A forward operator and its adjoint for GPS slant total delays
نویسندگان
چکیده
In a recent study we developed a fast and accurate algorithm to compute Global Positioning System (GPS) Slant Total Delay (STDs) utilizing numerical weather model data. Having developed a forward operator we construct in this study the tangent linear (adjoint) operator by application of the chain rule of differential calculus in forward (reverse) mode. Armed with these operators we show in a simulation study the potential benefit of GPS STDs in inverse modeling. We conclude that the developed operators are tailored for three (four)-dimensional variational data assimilation and/or travel time tomography.
منابع مشابه
Development and optimization of the IPMMM5 GPS slant path 4DVAR system
This article describes the development of tools for routine 4-dimensional variational data assimilation of Global Positioning System Slant Total Delay (STD) data in the framework of the MM5 system at the Institute of Physics and Meteorology of the University of Hohenheim. The Slant Total Delay forward operator is introduced which allows model validation and the assimilation in the Message-Passi...
متن کاملWeighted slant Toep-Hank Operators
A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...
متن کاملInvestigations into the Estimation of Tropospheric Delay and Wet Refractivity Using GPS Measurements
The principal error source in the GPS technology is a delay experienced by the GPS signal in propagating through the electrically neutral atmosphere, usually referred to as a tropospheric delay. This delay is normally calculated in the zenith direction, and is referred to as a zenith tropospheric delay. The delay consists of a zenith hydrostatic delay, which can be modeled accurately using surf...
متن کاملOn Generalization of Sturm-Liouville Theory for Fractional Bessel Operator
In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...
متن کاملOperator-valued tensors on manifolds
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
متن کامل