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NASA NTRS2006

Algorithms for Maneuvering Spacecraft Around Small Bodies

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Acikmese, A. Bechet↗
NASA NTRS2011

SMOS/SMAP Synergy for SMAP Level 2 Soil Moisture Algorithm Evaluation

Soil Moisture Active Passive (SMAP) satellite has been proposed to provide global measurements of soil moisture and land freeze/thaw state at 10 km and 3 km resolutions, respectively. SMAP would also provide a radiometer-only soil moisture product at 40-km spatial resolution. This product and the supporting brightness temperature observations are common to both SMAP and European Space Agency's Soil Moisture and Ocean Salinity (SMOS) mission. As a result, there are opportunities for synergies between the two missions. These include exploiting the data for calibration and validation and establishing longer term L-band brightness temperature and derived soil moisture products. In this investigation we will be using SMOS brightness temperature, ancillary data, and soil moisture products to develop and evaluate a candidate SMAP L2 passive soil moisture retrieval algorithm. This work will begin with evaluations based on the SMOS product grids and ancillary data sets and transition to those that will be used by SMAP. An important step in this analysis is reprocessing the multiple incidence angle observations provided by SMOS to a global brightness temperature product that simulates the constant 40 degree incidence angle observations that SMAP will provide. The reprocessed brightness temperature data provide a basis for evaluating different SMAP algorithm alternatives. Several algorithms are being considered for the SMAP radiometer-only soil moisture retrieval. In this first phase, we utilized only the Single Channel Algorithm (SCA), which is based on the radiative transfer equation and uses the channel that is most sensitive to soil moisture (H-pol). Brightness temperature is corrected sequentially for the effects of temperature, vegetation, roughness (dynamic ancillary data sets) and soil texture (static ancillary data set). European Centre for Medium-Range Weather Forecasts (ECMWF) estimates of soil temperature for the top layer (as provided as part of the SMOS ancillary data) were used to correct for surface temperature effects and to derive microwave emissivity. ECMWF data were also used for precipitation forecasts, presence of snow, and frozen ground. Vegetation options are described below. One year of soil moisture observations from a set of four watersheds in the U.S. were used to evaluate four different retrieval methodologies: (1) SMOS soil moisture estimates (version 400), (2) SeA soil moisture estimates using the SMOS/SMAP data with SMOS estimated vegetation optical depth, which is part of the SMOS level 2 product, (3) SeA soil moisture estimates using the SMOS/SMAP data and the MODIS-based vegetation climatology data, and (4) SeA soil moisture estimates using the SMOS/SMAP data and actual MODIS observations. The use of SMOS real-world global microwave observations and the analyses described here will help in the development and selection of different land surface parameters and ancillary observations needed for the SMAP soil moisture algorithms. These investigations will greatly improve the quality and reliability of this SMAP product at launch.

Bindlish, Rajat↗
NASA NTRS2011

The NASA Soil Moisture Active Passive (SMAP) Mission - Algorithm and Cal/Val Activities and Synergies with SMOS and Other L-Band Missions

NASA's Soil Moisture Active Passive (SMAP) mission, planned for launch in late 2014, has as its key measurement objective the frequent, global mapping of near-surface soil moisture and its freeze-thaw state. SMAP soil moisture and freeze/thaw measurements at 10 km and 3 km resolutions respectively, would enable significantly improved estimates of water, energy and carbon transfers between the land and atmosphere. Soil moisture control of these fluxes is a key factor in the performance of atmospheric models used for weather forecasts and climate projections Soil moisture measurements are also of great importance in assessing floods and for monitoring drought. In addition, observations of soil moisture and freeze/thaw timing over the boreal latitudes can help reduce uncertainties in quantifying the global carbon balance. The SMAP measurement concept utilizes an L-band radar and radiometer sharing a rotating 6-meter mesh reflector antenna. The SMAP radiometer and radar flight hardware and ground processing designs are incorporating approaches to identify and mitigate potential terrestrial radio frequency interference (RFI). The radar and radiometer instruments are planned to operate in a 680 km polar orbit, viewing the surface at a constant 40-degree incidence angle with a 1000-km swath width, providing 3-day global coverage. Data from the instruments would yield global maps of soil moisture and freeze/thaw state to be provided at 10 km and 3 km resolutions respectively, every two to three days. Plans are to provide also a radiometer-only soil moisture product at 40-km spatial resolution. This product and the underlying brightness temperatures have characteristics similar to those provided by the Soil Moisture and Ocean Salinity (SMOS) mission. As a result, there are unique opportunities for common data product development and continuity between the two missions. SMAP also has commonalities with other satellite missions having L-band radiometer and/or radar sensors applicable to soil moisture measurement, such as Aquarius, SAO COM, and ALOS-2. The algorithms and data products for SMAP are being developed in the SMAP Science Data System (SDS) Testbed. The algorithms are developed and evaluated in the SDS Testbed using simulated SMAP observations as well as observational data from current airborne and spaceborne L-band sensors including SMOS. The SMAP project is developing a Calibration and Validation (Cal/Val) Plan that is designed to support algorithm development (pre-launch) and data product validation (post-launch). A key component of the Cal/Val Plan is the identification, characterization, and instrumentation of sites that can be used to calibrate and validate the sensor data (Level I) and derived geophysical products (Level 2 and higher). In this presentation we report on the development status of the SMAP data product algorithms, and the planning and implementation of the SMAP Cal/Val program. Several components of the SMAP algorithm development and Cal/Val plans have commonality with those of SMOS, and for this reason there are shared activities and resources that can be utilized between the missions, including in situ networks, ancillary data sets, and long-term monitoring sites.

Njoku, Eni↗
NASA NTRS2011

POSE Algorithms for Automated Docking

POSE (relative position and attitude) can be computed in many different ways. Given a sensor that measures bearing to a finite number of spots corresponding to known features (such as a target) of a spacecraft, a number of different algorithms can be used to compute the POSE. NASA has sponsored the development of a flash LIDAR proximity sensor called the Vision Navigation Sensor (VNS) for use by the Orion capsule in future docking missions. This sensor generates data that can be used by a variety of algorithms to compute POSE solutions inside of 15 meters, including at the critical docking range of approximately 1-2 meters. Previously NASA participated in a DARPA program called Orbital Express that achieved the first automated docking for the American space program. During this mission a large set of high quality mated sensor data was obtained at what is essentially the docking distance. This data set is perhaps the most accurate truth data in existence for docking proximity sensors in orbit. In this paper, the flight data from Orbital Express is used to test POSE algorithms at 1.22 meters range. Two different POSE algorithms are tested for two different Fields-of-View (FOVs) and two different pixel noise levels. The results of the analysis are used to predict future performance of the POSE algorithms with VNS data.

Heaton, Andrew F.↗
NASA NTRS2005

Fast Algorithms for Model-Based Diagnosis

Two improved new methods for automated diagnosis of complex engineering systems involve the use of novel algorithms that are more efficient than prior algorithms used for the same purpose. Both the recently developed algorithms and the prior algorithms in question are instances of model-based diagnosis, which is based on exploring the logical inconsistency between an observation and a description of a system to be diagnosed. As engineering systems grow more complex and increasingly autonomous in their functions, the need for automated diagnosis increases concomitantly. In model-based diagnosis, the function of each component and the interconnections among all the components of the system to be diagnosed (for example, see figure) are represented as a logical system, called the system description (SD). Hence, the expected behavior of the system is the set of logical consequences of the SD. Faulty components lead to inconsistency between the observed behaviors of the system and the SD. The task of finding the faulty components (diagnosis) reduces to finding the components, the abnormalities of which could explain all the inconsistencies. Of course, the meaningful solution should be a minimal set of faulty components (called a minimal diagnosis), because the trivial solution, in which all components are assumed to be faulty, always explains all inconsistencies. Although the prior algorithms in question implement powerful methods of diagnosis, they are not practical because they essentially require exhaustive searches among all possible combinations of faulty components and therefore entail the amounts of computation that grow exponentially with the number of components of the system.

Fijany, Amir↗
NASA NTRS2011

A General Event Location Algorithm with Applications to Eclispe and Station Line-of-Sight

A general-purpose algorithm for the detection and location of orbital events is developed. The proposed algorithm reduces the problem to a global root-finding problem by mapping events of interest (such as eclipses, station access events, etc.) to continuous, differentiable event functions. A stepping algorithm and a bracketing algorithm are used to detect and locate the roots. Examples of event functions and the stepping/bracketing algorithms are discussed, along with results indicating performance and accuracy in comparison to commercial tools across a variety of trajectories.

Parker, Joel J. K.↗
NASA NTRS2010

Evaluation of the VIIRS Land Algorithms at Land PEATE

The Land Product Evaluation and Algorithm Testing Element (Land PEATE), a component of the Science Data Segment of the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP), is being developed at the NASA Goddard Space Flight Center (GSFC). The primary task of the Land PEATE is to assess the quality of the Visible Infrared Imaging Radiometer Suite (VIIRS) Land data products made by the Interface Data Processing System (IDPS) using the Operational (OPS) Code during the NPP era and to recommend improvements to the algorithms in the IDPS OPS code. The Land PEATE uses a version of the MODIS Adaptive Processing System (MODAPS), NPPDAPS, that has been modified to produce products from the IDPS OPS code and software provided by the VIIRS Science Team, and uses the MODIS Land Data Operational Product Evaluation (LDOPE) team for evaluation of the data records generated by the NPPDAPS. Land PEATE evaluates the algorithms by comparing data products generated using different versions of the algorithm and also by comparing to heritage products generated from different instrument such as MODIS using various quality assessment tools developed at LDOPE. This paper describes the Land PEATE system and some of the approaches used by the Land PEATE for evaluating the VIIRS Land algorithms during the pre-launch period of the NPP mission and the proposed plan for long term monitoring of the quality of the VIIRS Land products post-launch.

Wolfe, Robert E.↗
NASA NTRS2004

Algorithm for Training a Recurrent Multilayer Perceptron

An improved algorithm has been devised for training a recurrent multilayer perceptron (RMLP) for optimal performance in predicting the behavior of a complex, dynamic, and noisy system multiple time steps into the future. [An RMLP is a computational neural network with self-feedback and cross-talk (both delayed by one time step) among neurons in hidden layers]. Like other neural-network-training algorithms, this algorithm adjusts network biases and synaptic-connection weights according to a gradient-descent rule. The distinguishing feature of this algorithm is a combination of global feedback (the use of predictions as well as the current output value in computing the gradient at each time step) and recursiveness. The recursive aspect of the algorithm lies in the inclusion of the gradient of predictions at each time step with respect to the predictions at the preceding time step; this recursion enables the RMLP to learn the dynamics. It has been conjectured that carrying the recursion to even earlier time steps would enable the RMLP to represent a noisier, more complex system.

Parlos, Alexander G.↗
NASA NTRS2003

Using a Portfolio of Algorithms for Planning and Scheduling

The Automated Scheduling and Planning Environment (ASPEN) software system, aspects of which have been reported in several previous NASA Tech Briefs articles, includes a subsystem that utilizes a portfolio of heuristic algorithms that work synergistically to solve problems. The nature of the synergy of the specific algorithms is that their likelihoods of success are negatively correlated: that is, when a combination of them is used to solve a problem, the probability that at least one of them will succeed is greater than the sum of probabilities of success of the individual algorithms operating independently of each other. In ASPEN, the portfolio of algorithms is used in a planning process of the iterative repair type, in which conflicts are detected and addressed one at a time until either no conflicts exist or a user-defined time limit has been exceeded. At each choice point (e.g., selection of conflict; selection of method of resolution of conflict; or choice of move, addition, or deletion) ASPEN makes a stochastic choice of a combination of algorithms from the portfolio. This approach makes it possible for the search to escape from looping and from solutions that are locally but not globally optimum.

Sherwood, Robert↗
NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC): 2. Aerosol Algorithm

An aerosol component of a new multiangle implementation of atmospheric correction (MAIAC) algorithm is presented. MAIAC is a generic algorithm developed for the Moderate Resolution Imaging Spectroradiometer (MODIS), which performs aerosol retrievals and atmospheric correction over both dark vegetated surfaces and bright deserts based on a time series analysis and image-based processing. The MAIAC look-up tables explicitly include surface bidirectional reflectance. The aerosol algorithm derives the spectral regression coefficient (SRC) relating surface bidirectional reflectance in the blue (0.47 micron) and shortwave infrared (2.1 micron) bands; this quantity is prescribed in the MODIS operational Dark Target algorithm based on a parameterized formula. The MAIAC aerosol products include aerosol optical thickness and a fine-mode fraction at resolution of 1 km. This high resolution, required in many applications such as air quality, brings new information about aerosol sources and, potentially, their strength. AERONET validation shows that the MAIAC and MOD04 algorithms have similar accuracy over dark and vegetated surfaces and that MAIAC generally improves accuracy over brighter surfaces due to the SRC retrieval and explicit bidirectional reflectance factor characterization, as demonstrated for several U.S. West Coast AERONET sites. Due to its generic nature and developed angular correction, MAIAC performs aerosol retrievals over bright deserts, as demonstrated for the Solar Village Aerosol Robotic Network (AERONET) site in Saudi Arabia.

Lyapustin, A.↗
NASA NTRS2011

Chlorophyll-a Algorithms for Oligotrophic Oceans: A Novel Approach Based on Three-Band Reflectance Difference

A new empirical algorithm is proposed to estimate surface chlorophyll-a concentrations (Chl) in the global ocean for Chl less than or equal to 0.25 milligrams per cubic meters (approximately 77% of the global ocean area). The algorithm is based on a color index (CI), defined as the difference between remote sensing reflectance (R(sub rs), sr(sup -1) in the green and a reference formed linearly between R(sub rs) in the blue and red. For low Chl waters, in situ data showed a tighter (and therefore better) relationship between CI and Chl than between traditional band-ratios and Chl, which was further validated using global data collected concurrently by ship-borne and SeaWiFS satellite instruments. Model simulations showed that for low Chl waters, compared with the band-ratio algorithm, the CI-based algorithm (CIA) was more tolerant to changes in chlorophyll-specific backscattering coefficient, and performed similarly for different relative contributions of non-phytoplankton absorption. Simulations using existing atmospheric correction approaches further demonstrated that the CIA was much less sensitive than band-ratio algorithms to various errors induced by instrument noise and imperfect atmospheric correction (including sun glint and whitecap corrections). Image and time-series analyses of SeaWiFS and MODIS/Aqua data also showed improved performance in terms of reduced image noise, more coherent spatial and temporal patterns, and consistency between the two sensors. The reduction in noise and other errors is particularly useful to improve the detection of various ocean features such as eddies. Preliminary tests over MERIS and CZCS data indicate that the new approach should be generally applicable to all existing and future ocean color instruments.

Hu, Chuanmin↗
NASA NTRS2012

Algorithm for Simulating Atmospheric Turbulence and Aeroelastic Effects on Simulator Motion Systems

Atmospheric turbulence produces high frequency accelerations in aircraft, typically greater than the response to pilot input. Motion system equipped flight simulators must present cues representative of the aircraft response to turbulence in order to maintain the integrity of the simulation. Currently, turbulence motion cueing produced by flight simulator motion systems has been less than satisfactory because the turbulence profiles have been attenuated by the motion cueing algorithms. This report presents a new turbulence motion cueing algorithm, referred to as the augmented turbulence channel. Like the previous turbulence algorithms, the output of the channel only augments the vertical degree of freedom of motion. This algorithm employs a parallel aircraft model and an optional high bandwidth cueing filter. Simulation of aeroelastic effects is also an area where frequency content must be preserved by the cueing algorithm. The current aeroelastic implementation uses a similar secondary channel that supplements the primary motion cue. Two studies were conducted using the NASA Langley Visual Motion Simulator and Cockpit Motion Facility to evaluate the effect of the turbulence channel and aeroelastic model on pilot control input. Results indicate that the pilot is better correlated with the aircraft response, when the augmented channel is in place.

Ercole, Anthony V.↗
NASA NTRS2012

Assessment of Polarization Effect on Efficiency of Levenberg-Marquardt Algorithm in Case of Thin Atmosphere Over Black Surface

The Levenberg-Marquardt algorithm [1, 2] provides a numerical iterative solution to the problem of minimization of a function over a space of its parameters. In our work, the Levenberg-Marquardt algorithm retrieves optical parameters of a thin (single scattering) plane parallel atmosphere irradiated by collimated infinitely wide monochromatic beam of light. Black ground surface is assumed. Computational accuracy, sensitivity to the initial guess and the presence of noise in the signal, and other properties of the algorithm are investigated in scalar (using intensity only) and vector (including polarization) modes. We consider an atmosphere that contains a mixture of coarse and fine fractions. Following [3], the fractions are simulated using Henyey-Greenstein model. Though not realistic, this assumption is very convenient for tests [4, p.354]. In our case it yields analytical evaluation of Jacobian matrix. Assuming the MISR geometry of observation [5] as an example, the average scattering cosines and the ratio of coarse and fine fractions, the atmosphere optical depth, and the single scattering albedo, are the five parameters to be determined numerically. In our implementation of the algorithm, the system of five linear equations is solved using the fast Cramer s rule [6]. A simple subroutine developed by the authors, makes the algorithm independent from external libraries. All Fortran 90/95 codes discussed in the presentation will be available immediately after the meeting from sergey.v.korkin@nasa.gov by request.

Korkin, S.↗
NASA NTRS2012

SBUV version 8.6 Retrieval Algorithm: Error Analysis and Validation Technique

SBUV version 8.6 algorithm was used to reprocess data from the Back Scattered Ultra Violet (BUV), the Solar Back Scattered Ultra Violet (SBUV) and a number of SBUV/2 instruments, which 'span a 41-year period from 1970 to 2011 (except a 5-year gap in the 1970s)[see Bhartia et al, 2012]. In the new version Daumont et al. [1992] ozone cross section were used, and new ozone [McPeters et ai, 2007] and cloud climatologies Doiner and Bhartia, 1995] were implemented. The algorithm uses the Optimum Estimation technique [Rodgers, 2000] to retrieve ozone profiles as ozone layer (partial column, DU) on 21 pressure layers. The corresponding total ozone values are calculated by summing ozone columns at individual layers. The algorithm is optimized to accurately retrieve monthly zonal mean (mzm) profiles rather than an individual profile, since it uses monthly zonal mean ozone climatology as the A Priori. Thus, the SBUV version 8.6 ozone dataset is better suited for long-term trend analysis and monitoring ozone changes rather than for studying short-term ozone variability. Here we discuss some characteristics of the SBUV algorithm and sources of error in the SBUV profile and total ozone retrievals. For the first time the Averaging Kernels, smoothing errors and weighting functions (or Jacobians) are included in the SBUV metadata. The Averaging Kernels (AK) represent the sensitivity of the retrieved profile to the true state and contain valuable information about the retrieval algorithm, such as Vertical Resolution, Degrees of Freedom for Signals (DFS) and Retrieval Efficiency [Rodgers, 2000]. Analysis of AK for mzm ozone profiles shows that the total number of DFS for ozone profiles varies from 4.4 to 5.5 out of 6-9 wavelengths used for retrieval. The number of wavelengths in turn depends on solar zenith angles. Between 25 and 0.5 hPa, where SBUV vertical resolution is the highest, DFS for individual layers are about 0.5.

Kramarova, N. A.↗
NASA NTRS2013

SDR Input Power Estimation Algorithms

The General Dynamics (GD) S-Band software defined radio (SDR) in the Space Communications and Navigation (SCAN) Testbed on the International Space Station (ISS) provides experimenters an opportunity to develop and demonstrate experimental waveforms in space. The SDR has an analog and a digital automatic gain control (AGC) and the response of the AGCs to changes in SDR input power and temperature was characterized prior to the launch and installation of the SCAN Testbed on the ISS. The AGCs were used to estimate the SDR input power and SNR of the received signal and the characterization results showed a nonlinear response to SDR input power and temperature. In order to estimate the SDR input from the AGCs, three algorithms were developed and implemented on the ground software of the SCAN Testbed. The algorithms include a linear straight line estimator, which used the digital AGC and the temperature to estimate the SDR input power over a narrower section of the SDR input power range. There is a linear adaptive filter algorithm that uses both AGCs and the temperature to estimate the SDR input power over a wide input power range. Finally, an algorithm that uses neural networks was designed to estimate the input power over a wide range. This paper describes the algorithms in detail and their associated performance in estimating the SDR input power.

Nappier, Jennifer M.↗
NASA NTRS2013

Automatic Data Filter Customization Using a Genetic Algorithm

This work predicts whether a retrieval algorithm will usefully determine CO2 concentration from an input spectrum of GOSAT (Greenhouse Gases Observing Satellite). This was done to eliminate needless runtime on atmospheric soundings that would never yield useful results. A space of 50 dimensions was examined for predictive power on the final CO2 results. Retrieval algorithms are frequently expensive to run, and wasted effort defeats requirements and expends needless resources. This algorithm could be used to help predict and filter unneeded runs in any computationally expensive regime. Traditional methods such as the Fischer discriminant analysis and decision trees can attempt to predict whether a sounding will be properly processed. However, this work sought to detect a subsection of the dimensional space that can be simply filtered out to eliminate unwanted runs. LDAs (linear discriminant analyses) and other systems examine the entire data and judge a "best fit," giving equal weight to complex and problematic regions as well as simple, clear-cut regions. In this implementation, a genetic space of "left" and "right" thresholds outside of which all data are rejected was defined. These left/right pairs are created for each of the 50 input dimensions. A genetic algorithm then runs through countless potential filter settings using a JPL computer cluster, optimizing the tossed-out data s yield (proper vs. improper run removal) and number of points tossed. This solution is robust to an arbitrary decision boundary within the data and avoids the global optimization problem of whole-dataset fitting using LDA or decision trees. It filters out runs that would not have produced useful CO2 values to save needless computation. This would be an algorithmic preprocessing improvement to any computationally expensive system.

Mandrake, Lukas↗
NASA NTRS2013

A TCAS-II Resolution Advisory Detection Algorithm

The Traffic Alert and Collision Avoidance System (TCAS) is a family of airborne systems designed to reduce the risk of mid-air collisions between aircraft. TCAS~II, the current generation of TCAS devices, provides resolution advisories that direct pilots to maintain or increase vertical separation when aircraft distance and time parameters are beyond designed system thresholds. This paper presents a mathematical model of the TCAS~II Resolution Advisory (RA) logic that assumes accurate aircraft state information. Based on this model, an algorithm for RA detection is also presented. This algorithm is analogous to a conflict detection algorithm, but instead of predicting loss of separation, it predicts resolution advisories. It has been formally verified that for a kinematic model of aircraft trajectories, this algorithm completely and correctly characterizes all encounter geometries between two aircraft that lead to a resolution advisory within a given lookahead time interval. The RA detection algorithm proposed in this paper is a fundamental component of a NASA sense and avoid concept for the integration of Unmanned Aircraft Systems in civil airspace.

Munoz, Cesar↗
NASA NTRS2015

A Comparison of Three Algorithms for Orion Drogue Parachute Release

The Orion Multi-Purpose Crew Vehicle is susceptible to ipping apex forward between drogue parachute release and main parachute in ation. A smart drogue release algorithm is required to select a drogue release condition that will not result in an apex forward main parachute deployment. The baseline algorithm is simple and elegant, but does not perform as well as desired in drogue failure cases. A simple modi cation to the baseline algorithm can improve performance, but can also sometimes fail to identify a good release condition. A new algorithm employing simpli ed rotational dynamics and a numeric predictor to minimize a rotational energy metric is proposed. A Monte Carlo analysis of a drogue failure scenario is used to compare the performance of the algorithms. The numeric predictor prevents more of the cases from ipping apex forward, and also results in an improvement in the capsule attitude at main bag extraction. The sensitivity of the numeric predictor to aerodynamic dispersions, errors in the navigated state, and execution rate is investigated, showing little degradation in performance.

Matz, Daniel A.↗