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Mortari, Daniele

Publications and source records attributed to Mortari, Daniele.

8 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

A Functional Interpolation Approach to Compute Period Orbits in the Circular Restricted Three-body Problem

In this paper, we develop a method to solve for periodic orbits, i.e., Lyapunov and Halo orbits, using a functional interpolation scheme called the Theory of Func- tional Connections (TFC). Using this technique, a periodic constraint is analyti- cally embedded into the TFC constrained expression. By doing this, the system of differential equations governing the three-body problem is transformed into an unconstrained optimization problem where simple numerical schemes can be used to find a solution, e.g., nonlinear least-squares is used. This allows for a simpler numerical implementation with comparable accuracy and speed to the traditional differential corrector method.

Mortari, Daniele↗
NASA NTRS2018

Applications of the Dynamic N-Dimensional K-Vector

The n-dimensional k-vector (NDKV) is an appealing alternative to binary tress for resolving complex queries in large relational databases. The method has excelled in several applications involving static databases. The present paper extends the theory supporting the NDKV to handle dynamic databases, where the data is updated frequently. This includes deleting records, adding new entries, or editing existing elements. The merit of this new version of the NDKV, the dynamic n-dimensional k-vector (DNDKV), is that it is no longer necessary to recompute the entire k-vector (the main structure that indexes the data) every time a record changes. The algorithm updates the four constituents of the standard NDKV on the fly: the database, sorted database, index, and k-vector tables. As a result, the DNDKV becomes comparable in terms of capabilities and flexibility to stateof-the-art storage engines relying on structured query languages (SQL). The performance of the DNDKV is assessed by running typical read/write operations on a database that contains millions of pre-computed missions to celestial bodies. This database requires frequent updates whenever an orbit solution is refined or new bodies are discovered. The DNDKV is faster than rebuilding the k-vector tables completely, provided that the number of elements being added or removed is not excessively large. Direct runtime comparisons with MySQL suggest that the DNDKV is several times faster for reading but might be slower for writing and updating the database. One limit of the technique is the elements being added must be within the range of the current k-vector tables. If this is not the case, the technique cannot be used and the k-vector tables must be rebuilt from scratch.

Mortari, Daniele↗
NASA NTRS2015

Position Estimation Using Image Derivative

This paper describes an image processing algorithm to process Moon and/or Earth images. The theory presented is based on the fact that Moon hard edge points are characterized by the highest values of the image derivative. Outliers are eliminated by two sequential filters. Moon center and radius are then estimated by nonlinear least-squares using circular sigmoid functions. The proposed image processing has been applied and validated using real and synthetic Moon images.

Mortari, Daniele↗
NASA NTRS2003

System and method for attitude determination based on optical imaging

A method and apparatus is provide for receiving a first set of optical data from a first field of view and receiving a second set of optical data from a second field of view. A portion of the first set of optical data is communicated and a portion of the second set of optical data is reflected, both toward an optical combiner. The optical combiner then focuses the portions onto the image plane such that information at the image plane that is associated with the first and second fields of view is received by an optical detector and used to determine an attitude characteristic.

Junkins, John L.↗
NASA NTRS2000

New Developments in Quaternion Estimation from Vector Observations

This paper contains a critical comparison of estimators minimizing Wahba's loss function. Some new results are presented for the QUaternion ESTimator (QUEST) and EStimators of the Optimal Quaternion (ESOQ and ESOQ2) to avoid the computational burden of sequential rotations in these algorithms. None of these methods is as robust in principle as Davenport's q method or the Singular Value Decomposition (SVD) method, which are significantly slower. Robustness is only an issue for measurements with widely differing accuracies, so the fastest estimators, the modified ESOQ and ESOQ2, are well suited to sensors that track multiple stars with comparable accuracies. More robust forms of ESOQ and ESOQ2 are developed that are intermediate in speed.

Markley, F. Landis↗
NASA NTRS1999

How to Estimate Attitude from Vector Observations

In many spacecraft attitude systems, the attitude observations are naturally represented as unit vectors. Typical examples are the unit vectors giving the direction to the sun or a star and the unit vector in the direction of the Earth's magnetic field. In 1965, Grace Wahba, proposed the following problem: Find the orthogonal matrix A with determinant +1 that minimizes the loss function L(A) is identity with 1/2(Sum from i a(sub i) (absolute value of b(sub i - A(r(sub i))(exp 2))) where the set of b(sub i) is a set of unit vectors measured in a spacecraft's body frame, the set of r(sub i) are the corresponding unit vectors in a reference frame, and the set of a(sub i) are non-negative weights. Wahba's problem can be related to Maximum Likelihood Estimation if the weights are chosen to be inverse variances, a(sub i) = sigma((sub -2). Wahba didn't assume this, but it will be convenient to assume it in this paper. Wahba'soptimality condition has provided the basis for many attitude determination algorithms. The purpose of this paper is to give an overview of the most popular and most promising algorithm and to provide accuracy and speed comparisons.

Markley,F. Landis↗
NASA NTRS1999

How to Estimate Attitude from Vector Observations

The most robust estimators minimizing Wahba's loss function are Davenport's q method and the Singular Value Decomposition (SVD) method. The q method is faster than the SVD method with three or more measurements. The other algorithms are less robust since they solve the characteristic polynomial equation to find the maximum eigenvalue of Davenport's K matrix. They are only preferable when speed or processor power is an important consideration. Of these, Fast Optimal Attitude Matrix (FOAM) is the most robust and faster than the q method. Robustness is only an issue for measurements with widely differing accuracies, so the fastest algorithms, Quaternion ESTimator (QUEST), EStimator of the Optimal Quaternion (ESOQ), and ESOQ2, are well suited to star sensor applications.

Markley, F. Landis↗