Attitude Determination
Attitude estimation is the process of determining the spatial orientation of an object. A system formed by multiple Global Navigation Satellite System (GNSS ) antennas placed at known relative positions acts as an attitude sensor. This chapter provides an
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Attitude Dete 27. Attitude Determination
Gabriele Giorgi
27.1 27.2 27.2.1 27.2.2 27.3 27.3.1
Six Degrees of Freedom ..................... Attitude Parameterization ................. The Space of Rotations ....................... Parameterization of the Rotation Matrix .............................................. Attitude Estimation from Baseline Observations .................................... Estimation of the Orthonormal Matrix of Rotations ......................................
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27.3.2 27.3.3
Orthogonal Procrustes Problem ........... Weighted Orthogonal Procrustes Problem............................................ 27.3.4 Attitude Estimation with Fully Populated Weight Matrix.................... 27.3.5 On the Precision of Attitude Estimation 27.4 27.4.1
The GNSS Attitude Model ................... Potential Model Errors and Misspecification.......................... 27.4.2 Resolution of the GNSS Attitude Model 27.4.3 The GNSS Ambiguity and Attitude Estimation ........................................ 27.4.4 The Quality of Ambiguity and Attitude Estimations .......................................
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27.5 27.5.1 27.5.2 27.5.3 27.5.4
Applications ..................................... Space Operations ............................... Aeronautics Applications .................... Marine Navigation ............................. Land Applications ..............................
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27.6
An Overview of GNSS/INS Sensor Fusion for Attitude Determination .....
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References...................................................
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27.1 Six Degrees of Freedom The pose of a rigid body in a three dimensional space can be described by six independent parameters, of which three refer to the absolute position of a body reference point and three describe the body orientation. Whereas positioning deals with the estimation of the absolute location, attitude estimation is the process of determining the orientation of the body with respect to a reference frame. The combination of absolute position and orientation enables a complete static characterization of a rigid body in space, as shown in Fig. 27.1. Several attitude sensors are available to obtain the spatial orientation of a body. These can be classified in two distinct categories: relative and absolute sensors. Relative attitude sensors detect changes in the body dynamics by exploiting internal devices, and keep track of rotational accelerations induced by the body mo-
tion, generating an output proportional to the magnitude of the rotations. The absolute orientation of the body is then obtained by continuously propagating a known initial state. Due to the accumulation of measurement errors, the integration process causes estimation biases that tend to increase over time, thus requiring periodic recalibrations. An example of a relative attitude sensor is the gyroscope, which reacts to variations of the body orientation by opposing a measurable gyroscopic resistance force. Absolute attitude se
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