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NASA NTRS2009

Progress of the NASA/USGS Lunar Regolith Simulant Project

Beginning in 2004 personnel at MSFC began serious efforts to develop a new generation of lunar simulants. The first two products were a replication of the previous JSC-1 simulant under a contract to Orbitec and a major workshop in 2005 on future simulant development. Beginning in 2006 the project refocused its efforts and approached simulant development in a new and more comprehensive manner, examining new approaches in simulant development and ways to more accurately compare simulants to actual lunar materials. This led to a multi-year effort with five major tasks running in parallel. The five tasks are Requirements, Lunar Analysis, Process Development, Feed Stocks, and Standards. Major progress has been made in all five areas. A substantial draft of a formal requirements document now exists and has been largely stable since 2007. It does evolve as specific details of the standards and Lunar Analysis efforts proceed. Lunar Analysis has turned out to be vastly more difficult than anticipated. After great effort to mine existing published and gray literature, the team has realized the necessity of making new measurements of the Apollo samples, an effort that is currently in progress. Process development is substantially ahead of expectations in 2006. It is now practical to synthesize glasses of appropriate composition and purity. It is also possible to make agglutinate particles in significant quantities. A series of minerals commonly found on the Moon has been synthesized. Separation of mineral constituents from starting rock material is also proceeding. Customized grinding and mixing processes have been developed and tested are now being documented. Identification and development of appropriate feedstocks has been both easier and more difficult than anticipated. The Stillwater Mining Company, operating in the Stillwater layered mafic intrusive complex of Montana, has been an amazing resource for the project, but finding adequate sources for some of the components remains a difficult problem. For example the ratio of clino- to ortho-pyroxenes in the Stillwater is not an exact match for lunar materials. One of the sources being examined as an alternative pyroxene source is the Bushveld Complex in South Africa. Standards have been a major success for the project. The Figure of Merit algorithms have been created, tested, and are being considered for an ISO standard. Agreement has been reached in the community about how to make many of the critical measurements. There remains much work to do: (1) driving down the cost of simulants remains a major obstacle; (2) documentation and cost data analysis have not kept up with progress; (3) educating users in the complexity of the lunar regolith and the use of simulants remains a major task. In summary the project has made enormous progress and is successfully placing simulant development and use on a rigorous, scientifically defensible, engineering basis.

Rickman, Doug↗

NASA NTRS2009

Progressive Band Selection

Progressive band selection (PBS) reduces spectral redundancy without significant loss of information, thereby reducing hyperspectral image data volume and processing time. Used onboard a spacecraft, it can also reduce image downlink time. PBS prioritizes an image's spectral bands according to priority scores that measure their significance to a specific application. Then it uses one of three methods to select an appropriate number of the most useful bands. Key challenges for PBS include selecting an appropriate criterion to generate band priority scores, and determining how many bands should be retained in the reduced image. The image's Virtual Dimensionality (VD), once computed, is a reasonable estimate of the latter. We describe the major design details of PBS and test PBS in a land classification experiment.

Fisher, Kevin↗

NASA NTRS2009

Lunar Mapping and Modeling Project

Noble, Sarah K.↗

NASA NTRS2009

An Effective Health and Medical Technical Authority

The NASA Governance model directed the formation of three Technical Authorities, Engineering; Safety and Mission Assurance; and Health and Medical, to ensure that risks are identified and adjudicated efficiently and transparently in concert with the spaceflight programs and projects. The Health and Medical Technical Authority (HMTA) has been implemented at the Johnson Space Center (JSC) and consists of the Chief Medical Office (CMO), the Deputy CMO, and HMTA Delegates. The JSC HMTA achieves the goals of risk identification and adjudication through the discharge of the appropriate technical expertise to human space flight programs and projects and the escalation of issues within program and technical authority boards. The JSC HMTA relies on subject matter experts (SMEs) in the Space Life Sciences Directorate at JSC as well as experts from other Centers to work crew health and performance issues at the technical level, develop requirements, oversee implementation and validation of requirements, and identify risks and non-compliances. Once a risk or potential noncompliance has been identified and reported to the programs or projects, the JSC HMTA begins to track it and closely monitor the program's or project's response. As a risk is developed or a non-compliance negotiated, positions from various levels of decision makers are sought at the program and project control boards. The HMTA may support a program or project position if it is satisfied with the decision making and vetting processes (ex. the subject matter expert voiced his/her concerns and all dissenting opinions were documented) and finds that the position both acknowledges the risk and cost of the mitigation and resolves the issue without changing NASA risk posture. The HMTA may disagree with a program or project position if the NASA risk posture has been elevated or obfuscated. If the HMTA does disagree with the program or project position, it will appeal to successively higher levels of authority so that risk acceptance and risk trades will be acknowledged and sanctioned at the highest appropriate level; this includes Program Managers, Mission Directorate Associate Administrators and the Agency Administrator.

Fogarty, Jennifer A.↗

NASA NTRS2009

Developing Dual Polarization Applications For 45th Weather Squadron's (45 WS) New Weather Radar: A Cooperative Project With The National Space Science and Technology Center (NSSTC)

A new weather radar is being acquired for use in support of America s space program at Cape Canaveral Air Force Station, NASA Kennedy Space Center, and Patrick AFB on the east coast of central Florida. This new radar includes dual polarization capability, which has not been available to 45 WS previously. The 45 WS has teamed with NSSTC with funding from NASA Marshall Spaceflight Flight Center to improve their use of this new dual polarization capability when it is implemented operationally. The project goals include developing a temperature profile adaptive scan strategy, developing training materials, and developing forecast techniques and tools using dual polarization products. The temperature profile adaptive scan strategy will provide the scan angles that provide the optimal compromise between volume scan rate, vertical resolution, phenomena detection, data quality, and reduced cone-of-silence for the 45 WS mission. The mission requirements include outstanding detection of low level boundaries for thunderstorm prediction, excellent vertical resolution in the atmosphere electrification layer between 0 C and -20 C for lightning forecasting and Lightning Launch Commit Criteria evaluation, good detection of anvil clouds for Lightning Launch Commit Criteria evaluation, reduced cone-of-silence, fast volume scans, and many samples per pulse for good data quality. The training materials will emphasize the appropriate applications most important to the 45 WS mission. These include forecasting the onset and cessation of lightning, forecasting convective winds, and hopefully the inference of electrical fields in clouds. The training materials will focus on annotated radar imagery based on products available to the 45 WS. Other examples will include time sequenced radar products without annotation to simulate radar operations. This will reinforce the forecast concepts and also allow testing of the forecasters. The new dual polarization techniques and tools will focus on the appropriate applications for the 45 WS mission. These include forecasting the onset of lightning, the cessation of lightning, convective winds, and hopefully the inference of electrical fields in clouds. This presentation will report on the results achieved so far in the project.

Roeder, W.P.↗

NASA NTRS2009

Adaptable DC offset correction

Methods and systems for adaptable DC offset correction are provided. An exemplary adaptable DC offset correction system evaluates an incoming baseband signal to determine an appropriate DC offset removal scheme; removes a DC offset from the incoming baseband signal based on the appropriate DC offset scheme in response to the evaluated incoming baseband signal; and outputs a reduced DC baseband signal in response to the DC offset removed from the incoming baseband signal.

Golusky, John M.↗

NASA NTRS2010

Inferring Properties of Ancient Cyanobacteria from Biogeochemical Activity and Genomes of Siderophilic Cyanobacteria

Interrelationships between life and the planetary system could have simultaneously left landmarks in genomes of microbes and physicochemical signatures in the lithosphere. Verifying the links between genomic features in living organisms and the mineralized signatures generated by these organisms will help to reveal traces of life on Earth and beyond. Among contemporary environments, iron-depositing hot springs (IDHS) may represent one of the most appropriate natural models [1] for insights into ancient life since organisms may have originated on Earth and probably Mars in association with hydrothermal activity [2,3]. IDHS also seem to be appropriate models for studying certain biogeochemical processes that could have taken place in the late Archean and,-or early Paleoproterozoic eras [4, 5]. It has been suggested that inorganic polyphosphate (PPi), in chains of tens to hundreds of phosphate residues linked by high-energy bonds, is environmentally ubiquitous and abundant [6]. Cyanobacteria (CB) react to increased heavy metal concentrations and UV by enhanced generation of PPi bodies (PPB) [7], which are believed to be signatures of life [8]. However, the role of PPi in oxygenic prokaryotes for the suppression of oxidative stress induced by high Fe is poorly studied. Here we present preliminary results of a new mechanism of Fe mineralization in oxygenic prokaryotes, the effect of Fe on the generation of PPi bodies in CB, as well as preliminary analysis of the diversity and phylogeny of proteins involved in the prevention of oxidative stress in phototrophs inhabiting IDHS.

McKay, David S.↗

NASA NTRS2009

Lunar Mapping and Modeling Project

The Lunar Mapping and Modeling Project (LMMP) has been created to manage the development of a suite of lunar mapping and modeling products that support the Constellation Program (CxP) and other lunar exploration activities, including the planning, design, development, test and operations associated with lunar sortie missions, crewed and robotic operations on the surface, and the establishment of a lunar outpost. The information provided through LMMP will assist CxP in: planning tasks in the areas of landing site evaluation and selection, design and placement of landers and other stationary assets, design of rovers and other mobile assets, developing terrain-relative navigation (TRN) capabilities, and assessment and planning of science traverses. The project draws on expertise from several NASA and non-NASA organizations (MSFC, ARC, GSFC, JPL, CRREL US Army Cold Regions Research and Engineering Laboratory, and the USGS). LMMP will utilize data predominately from the Lunar Reconnaissance Orbiter, but also historical and international lunar mission data (e.g. Apollo, Lunar Orbiter, Kaguya, Chandrayaan-1), as available and appropriate, to meet Constellation s data needs. LMMP will provide access to this data through a single intuitive and easy to use NASA portal that transparently accesses appropriately sanctioned portions of the widely dispersed and distributed collections of lunar data, products and tools. Two visualization systems are being developed, a web-based system called Lunar Mapper, and a desktop client, ILIADS, which will be downloadable from the LMMP portal. LMMP will provide such products as local and regional imagery and DEMs, hazard assessment maps, lighting and gravity models, and resource maps. We are working closely with the LRO team to prevent duplication of efforts and to ensure the highest quality data products. While Constellation is our primary customer, LMMP is striving to be as useful as possible to the lunar science community, the lunar commercial community, the lunar education and public outreach (E/PO) community, and anyone else interested in accessing or utilizing lunar data. A beta version of the portal and visualization systems is expected to be released in late 2009, with a version 1 release planned for early 2011.

Noble, Sarah K.↗

NASA NTRS1992

Optimal Estimation of Rain Rate Profiles from Single-Frequency Radar Echoes

The significant ambiguities inherent in the determination of a particular vertical rain intensity profile from a given time profile of radar echo powers measured by a downward-looking (spaceborne or airborne) radar at a single attenuating frequency are well-documented. Indeed, one already knows that by appropriately varying the parameters of the reflectivity-rain-rate (Z - R) and/or attenuation-rain-rate (k - R) relationships, one can produce several substantially different hypothetical rain rate profiles which would have the same radar power profile. Imposing the additional constraint that the path-averaged rain-rate be a given fixed number does reduce the ambiguities but falls far short of eliminating them. While we now know how to generate as many mutually ambiguous rain-rate profiles from a given profile of received radar reflectivities as we like, there remains to produce a quantitative measure to assess how likely each of these profiles is, what the appropriate 'average' profile should be, and what the 'variance' of these multiple solutions is. Of course, in order to do this, one needs to spell out the stochastic constraints that can allow us to make sense of the words 'average' and 'variance' in a mathematically rigorous way. Such a quantitative approach would be particularly well-suited for such systems as the proposed Precipitation Radar of the Tropical Rainfall Measuring Mission (TRMM). Indeed, one would then be able to use the radar reflectivities measured by the TRMM radar from one particular look in order to estimate the most likely rain-rate profile that would have produced the measurements, as well as the uncertainty in the estimated rain-rates as a function of range. Such an optimal approach is described in this paper.

deep space flight computer real-time advanced spac↗

NASA NTRS2010

Using the Integrated Vehicle Health Management Research Test and Integration Plan Wiki to Identify Synergistic Test Opportunities

The National Aeronautics and Space Administration (NASA) and the aviation industry have recognized a need for developing a method to identify and combine resources to carry out research and testing more efficiently. The Integrated Vehicle Health Management (IVHM) Research Test and Integration Plan (RTIP) Wiki is a tool that is used to visualize, plan, and accomplish collaborative research and testing. Synergistic test opportunities are developed using the RTIP Wiki, and include potential common resource testing that combines assets and personnel from NASA, industry, academia, and other government agencies. A research scenario is linked to the appropriate IVHM milestones and resources detailed in the wiki, reviewed by the research team members, and integrated into a collaborative test strategy. The scenario is then implemented by creating a test plan when appropriate and the research is performed. The benefits of performing collaborative research and testing are achieving higher Technology Readiness Level (TRL) test opportunities with little or no additional cost, improved quality of research, and increased communication among researchers. In addition to a description of the method of creating these joint research scenarios, examples of the successful development and implementation of cooperative research using the IVHM RTIP Wiki are given.

Koelfgen, Syri J.↗

NASA NTRS2010

A Comparison of Flow-Through Versus Non-Flow-Through Proton Exchange Membrane Fuel Cell Systems for NASA's Exploration Missions

As part of the Exploration Technology Development Program (ETDP) under the auspices of the Exploration Systems Mission Directorate (ESMD), NASA is developing both primary fuel cell power systems and regenerative fuel cell (RFC) energy storage systems within the fuel cell portion of the Energy Storage Project. This effort is being led by the NASA Glenn Research Center (GRC) in partnership with the NASA Johnson Space Center (JSC), Jet Propulsion Laboratory (JPL), NASA Kennedy Space Center (KSC), and industrial partners. The development goals are to improve fuel cell and electrolysis stack electrical performance, reduce system mass, volume, and parasitic power requirements, and increase system life and reliability. A major focus of this effort has been the parallel development of both flow-through and non-flow-through proton exchange membrane (PEM) primary fuel cell power systems. The plan has been, at the appropriate time, to select a single primary fuel cell technology for eventual flight hardware development. Ideally, that appropriate time would occur after both technologies have achieved a technology readiness level (TRL) of six, which represents an engineering model fidelity PEM fuel cell system being successfully tested in a relevant environment. Budget constraints in fiscal year 2009 and beyond have prevented NASA from continuing to pursue the parallel development of both primary fuel cell options. Because very limited data exists for either system, a toplevel, qualitative assessment based on engineering judgement was performed expeditiously to provide guidance for a selection. At that time, the non-flow-through technology was selected for continued development because of potentially major advantages in terms of weight, volume, parasitic power, reliability, and life. This author believes that the advantages are significant enough, and the potential benefits great enough, to offset the higher state of technology readiness of flow-through technology. This paper summarizes the technical considerations which helped form the engineering judgement that led to the final decision.

Hoberecht, Mark A.↗

NASA NTRS2010

Low Mass Printable Devices for Energy Capture, Storage, and Use

The energy-efficient, environmentally friendly technology that will be presented is the result of a Space Act Agreement between NthDegree Technologies Worldwide, Inc., and the National Aeronautics and Space Administration's (NASA's) Marshall Space Flight Center (MSFC). The work combines semiconductor and printing technologies to advance lightweight electronic and photonic devices having excellent potential for commercial and exploration applications. Device development involves three projects that relate to energy generation and consumption: (1) a low-mass efficient (low power, low heat emission) micro light-emitting diode (LED) area lighting device; (2) a low-mass omni-directional efficient photovoltaic (PV) device with significantly improved energy capture; and (3) a new approach to building super-capacitors. These three technologies, energy capture, storage, and usage (e.g., lighting), represent a systematic approach for building efficient local micro-grids that are commercially feasible; furthermore, these same technologies, appropriately replacing lighting with lightweight power generation, will be useful for enabling inner planetary missions using smaller launch vehicles and to facilitate surface operations during lunar and planetary surface missions. The PV device model is a two sphere, light trapped sheet approximately 2-mm thick. The model suggests a significant improvement over current thin film systems. For lighting applications, all three technology components are printable in-line by printing sequential layers on a standard screen or flexographic direct impact press using the three-dimensional printing technique (3DFM) patented by NthDegree. One primary contribution to this work in the near term by the MSFC is to test the robustness of prototype devices in the harsh environments that prevail in space and on the lunar surface. It is anticipated that this composite device, of which the lighting component has passed off-gassing testing, will function appropriately in such environments consistent with NASA s exploration missions. Advanced technologies such as this show promise for both space flight and terrestrial applications.

Frazier, Donald O.↗

NASA NTRS2010

Random Vibrations

Ares I Zonal Random vibration environments due to acoustic impingement and combustion processes are develop for liftoff, ascent and reentry. Random Vibration test criteria for Ares I Upper Stage pyrotechnic components are developed by enveloping the applicable zonal environments where each component is located. Random vibration tests will be conducted to assure that these components will survive and function appropriately after exposure to the expected vibration environments. Methodology: Random Vibration test criteria for Ares I Upper Stage pyrotechnic components were desired that would envelope all the applicable environments where each component was located. Applicable Ares I Vehicle drawings and design information needed to be assessed to determine the location(s) for each component on the Ares I Upper Stage. Design and test criteria needed to be developed by plotting and enveloping the applicable environments using Microsoft Excel Spreadsheet Software and documenting them in a report Using Microsoft Word Processing Software. Conclusion: Random vibration liftoff, ascent, and green run design & test criteria for the Upper Stage Pyrotechnic Components were developed by using Microsoft Excel to envelope zonal environments applicable to each component. Results were transferred from Excel into a report using Microsoft Word. After the report is reviewed and edited by my mentor it will be submitted for publication as an attachment to a memorandum. Pyrotechnic component designers will extract criteria from my report for incorporation into the design and test specifications for components. Eventually the hardware will be tested to the environments I developed to assure that the components will survive and function appropriately after exposure to the expected vibration environments.

Messaro. Semma↗

NASA NTRS2010

Analysis, Simulation, and Verification of Knowledge-Based, Rule-Based, and Expert Systems

Mathematically sound techniques are used to view a knowledge-based system (KBS) as a set of processes executing in parallel and being enabled in response to specific rules being fired. The set of processes can be manipulated, examined, analyzed, and used in a simulation. The tool that embodies this technology may warn developers of errors in their rules, but may also highlight rules (or sets of rules) in the system that are underspecified (or overspecified) and need to be corrected for the KBS to operate as intended. The rules embodied in a KBS specify the allowed situations, events, and/or results of the system they describe. In that sense, they provide a very abstract specification of a system. The system is implemented through the combination of the system specification together with an appropriate inference engine, independent of the algorithm used in that inference engine. Viewing the rule base as a major component of the specification, and choosing an appropriate specification notation to represent it, reveals how additional power can be derived from an approach to the knowledge-base system that involves analysis, simulation, and verification. This innovative approach requires no special knowledge of the rules, and allows a general approach where standardized analysis, verification, simulation, and model checking techniques can be applied to the KBS.

Hinchey, Mike↗

NASA NTRS2000

A Primary Care Approach to the Diagnosis and Management of Peripheral Arterial Disease

The objectives of this work are: (1) Be able to recognize characteristic symptoms of intermittent claudication (2) Diagnose PAD on the basis of history, physical exam, and simple limb blood pressure measurements (3) Recognize the significance of peripheral artery disease as a marker for coronary or cerebrovascular atherosclerosis (4) Provide appropriate medical management of atherosclerosis risk factors-- including use of antiplatelet therapy to reduce risk of myocardial infarction, stroke and death (5) Manage symptoms of intermittent claudication with program of smoking cessation, exercise, and medication The diagnosis of intermittent claudication secondary to peripheral artery disease (PAD) can often be made on the basis of history and physical examination. Additional evaluation of PAD is multi-modal and the techniques used will vary depending on the nature and severity of the patient's presenting problem. Most patients can be appropriately managed without referral for specialized diagnostic services or interventions.

Dawson, David L.↗

NASA NTRS2010

NASA 14 Day Undersea Missions: A Short-Duration Spaceflight Analog for Immune System Dysregulation

BACKGROUND Spaceflight-associated immune dysregulation (SAID) occurs during spaceflight and may represent specific clinical risks for exploration-class missions. An appropriate ground analog for spaceflight-associated immune dysregulation would offer a platform for ground-evaluation of various potential countermeasures. This study evaluated the NASA Undersea Mission Operations ( NEEMO ), consisting of 14 day undersea deployment at the Aquarius station, as an analog for SAID. Sixteen Aquanauts from missions NEEMO-12, 13 and 14 participated in the study. RESULTS Mid-mission alterations leukocyte distribution occurred, including granulocytosis and elevations in central-memory CD8+ T-cells. General T cell function was reduced during NEEMO missions in roughly 50% of subjects. Secreted cytokines profiles were evaluated following whole blood stimulation with CD3/CD28 (T cells) or LPS (monocytes). T cell production of IFNg, IL-5, IL-10, IL-2, TNFa and IL-6 were all reduced before and during the mission. Conversely, monocyte production of TNFa, IL-10, IL-6, IL-1b and IL-8 were elevated during mission, moreso at the MD-14 timepoint. Antibodies to Epstein-Barr virus (EBV) viral capsid antigen and early antigen were increased in approximately 40% of the subjects. Changes in EBV tetramer-positive CD8+ T-cells exhibited a variable pattern. Antibodies against Cytomegalovirus (CMV) were marginally increased during the mission. Herpesvirus reactivation was determined by PCR. EBV viral load was generally elevated at L-6. Higher levels of salivary EBV were found during the NEEMO mission than before and after as well as than the healthy controls. No VZV or CMV was found in any pre, during and after NEEMO mission or control samples. Plasma cortisol was elevated at L-6. CONCLUSION Unfortunately, L-6 may be too near to mission start to be an appropriate baseline measurement. The general immune changes in leukocyte distribution, T cell function, cytokine production, virus specific immunity and viral reactivation are similar to those observed during or following spaceflight. The NEEMO platform may thus have utility for short-duration, ground-based spaceflight-immune research, such as investigations of mechanism or countermeasures validation.

Crucian, B. E.↗

NASA NTRS2010

Design and Implementation of the Boundary Layer Transition Flight Experiment on Space Shuttle Discovery

In an effort to better the understanding of high speed aerodynamics, a series of flight experiments were installed on Space Shuttle Discovery during the STS-119 and STS-128 missions. This experiment, known as the Boundary Layer Transition Flight Experiment (BLTFE), provided the technical community with actual entry flight data from a known height protuberance at Mach numbers at and above Mach 15. Any such data above Mach 15 is irreproducible in a laboratory setting. Years of effort have been invested in obtaining this valuable data, and many obstacles had to be overcome in order to ensure the success of implementing an Orbiter modification. Many Space Shuttle systems were involved in the installation of appropriate components that revealed 'concurrent engineering' was a key integration tool. This allowed the coordination of all various parts and pieces which had to be sequenced appropriately and installed at the right time. Several issues encountered include Orbiter configuration and access, design requirements versus current layout, implementing the modification versus typical processing timelines, and optimizing the engineering design cycles and changes. Open lines of communication within the entire modification team were essential to project success as the team was spread out across the United States, from NASA Kennedy Space Center in Florida, to NASA Johnson Space Center in Texas, to Boeing Huntington Beach, California among others. The forum permits the discussion of processing concerns from the design phase to the implementation phase, which eventually saw the successful flights and data acquisition on STS-119 in March 2009 and on STS-128 in September 2009.

Spanos, Theodoros A.↗

NASA NTRS2011

An Empirical State Error Covariance Matrix for Batch State Estimation

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).

Frisbee, Joseph H., Jr.↗