Angular Rate Estimation Using a Distributed Set of Accelerometers

A distributed set of accelerometers based on the minimum number of 12 accelerometers allows for computation of the magnitude of angular rate without using the integration operation. However, it is not easy to extract the magnitude of angular rate in the presence of the accelerometer noises, and even worse, it is difficult to determine the direction of a rotation because the angular rate is present in its quadratic form within the inertial measurement system equations. In this paper, an extended Kalman filter scheme to correctly estimate both the direction and magnitude of the angular rate through fusion of the angular acceleration and quadratic form of the angular rate is proposed. We also provide observability analysis for the general distributed accelerometers-based inertial measurement unit, and show that the angular rate can be correctly estimated by general nonlinear state estimators such as an extended Kalman filter, except under certain extreme conditions.

[1]  B. Ravani,et al.  Design and Implementation of a Mechatronic, All-Accelerometer Inertial Measurement Unit , 2007, IEEE/ASME Transactions on Mechatronics.

[2]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[3]  A. King,et al.  Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers , 1975 .

[4]  Sou-Chen Lee,et al.  Gyroscope Free Strapdown Inertial Measurement Unit by Six Linear Accelerometers , 1994 .

[5]  Sungsu Park,et al.  Design of accelerometer-based inertial navigation systems , 2005, IEEE Transactions on Instrumentation and Measurement.

[6]  Stefano Rossi,et al.  A Redundant Accelerometric Cluster for the Measurement of Translational and Angular Acceleration and Angular Velocity of the Head , 2007 .

[7]  Sungsu Park,et al.  A scheme for improving the performance of a gyroscope-free inertial measurement unit , 2005 .

[8]  Stefano Rossi,et al.  Two calibration procedures for a gyroscope-free inertial measurement system based on a double-pendulum apparatus , 2008 .

[9]  G. Legnani,et al.  On the Number and Placement of Accelerometers for Angular Velocity and Acceleration Determination , 2001 .

[10]  Jorma Rissanen.  Optimal Estimation , 2011, ALT.

[11]  Yiannos Manoli,et al.  Design, geometry evaluation, and calibration of a gyroscope-free inertial measurement unit , 2010 .

[12]  Pei-Chun Lin,et al.  State Derivation of a 12-Axis Gyroscope-Free Inertial Measurement Unit , 2011, Sensors.

[13]  Daniel E. Koditschek,et al.  Sensor data fusion for body state estimation in a hexapod robot with dynamical gaits , 2005, IEEE Transactions on Robotics.

[14]  P. Cardou,et al.  A Nonlinear Program for Angular-Velocity Estimation From Centripetal-Acceleration Measurements , 2011, IEEE/ASME Transactions on Mechatronics.

[15]  Ralf Srama,et al.  Low-charge detector for the monitoring of hyper-velocity micron-sized dust particles , 2008 .