Microfinance and Small Deposit Mobilization: Fact or Fiction?

Two primary arguments can be made for voluntary deposit mobilization among microfinance institutions (MFIs). First, deposit mobilization is an alternative source of funds that was neglected by most MFIs until a few years ago. From this perspective, voluntary deposit mobilization helps MFIs achieve independence from donors and investors, which is particularly important in periods of liquidity constraints. Second, poor households benefit greatly from having access to deposit mechanisms, and the benefits can be even greater than those derived from access to credit. On the funding side, the industry has demonstrated great progress, with savings mobilization now representing more than half of the assets reported by deposit mobilizing MFIs, even though this share seems to have decreased a bit during the last three years

The celestial mechanics approach: application to data of the GRACE mission

The celestial mechanics approach (CMA) has its roots in the Bernese GPS software and was extensively used for determining the orbits of high-orbiting satellites. The CMA was extended to determine the orbits of Low Earth Orbiting satellites (LEOs) equipped with GPS receivers and of constellations of LEOs equipped in addition with inter-satellite links. In recent years the CMA was further developed and used for gravity field determination. The CMA was developed by the Astronomical Institute of the University of Bern (AIUB). The CMA is presented from the theoretical perspective in (Beutler etal. 2010). The key elements of the CMA are illustrated here using data from 50 days of GPS, K-Band, and accelerometer observations gathered by the Gravity Recovery And Climate Experiment (GRACE) mission in 2007. We study in particular the impact of (1) analyzing different observables [Global Positioning System (GPS) observations only, inter-satellite measurements only], (2) analyzing a combination of observations of different types on the level of the normal equation systems (NEQs), (3) using accelerometer data, (4) different orbit parametrizations (short-arc, reduced-dynamic) by imposing different constraints on the stochastic orbit parameters, and (5) using either the inter-satellite ranges or their time derivatives. The so-called GRACE baseline, i.e., the achievable accuracy of the GRACE gravity field for a particular solution strategy, is established for the CM

The celestial mechanics approach: theoretical foundations

Gravity field determination using the measurements of Global Positioning receivers onboard low Earth orbiters and inter-satellite measurements in a constellation of satellites is a generalized orbit determination problem involving all satellites of the constellation. The celestial mechanics approach (CMA) is comprehensive in the sense that it encompasses many different methods currently in use, in particular so-called short-arc methods, reduced-dynamic methods, and pure dynamic methods. The method is very flexible because the actual solution type may be selected just prior to the combination of the satellite-, arc- and technique-specific normal equation systems. It is thus possible to generate ensembles of substantially different solutions—essentially at the cost of generating one particular solution. The article outlines the general aspects of orbit and gravity field determination. Then the focus is put on the particularities of the CMA, in particular on the way to use accelerometer data and the statistical information associated with i

Comparison of empirical noise models for GRACE Follow-On derived with the Celestial Mechanics Approach

A key component of any model is the accurate specification of its quality. In gravity field modelling from satellite data, as it is done with the observation collected by GRACE Follow-On, usually least-squares adjustments are performed to obtain a monthly solution of the Earth's gravity field. However, the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. We take the Celestial Mechanics Approach (CMA), developed at the Astronomical Institute, University of Bern (AIUB), and extend it by an empirical modelling of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals. We compare and validate the solutions that employ empirical modelling with solutions that do not contain sophisticated noise modelling by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence of the empirically weighted solutions in a combination of monthly gravity fields based on other approaches as it is done in the COST-G framework

Variance component estimation for co-estimated noise parameters in GRACE Follow-On gravity field recovery

Temporal gravity field modelling from GRACE Follow-On has to cope with several noise sources contaminating not only the observations but also the observation equations via mis-modellings in the underlying background force models. One way to deal with such deficiencies is to extend the parameter space by additional quantities, such as pseudo-stochastic parameters, which are co-estimated in the Least-Squares Adjustment (LSA). These parameters are meant to absorb any kind of noise while retaining the signal in the gravity field and orbit parameters. In the Celestial Mechanics Approach (CMA) such pseudo-stochastic parameters are typically set-up as Piece-wise Constant Accelerations (PCA) in regular intervals of e.g., 15 min. The stochastic behaviour of these parameters is unknown because they reflect an accumulation of a variety of noise sources. In the CMA fictitious artificial zero-observations are appended to the vector of observations together with an empirically determined variance to introduce a stochastic model for the PCAs. In order to also co-estimate a stochastic model for the pseudo-stochastic parameters in the LSA we use Variance Component Estimation (VCE) as a well established tool to assign variance components to individual groups of observation. In the simplest case the magnitude of the constraints of the pseudo-stochastic parameters can be determined fully automatically. We present results for GRACE Follow-On gravity field recovery when extending the CMA by stochastic models for the piece-wise constant accelerations computed with VCE and provide noise and signal assessment applying the quality control tools routinely used in the frame of the Combination Service for Time-variable gravity fields (COST-G)

The new COST-G deterministic signal model

The precise orbit determination (POD) of Low Earth Orbiters (LEO), e.g. the Copernicus Sentinel Earth observation satellites, relies on the precise knowledge of the Earth gravity field and its variations with time. The most precise observation of time-variable gravity on a global scale is currently provided by the GRACE-FO satellites. But the monthly gravity field solutions are released with a latency of approx. 2 months, therefore they cannot be used for operational POD. We present a deterministic signal model (DSM) that is fitted to the time-series of COST-G combined monthly gravity fields and describe the differences with respect to the available long-term gravity models including seasonal and secular time-variations. To validate the DSM, dynamic POD of the Sentinel-2B, -3B and -6A satellites is performed based on long-term or monthly gravity field models, and on the COST-G DSM. We evaluate the model quality on the basis of carrier phase residuals, orbit overlap analysis and independent satellite laser ranging observations, and study the limitation on orbit altitude posed by the reduced spherical harmonic resolution of the monthly models and the DSM. The COST-G DSM is updated quarterly with the most recent GRACE-FO combined monthly gravity fields. It is foreseen to apply a sliding window approach with flexible window length to allow for an optimal adjustment in case of singular events like major earthquakes

Variance component estimation for co-estimated noise parameters in GRACE Follow-On gravity field recovery

Temporal gravity field modelling from GRACE Follow-On deals with several noise sources polluting the observations and the system of equations, be it actual measurement noise or mis-modellings in the underlying background models. One way to collect such deficiencies is to co-estimate additional pseudo-stochastic parameters in the least-squares adjustment which are meant to absorb any kind of noise while retaining the signal in the gravity field and orbit parameters. In the Celestial Mechanics Approach (CMA) such pseudo-stochastic parameters are typically piece-wise constant accelerations set up in regular intervals of e.g., 15 min, and an empirically determined constraint is added to confine the impact of the additional quantities. As the stochastic behaviour of these parameters is unknown because they reflect an accumulation of a variety of noise sources, Variance Component Estimation (VCE) is a well established tool to assign a stochastic model to the pseudo-stochastic orbit parameters driven by the observations. In the simplest case the magnitude of the constraints of the pseudo-stochastic orbit parameters can be determined fully automatically. We present results for GRACE Follow-On gravity field recovery when extending the CMA by stochastic models for the piece-wise constant accelerations computed with VCE and provide noise and signal assessment applying the quality control tools routinely used in the frame of the Combination Service for Time-variable gravity fields (COST-G)

Time-variable gravity field determination from GRACE Follow-On data usingthe Celestial Mechanics Approach extended by empirical noise modelling

We study gravity field determination from GRACE Follow-On satellite-to-satellite tracking using the inter-satellite K-band link and kinematic positions of the satellites as observations and pseudo- observations respectively. A key component of any model is the accurate specification of its quality. In the case of gravity field modelling from satellite data with the Celestial Mechanics Approach (CMA) a least-squares adjustment is performed to obtain a monthly solution of the Earthâ?Ts gravity field. However, the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. We present gravity field solutions computed with the CMA and extend it by an empirical modelling of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals. We compare and validate the solutions that use empirical modelling with solutions from the operational GRACE Follow-On processing at AIUB by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence of the empirically weighted solutions in a combination of monthly gravity fields based on other approaches as it is done by the Combination Service for Time-variable Gravity fields (COST-G) and make use of noise and signal assessment applying the quality control tools routinely used in the frame of COST-G

On the co-estimation of static and monthly gravity field solutions from GRACE Follow-On data

Temporal gravity field modelling from GRACE Follow-On data is usually performed by computing monthly snapshots of spherical harmonic coefficients representing the state of the Earthâ?Ts gravity field. Associated to this, the spherical harmonic series has to be truncated at a certain point, commonly at degree/order 96. Higher degrees and orders are fixed to the a priori used background gravity field model. We present an investigation on the influence of the high degrees and orders of different a priori background gravity field models on monthly gravity field model computations from GRACE Follow-On data. Furthermore, we extend the temporal gravity field modelling to additionally co-estimate a static gravity field for the GRACE Follow-On satellite mission along with the monthly snapshots to provide for a consistent handling of correlations between temporal and static gravity field coefficients. Moreover, we model the stochastic noise of the data with an empirical description of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals, to further study the influence of the high degrees and orders of the a priori background gravity field model on such noise models. We compare and validate the monthly solutions with the models from the operational GRACE Follow-On processing at AIUB by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence in a combination of monthly gravity fields based on other approaches as it is done by the Combination Service for Time-variable Gravity fields (COST-G) and make use of noise and signal assessment applying the quality control tools routinely used in the frame of COST-G