As: r – r B,0 r – r B,i i TiA B,cs = -x Re y ny -x(5)Sensors 2021, 21,7 ofwhere r will be the position on the satellite i at observation time, and r B,0 will be the initial position value of antenna B. They may be vectors of dimension three 1. By solving the Equation (4), sin , cos along with the float option of double-differenced ambiguity can be obtained. It really should be noted that the computed sin and cos are 2 two ordinarily inaccurate and can’t meet (sin ) + (cos ) = 1. The obtained ambiguity float solution and variance matrix can be used within the conventional LAMBDA look for the integer solution. It truly is anticipated that the geometric constraint can assist lower the amount of equation unknowns and strengthen the ambiguity search overall performance specially when the amount of out there satellites is small. two.two.two. Interpolation Calculation and Secondary Processing Following checking the baseline vectors as described in Section two.1, the precise position options of each and every dynamic antenna may be obtained. Thinking about that the platform rotation speed is comparatively stable, it really is assumed that the second derivative (angular acceleration) from the platform azimuth should be first-order differentiable. Moreover, the velocity derived from Doppler observations is precise. As a result, the cubic spline interpolation can be performed for the platform azimuth to compute the missing position in the dynamic antenna. Right after the interpolation calculation, as a way to decrease the amount of unsolvable epochs further, carry out secondary processing as outlined by the following measures: (a) (b)Sensors 2021, 21, x FOR PEER Evaluation (c)iTake the interpolated antenna position as the initial position, after which solve the float ambiguity calculation equation. Use LAMBDA to search the fixed ambiguity answer. Because the initial worth is much more correct, the achievement price of this step will boost. Integrate the outcomes of other antennae to receive the correct position. The schematic diagram is shown in Figure 6.Observation dataGeometric constraints aided ambiguity searchingEliminating gross errors, detecting cycle slips As the initial positionCoordinates of dynamic antennas in the body coordinates program of rotating platform Combined with the rotation speedSearch for integer ambiguityCalculate the baseline vectorIntegrate the successful positioning outcomes and calculate the azimuthInterpolate the azimuth at non-solution epochThe position of dynamic antennasPositioning final MK-2206 Autophagy results of four dynamic receiversNoCalculation first round YesFigure 6. six. The system of enhancing therate of precise relative positioning. Figure The process of improving the good results results price of precise relativepositioning.two.3. Utilizing the Mixture of Gaussian Distribution to Model Carrier-Phase Cycle SlipsAt present, all cycle-slip detection solutions can not assure that they w miss the alarm. Hence, analyzing the characteristics of cycle slip is conducive toSensors 2021, 21,8 of2.three. Employing the Mixture of Gaussian Distribution to Model Carrier-Phase Cycle Slips At present, all cycle-slip detection procedures can not assure that they may by no means miss the alarm. As a result, analyzing the traits of cycle slip is conducive to achieving both the integrity and availability indicators at the very same time. Cycle slips are characteristically have sharp peaks and heavy tails, and usually do not comply together with the typical distribution. However, it really is also improper to fit its statistical qualities employing the Elesclomol MedChemExpress skew-normal distribution model by knowledge. This pa.