Bradford W. Parkinson

A gyro-free quaternion-based attitude determination system suitable for implementation using low cost sensors

Attitude determination systems that use inexpensive sensors and are based on computationally efficient and robust algorithms are indispensable for real-time vehicle navigation, guidance and control applications. This paper describes an attitude determination system that is based on two vector measurements of non-zero, non-colinear vectors. The algorithm is based on a quaternion formulation of Wahbas (1966) problem, whereby the error quaternion (q/sub e/) becomes the observed state and can be cast into a standard linear measurement equation. Using the Earths magnetic field and gravity as the two measured quantities, a low-cost attitude determination system is proposed. An iterated least-squares solution to the attitude determination problem is tested on simulated static cases, and shown to be globally convergent. A time-varying Kalman filter implementation of the same formulation is tested on simulated data and experimental data from a maneuvering aircraft. The time-varying Kalman filter implementation of this algorithm is exercised on simulated and real data collected from an inexpensive triad of accelerometers and magnetometers. The accelerometers in conjunction with the derivative of GPS velocity provided a measure of the gravitation field vector and the magnetometers measured the Earths magnetic field vector. Tracking errors on experimental data are shown to be less than 1 degree mean and standard deviation of approximately 11 degrees in yaw, and 3 degrees in pitch and roll. Best case performance of the system during maneuvering is shown to improve standard deviations to approximately 3 degrees in yaw, and 1.5 degrees in pitch and roll.

Cascaded Kalman Filters for Accurate Estimation of Multiple Biases, Dead-Reckoning Navigation, and Full State Feedback Control of Ground Vehicles

This paper develops a cascaded estimation algorithm for estimating all of the biases and states for full state feedback and dead reckoning of a farm tractor through short global positioning system (GPS) outages. First, a conventional (one stage) estimation scheme is presented. The single state estimation scheme is shown to have degraded performance in bias state estimation and dead-reckoning due to vehicle model errors. However, the states for position and velocity are not highly coupled to the tractor dynamic states, allowing for separation of the estimators. Therefore, the state estimation algorithms are divided into two cascaded estimators in order to prevent the errors in the vehicle model from corrupting the navigation states. A dead reckoning (or navigation) estimator estimates all of the inertial sensor biases while GPS is available. When GPS is not available, the dead reckoning estimator integrates rate measurements to provide position and heading estimates in order to maintain continuous control of the vehicle through these GPS outages. A second estimator is then used to estimate the additional states needed for full state feedback control algorithms. Bias estimates from the dead reckoning estimator are used to correct the sensor measurement used in the second estimator. An extended kalman filter (EKF) is utilized for each of the estimators. Results are given, showing that the cascaded estimation technique provides better estimation of the vehicle states over a conventional estimation scheme, especially during a GPS outage. Results are also given which verify the ability of the estimation algorithm to estimate all of the system biases and provide continuous control of the tractor through a short GPS outage

Optimal Recursive Iterative Algorithm for Discrete Nonlinear Least-Squares Estimation

The estimation algorithm developed offers an alternative to standard recursive nonlinear estimators such as the extended Kalman filter and the iterated extended Kalman filter. The algorithm, which is developed from a quadratic cost function basis, splits the problem of cost function minimization into a linear first step and a nonlinear second step by defining new first-step states that are nonlinear combinations of the unknown states. Estimates of the firststep states are obtained by minimizing the first-step cost function using a Kalman filter formulation. Estimates of the unknown, or second-step, states are obtained by minimizing the second-step cost function using an iterative Gauss-Newton algorithm. The two-step estimator is shown to be optimal for static problems in which the time variation of the measurement equation can be separated from the unknowns. This method is then generalized by approximating the nonlinearity as a perturbation of the dynamic update, while keeping the measurement cost function the same. In contrast, the extended Kalman filter and the iterated extended Kalman filter linearize the measurement cost function, resulting in suboptimal estimates. Two example applications confirm these analytical results.

The gravity-probe-b relativity gyroscope experiment: Development of the prototype flight instrument

The Gravity-Probe-B Relativity Gyroscope Experiment (GP-B) will measure the geodetic and frame-dragging precession rates of gyroscopes in a 650 km high polar orbit about the earth. The goal is to measure these two effects, which are predicted by Einsteins General Theory of Relativity, to 0.01% (geodetic) and 1% (frame-dragging). This paper presents the development progress for full-size prototype flight hardware including the gyroscopes, gyro readout and magnetic shielding system, and an integrated ground test instrument. Results presented include gyro rotor mass-unbalance values (15–86 nm) due the thickness variations of the thin niobium coating on the rotor, interior sphericities (163–275 nm peak-to-valley) of fused-quartz gyro housings produced by tumble lapping, gyro precession rates (gyroscopes at 5 K) which imply low mass-unbalance components parallel to the gyro axis (23–62 nm), and demonstration of a magnetic shielding factor of 2×1010 for the gyro readout system with one shielding component missing (the gyro rotor). All of these results are at or near flight requirements for the GP-B Science Mission, which is expected to be launched in 1995.

Parity space methods for autonomous fault detection and exclusion using GPS carrier phase

Kinematic carrier phase positioning provides navigation integrity. The sub-centimeter precision of carrier phase measurements can be used to leverage receiver autonomous integrity monitoring (RAIM) in the sense that extremely tight fault detection thresholds can be set on the least-squares residual (ensuring navigation integrity) without incurring high false alarm rates. In addition, the high precision of carrier phase, when compared with code phase, lowers the integrity risk associated with the fault identification process. This is true because carrier phase provides a much cleaner observation of the effect of a given failure on the residual. Thus, for the same improvement in navigation continuity (obtained from fault isolation), misidentification will be less likely. This paper is focused on the use of parity space methods to investigate the limits of high-integrity and high-continuity GPS performance. In this regard, prototype algorithms for receiver autonomous fault detection and exclusion were developed with the goal of maximizing navigation continuity subject to the constraint of maintaining high integrity (by repressing mis-identifications). Fault detection and exclusion performance was demonstrated through analysis and extensive simulation. In addition, the prototype algorithms were implemented in a real-time airborne kinematic positioning architecture and tested by deliberately inducing failures in the post-processing of raw flight data.

Autonomous fault detection and removal using GPS carrier phase

This paper is focused on the use of carrier phase measurements and parity space methodology to investigate the limits of high-integrity and high-continuity satellite-based navigation performance. In this regard, a new algorithm for receiver autonomous fault detection and removal is developed with the specific goal of attaining the high levels of integrity and continuity required for aircraft precision approach and landing applications. Fault detection and removal algorithm performance is demonstrated through analysis and simulation, and the results of tests using deliberately induced failures in raw night data are presented.

Wide area differential GPS (WADGPS): future navigation system

Conventional differential Global Positioning System (DGPS) usually has accuracies of 1-3 within 100 km of the reference station wide area differential GPS (WADGPS) can achieve the same accuracy as DGPS in much wider area while reducing the number of reference stations and increasing the integrity substantially. Test results have shown 1.5-4 m positioning accuracy for a dual frequency user with 10-20 s of age using WADGPS, which in this case has six monitor stations with a 1632 km minimum baseline.

A New Yaw Dynamic Model for Improved High Speed Control of a Farm Tractor

This paper presents the system identification of a new model for the farm tractors yaw dynamics in order to improve automatic control at higher speeds and understand controller limitations from neglecting these dynamics.As speed increases, higher order models are required to maintain accurate lateral control of the vehicle. Neglecting these dynamics can cause the controller to become unstable at the bandwidths required for accurate control at higher speeds. The yaw dynamic model, which is found to be dominated by a second order response, is identified for multiple speeds to determine the effect of velocity on the model. The second order yaw dynamics cannot be represented by the traditional bicycle model. An analytical derivation shows that the model characteristics can, however, be captured by a model consisting of a significant (non-negligible) relaxation length in the front tire. Experimental results are presented showing that the new yaw dynamic model can provide lateral control of the tractor to within 4 cm (1σ) at speeds up to 8 m/s. These results are shown to be an improvement, at high speeds, over controllers based on models (such as a kinematic model) previously used for control of farm equipment.

Origins, Evolution, and Future of Satellite Navigation

The Global Positioning System (GPS or NAVSTAR) has been called the most significant civil spin-off of the cold war. It evolved from technology efforts in the Navy and in the Air Force but was almost canceled before gaining approval by the Department of Defense. While it offers phenomenal accuracy (centimeters for landing aircraft), it still requires some expansions to satisfy integrity, continuity, and availability requirements. Most of all, for this system to be formally accepted (and certified) internationally, the world will need greater confidence in commitments by the U.S. and greater participation by the world community. (Author)

A system using LEO telecommunication satellites for rapid acquisition of integer cycle ambiguities

This paper addresses the design of a cm-level carrier-phase navigation system which employs Low Earth Orbit (LEO) satellites for rapid resolution of integer-cycle ambiguities. In the short term, the system aims to combine the Navstar GPS fleet with satellites of the Globalstar Telecommunications constellation. We describe how cm-level carrier-phase positioning can be achieved using signals that were not designed for navigation. Our objective is to perform precision navigation without requiring alteration of the communication payload onboard the satellites. The technique accommodates the beam configuration of the satellite downlink, the bent-pipe architecture of the communication payload, the instabilities of the satellite oscillators and the frequency-dependent phase lags in the user and reference receiver front ends. The object of this paper is to characterize those components of the system necessary to achieve high-integrity high-precision performance objectives.