Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #1

AN IMPROVED KNIGHT METHOD FOR INSTANTANEOUS AMBIGUITY RESOLUTION IN ATTITUDE DETERMINATION USING GPS:
Y. Li, M. Murata, National Aerospace Laboratory, Japan

The instantaneous integer ambiguity resolution (IIAR) is crucial to the GPS-based attitude determination in some real-time applications, i.e. spacecraft attitude control. An IIAR method should have the capability to determine the ambiguities only utilizing the measurements at an epoch. One this kind of method was proposed by Mr. Knight method in 1994 (In: proceedings of ION GPS-94), which reformulated the fit residuals and employed a recursive procedure to eliminate some unreasonable search branches and decrease the search burden successfully. Even if Knight algorithm improves the search speed greatly, the reliability of solution still relies on the volume of search space. When there are many satellites in tracking or long baselines in structuring, the search volume would be very large. It means that the right solution will suffer more interferences and its reliability will be reduced. One method to limit the search space is that to utilize a coarse initial attitude with certain uncertainty, i.e. 30a. This paper proposes a new method to narrow the search space. It employs a recursive procedure to determine the search ranges, similar to the FASF method (D.Chen and G.Lachapelle, 1995; In: Navigation: Journal of Institute of Navigation). Differing from the FASF, new method only considers the geometrical constraints of satellites.

In fact, the search space can be not only determined by the length of baseline, but also constrained by the other integer ambiguities. It means that the ith sub-space will be restricted by the j integer ambiguities, where j is equal to i-1. One can derive the relationship between ith sub-space and j assumed integers by considering the satellites geometrical configuration. Let us explain it in a geometrical view. If only the length of baseline beening considered, the angle between a satellite and a baseline will vary in the range from 0a to 180a. Once the value of this angle is fixed, i.e. a, the corresponding integer ambiguity will be determined. This angle a and LOS (line-of-sight) vector determine a circular cone that the LOS vector is its rotation axis and a is its inclination angle. The baseline vector lie in the surface of the cone. Taking into account this point and the geometrical configuration of satellites simultaneously, the angle between the baseline and another satellite's LOS vector will be narrowed to a smaller range compared with the previous range varying from 0a to 180a. It means that the search space has been narrowed. The similar constraint will affect on the behind satellites in the same way. The constraints can be formulated by a recursive procedure that is very suitable to be inserted into the search loop of Knight algorithm.

Results of experiments demonstrate that the method can improve the solution rate and reduce the error rate. One result shows that referencing the normal Knight algorithm, the solution rate can be improved 45%, and the error rate can be reduced 48%.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #2

A TRUSTFUL ATTITUDE DETERMINATION ALGORITHM GIVING CONFIDENCE LEVEL OF THE SOLUTION:
C. Kee, Y. Sohn, Seoul National University, Korea

Global Positioning System (GPS) was originally designed mainly for position applications. Recently researches for attitude determination using GPS were gradually increased and now it is already implemented and operational in attitude determination of many applications including Globalstar satellites. In near future attitude sensors using GPS are expected to be used as primary sensors in airplanes, ships, farming machines and etc.

So far, almost all the papers about attitude determination developed algorithms to reduce cycle ambiguity search space in terms of mathematical formulation. Those conventional techniques have some problems. They need big computational efforts comparatively and can not guarantee 100% if the solution is correct or not (i.e., there is no confidence indicator), which may cause serious operational problems in most safety critical applications. Besides success ratio and computational load are sensitive to number of visible satellites (the more visible satellites, the bigger computational load) and in multi-baseline case, computational load increases proportional to the number of baselines. We recently resolved the above problems by newly developed algorithm.

In this paper, we found a trustful method to solve cycle ambiguity by using geometrical formulation. Through this, we found that our new SNUGLAD (Seoul National University GPS Laboratory attitude determination) algorithm out-performs the existing algorithms even in case of a few visible satellites and determine baseline_s attitude with first epoch in high accuracy comparatively. Computational load is insensitive to the number of visible satellites. The most distinctive advantage of SNUGLAD is that it can show the confidence level of the solution by setting Green, , Yellow, or Red light sign. If there is only one solution, which satisfies pre-determined probability criterion at first epoch, it is selected as true solution directly and SNUGLAD sets its confidence level as Green light. Results show that all the green solutions agree with true ones. In the case that there are two or more solutions (Yellow light), SNUGLAD hands over the candidate solutions to next epoch and can determine solution by our particular multi-epoch method.

We confirmed our algorithm by simulations and also experiments. The results proved that SNUGLAD finds the right cycle ambiguities at the first epoch most of time and it guarantees the solution with 100% confidence level without additional computational load.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #3

AN ANTENNA ARRAY BASED APPROACH TO ATTITUDE DETERMINATION IN A JAMMED ENVIRONMENT:
M. Markel, Sverdrup Technology; E. Sutton, H. Zmuda, University of Florida

This work provides the mathematical basis for a GPS based attitude determination (AD) system that performs even in the presence of strong external interference. Typical methods for using GPS to determine attitude involve measuring the sensor-to-sensor phase difference for several satellites. These phase differences contain the projections of the known line-of-sight (LOS) vectors to the satellites onto the unknown baseline sensor-to-sensor vectors, and from them attitude can be determined. This approach performs well when the GPS signals alone are present in the received data, and the spread spectrum waveform and receiver design offer a modest inherent tolerance to jamming. However, in many realistic situations the jamming power may exceed the receivers inherent jammer tolerance, resulting in failure to produce an accurate attitude estimate. In addition, phase detection is non-linear, therefore even if some aspects of the jammer are known (power, LOS, etc.) it is not possible to extract the phase of the GPS signal from the phase of the composite sum. It is clear then that a new approach is required to provide AD in a jammed environment. The objective of this paper is to present an approach that provides an attitude capability in the presence of intentional jamming.

It is well known that adaptive antenna arrays (often called "Smart Antennas" for communications systems) can provide significant resistance to unintentional interference / jammers for both signal extraction and direction finding. This performance comes at the cost of additional sensors and of course processing capability. An AD system, however, by necessity requires multiple sensors. Therefore, it is natural to examine the jammer resistant (anti-jam) complement to attitude determination, i.e. taking maximum advantage of the presence of the sensor array. This paper shows that anti-jam attitude determination can be posed as a special case of multi-source direction finding with an antenna array.

In this paper we develop a data model for the GPS signal using the known GPS waveforms and LOS directions to the satellites and the unknown body attitude and jammer locations and powers. From this model we develop a maximum likelihood estimator for the body attitude from a block of data comprised of several snapshots of sensor data vectors. Recent research has shown that if the signal waveforms are known and uncorrelated, as is the case for GPS, the maximum likelihood estimator reduces to a series of independent searches for the individual LOS directions to the sources. We continue the derivation in this manner and show that the estimation can be performed without the requirement of direction-finding each satellite. In addition, unlike sub-space direction finding algorithms our approach provides graceful degradation in performance as the number of jammers increases. This paper discusses methods of implementing this estimator, including techniques to estimate the nuisance parameters of the jammers spatial covariance, and issues of convergence.

This paper presents the results of simulations of this new approach for several jammer powers, satellite constellations, and array topologies. These results show the capability and accuracy of attitude determination in a jammed environment.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #4

OBTAINING 3-AXIS ATTITUDE SOLUTIONS FROM GPS SIGNAL TO NOISE RATIO MEASUREMENTS:
J. Madsen, The University of Texas at Austin

ION Sponsored Student Paper
This paper investigates the performance of an algorithm which uses Kalman filtered signal to noise ratio (SNR) measurements from two GPS antennas at differing angles to derive a full 3 axis attitude solution for a rigid body such as a spacecraft. This algorithm could be used by low-earth orbiting satellites which have rather coarse attitude requirements, or utilized as a back-up method of attitude determination when more accurate, but less robust methods, fail.

Performance of the algorithm is investigated during static attitude states as well as during periods of attitude maneuvers. Evaluations are also done on the effects of varying the constants used by the filter as well as the effects of varying the offset angle between the antennas. Finally, the impact of various expected error sources are investigated.

The analysis demonstrates that a Kalman filtered SNR algorithm can provide surprisingly accurate measurements of attitude from GPS signal sources. Additionally, the results show that this approach is relatively robust in the presence of many types of error sources.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #5

GPS ATTITUDE DETERMINATION OF AN UNMANNED AERIAL VEHICLE USING EXTREMELY SHORT BASELINES:
M. Harris, Ohio University

This paper presents a carrier-phase attitude determination system with baseline lengths of approximately half of one wavelength that was designed for use in an unmanned aerial vehicle (UAV). A navigation system was implemented using three L1 GPS receivers with antennas placed in a triangular pattern for the purpose of providing a small, inexpensive, high integrity attitude solution for a UAV. Differential carrier phase measurements were used to determine the aircraft pitch, roll, and azimuth by a miniaturized personal computer running a real time operating system. Because a common receiver clock was not used, double-differenced carrier phase measurements were necessary in order to cancel receiver clock biases.

The short baseline lengths aid carrier phase integer ambiguity resolution significantly, but they do not eliminate the ambiguities completely. The cost for such aiding, however, is a relatively large error in the attitude calculations as the magnitude of the carrier phase noise approaches the magnitude of the baseline length. Noise levels with a standard deviation of approximately one degree were experienced on the attitude measurements. The methods and considerations used in implementing the attitude determination system are discussed, and results from testing of the attitude determination system are presented.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #6

GPS/MAGNETOMETER BASED SATELLITE NAVIGATION AND ATTITUDE DETERMINATION:
J. Deutschmann, R. Harman, NASA GSFC; I. Bar-Itzhack, Faculty of Aerospace Engineering, Israel

In recent years algorithms were developed for orbit, attitude and angular-rate determination of Low Earth Orbiting (LEO) satellites [1, 2, 3]. Those algorithms rely on measurements of magnetometers, which are standard, relatively inexpensive, sensors that are normally installed on every LEO satellite. Although magnetometers alone are sufficient for obtaining the desired information, the convergence of the algorithms to the right values of the satellite orbital parameters, position, attitude and angular velocity is very slow. The addition of sun sensors reduces the convergence time considerably [4]. However, for many LEO satellites the sun data is not available during portions of the orbit when the spacecraft (SC) is in the earth shadow. It is here where the GPS space vehicles (SV) can provide valuable support. This is clearly demonstrated in the present paper. Although GPS measurements alone can be used to obtain SC position, velocity, attitude and angular-rate, the use of magnetometers improve the results due to the synergistic effect of sensor fusion. Moreover, it is possible to obtain these results with less than three SVs.

In this paper we introduce an estimation algorithm, which is a combination of an Extended Kalman Filter (EKF) and a Pseudo Linear Kalman Filter (PSELIKA) [5]. The measurements, which are processed by the algorithm, are the following ones:
1. Magnetometer readings,
2. GPS pseudo range,
3. GPS range-rate,
4. GPS phase measurements.
Although data from one SV only are sufficient, the improvement achieved when two SVs are used, is examined.

The incorporation of SV phase measurements for estimating the SC angular-rate requires the use of the rate-of-change of the measured phase-angle. Using the derivative approach [6], this data is obtained by differentiation; however, when the estimation approach [6] is used, there is no need to differentiate the GPS phase measurements. In this paper both approaches for estimating the SC angular-rate, are examined.

The algorithm is tested using simulated data. The test results yield the following conclusions:
1. In the absence of sun sensor data the use of GPS is essential.
2. A three-axis-magnetometer (TAM) and one SV are sufficient for obtaining good estimate of a LEO SC orbit, location, attitude and angular-rate.
3. As expected, when using two SVs, the SC orbit and location converge much faster and to smaller errors. The use of two versus one SV shortens the convergence of the attitude and the angular-rate estimates, but does not reduce their final estimation error.
4. Comparing the use of the estimation approach with the derivative approach for estimating the SC angular-rate, reveals that both approaches give similar results with the estimation approach yielding angular-rate estimates which appear less noisy, as expected.

References
1. Psiaki, M.L., Huang, L., and Fox, S.M., "Ground Tests of Magnetometer Based Autonomous Navigation (MAGNAV) for Low-Earth-Orbiting Spacecraft," Journal of Guidance, Control, and Dynamics, Vol. 16, No. 1 Jan.-Feb., 1993, pp. 206-214.
2. Shorshi, G. and Bar-Itzhack, I., "Satellite Autonomous Navigation Based on Magnetic Field Measurements", Journal of Guidance, Control, and Dynamics, Vol. 18, No. 4 July-August, 1995, pp. 843-850.
3. Deutschmann, J., and I. Bar-Itzhack, "Comprehensive Evaluation of Attitude and Orbit Estimation Using Real Earth Magnetic Field Data", Proceedings of the 11th Annual AIAA/USU Conference on Small Satellites, Logan, UT, September 15-18, 1997.
4. Deutschmann, J., R. Harman, and I. Bar-Itzhack, "An Innovative Method for Low Cost, Autonomous Navigation for Low Earth Orbit Satellites", Proceedings of the AAS/AIAA Astrodynamics Specialists Conference, Boston, MA, August 10-12, 1998.
5. R. Harman and I.Y. Bar-Itzhack, "Pseudolinear and State-Dependent Riccati Equation Filters for Angular Rate Estimation", AIAA J. of Guidance, Control, and Dynamics, Vol. 22, No. 5, Sept.-Oct. 1999, pp. 723-725. (Engineering Note).
6. Bar-Itzhack, I., "Classification of Algorithms for Angular Velocity Estimation", to appear in Journal of Guidance, Dynamics, and Control, Vol. 24, No. 2, March-April. 2001.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #7

GPS BASED STAR SENSOR AIDING FOR ATTITUDE DETERMINATION IN HIGH DYNAMICS:
C. Arbinger, W. Enderle, German Aerospace Center, German Space Operations Center, Germany; O. Wagner, TU Muenchen, Institute of Flight Mechanics, Germany

The applications of GPS in space, such as orbit and attitude determination, offer several advantages, e.g. complete navigation information on board, low weight, volume and power consumption.

GPS used for spacecraft attitude determination has many important advantages like the fast and reliable initial acquisition, the resistance against high spin rates and the fact, that at least two satellites for deterministic attitude determination are visible for most of the mission duration. GPS could also be used as a safe mode sensor. Therefore GPS based attitude determination seems very promising.

Due to the achievable accuracy, depending on the baseline length and the signal noise figure, a GPS attitude sensor cannot be used for missions were high accurate attitude measurements are needed and the baseline lengths are restricted.

A particular field of interest is the broad and evolving area of earth observation missions and their corresponding requirements for a high position and attitude accuracy related to image processing.

For these missions, a star sensor will be the adequate attitude sensor. Star sensors are highly accurate and well-established algorithms are available. The disadvantages using star sensors are e.g. restricted field of view, operation only at low angular rates, sensor performance degradation and sensitive to problems related to star pattern recognition.

Taking all these individual advantages and disadvantages into account, the combination of a GPS attitude sensor and a star sensor seems extremely promising, because such a sensor combination can be applied to a broad area of missions and their requirements of a high accurate attitude.

This paper presents results from a software simulation, showing the increase of performance by the support of the star sensor through GPS measurements. The GPS attitude sensor aids the star sensor within the star pattern recognition process, resulting in improvement of accuracy and robustness with respect to the attitude solution. This can even be achieved in scenarios with high angular rates.

Due to the fact that the star sensors used in this research did not support the input of reference attitude data for aiding, a software simulation approach was set up.

GPS based attitude measurements are fed into the star sensor software model in order to increase the area of applicability.

Open night sky tests with a real star sensor underlay the conservative assumptions made in the software simulation.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Paper #8

TWO ANTENNAE GPS AND LOW COST INS TIGHT INTEGRATION FOR ATTITUDE DETERMINATION:
Y. Yang, J.A. Farrell, University of California, Riverside

Methods of attitude determination can be classified into three broad categories according to sensors and theories on which the attitude determination is based. They are:
1. Attitude determination by integrating angle rate from gyroscope after initialization and alignment;
2. Attitude determination by measuring baseline vectors in navigation frame with differential carrier phase GPS measurement and estimating the rotation matrix with respect to the known baseline vector in vehicle frame;
3. Attitude Determination by combining terms 1 and 2.

The third approach by tightly integrating two antennae GPS with low cost INS for attitude determination is considered in this article. This approach has several advantages. They are:
1. High accuracy for both short time and long time;
2. Real time and low latency;
3. High frequency outputs;
4. Full vehicle state estimate;
5. Quick INS initialization and alignment by differential carrier phase GPS aiding;
6. Redundancy and robustness by multi-sensor tight integration.

The article here presents a methodology for tight integration of two antennae GPS/INS for attitude determination. Based on the dynamical model of INS, the two antennae attitude observation model is derived, and a recursive extended Kalman filter algorithm is developed. The observability, which is a main issue of the state estimation, is analyzed with a focus on attitude estimates.

The attitude determination performance is shown by both covariance analysis and experiment results. The standard deviation of the attitude angles (roll, pitch and yaw) is determined by several factors. They are the performance of the Inertial Measurement Unit (IMU) and GPS receivers, system configuration and the length of the short baseline. For the system implemented here, the standard deviation of roll is 0.1 degree, while those of pitch and yaw are within 0.15 degree with 0.96 meters short baseline.

Although the system, presented in this article, is designed for a high dynamics automated vehicle control, it is applicable to all the systems that need real-time high accuracy navigation information in all the moving cases, such as aviation, automatic mining and precise farming. With GPS modernization and MEMS technology application in IMU, the system will be more affordable.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Alternate #1

COMPARING AZIMUTHS OBTAINED BY CLASSICAL ASTRONOMY AND GPS TECHNOLOGY:
P.C.L. Segantine, C.P. Rocha, Sao Carlos Engineering School, Brazil

Astronomy and Geodesy are sciences that interact in geographical positioning field, but differing in relation to mathematical models adopted for those representations. The advent of GPS technology has changed the concept to measure azimuths and others applications. The essential objective of this paper is to characterize which methods and processes should be used to obtain better results of the azimuths under optics of the Classical Astronomy and using GPS, taking into account the different natures of the treatment applied in the observations. Comparing the quality of azimuths obtained by Classic Astronomy and by GPS, it is not an easy task because those parameters are referenced to different surfaces and need a complex mathematical treatment. It was also tried to establish the border in the base lines length, where the results gotten through Classic Astronomy process should be better in quality than those obtained by GPS. It is presented an experiment that collected astronomical and GPS data in the field and the reached difference between those methods. The results showed, after Laplace correction, that the azimuth obtained by classical Astronomy is little bit higher than obtained by GPS.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Alternate #2

TACTICAL FAR TARGET LOCATION USING POSITION AND AZIMUTH FROM A P(Y) CODE GPS ATTITUDE DETERMINATION SYSTEM:
C.J. Pruszynski, Raytheon Systems Company; K.W. Ulmer, C.W. Phelps, Rockwell Collins Government Systems; M.P. St. Peter, PM NV/RSTA

The Long Range Advanced Scout Surveillance System (LRAS3) is a battlefield reconnaissance and surveillance sensor system developed for U.S. Army Project Manager Night Vision/Reconnaissance, Surveillance and Target Acquisition (PM NV/RSTA) by Raytheon Electronic Systems (RES). The LRAS3 sight integrates the Army's Second Generation HTI FLIR technology, a day TV camera, and an eyesafe laser rangefinder into a large, single aperture optical system to provide a high performance day/night target acquisition capability. The LRAS3 will be deployed on the High Mobility Multi-purpose Wheeled Vehicle (HMMWV) in the current force and on the reconnaissance variant of the Interim Armored Vehicle (IAV) in the Interim Brigade Combat Team (BCT) for use by Army scouts to detect, identify and locate tactical threat targets at extended ranges.

The LRAS3 includes a Far Target Location (FTL) capability that enables the scout to determine the geodetic location of any detected target with a very high degree of accuracy. Far Target Location requires three pieces of information; own location, target range and lastly target bearing. The first two elements are easily provided by a GPS receiver and laser rangefinder. Predecessor systems have typically employed either a digital magnetic compass or an inertial sensor for the bearing determination task. The digital magnetic compass has been the long standing, low cost azimuth sensor solution, but it is handicapped by unpredictable behavior and marginal accuracy performance in vehicle installations. Inertial sensors can provide high accuracy and reliability, but with the penalties of higher cost, weight and power consumption. GPS Attitude Determination Systems provide the systems engineer with a new intermediate level of azimuth determination capability that can be employed in this and related direction-finding sensor applications.

This new approach to the target location problem has been successfully developed, demonstrated and is now entering production in a military tactical application. In the LRAS3, the sight sensor position and target bearing are determined by a Rockwell Collins P(Y)-code GPS attitude determination system that is fully integrated into the sensor sight housing. Data from the two antenna, 0.5 meter baseline, GPS system is combined with data from a two-axis pitch-roll inclinometer to provide a complete 3-dimensional attitude solution for the sensor optical line of sight.

This paper describes the configuration of the GPS Interferometer Subsystem (GPSIS) and its integration into the LRAS3 sight system housing. Various lessons learned during the integration of the system are described, including the use of a software-based compensation method to correct the carrier phase measurement distortions introduced by the physically constrained antenna and ground plane installation. Summary test results of the LRAS3 Far Target Location performance are presented.
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Session C6: ATTITUDE DETERMINATION SYSTEMS
Alternate #3

OCTOPUS: FOUR-ANTENNAE RTK SYSTEM AND NEW QUATERNIONS BASED ATTITUDE DETERMINATION TECHNIQUE:
J. Ashjaee, L. Rapoport, I. Barabanov, V. Mogilnitsky, Javad Navigation Systems, Russia

New quaternion-based technique is proposed for implementation in the four-antennae RTK system OCTPUS. The system is composed of four dual bands GPS or GPS/GLONASS receivers and provides attitude solutions at up to 20Hz rate. It performs simultaneous carrier phase differential positioning of three slave antennae relative to the master antenna. The master receiver calculates attitude solutions on the base of three RTK single base line solutions. There are two methods for such calculations:

(1) Decomposed method. Rotations from the body frame to the local horizon frame are calculated using three RTK vector solutions. The analytic solution using quaternion technique is proposed to solve this problem. To calculate the corresponding quaternion one needs to solve certain four dimensional eigenvalue problem and take the eigenvector corresponding the largest eigenvalue.
(2) General case method. Slave receivers resolve ambiguity and send measurements to the master receiver. The master calculates attitude on the base of unbiased carrier phase measurements from three slave receiver. To calculate the quaternion one needs to minimize the non-linear cost function using Newton or Quasi-Newton algorithm.

It is shown that first decomposed solution is derived from the second general case solution using some certain weighting matrix. The weighting matrix is then parameterized by one scalar parameter taking values from zero to one. The zero value supposes the decomposed solution. The value one supposes second solution with some pre-defined weighting matrix. New technique is proposed that tracks the attitude solution starting with decomposed analytic solution to the second general case solution, as parameter growth from zero to one.

The paper is organized the following way. The numerical method is discussed at first. Then the performance results are included. Mathematical details are given in Appendixes.
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