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The sensor calibration methods used and the resulting attitude determination accuracy achieved with this system is discussed in Chapter 6 kingston hospital pain treatment center aspirin 100pills without prescription. In this chapter midwest pain treatment center wausau order aspirin 100 pills on-line, we present a method for attitude-independent advanced pain treatment center ohio buy generic aspirin 100pills, on-orbit magnetometer calibration that mitigates the effect of time-varying magnetic fields produced by electronics on-board a spacecraft active pain treatment knoxville tn best aspirin 100 pills. This method is attitude-independent in the sense that it neither requires attitude knowledge nor estimates attitude during the calibration process. The calibration significantly increases the accuracy of measurements from magnetometers embedded within a satellite, enabling them to make accurate measurements of the geomagnetic field without imposing location constraints on the sensor. Additionally, since the calibration requires only on-orbit data, it mitigates the need for pre-flight calibration. In this work, calibration was motivated by improved magnetometer-based attitude determination on satellites, but the calibration is applicable to other magnetometer-based sensing systems on a variety of platforms, such as air-, ground-, or water-based vehicles [38]. The purpose of calibration is to quantify the statistical properties of the magnetometer errors [39, 40]. Magnetometers are subject to both constant and time-varying errors, including errors caused by hard iron, soft iron, null shift, scale factors, non-orthogonality, and nearby electronics. Various algorithms exist to estimate the time-invariant errors, which are captured by three general error types: bias, scale factors, and non-orthogonality. The first step is a centering approximation to provide an initial estimate of the calibration parameters, and the second step is a Gauss-Newton method to iteratively refine the parameters. In similar work, [44] utilizes a geometric approach to formulate the problem of compensating for magnetometer errors by estimating parameters lying on an ellipsoid. A simpler method that utilizes least-squares minimization to estimate bias, scale factors, and non-orthogonality is developed in [45, 46]. Realtime implementations of [43] using non-linear Kalman filtering techniques are developed in [47]. The above calibration techniques are attitude-independent, meaning no attitude knowledge is required for the calibration. This is critical when magnetometers are used to estimate attitude, and thus attitude measurements are not available before calibration. The sensor calibration is typically carried out in a coordinate system attached to the magnetometer. However, the calibration methods presented in [44] and [49], an extension of [46], include an additional step to estimate the alignment of the magnetometer relative to the vehicle body frame. The existing algorithms have been shown to work well in compensating for constant sources of magnetometer error [43, 44, 46]. In practice, the time-varying bias caused by nearby electronics can result in additional magnetometer errors. Traditionally, this bias is mitigated by either using a boom to physically separate the magnetometer from the spacecraft, or by using design and manufacturing practices to minimize the effect of electronic components (for example, [50]). These design practices increase the satellite development time and cost, and with the trend toward smaller spacecraft with reduced development times and costs, it may be impossible to physically separate a magnetometer from other spacecraft electronics. The original contribution of this work is an attitude-independent, on-orbit method to estimate magnetometer bias caused by nearby electronics. In particular, the work of Foster and Elkaim [46] is expanded to include time-varying bias in the calibration. This is accomplished by including measurements of spacecraft electric currents in the sensor model and estimating constant parameters that map time-varying current to magnetometer bias. In similar work, Kim et al [51] estimate the bias resulting from a magnetic torque coil by 27 expanding the model of [43] to include the magnetic dipole moment produced by the torque coil. Our method is more general in that the bias caused by any electronic component can be estimated. The current measurements used in the calibration are typically already part of spacecraft health monitoring, so no additional sensors are needed.

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