Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

Systems and methods according to the present invention describe 3D pointing devices which enhance usability by transforming sensed motion data from a first frame of reference (e.g., the body of the 3D pointing device) into a second frame of reference (e.g., a user's frame of reference). One exemplary embodiment of the present invention removes effects associated with a tilt orientation in which the 3D pointing device is held by a user.

3D pointing devices with orientation compensation and improved usability

Systems and methods according to the present invention address these needs and others by providing a handheld device, e.g., a 3D pointing device, which uses at least one sensor to detect motion of the handheld device. The detected motion can then be mapped into a desired output, e.g., cursor movement.

3D pointing devices and methods

Observability properties of errors in an integrated navigation system are studied with a control-theoretic approach in this paper. A navigation system with a low-grade inertial measurement unit and an accurate single-antenna Global Positioning System (GPS) measurement system is considered for observability analysis. Uncertainties in attitude, gyro bias, and GPS antenna lever arm were shown to determine unobservable errors in the position, velocity, and accelerometer bias. It was proved that all the errors can be made observable by maneuvering. Acceleration changes improve the estimates of attitude and gyro bias. Changes in angular velocity enhance the lever arm estimate. However, both the motions of translation and constant angular velocity have no influence on the estimation of the lever arm. A covariance simulation with an extended Kalman filter was performed to confirm the observability analysis.

Observability of error States in GPS/INS integration

Ieee transactions® on aerospace and electronic systems

Misalignment can be an important error source in the integration of the global positioning system (GPS) and inertial navigation systems. This paper presents car test results on the estimation of alignment errors in the integration of a low-grade inertial measurement unit (IMU) with accurate GPS measurement systems. The car test was conducted with a low-cost solid-state IMU and carrier-phase differential GPS measurement systems. Test results showed that changes in the angular velocity improve the estimation of the lever arm between the GPS antenna and IMU. They also showed that changes in acceleration improve the estimation of the relative attitude between the GPS antenna array and IMU. The lever arm was estimated with a 10-cm error. The relative attitude was estimated with a half-degree error. An iterative scheme was used to improve the estimation of the alignment errors during postprocessing. The scheme was shown to be useful when the test car could not have sufficient changes in motion due to limitations in its path. With the given set of test data, the estimation error decreased as the number of iterations increased.

A car test for the estimation of GPS/INS alignment errors

Lever-arm uncertainty can be an important error source in the integration of the Global Positioning System (GPS) and inertial navigation system (INS). This paper presents both numerical and experimental studies on the estimation of the lever arm in the integration of a very-low-grade inertial measurement unit (IMU) with an accurate single-antenna GPS measurement system. Covariance simulation results showed that maneuvers play an important role on the estimation of the lever arm and attitude. The length of the lever arm has a rather insignificant effect on the estimation of these. Experimental tests conducted with a low-cost microelectromechanical system (MEMS) IMU and a carrier-phase differential GPS (CDGPS) measurement system showed that the lever arm can be estimated with centimeter-level accuracy. The test results confirmed that angular motions and horizontal accelerations improve the estimates of the lever arm and yaw angle, respectively.

Experimental study on the estimation of lever arm in GPS/INS

In this paper, two observability measures are introduced for a discrete linear system. The degrees of observability of both the system and its subspaces can be examined with these measures. The measures are well conditioned to perturbation and applicable to multi-input/multi-output time-varying systems. The relations among observability, observability measures, error covariance, and the information matrix are presented. It is shown that the measures have direct connections with the singular value decomposition of the information matrix. In contrast to the error covariance, the measures are determined by the system model and independent of the initial error covariance. An example of the observability analysis of the Global Positioning System/inertial navigation system is given. The measures are confirmed to be less sensitive to the system model perturbation. It is also shown that the vertical component of the gyro bias can be considered unobservable with a tactical-grade inertial measurement unit for a horizontal constant-speed motion.

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Observability Measures and Their Application to GPS/INS

A double-quenching (D/Q) process is proposed for heat-treating high carbon-chromium bearing steels to improve the fatigue properties through refinement of the microstructure. The new heat treatment method has two steps: The first step is a nitrocarburizing process that results in high surface hardness and lowers the transformation temperature. The second step is the same as in the conventional quenching process but can be conducted at a considerably lower temperature than in conventional quenching. The microstructure in the material that is caused by the D/Q heat treatment is much finer than in the conventional Q/T (quenching and tempering) process. In order to quantify the performance of the proposed heat-treatment process, various mechanical property tests are carried out. The rolling contact fatigue life of double-quenched bearing steels was eight times higher than in bearing steels that were treated by conventional Q/T.

Sinpyo Hong

Papers

Observability of error States in GPS/INS integration

A car test for the estimation of GPS/INS alignment errors

Experimental study on the estimation of lever arm in GPS/INS

Observability Measures and Their Application to GPS/INS

Grain refinement in bearing steels using a double-quenching heat-treatment process