Geomagnetic orbit determination: EKF or UKF?

Purpose Autonomous orbit determination using geomagnetic measurements is an important backup technique for safe spacecraft navigation with a mere magnetometer. The geomagnetic model is used for the state estimation of orbit elements, but this model is highly nonlinear. Therefore, many efforts have been paid to developing nonlinear filters based on extended Kalman filter (EKF) and unscented Kalman filter (UKF). This paper aims to analyze whether to use UKF or EKF in solving the geomagnetic orbit determination problem and try to give a general conclusion. Design/methodology/approach This paper revisits the problem and from both the theoretical and engineering results, the authors show that the EKF and UKF show identical estimation performances in the presence of nonlinearity in the geomagnetic model. Findings While EKF consumes less computational time, the UKF is computationally inefficient but owns better accuracy for most nonlinear models. It is also noted that some other navigation techniques are also very similar with the geomagnetic orbit determination. Practical implications The intrinsic reason of such equivalence is because of the orthogonality of the spherical harmonics which has not been discovered in previous studies. Thus, the applicability of the presented findings are not limited only to the major problem in this paper but can be extended to all those schemes with spherical harmonic models. Originality/value The results of this paper provide a fact that there is no need to choose UKF as a preferred candidate in orbit determination. As UKF achieves almost the same accuracy as that of EKF, its loss in computational efficiency will be a significant obstacle in real-time implementation.

High-resolution GRACE Monthly Gravity Field Solutions Expressed as Geopotential Coefficients

<p>The commonly used filters (e.g. Gaussian smoothing, decorrelation and DDK filtering) applied to GRACE spherical harmonic gravity field solutions generally lead to reduced resolution, signal damping and leakage. This work is dedicated to improving spatial resolution and reducing signal damping by developing a regularization method with spectral constraints to spherical harmonics. Before constructing the spectral constraints, we create spatial constraints over global grids (covering lands, oceans and the boundaries between lands and oceans) from the a priori information of GRACE spherical harmonic models. Since we are solving geopotential coefficients rather than mascon grids, we further transfer the spatial constraints into the spectral domain according to the law of variance-covariance propagation, leading to spectral constraints regarding geopotential coefficients. In our work, the regularization method with spectral constraints was demonstrated to have comparable ability as mascon modelling method to enhance the spatial resolution and signal power besides reducing signal leakage. Applying the presented method with spatial constraints, we produced the first time series of high-resolution gravity field solutions expressed as geopotential coefficients complete to degree and order 180. Our analyses over the global and regional areas show that our high-resolution solutions are in good agreement with CSR and JPL mascon solutions.</p>

Harmonic analysis of surface instability patterns on colloidal particles

Spectral topographical analysis of wrinkled and crumpled colloidal particle surfaces utilizing cryo-electron tomography and spherical harmonic models.

Using isostatic gravity anomalies from spherical harmonic models and elastic plate compensation to interpret the lithosphere of the Bolivian Andes

We have determined for the Bolivian Andes that the new global gravity models derived from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission may be used directly to study lithospheric structure. Toward this end, we have formulated Bouguer and isostatic gravity anomalies in spherical approximation, rather than in the usual planar approach, using spherical harmonic series consistent with the satellite-derived gravitational models. From the approximate equivalency of topographic masses and surface density layers using the Helmert condensation method we further derived and used isotropic transfer relations between the spherical spectra of topographic loads and elastic spherical shell deflections, where the Airy isostatic compensation is the special case of no flexural rigidity. A numerical comparison of these spherical harmonic models to conventional three-dimensional modeling based on topographic data and newly acquired surface gravity data in Bolivia confirmed their suitability for lithospheric interpretation. Specifically, the relatively high and uniform resolution of the satellite gravitational model (better than 83 km) produces detailed maps of the isostatic anomaly that clearly delineate the flexure of the Brazilian shield that is thrust under the Sub-Andes. Inferred values of the thickness of Airy-type roots and the flexural rigidity of the elastic lithosphere agree reasonably with published results based on seismic and surface gravity data. In addition, a local minimum in the flexural rigidity is evident at the sharp bend of the eastern margins of the Sub-Andes in Bolivia. This feature is consistent with earlier theories for counter rotations about a vertical axis at this minimum, associated with the confluence of the subducted Nazca plate and the Brazilian craton. The GOCE model thus generates high-resolution isostatic anomaly maps that offer additional structural detail not seen as clearly from previous seismic and gravity investigations in this region.

Texture and structural refinement using neutron diffraction data from molybdite (MoO3) and calcite (CaCO3) powders and a Ni-rich Ni50.7Ti49.30 alloy

Preferred orientation or texture is a common feature of experimental powder patterns. The mathematics of two commonly used models for preferred orientation—the March-Dollase and the generalized spherical-harmonic models—is reviewed. Both models were applied individually to neutron powder data from uniaxially pressed molybdite (MoO3) and calcite (CaCO3) powders in Rietveld analyses, as well as the as-received powders. The structural refinement results are compared to single-crystal structures. The results indicate that reasonable refinement of crystal structures can be obtained using either the March model or generalized spherical-harmonic description. However, the generalized spherical-harmonic description provided better Rietveld fits than the March model for the molybdite and calcite. Therefore, the generalized spherical-harmonic description is recommended for correction of preferred orientation in neutron diffraction analysis for both crystal structure refinement and phase composition analysis. Subsequently, the generalized spherical-harmonic description is extended to crystal structure refinement of annealed and the aged polycrystalline Ni-rich Ni50.7Ti49.30 shape memory alloys.