Recursive Attitude Determination from Vector Observations: Direction Cosine Matrix Identification

Bar-Itzhack, Itzhack Y.; Reiner, John M.

doi:10.2514/3.56362

Cited by 51 publications

(43 citation statements)

References 9 publications

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“…The quaternions in (33) are the complements of the quaternions in (21). Equation (33) can be used to write the b to n transformation as…”

Section: Linearization In the Body Framementioning

confidence: 99%

“…In this approach, the attitude determination problem is cast in the form of an observer or filter. Specific examples of this approach are given in [19] (Euler angle filter), [21] (direction cosine matrix filter), [22] (Rodrigues parameter filter), and [20], [23] (quaternion filters). While the classical approaches to the problem provide an exact solution, they cannot easily accommodate a dynamic model or sensor errors into their formulation.…”

Section: Introductionmentioning

confidence: 99%

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MAV attitude determination by vector matching

Gebre-Egziabher

Elkaim

2008

IEEE Trans. Aerosp. Electron. Syst.

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INTRODUCTIONAttitude is the term used to describe a rigid body's orientation in three-dimensional space. In a more general sense, it is the description of the relative orientation of two coordinate frames. In vehicle guidance, navigation, and control (GNC) applications near Earth's surface (e.g., applications involving airplanes, marine vessels, etc.) the two coordinate frames of interest are sometimes referred to as the body and navigation reference frames. The body frame is rigidly attached to and moves with the vehicle. The navigation frame is normally a locally level (or tangent) coordinate frame. That is, it has an origin attached to Earth's surface and located directly below the vehicle's current position. Its x-y-z axes are lined-up with North, East, and Down (along the local vertical) directions, respectively. Attitude determination systems are used to measure or estimate the relative orientation of these two frames. The information generated by attitude determination systems is indispensable in many GNC applications. A few examples of applications requiring attitude information include pilot-in-the-loop control of manned aircraft, accurate payload pointing on remote sensing platforms, and autonomous navigation and guidance of uninhabited aerial, ground, and marine vehicles.The recent interest in high performance, micro aerial vehicles (MAVs) has necessitated the design of compact, accurate, and inexpensive attitude determination systems. MAVs are designed to be disposable and are very small in size and weight (largest dimensions no greater than 15 cm) [1,2]. At these scales, the avionics and sensor payloads can represent a significant fraction of the overall vehicle dimension and weight. To address this need, many inexpensive rate-gyro based attitude determination systems have been developed [3][4][5]. However, inexpensive and miniature solid-state rate gyros (< $1000 per axis) tend to be low-performance sensors which have outputs subject to wideband noise and rate instabilities on the order of 10 to 100 ± /hr [6,7]. In order to determine attitude, the rate gyro outputs must be integrated to give attitude and this leads to unbounded attitude errors. Thus, successful implementation of an attitude determination system that relies solely on rate gyros requires the use of sensors with exceptionally accurate and stable outputs. These types of gyros would have output errors less than 0:1 ± /hr and tend to be 1) prohibitively expensive, 2) have high power consumption, and/or 3) be physically too large for many miniature vehicle applications.An alternative to relying on accurate and expensive rate gyros is to devise a system which fuses miniature, low-performance (and low-cost and low-power) gyros with a gyro-free aiding system using a complementary filter architecture as shown in Fig. 1. The gyro-free aiding system provides either one of two types of information. It can provide 1) a noisy but unbiased direct attitude measurement periodically (i.e., a low bandwidth attitude update), or 2) it can provide indire...

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“…The quaternions in (33) are the complements of the quaternions in (21). Equation (33) can be used to write the b to n transformation as…”

Section: Linearization In the Body Framementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

MAV attitude determination by vector matching

Gebre-Egziabher

Elkaim

2008

IEEE Trans. Aerosp. Electron. Syst.

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“…[2][3][4][5] There are various attitude representation methods. 6) As some examples, the Direction Cosine Matrix (DCM), 7) the Euler angle, 8) the quaternion, 9) and the Rodrigues parameters 10) are used to express the attitude. Although the attitude representation method and the estimation scheme are different, the attitude is evaluated with the observation vectors in all of the above-mentioned methods.…”

Section: Introductionmentioning

confidence: 99%

Initial Attitude Determination Using a Single Star Sensor

Wang

Cho

Chun

2007

Trans. Japan Soc. Aero. S Sci.

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An initial quaternion estimation method for the attitude determination of a spacecraft using an onboard star sensor is presented. In this method, we use a sequence of the number of stars in the field of view (FOV) of the star sensor as the measurement instead of the direction vector pairs of stars. A new statistical observation model is derived and coupled with the kinematics model of attitude to develop a cost function of the estimated initial quaternion. The attitude acquisition method proposed herein exploits generalized simulated annealing to optimize the cost function and find the initial quaternion. In addition, a virtual sub-FOV and its shuffling procedure for a more accurate estimation are presented. The performance of the proposed method is quantified using an extensive simulation.

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“…In other words, the uncertainty is a 16-dimensional state which corresponds to each element in the transformation matrix. This is a straightforward generalization of the approach of Bar-Itzhack for direction cosine matrices [3].…”

Section: Error Representation and Propagationmentioning

confidence: 99%

“…Specifically, let M j i be the true relative transformation from node i to node j , Each element can take arbitrary values. 3 To parameterize such a general matrix, a number of authors have developed methods to decompose an arbitrary matrix into a set of primitive operations including rotation, translation and scale [12,6]. However, these decompositions are constructed by applying potentially expensive nonlinear operations (such as single value decomposition).…”

Section: Error Representation and Propagationmentioning

confidence: 99%