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NASA NTRS2003

Algorithm Updates for the Fourth SeaWiFS Data Reprocessing

The efforts to improve the data quality for the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) data products have continued, following the third reprocessing of the global data set in May 2000. Analyses have been ongoing to address all aspects of the processing algorithms, particularly the calibration methodologies, atmospheric correction, and data flagging and masking. All proposed changes were subjected to rigorous testing, evaluation and validation. The results of these activities culminated in the fourth reprocessing, which was completed in July 2002. The algorithm changes, which were implemented for this reprocessing, are described in the chapters of this volume. Chapter 1 presents an overview of the activities leading up to the fourth reprocessing, and summarizes the effects of the changes. Chapter 2 describes the modifications to the on-orbit calibration, specifically the focal plane temperature correction and the temporal dependence. Chapter 3 describes the changes to the vicarious calibration, including the stray light correction to the Marine Optical Buoy (MOBY) data and improved data screening procedures. Chapter 4 describes improvements to the near-infrared (NIR) band correction algorithm. Chapter 5 describes changes to the atmospheric correction and the oceanic property retrieval algorithms, including out-of-band corrections, NIR noise reduction, and handling of unusual conditions. Chapter 6 describes various changes to the flags and masks, to increase the number of valid retrievals, improve the detection of the flag conditions, and add new flags. Chapter 7 describes modifications to the level-la and level-3 algorithms, to improve the navigation accuracy, correct certain types of spacecraft time anomalies, and correct a binning logic error. Chapter 8 describes the algorithm used to generate the SeaWiFS photosynthetically available radiation (PAR) product. Chapter 9 describes a coupled ocean-atmosphere model, which is used in one of the changes described in Chapter 4. Finally, Chapter 10 describes a comparison of results from the third and fourth reprocessings along the US. Northeast coast.

Hooker, Stanford, B.↗
NASA NTRS2003

Quantum Adiabatic Algorithms and Large Spin Tunnelling

We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.

Boulatov, A.↗
NASA NTRS2003

GOME Total Ozone and Calibration Error Derived Usign Version 8 TOMS Algorithm

The Global Ozone Monitoring Experiment (GOME) is a hyper-spectral satellite instrument measuring the ultraviolet backscatter at relatively high spectral resolution. GOME radiances have been slit averaged to emulate measurements of the Total Ozone Mapping Spectrometer (TOMS) made at discrete wavelengths and processed using the new TOMS Version 8 Ozone Algorithm. Compared to Differential Optical Absorption Spectroscopy (DOAS) techniques based on local structure in the Huggins Bands, the TOMS uses differential absorption between a pair of wavelengths including the local stiucture as well as the background continuum. This makes the TOMS Algorithm more sensitive to ozone, but it also makes the algorithm more sensitive to instrument calibration errors. While calibration adjustments are not needed for the fitting techniques like the DOAS employed in GOME algorithms, some adjustment is necessary when applying the TOMS Algorithm to GOME. Using spectral discrimination at near ultraviolet wavelength channels unabsorbed by ozone, the GOME wavelength dependent calibration drift is estimated and then checked using pair justification. In addition, the day one calibration offset is estimated based on the residuals of the Version 8 TOMS Algorithm. The estimated drift in the 2b detector of GOME is small through the first four years and then increases rapidly to +5% in normalized radiance at 331 nm relative to 385 nm by mid 2000. The lb detector appears to be quite well behaved throughout this time period.

Gleason, J.↗
NASA NTRS2003

Ocean Primary Production Estimates from Terra MODIS and Their Dependency on Satellite Chlorophyll Alpha Algorithms

Simplistic models relating global satellite ocean color, temperature, and light to ocean net primary production (ONPP) are sensitive to the accuracy and limitations of the satellite estimate of chlorophyll and other input fields, as well as the primary productivity model. The standard MODIS ONPP product uses the new semi-analytic chlorophyll algorithm as its input for two ONPP indexes. The three primary MODIS chlorophyll Q estimates from MODIS, as well as the SeaWiFS 4 chlorophyll product, were used to assess global and regional performance in estimating ONPP for the full mission, but concentrating on 2001. The two standard ONPP algorithms were examined with 8-day and 39 kilometer resolution to quantify chlorophyll algorithm dependency of ONPP. Ancillary data (MLD from FNMOC, MODIS SSTD1, and PAR from the GSFC DAO) were identical. The standard MODIS ONPP estimates for annual production in 2001 was 59 and 58 GT C for the two ONPP algorithms. Differences in ONPP using alternate chlorophylls were on the order of 10% for global annual ONPP, but ranged to 100% regionally. On all scales the differences in ONPP were smaller between MODIS and SeaWiFS than between ONPP models, or among chlorophyll algorithms within MODIS. Largest regional ONPP differences were found in the Southern Ocean (SO). In the SO, application of the semi-analytic chlorophyll resulted in not only a magnitude difference in ONPP (2x), but also a temporal shift in the time of maximum production compared to empirical algorithms when summed over standard oceanic areas. The resulting increase in global ONPP (6-7 GT) is supported by better performance of the semi-analytic chlorophyll in the SO and other high chlorophyll regions. The differences are significant in terms of understanding regional differences and dynamics of ocean carbon transformations.

Essias, Wayne E.↗
NASA NTRS1997

Developments in Human Centered Cueing Algorithms for Control of Flight Simulator Motion Systems

The authors conducted further research with cueing algorithms for control of flight simulator motion systems. A variation of the so-called optimal algorithm was formulated using simulated aircraft angular velocity input as a basis. Models of the human vestibular sensation system, i.e. the semicircular canals and otoliths, are incorporated within the algorithm. Comparisons of angular velocity cueing responses showed a significant improvement over a formulation using angular acceleration input. Results also compared favorably with the coordinated adaptive washout algorithm, yielding similar results for angular velocity cues while eliminating false cues and reducing the tilt rate for longitudinal cues. These results were confirmed in piloted tests on the current motion system at NASA-Langley, the Visual Motion Simulator (VMS). Proposed future developments by the authors in cueing algorithms are revealed. The new motion system, the Cockpit Motion Facility (CMF), where the final evaluation of the cueing algorithms will be conducted, is also described.

Houck, Jacob A.↗
NASA NTRS2005

A Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations

A parallel Particle Swarm Optimization (PSO) algorithm is presented. Particle swarm optimization is a fairly recent addition to the family of non-gradient based, probabilistic search algorithms that is based on a simplified social model and is closely tied to swarming theory. Although PSO algorithms present several attractive properties to the designer, they are plagued by high computational cost as measured by elapsed time. One approach to reduce the elapsed time is to make use of coarse-grained parallelization to evaluate the design points. Previous parallel PSO algorithms were mostly implemented in a synchronous manner, where all design points within a design iteration are evaluated before the next iteration is started. This approach leads to poor parallel speedup in cases where a heterogeneous parallel environment is used and/or where the analysis time depends on the design point being analyzed. This paper introduces an asynchronous parallel PSO algorithm that greatly improves the parallel e ciency. The asynchronous algorithm is benchmarked on a cluster assembled of Apple Macintosh G5 desktop computers, using the multi-disciplinary optimization of a typical transport aircraft wing as an example.

Venter, Gerhard↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗
NASA NTRS2005

The Optimization of Trained and Untrained Image Classification Algorithms for Use on Large Spatial Datasets

The HARVIST project seeks to automatically provide an accurate, interactive interface to predict crop yield over the entire United States. In order to accomplish this goal, large images must be quickly and automatically classified by crop type. Current trained and untrained classification algorithms, while accurate, are highly inefficient when operating on large datasets. This project sought to develop new variants of two standard trained and untrained classification algorithms that are optimized to take advantage of the spatial nature of image data. The first algorithm, harvist-cluster, utilizes divide-and-conquer techniques to precluster an image in the hopes of increasing overall clustering speed. The second algorithm, harvistSVM, utilizes support vector machines (SVMs), a type of trained classifier. It seeks to increase classification speed by applying a "meta-SVM" to a quick (but inaccurate) SVM to approximate a slower, yet more accurate, SVM. Speedups were achieved by tuning the algorithm to quickly identify when the quick SVM was incorrect, and then reclassifying low-confidence pixels as necessary. Comparing the classification speeds of both algorithms to known baselines showed a slight speedup for large values of k (the number of clusters) for harvist-cluster, and a significant speedup for harvistSVM. Future work aims to automate the parameter tuning process required for harvistSVM, and further improve classification accuracy and speed. Additionally, this research will move documents created in Canvas into ArcGIS. The launch of the Mars Reconnaissance Orbiter (MRO) will provide a wealth of image data such as global maps of Martian weather and high resolution global images of Mars. The ability to store this new data in a georeferenced format will support future Mars missions by providing data for landing site selection and the search for water on Mars.

Kocurek, Michael J.↗
NASA NTRS2006

Automated Antenna Design with Evolutionary Algorithms

Current methods of designing and optimizing antennas by hand are time and labor intensive, and limit complexity. Evolutionary design techniques can overcome these limitations by searching the design space and automatically finding effective solutions. In recent years, evolutionary algorithms have shown great promise in finding practical solutions in large, poorly understood design spaces. In particular, spacecraft antenna design has proven tractable to evolutionary design techniques. Researchers have been investigating evolutionary antenna design and optimization since the early 1990s, and the field has grown in recent years as computer speed has increased and electromagnetic simulators have improved. Two requirements-compliant antennas, one for ST5 and another for TDRS-C, have been automatically designed by evolutionary algorithms. The ST5 antenna is slated to fly this year, and a TDRS-C phased array element has been fabricated and tested. Such automated evolutionary design is enabled by medium-to-high quality simulators and fast modern computers to evaluate computer-generated designs. Evolutionary algorithms automate cut-and-try engineering, substituting automated search though millions of potential designs for intelligent search by engineers through a much smaller number of designs. For evolutionary design, the engineer chooses the evolutionary technique, parameters and the basic form of the antenna, e.g., single wire for ST5 and crossed-element Yagi for TDRS-C. Evolutionary algorithms then search for optimal configurations in the space defined by the engineer. NASA's Space Technology 5 (ST5) mission will launch three small spacecraft to test innovative concepts and technologies. Advanced evolutionary algorithms were used to automatically design antennas for ST5. The combination of wide beamwidth for a circularly-polarized wave and wide impedance bandwidth made for a challenging antenna design problem. From past experience in designing wire antennas, we chose to constrain the evolutionary design to a monopole wire antenna. The results of the runs produced requirements-compliant antennas that were subsequently fabricated and tested. The evolved antenna has a number of advantages with regard to power consumption, fabrication time and complexity, and performance. Lower power requirements result from achieving high gain across a wider range of elevation angles, thus allowing a broader range of angles over which maximum data throughput can be achieved. Since the evolved antenna does not require a phasing circuit, less design and fabrication work is required. In terms of overall work, the evolved antenna required approximately three person-months to design and fabricate whereas the conventional antenna required about five. Furthermore, when the mission was modified and new orbital parameters selected, a redesign of the antenna to new requirements was required. The evolutionary system was rapidly modified and a new antenna evolved in a few weeks. The evolved antenna was shown to be compliant to the ST5 mission requirements. It has an unusual organic looking structure, one that expert antenna designers would not likely produce. This antenna has been tested, baselined and is scheduled to fly this year. In addition to the ST5 antenna, our laboratory has evolved an S-band phased array antenna element design that meets the requirements for NASA's TDRS-C communications satellite scheduled for launch early next decade. A combination of fairly broad bandwidth, high efficiency and circular polarization at high gain made for another challenging design problem. We chose to constrain the evolutionary design to a crossed-element Yagi antenna. The specification called for two types of elements, one for receive only and one for transmit/receive. We were able to evolve a single element design that meets both specifications thereby simplifying the antenna and reducing testing and integration costs. The highest performance antenna found using a getic algorithm and stochastic hill-climbing has been fabricated and tested. Laboratory results correspond well with simulation. Aerospace component design is an expensive and important step in space development. Evolutionary design can make a significant contribution wherever sufficiently fast, accurate and capable software simulators are available. We have demonstrated successful real-world design in the spacecraft antenna domain; and there is good reason to believe that these results could be replicated in other design spaces.

Hornby, Gregory S.↗
NASA NTRS2006

Plasmapause Equatorial Shape Determination via the Minimum L Algorithm: Description and Evaluation

The Minimum L Algorithm for determining the equatorial shape of the plasmapause using NASA IMAGE Extreme Ultraviolet (EUV) imagery is described and analyzed. The algorithm operates without human intervention given a single EUV image in which the plasmasphere silhouette boundary has been identified. For each line of sight (LOS) through pixels on the 13 plasmasphere silhouette boundary, the algorithm first finds all magnetic dipole 14 field lines intersected by the LOS and then returns as the plasmasphere s boundary the field line with the minimum L value. The analysis considers the reasonableness, applicability, and accuracy of the algorithm and contrasts it with 17 the well-known Edge Algorithm is also introduced. Application of all three algorithms to real EUV imagery is demonstrated.

Newman, Timothy S.↗
NASA NTRS2007

Integration of On-Line and Off-Line Diagnostic Algorithms for Aircraft Engine Health Management

This paper investigates the integration of on-line and off-line diagnostic algorithms for aircraft gas turbine engines. The on-line diagnostic algorithm is designed for in-flight fault detection. It continuously monitors engine outputs for anomalous signatures induced by faults. The off-line diagnostic algorithm is designed to track engine health degradation over the lifetime of an engine. It estimates engine health degradation periodically over the course of the engine s life. The estimate generated by the off-line algorithm is used to update the on-line algorithm. Through this integration, the on-line algorithm becomes aware of engine health degradation, and its effectiveness to detect faults can be maintained while the engine continues to degrade. The benefit of this integration is investigated in a simulation environment using a nonlinear engine model.

Kobayashi, Takahisa↗
NASA NTRS2003

cWINNOWER Algorithm for Finding Fuzzy DNA Motifs

The cWINNOWER algorithm detects fuzzy motifs in DNA sequences rich in protein-binding signals. A signal is defined as any short nucleotide pattern having up to d mutations differing from a motif of length l. The algorithm finds such motifs if multiple mutated copies of the motif (i.e., the signals) are present in the DNA sequence in sufficient abundance. The cWINNOWER algorithm substantially improves the sensitivity of the winnower method of Pevzner and Sze by imposing a consensus constraint, enabling it to detect much weaker signals. We studied the minimum number of detectable motifs qc as a function of sequence length N for random sequences. We found that qc increases linearly with N for a fast version of the algorithm based on counting three-member sub-cliques. Imposing consensus constraints reduces qc, by a factor of three in this case, which makes the algorithm dramatically more sensitive. Our most sensitive algorithm, which counts four-member sub-cliques, needs a minimum of only 13 signals to detect motifs in a sequence of length N = 12000 for (l,d) = (15,4).

Liang, Shoudan↗
NASA NTRS2009

Algorithm for Detecting a Bright Spot in an Image

An algorithm processes the pixel intensities of a digitized image to detect and locate a circular bright spot, the approximate size of which is known in advance. The algorithm is used to find images of the Sun in cameras aboard the Mars Exploration Rovers. (The images are used in estimating orientations of the Rovers relative to the direction to the Sun.) The algorithm can also be adapted to tracking of circular shaped bright targets in other diverse applications. The first step in the algorithm is to calculate a dark-current ramp a correction necessitated by the scheme that governs the readout of pixel charges in the charge-coupled-device camera in the original Mars Exploration Rover application. In this scheme, the fraction of each frame period during which dark current is accumulated in a given pixel (and, hence, the dark-current contribution to the pixel image-intensity reading) is proportional to the pixel row number. For the purpose of the algorithm, the dark-current contribution to the intensity reading from each pixel is assumed to equal the average of intensity readings from all pixels in the same row, and the factor of proportionality is estimated on the basis of this assumption. Then the product of the row number and the factor of proportionality is subtracted from the reading from each pixel to obtain a dark-current-corrected intensity reading. The next step in the algorithm is to determine the best location, within the overall image, for a window of N N pixels (where N is an odd number) large enough to contain the bright spot of interest plus a small margin. (In the original application, the overall image contains 1,024 by 1,024 pixels, the image of the Sun is about 22 pixels in diameter, and N is chosen to be 29.)

Source record↗
NASA NTRS2009

Experimental Performance of a Genetic Algorithm for Airborne Strategic Conflict Resolution

The Autonomous Operations Planner, a research prototype flight-deck decision support tool to enable airborne self-separation, uses a pattern-based genetic algorithm to resolve predicted conflicts between the ownship and traffic aircraft. Conflicts are resolved by modifying the active route within the ownship s flight management system according to a predefined set of maneuver pattern templates. The performance of this pattern-based genetic algorithm was evaluated in the context of batch-mode Monte Carlo simulations running over 3600 flight hours of autonomous aircraft in en-route airspace under conditions ranging from typical current traffic densities to several times that level. Encountering over 8900 conflicts during two simulation experiments, the genetic algorithm was able to resolve all but three conflicts, while maintaining a required time of arrival constraint for most aircraft. Actual elapsed running time for the algorithm was consistent with conflict resolution in real time. The paper presents details of the genetic algorithm s design, along with mathematical models of the algorithm s performance and observations regarding the effectiveness of using complimentary maneuver patterns when multiple resolutions by the same aircraft were required.

Karr, David A.↗
NASA NTRS2009

Guaranteeing Failsafe Operation of Extended-Scene Shack-Hartmann Wavefront Sensor Algorithm

A Shack-Hartmann sensor (SHS) is an optical instrument consisting of a lenslet array and a camera. It is widely used for wavefront sensing in optical testing and astronomical adaptive optics. The camera is placed at the focal point of the lenslet array and points at a star or any other point source. The image captured is an array of spot images. When the wavefront error at the lenslet array changes, the position of each spot measurably shifts from its original position. Determining the shifts of the spot images from their reference points shows the extent of the wavefront error. An adaptive cross-correlation (ACC) algorithm has been developed to use scenes as well as point sources for wavefront error detection. Qualifying an extended scene image is often not an easy task due to changing conditions in scene content, illumination level, background, Poisson noise, read-out noise, dark current, sampling format, and field of view. The proposed new technique based on ACC algorithm analyzes the effects of these conditions on the performance of the ACC algorithm and determines the viability of an extended scene image. If it is viable, then it can be used for error correction; if it is not, the image fails and will not be further processed. By potentially testing for a wide variety of conditions, the algorithm s accuracy can be virtually guaranteed. In a typical application, the ACC algorithm finds image shifts of more than 500 Shack-Hartmann camera sub-images relative to a reference sub -image or cell when performing one wavefront sensing iteration. In the proposed new technique, a pair of test and reference cells is selected from the same frame, preferably from two well-separated locations. The test cell is shifted by an integer number of pixels, say, for example, from m= -5 to 5 along the x-direction by choosing a different area on the same sub-image, and the shifts are estimated using the ACC algorithm. The same is done in the y-direction. If the resulting shift estimate errors are less than a pre-determined threshold (e.g., 0.03 pixel), the image is accepted. Otherwise, it is rejected.

Sidick, Erikin↗
NASA NTRS2009

A Local Scalable Distributed Expectation Maximization Algorithm for Large Peer-to-Peer Networks

This paper offers a local distributed algorithm for expectation maximization in large peer-to-peer environments. The algorithm can be used for a variety of well-known data mining tasks in a distributed environment such as clustering, anomaly detection, target tracking to name a few. This technology is crucial for many emerging peer-to-peer applications for bioinformatics, astronomy, social networking, sensor networks and web mining. Centralizing all or some of the data for building global models is impractical in such peer-to-peer environments because of the large number of data sources, the asynchronous nature of the peer-to-peer networks, and dynamic nature of the data/network. The distributed algorithm we have developed in this paper is provably-correct i.e. it converges to the same result compared to a similar centralized algorithm and can automatically adapt to changes to the data and the network. We show that the communication overhead of the algorithm is very low due to its local nature. This monitoring algorithm is then used as a feedback loop to sample data from the network and rebuild the model when it is outdated. We present thorough experimental results to verify our theoretical claims.

Bhaduri, Kanishka↗
NASA NTRS2009

An Algorithm for Obtaining the Distribution of 1-Meter Lightning Channel Segment Altitudes for Application in Lightning NOx Production Estimation

An algorithm has been developed to estimate the altitude distribution of one-meter lightning channel segments. The algorithm is required as part of a broader objective that involves improving the lightning NOx emission inventories of both regional air quality and global chemistry/climate models. The algorithm was tested and applied to VHF signals detected by the North Alabama Lightning Mapping Array (NALMA). The accuracy of the algorithm was characterized by comparing algorithm output to the plots of individual discharges whose lengths were computed by hand; VHF source amplitude thresholding and smoothing were applied to optimize results. Several thousands of lightning flashes within 120 km of the NALMA network centroid were gathered from all four seasons, and were analyzed by the algorithm. The mean, standard deviation, and median statistics were obtained for all the flashes, the ground flashes, and the cloud flashes. One-meter channel segment altitude distributions were also obtained for the different seasons.

Peterson, Harold↗
NASA NTRS2007

Mapped Landmark Algorithm for Precision Landing

A report discusses a computer vision algorithm for position estimation to enable precision landing during planetary descent. The Descent Image Motion Estimation System for the Mars Exploration Rovers has been used as a starting point for creating code for precision, terrain-relative navigation during planetary landing. The algorithm is designed to be general because it handles images taken at different scales and resolutions relative to the map, and can produce mapped landmark matches for any planetary terrain of sufficient texture. These matches provide a measurement of horizontal position relative to a known landing site specified on the surface map. Multiple mapped landmarks generated per image allow for automatic detection and elimination of bad matches. Attitude and position can be generated from each image; this image-based attitude measurement can be used by the onboard navigation filter to improve the attitude estimate, which will improve the position estimates. The algorithm uses normalized correlation of grayscale images, producing precise, sub-pixel images. The algorithm has been broken into two sub-algorithms: (1) FFT Map Matching (see figure), which matches a single large template by correlation in the frequency domain, and (2) Mapped Landmark Refinement, which matches many small templates by correlation in the spatial domain. Each relies on feature selection, the homography transform, and 3D image correlation. The algorithm is implemented in C++ and is rated at Technology Readiness Level (TRL) 4.

Johnson, Andrew↗