser scanner and actuator.

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