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At least 631 records · Page 35

DEUTERIUM BURNING IN MASSIVE GIANT PLANETS AND LOW-MASS BROWN DWARFS FORMED BY CORE-NUCLEATED ACCRETION

Using detailed numerical simulations, we study the formation of bodies near the deuterium-burning limit according to the core-nucleated giant planet accretion scenario. The objects, with heavy-element cores in the range 5-30 M{sub Circled-Plus }, are assumed to accrete gas up to final masses of 10-15 Jupiter masses (M{sub Jup}). After the formation process, which lasts 1-5 Myr and which ends with a ''cold-start'', low-entropy configuration, the bodies evolve at constant mass up to an age of several Gyr. Deuterium burning via proton capture is included in the calculation, and we determined the mass, M{sub 50}, above which more than 50% of the initial deuterium is burned. This often-quoted borderline between giant planets and brown dwarfs is found to depend only slightly on parameters, such as core mass, stellar mass, formation location, solid surface density in the protoplanetary disk, disk viscosity, and dust opacity. The values for M{sub 50} fall in the range 11.6-13.6 M{sub Jup}, in agreement with previous determinations that do not take the formation process into account. For a given opacity law during the formation process, objects with higher core masses form more quickly. The result is higher entropy in the envelope at the completion of accretion, yielding lower values of M{sub 50}. For masses above M{sub 50}, during the deuterium-burning phase, objects expand and increase in luminosity by one to three orders of magnitude. Evolutionary tracks in the luminosity versus time diagram are compared with the observed position of the companion to Beta Pictoris.

79 ASTRONOMY AND ASTROPHYSICS↗

NEW DETERMINATION OF THE {sup 13}C({alpha}, n){sup 16}O REACTION RATE AND ITS INFLUENCE ON THE s-PROCESS NUCLEOSYNTHESIS IN AGB STARS

We present a new measurement of the {alpha}-spectroscopic factor (S{sub {alpha}}) and the asymptotic normalization coefficient for the 6.356 MeV 1/2{sup +} subthreshold state of {sup 17}O through the {sup 13}C({sup 11}B, {sup 7}Li){sup 17}O transfer reaction and we determine the {alpha}-width of this state. This is believed to have a strong effect on the rate of the {sup 13}C({alpha}, n){sup 16}O reaction, the main neutron source for slow neutron captures (the s-process) in asymptotic giant branch (AGB) stars. Based on the new width we derive the astrophysical S-factor and the stellar rate of the {sup 13}C({alpha}, n){sup 16}O reaction. At a temperature of 100 MK, our rate is roughly two times larger than that by Caughlan and Fowler and two times smaller than that recommended by the NACRE compilation. We use the new rate and different rates available in the literature as input in simulations of AGB stars to study their influence on the abundances of selected s-process elements and isotopic ratios. There are no changes in the final results using the different rates for the {sup 13}C({alpha}, n){sup 16}O reaction when the {sup 13}C burns completely in radiative conditions. When the {sup 13}C burns in convective conditions, as in stars of initial mass lower than {approx}2 M{sub Sun} and in post-AGB stars, some changes are to be expected, e.g., of up to 25% for Pb in our models. These variations will have to be carefully analyzed when more accurate stellar mixing models and more precise observational constraints are available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Aerobraking Maneuver (ABM) Report Generator

abmREPORT Version 3.1 is a Perl script that extracts vital summarization information from the Mars Reconnaissance Orbiter (MRO) aerobraking ABM build process. This information facilitates sequence reviews, and provides a high-level summarization of the sequence for mission management. The script extracts information from the ENV, SSF, FRF, SCMFmax, and OPTG files and burn magnitude configuration files and presents them in a single, easy-to-check report that provides the majority of the parameters necessary for cross check and verification during the sequence review process. This means that needed information, formerly spread across a number of different files and each in a different format, is all available in this one application. This program is built on the capabilities developed in dragReport and then the scripts evolved as the two tools continued to be developed in parallel.

Fisher, Forrest↗

Incorporating an Interactive Fire Plume-Rise Model in the DOE's Energy Exascale Earth System Model Version 1 (E3SMv1) and Examining Aerosol Radiative Effect

The vertical distribution of biomass burning aerosol (BBA) is important in regulating their impacts on weather and climate. The plume-rise process affects the injection height of BBA and interacts with the air parcel lifting and cloud processes. However, these processes are not represented in most global climate models. In this study, we replaced the fixed vertical profiles of monthly BBA emissions in the Department of Energy's Energy Exascale Earth System Model version 1 (E3SMv1) with an interactive fire plume-rise model. The vertical distribution of BBA emissions was calculated as a function of ambient thermodynamic conditions from the host E3SMv1, with distributions of fire sizes and sensible heat fluxes derived from the observations. The maximum fire radiative power (FRP) technique was used to determine the fire size. Scaling-FRP technique is used to calculate the wildfire heat release. Daily BBA emission, superimposed with a fire diurnal cycle retrieved from the satellite observation, was included in model simulations. The model shows improved agreement with satellite retrievals and in situ measurement during the National Oceanic and Atmospheric Administration Wildfire Experiment for Cloud chemistry, Aerosol absorption, and Nitrogen campaign. The model-observation comparison demonstrates the importance of the plume-rise model and fire diurnal cycle assumption in determining the BBA fields. We also find that E3SMv1 with new features produces a larger carbonaceous aerosol burden, leading to 0.13 W m –2 warming at the top of atmosphere compared to the default E3SMv1. This highlights the importance of accurately representing the BBA injection height and indicates a no-linear nature in the BBA-induced radiative effect.

54 ENVIRONMENTAL SCIENCES↗

Measuring Response Of Propellant To Oscillatory Heat Flux

Apparatus for research in combustion of solid propellants measures oscillatory response of rate of burning to oscillating thermal radiation from modulated CO2 laser. Determines response to rate of burning to equivalent oscillation in pressure. Rod of propellant mounted in burner assembly including waveguide at one end and infrared window at other end. Microwave Doppler velocimeter measures motion of combustion front. Microwave, laser-current, and heat-flux signals processed into and recorded in forms useful in determining desired response of propellent.

Strand, Leon D.↗

Identifying Challenges in Safeguards for Metallic Fuel Fabrication Facilities

As new advanced reactors gain popularity, there is an increasing interest in metallic fuel fabrication for fast reactors. While metallic fuels themselves are not a new idea, as many of the first reactors employed metallic fuels, new designs, compositions, and fabrication methods are appearing throughout the nuclear community. As the interest grows and facilities are constructed, both domestic and international safeguards will need to be heavily involved to support safeguards-by-design (SBD) measures from the start. This work compiles a review of historical and modern fuel types and fabrication methods, fabrication processes, safeguards gaps, and potential safeguards solutions. Metallic nuclear fuel types have been around for many decades and were included in some of the first reactors including the Experimental Breeder Reactor (EBR)-I and -II, the Fermi 1 reactor, the Integral Fast Reactor (IFR), and the Dounreay Fast Reactor (DFR). These reactors used various compositions including pure uranium (U) metal, U-zirconium (Zr) alloys, plutonium (Pu)-aluminum (Al) alloys, U-fissium (Fs) alloys, U-Pu-Zr alloys, and U-molybdenum (Mo) alloys [1, 2, 3, 4, 5]. These small alloying additions are included to improve the material properties of the pure U metal. The alpha-phase U (stable below 661C) suffers elongation in one direction causing grain boundary cracking and increasing creep rate due to irradiation growth, thermal cycling, and preferential crystal orientation. It is ideal to utilize the gamma-phase U (typically stable above 769C) by adding small amounts of alloying elements such as Zr or Mo to stabilize this phase down to room temperature [3]. Additionally, some research has been focused on U with transuranic (TRU) elements present, typically coming from the used fuel recycling process. Including these elements in fast reactor fuel can aid in the reduction of nuclear waste by burning minor long-lived actinides. However, the additions of TRU elements can cause concerns to arise when trying to fabrication or safeguard metallic fuels. A typical metallic fuel element is shown in Figure 1. Sodium is added into the cladding to create a thermal bond between the fuel slug and cladding wall. The fuel slug is then inserted and the end plug is welded on to the top of the fuel element. A gas plenum is left to create a headspace for gaseous fission products to escape rather than continue to build in the fuel itself [1, 5]. Other fuel element geometries exist as well, such as the Lightbridge twisted cruciform geometry shown in Figure 2 [6]. This design allows for better cooling performance and provides room for fuel rod swelling without impacting the fuel rod diameter. There are many different fabrication methods for metallic fuels, which is one of the many benefits of these fuel types. Many of these fabrication methods are relatively easy and cost-efficient. The most popular fabrication method is injection casting, sometimes called vacuum induction melting (VIM), shown in Figure 3 [4, 8, 9, 7, 10]. This method was largely used for EBR-II fuel fabrication. The injection casting system is contained inside of a vessel consisting of a Y2O3-coated graphite crucible surrounded by an induction coil with ZrO2-coated quartz molds suspended above the crucible. The fuel feedstock is placed inside of the graphite crucible and melted using the induction furnace. The induction furnace utilizes a dual frequency with the high frequency melting the feedstock and the low frequency causing stirring of the melted feedstock to form a homogeneous mixture. The mixture is heated to approximately 1600C in an argon environment. The vessel is evacuated and then the quartz molds are lowered into the graphite crucible containing the molten metal and the vessel is repressurized to inject the metal fuel upwards into the molds. The molds are removed and then shattered to release the fuel slugs. This fabrication method was used to fabricate 39,000 metallic fuel pins for EBR-II. While injection casting has been the most common metallic fuel fabrication method throughout the decades, many other methods have been explored including low-pressure gravity casting, microwave casting, continuous casting, centrifugal casting, coextrusion, and many others [11, 12, 8, 13, 14, 15]. Some of these methods aim to mitigate challenges that arise with americium (Am) volatilization during the casting process for TRU-containing fuel feedstocks, an issue with injection casting. Coextrusion is one of the methods explored at the Idaho National Laboratory (INL) and has been utilized for the initial fabrication tests of Lightbridge's unique fuels, as well as other metallic fuels with cladding coextruded. In this process, large billets are formed and machined and then inserted into a molten salt bath for approximately 30 minutes. The billets are then loaded into the extrusion press and extruded. This process can be seen in Figure 4 [15].

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Airborne Observations of Aerosol Properties in Southeast Asia: Overview of Emissions, Cloud Processing, and Long Range Transport during NASA CAMP2Ex

The Southwest Monsoon represents an important synoptic scale meteorological feature that modulates precipitation throughout Southeast Asia. In addition, southwesterly flow can funnel large amounts of biomass burning aerosol into heavily populated areas throughout the Philippines, mixing with urban emissions and representing a significant air quality issue. From a climate perspective, understanding interactions between these particles and clouds has important societal ramifications through frequent extreme periods of flood and drought. Here we present airborne observations made in support of the NASA CAMP2Ex (Cloud and Aerosol Monsoonal Processes-Philippines Experiment) mission aboard the Wallops Flight Facility P-3 research aircraft, based at Clark International Airport in the Luzon region of Northern Philippines. Nineteen research flights were conducted in August-October of 2019. An extensive suite of aerosol microphysical, optical, and chemical instrumentation was deployed, along with trace gas and remote sensing measurements, to characterize aerosol emissions and their vertical/spatial variability associated with moderately convective marine cloud systems in the region. Analysis will focus on characterizing disparate aerosol sources with respect to derived chemical and optical properties relevant to global circulation modeling. For example, higher than expected mass scattering efficiencies for aged biomass burning emissions, derived from a combination of nephelometer and aerosol mass spectrometer measurements, are attributed to increased particle size and decreased density. Results will also illustrate the evolution of aerosols from Indonesian agricultural biomass burning activities into the Philippines region, in comparison with urban emissions from the megacity Manila and transported air masses from mainland Asia.

Luke David Ziemba↗

Scale up production of carbon fibers from petroleum mesophase pitch

This work investigates the scale-up of pitch precursors for the carbon fiber market using mesophase pitch formulated and produced by Advanced Carbon Products Technologies’ (ACPT’s) patented mesophase pitch processing technology. Through use of its patented process, ACPT developed strategic materials by converting petroleum-based pitch into a high-value, low-cost, carbon-rich feedstock for carbon fiber and other materials critical to our national security. The team successfully developed processing criteria for the tailored mesophase pitch material that can be processed further into precursor and carbon fiber. Processability of the mesophase pitch into precursor and carbon fiber was demonstrated at scale. The resulting materials sequester the carbon that would otherwise be burned and released into the atmosphere, making this an environmentally friendly way to produce these materials in the United States.Pitch-based carbon fibers offer a promising pathway toward cost-effective, high-performance materials for structural and high-modulus composite applications; however, adoption has been limited by challenges in precursor processability and scale-up. In this work, tailored isotropic and mesophase petroleum-derived pitch materials were developed and evaluated for precursor and carbon fiber production through a collaborative effort between Oak Ridge National Laboratory (ORNL) and ACPT. Processing conditions were established at ORNL’s Carbon Fiber Technology Facility to enable stable melt-blowing of pitch-based precursors under continuous operation. Mesophase pitch precursor fibers were produced following oxidation and carbonization, corresponding to a diameter shrinkage of approximately 12%–13% and an estimated mass yield of about 75%–80%. Continuous melt-blowing steady-state operation was demonstrated over time, indicating robust process stability. Melt-blowing was achieved at throughput rates of approximately 20 lb/h⁻¹, validating the commercial viability of petroleum-derived pitch feedstocks for fiber production. Further studies are required to tailor carbon fiber microstructure and properties for specific composite applications.

99 GENERAL AND MISCELLANEOUS↗

The evaluation of aluminum and iron metal oxide settling behaviors for Hanford insoluble solids waste preprocessing

The Hanford site is currently one of the largest and most expensive cleanup sites for hazardous, radioactive waste. Over 20% of the waste found at the Hanford site is in the form of a high activity sludge. The insoluble solids in the sludge will need to be concentrated prior to vitrification in the high-level waste (HLW) melter. This will minimize the amount of liquid that will be evaporated during the melting process and expedite the melter processing rate. One proposed option for concentrating the insoluble solids is gravity settling in the storage tanks. Metal oxide compounds containing aluminum and iron make up the majority of the insoluble solids in the sludge, therefore understanding the behavior of these compounds in various tank waste matrices can facilitate sludge pretreatment options. A study of non-radioactive slurry solutions containing Al(OH) 3 (gibbsite), AlO(OH) (boehmite), and Fe 2 O 3 (iron (III) oxide) was conducted to determine the time dependent interface behavior and settling rates of these compounds. Variations in solids loading and sodium concentration were evaluated to represent waste processing conditions and the results of these settling studies were compared with prior tank waste settling tests. Information gathered from these studies can be used to inform future decisions on sludge treatment processes of the insoluble solids processed at the Hanford site.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Leveraging design of experiments to build chemometric models for the quantification of uranium (VI) and HNO3 by Raman spectroscopy

Partial least squares regression (PLSR) and support vector regression (SVR) models were optimized for the quantification of U(VI) (10–320 g L −1 ) and HNO 3 (0.6–6 M) by Raman spectroscopy with optimized calibration sets chosen by optimal design of experiments. The designed approach effectively minimized the number of samples in the calibration set for PLSR and SVR by selecting sample concentrations with a quadratic process model, despite complex confounding and covarying spectral features in the spectra. The top PLS2 model resulted in percent root mean square errors of prediction for U(VI), HNO 3 , and NO 3 − of 3.7%, 3.6%, and 2.9%, respectively. PLS1 models performed similarly despite modeling an analyte with a majority linear response (i.e., uranyl symmetric stretch) and another with more covarying vibrational modes (i.e., HNO 3 ). Partial least squares (PLS) model loadings and regression coefficients were evaluated to better understand the relationship between weaker Raman bands and covarying spectral features. Support vector machine models outperformed PLS1 models, resulting in percent root mean square error of prediction values for U(VI) and HNO 3 of 1.5% and 3.1%, respectively. The optimal nonlinear SVR model was trained using a similar number of samples (11) compared with the PLSR model, even though PLS is a linear modeling approach. The generic D-optimal design presented in this work provides a robust statistical framework for selecting training set samples in disparate two-factor systems. This approach reinforces Raman spectroscopy for the quantification of species relevant to the nuclear fuel cycle and provides a robust chemometric modeling approach to bolster online monitoring in challenging process environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ANISAP: A three-dimensional finite element program for laminated composites subjected to mechanical loading

ANISAP is a 3-D finite element FORTRAN 77 computer code for linear elastic, small strain, analysis of laminated composites with arbitrary geometry including free edges and holes. Individual layers may be isotropic or transversely isotropic in material principal coordinates; individual layers may be rotated off-axis about a global z-axis. The laminate may be a hybrid. Three different isoparametric elements, variable order of gaussian integration, calculation of stresses at element boundaries, and loading by either nodal displacement of forces are included in the program capability. Post processing capability includes failure analysis using the tensor polynominal failure criterion.

Burns, S. W.↗

Orbital evolution of circumplanetary dust by resonant charge variations

Vast ethereal rings composed of micron-sized particles have been detected about the three giant planets so far visited by Voyager. An orbital evolution mechanism for gravitationally dominated circumplanetary dust is identified here that may temporarily overwhelm other processes. Evolution rates that agree with numerical integrations are derived, and it is suggested how this process could affect the location of the faint rings evident today.

Burns, Joseph A.↗

An Internet Protocol-Based Software System for Real-Time, Closed-Loop, Multi-Spacecraft Mission Simulation Applications

The paper will provide an overview of the web-based distributed simulation software system developed for end-to-end, multi-spacecraft mission design, analysis, and test at the NASA Goddard Space Flight Center (GSFC). This software system was developed for an internal research and development (IR&D) activity at GSFC called the Distributed Space Systems (DSS) Distributed Synthesis Environment (DSE). The long-term goal of the DSS-DSE is to integrate existing GSFC stand-alone test beds, models, and simulation systems to create a "hands on", end-to-end simulation environment for mission design, trade studies and simulations. The short-term goal of the DSE was therefore to develop the system architecture, and then to prototype the core software simulation capability based on a distributed computing approach, with demonstrations of some key capabilities by the end of Fiscal Year 2002 (FY02). To achieve the DSS-DSE IR&D objective, the team adopted a reference model and mission upon which FY02 capabilities were developed. The software was prototyped according to the reference model, and demonstrations were conducted for the reference mission to validate interfaces, concepts, etc. The reference model, illustrated in Fig. 1, included both space and ground elements, with functional capabilities such as spacecraft dynamics and control, science data collection, space-to-space and space-to-ground communications, mission operations, science operations, and data processing, archival and distribution addressed.

Davis, George↗

Analysis of Hydrodynamic (Landau) Instability in Liquid-Propellant Combustion at Normal and Reduced Gravity

The burning of liquid propellants is a fundamental combustion problem that is applicable to various types of propulsion and energetic systems. The deflagration process is often rather complex, with vaporization and pyrolysis occurring at the liquid/gas interface and distributed combustion occurring either in the gas phase or in a spray. Nonetheless, there are realistic limiting cases in which combustion may be approximated by an overall reaction at the liquid/gas interface. In one such limit, the gas flame occurs under near-breakaway conditions, exerting little thermal or hydrodynamic influence on the burning propellant. In another such limit, distributed combustion occurs in an intrusive regime, the reaction zone lying closer to the liquid/gas interface than the length scale of any disturbance of interest. Finally, the liquid propellant may simply undergo exothermic decomposition at the surface without any significant distributed combustion, such as appears to occur in some types of HydroxylAmmonium Nitrate (HAN)-based liquid propellants at low pressures. Such limiting models have recently been formulated,thereby significantly generalizing earlier classical models that were originally introduced to study the hydrodynamic stability of a reactive liquid/gas interface. In all of these investigations, gravity appears explicitly and plays a significant role, along with surface tension, viscosity, and, in the more recent models, certain reaction-rate parameters associated with the pressure and temperature sensitivities of the reaction itself. In particular, these parameters determine the stability of the deflagration with respect to not only classical hydrodynamic disturbances, but also with respect to reactive/diffusive influences as well. Indeed, the inverse Froude number, representing the ratio of buoyant to inertial forces, appears explicitly in all of these models, and consequently, in the dispersion relation that determines the neutral stability boundaries beyond which steady, planar burning is unstable to nonsteady, and/or nonplanar (cellular) modes of burning. These instabilities thus lead to a number of interesting phenomena, such as the sloshing type of waves that have been observed in mixtures of HAN and TriEthanolAmmonium Nitrate (TEAN) with water. Although the Froude number was treated as an O(1) quantity in these studies, the limit of small inverse Froude number corresponding to the microgravity regime is increasingly of interest and can be treated explicitly, leading to various limiting forms of the models, the neutral stability boundaries, and, ultimately, the evolution equations that govern the nonlinear dynamics of the propagating reaction front. In the present work, we formally exploit this limiting parameter regime to compare some of the features of hydrodynamic instability of liquid-propellant combustion at reduced gravity with the same phenomenon at normal gravity.

Margolis, Stephen B.↗

Los Alamos National Security, LLC Request for Information on how industry may partner with the Laboratory on KIVA software.

KIVA is a family of Fortran-based computational fluid dynamics software developed by LANL. The software predicts complex fuel and air flows as well as ignition, combustion, and pollutant-formation processes in engines. The KIVA models have been used to understand combustion chemistry processes, such as auto-ignition of fuels, and to optimize diesel engines for high efficiency and low emissions. Fuel economy is heavily dependent upon engine efficiency, which in turn depends to a large degree on how fuel is burned within the cylinders of the engine. Higher in-cylinder pressures and temperatures lead to increased fuel economy, but they also create more difficulty in controlling the combustion process. Poorly controlled and incomplete combustion can cause higher levels of emissions and lower engine efficiencies.

33 ADVANCED PROPULSION SYSTEMS↗

CFD simulation of MSW combustion and SNCR in a commercial incinerator

Highlights: • Presented a CFD scheme for modeling MSW incinerator including SNCR process. • Performed a sensitivity analysis of SNCR operating conditions. • Non-uniform distributions of gas velocity, temperature and NO{sub x} in the incinerator. • The injection position of reagent was critical for a desirable performance of SNCR. • A NSR 1.5 was recommended as a compromise of NO{sub x} reduction rates and NH{sub 3} slip. - Abstract: A CFD scheme was presented for modeling municipal solid waste (MSW) combustion in a moving-grate incinerator, including the in-bed burning of solid wastes, the out-of-bed burnout of gaseous volatiles, and the selective non-catalytic reduction (SNCR) process between urea (CO(NH{sub 2}){sub 2}) and NO{sub x}. The in-bed calculations provided 2-D profiles of the gas–solid temperatures and the gas species concentrations along the bed length, which were then used as inlet conditions for the out-of-bed computations. The over-bed simulations provided the profiles of incident radiation heat flux on the top of bed. A 3-dimensional benchmark simulation was conducted with a 750 t/day commercial incinerator using the present coupling scheme incorporating with a reduced SNCR reduction mechanism. Numerical tests were performed to investigate the effects of operating parameters such as injection position, injection speed and the normalized stoichiometric ratio (NSR) on the SNCR performance. The simulation results showed that the distributions of gas velocity, temperature and NO{sub x} concentration were highly non-uniform, which made the injection position one of the most sensitive operating parameters influencing the SNCR performance of moving grate incinerators. The simulation results also showed that multi-layer injections were needed to meet the EU2000 standard, and a NSR 1.5 was suggested as a compromise of a satisfactory NO{sub x} reduction and reasonable NH{sub 3} slip rates. This work provided useful guides to the design and operation of SNCR process in moving-grate incinerators.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Space Shuttle propulsion parameter estimation using optimal estimation techniques, volume 1

The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.

Source record↗