Sinpyo Hong

Observability of error States in GPS/INS integration

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.

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

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.

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

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.

Observability Measures and Their Application to 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.

Observability Analysis of INS with a GPS Multi-Antenna System

This paper investigates observability properties of strapdown INS aided by a GPS antenna array. The motivation to consider a GPS antenna array is that the lever-arms between the GPS antennas and IMU play an important role in the estimation of vehicle attitude and biases of IMU. It is shown that time-invariant INS error models are observable with measurements from at least three GPS antennas. It is also shown that time-varying error models are instantaneously observable with measurements from three antennas. Numerical simulation results are given to show the effectiveness of multiple GPS antennas on estimating vehicle attitude and biases of IMU when IMU has considerable magnitude of biases.

Observability analysis of alignment errors in GPS/INS

Misalignment can be an important problem in the integration of GPS/INS. Observability analysis of the alignment errors in the integration of low-grade inertial sensors and multiantenna GPS is presented in this paper. A control-theoretic approach is adopted to study the observability of time-varying error dynamics models. The relationship between vehicle motions and the observability of the errors in the lever arm and relative attitude between GPS antenna array and IMU is given. It is shown that alignment errors can be made observable through maneuvering. The change of acceleration makes the components of the relative attitude error that are orthogonal to the direction of the acceleration change observable. The change of angular velocity makes the components of the lever arm error that are orthogonal to the direction of the angular velocity observable. The motion of constant angular velocity has no influence on the estimation of the lever arm.

Vision based lateral control by yaw rate feedback

In an autonomous vehicle, the reference lane is continually detected by a machine vision system. The vehicle is steered to follow the reference yaw rates which are generated by the deviations of lateral distance and the yaw angle between the vehicle and the reference lane. To cope with the steering delay and the side-slip of vehicle, a PI controller is introduced for the yaw rate feedback. It is tuned by the simulation in which the vehicle is modeled as 2 DOF and 79 DOF and is verified by the results of an actual vehicle test. The lateral control algorithm by yaw rate feedback has good performances of lane tracking and passenger comfort.

Estimation of errors in INS with multiple GPS antennas

This paper presents a technique to estimate strapdown INS errors with a multi-antenna GPS receiver. A GPS measurement system is introduced in which a compromise between accuracy and computational load is achieved. The combination of differential pseudo-range measurement of vehicle position and differential carrier phase measurements of relative positions among antennas could be considered as a practical scheme for INS error correction. It is shown that position measurements from at least three GPS antennas are sufficient for the estimation of INS errors in time-invariant models. Additional velocity measurements do not change the unobservable subspace of the error models. Numerical simulation results are given to show the effectiveness of the proposed measurement scheme on the estimation of vehicle attitude and biases of low-cost IMU.

Estimation of errors in the integration of GPS and INS

Estimation of errors in the integrated navigation system that consists of a very low-grade inertial measurement unit (IMU) and a single antenna GPS measurement system is studied in this paper. Observability properties of the errors are investigated with a control-theoretic approach. The uncertainties in attitude, gyro bias, and GPS antenna lever arm are shown to cause errors in the estimates of position, velocity, and accelerometer bias. Changes in the acceleration of vehicles improve the estimates of attitude and gyro bias. Changes in the angular velocity enhance the lever arm estimate. Both the motions of translation and constant angular velocity have no influence on the estimation of the lever arm. A car test was performed to confirm the observability analysis.

Estimation of errors in inertial navigation systems with GPS measurements

In this paper, observability properties of a multiantenna GPS measurement system for the estimation of errors in INS are presented. It is shown that time-invariant INS error models are observable with measurements from at least three GPS antennas on the vehicle. There is at least one unobservable mode with two antennas. There are three unobservable modes with one antenna. It is also shown that time-varying INS error models are instantaneously observable with measurements from three GPS antennas. A numerical simulation results are given to verify the effectiveness of the multiantenna measurement system on the INS error estimation. In the simulation, a GPS measurement system is considered in which a trade-off between computational load and accuracy of estimation is achieved.