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Techniques are discussed for attitude determination using the global positioning system (GPS) differential phase measurements, assuming that the cycle integer ambiguities are known. The problem of attitude determination is posed as a parameter optimization problem. One proposed set of optimal solutions, which includes solutions of Wahba's problem, is based on least-squares t of some attitude parameters to a set of vector measurements. The use of these algorithms requires the conversion of the basic GPS scalar phase measurements into unit vectors. It is shown that when the GPS antennas constitute two axes of a Cartesian coordinate system, the conversion is immediate. When this is not the case, a more elaborate transformation is required. The necessary conversion formulae for both cases are developed and demonstrated in an example. Another possible approach is based on a least-squares t of the attitude quaternion to the GPS phase measurements themselves. The cost function of the t is given in the literature in the most straightforward formulation as a function of the attitude matrix. Conversion is presented of the matrix-based cost function to a quaternion-based cost function that corresponds to the cost function minimized by QUEST. However, unlike the QUEST cost function, the converted cost function is not a simple quadratic form; therefore, the simple QUEST solution is not applicable in this case. An iterative solution for nding the optimal quaternion is derived and demonstrated through numerical examples. The algorithms can handle cases of planar antenna arrays and, thus, cover a de ciency in earlier algorithms.

Objective: This study was designed to develop and prospectively validate a machine learning based algorithm that could predict patient response to the most common biologic drug classes used in the management of psoriasis patients. This type of tool would allow clinicians to have greater confidence that a given patient will respond to a specific drug class, which could lead to improved health outcomes and reduced wasted healthcare spend. Methods: Patients were enrolled into one of two observational studies (STAMP studies) where dermal biomarker patches (DBPs) were applied at baseline prior to drug exposure, followed by clinical evaluations at 12 weeks after exposure. PASI measurements were made at baseline and 12 weeks to evaluate clinical response to a clinical phenotype. Responders were defined as those who reached PASI75 at 12 weeks. The transcriptomes obtained from the DBPs were sequenced and analyzed to derive and/or validate classifiers for each biologic class, which were then combined to yield predictive responses for all three biologic drug classes (IL-23i, IL-17i, and TNFai). Results: A total of 242 psoriasis patients were enrolled in these studies, including 118 patients (49.6%) treated with IL-23i, 79 patients (33.2%) treated with IL-17i, 35 patients (14.7%) treated with TNFai, and 6 patients (2.5%) treated with IL-12/23i. The IL-23i predictive classifier was developed from the earlier enrolled patients and independently validated with the latter enrolled patients. IL-17i and TNFai predictive classifiers were developed using publicly available datasets and independently validated with patients from the STAMP studies. In the independent validation, positive predictive values for three classifiers (IL-23i, IL-17i, and TNFai) were 93.1%, 92.3% and 85.7% respectively. Over the entire cohort, 99.5% of patients were predicted to respond to at least one drug class. Conclusion: This study demonstrates the power of using baseline dermal biomarkers and machine learning methods as applied to the prediction of psoriasis biologic prior to drug exposure. Using this test, patients, physicians, and the health care system all can benefit in distinct ways. Precision medicine can be realized for individual patients as most will likely respond to their prescribed biologic the first time. Physicians can prescribe these drugs with increased confidence, and the healthcare system will realize lower net costs as well as greatly reduced wasted spend by significantly improving initial response rates to expensive biologic therapeutics.

Carrier-phase GPS techniques are capable of measuring positions with subcentimeter accuracy. With several antennae, carrier-phase GPS can be used to determine attitude. This paper presents a motion-based algorithm for resolving the integer ambiguities that is suitable for conditions of poor satellite visibility. In particular, this algorithm can use baselines with fewer than three common satellites visible. This algorithm was used very successfully in practice as the attitude sensor for an autonomous model helicopter and aircraft.

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