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Flight Performance and Stability of Space Launch System Core Stage Thrust Vector Control

The Space Launch System (SLS) Core Stage (CS) Thrust Vector Control (TVC) system is comprised of eight mechanical feedback Shuttle heritage Type III TVC actuators and four RS-25 engines, each attached to a Shuttle heritage gimbal block/bearing. The Core Stage TVC shares vehicle control authority with the SLS 5-segment Solid Rocket Boosters (SRBs) during boost phase flight, and is the sole means of vehicle flight control during in exoatmospheric flight following SRB separation. TVC responses during Green Run Hot Fire (GRHF) testing revealed that the TVC did not meet its performance specifications. Step and frequency responses exhibited unexpected departures from prior laboratory data and modeled behavior. Post-test analysis determined that the characteristics of the structure and gimbal friction are significantly influenced by the thrust-loaded conditions, and the command avionics exhibited a small but important gain nonlinearity. Using the available test data, the design team augmented the flight control TVC models to bound the observed results and include the additional fidelity needed for vehicle flight control analysis so as to build sufficient rationale for flight certification. Prior to the Green Run tests, “simplex” linear models typically used for flight control analysis did not include gimbal friction and other nonlinearities owing to long-standing assumptions that these effects were negligible in the Shuttle Orbiter TVC system. Following the Green Run findings, simulation analysis of the flight dynamics in the time and frequency domain revealed the propensity for a flight control limit cycle oscillation (LCO) if friction and structural compliances fell near the edges of test-predicted bounds. While the “most probable” models did not predict an in-flight LCO, the SLS Program conservatively proceeded with a system-wide evaluation and ultimate acceptance of the possibility for a small amplitude, low-frequency TVC LCO in flight. A final validation of the extensive test and modeling effort occurred when the first flight of SLS successfully demonstrated the fully integrated performance of the vehicle’s TVC system This paper is the final installment in a seven-paper series surveying the design, engineering, test validation, and flight performance of the Core Stage Thrust Vector Control system. In this paper, the development of flight rationale in light of the TVC responses observed in Green Run is discussed, along with a review of the flight telemetry illustrating the correlation of the preflight predictions with the observed performance.

John H. Wall↗

NASA NTRS1999

Membrane-Based Functions in the Origin of Cellular Life

Our objective is to help explain how the earliest ancestors of contemporary cells (protocells) performed their essential functions employing only the molecules available in the protobiological milieu. Our hypothesis is that vesicles, built of amphiphilic, membrane-forming materials, emerged early in protobiological evolution and served as precursors to protocells. We further assume that the cellular functions associated with contemporary membranes, such as capturing and, transducing of energy, signaling, or sequestering organic molecules and ions, evolved in these membrane environments. An alternative hypothesis is that these functions evolved in different environments and were incorporated into membrane-bound structures at some later stage of evolution. We focus on the application of the fundamental principles of physics and chemistry to determine how they apply to the formation of a primitive, functional cell. Rather than attempting to develop specific models for cellular functions and to identify the origin of the molecules which perform these functions, our goal is to define the structural and energetic conditions that any successful model must fulfill, therefore providing physico-chemical boundaries for these models. We do this by carrying out large-scale, molecular level computer simulations on systems of interest.

Chipot, Christophe↗

NASA NTRS1986

Characterization of real gas properties for space shuttle main engine fuel turbine and performance calculations

Real thermodynamic and transport properties of hydrogen, steam, the SSME mixture, and air are developed. The SSME mixture properties are needed for the analysis of the space shuttle main engine fuel turbine. The mixture conditions for the gases, except air, are presented graphically over a temperature range from 800 to 1200 K, and a pressure range from 1 to 500 atm. Air properties are given over a temperature range of 320 to 500 K, which are within the bounds of the thermodynamics programs used, in order to provide mixture data which is more easily checked (than H2/H2O). The real gas property variation of the SSME mixture is quantified. Polynomial expressions, needed for future computer analysis, for viscosity, Prandtl number, and thermal conductivity are given for the H2/H2O SSME fuel turbine mixture at a pressure of 305 atm over a range of temperatures from 950 to 1140 K. These conditions are representative of the SSME turbine operation. Performance calculations are presented for the space shuttle main engine (SSME) fuel turbine. The calculations use the air equivalent concept. Progress towards obtaining the capability to evaluate the performance of the SSME fuel turbine, with the H2/H2O mixture, is described.

Harloff, G. J.↗

DOE OSTI2020

Evaluation of H-Canyon Ventilation Exhaust Tunnel Inspection at the Savannah River Site - 20052

The Department of Energy (DOE) H-Canyon Facility at the Savannah River Site (SRS) is operated by Savannah River Nuclear Solutions (SRNS). The Facility Structural Integrity Program [1] provides a process to inspect, evaluate, and document the conditions of passive safety related structural systems and components, their degradation mechanisms and their impact on the safety envelope. The Structural Integrity Program performs periodic visual inspections to confirm the systems and components can perform their safety function and recommend corrective actions before the function is compromised. The H-Canyon Exhaust Tunnel is part of the H-Canyon Ventilation System and is periodically inspected under the Structural Integrity Program. The Tunnel performs a Safety Class passive design feature function that is available 100% of the time. The underground reinforced concrete Tunnel directs Canyon process air from the Canyon to the Sand Filter System. The radiological and chemical airborne activity coupled with the physical configuration of the tunnel precludes a manned entry into the tunnel to perform the inspection. Unlike active systems that can be subjected to physical testing to confirm capability, qualification calculations, including modeling, is performed to assess passive design feature capabilities relative to operational, accident and natural phenomena hazards events. Input for these calculations come from knowledge of field conditions, design drawings and conservative assumptions. The knowledge of field conditions comes from concrete and soil testing activities as well as inspection data. The use of cameras on crawlers to obtain inspection data and how that data is used in qualification calculations is the focus of this discussion. Remote Tunnel inspections have been performed using cameras on a stick, referred to as pole cameras, prior to Calendar Year 2003 (CY2003). Since CY2003, six camera equipped crawlers have been used. Crawlers have evolved and improved by incorporating lessons learned from the previous inspections. The latest 2019 crawler successfully traveled the entire length of the tunnel between the Canyon and Sand Filter System and captured images that were previously unseen, thus providing key visual data for the Structural Integrity Program report [2]. The inspection data serves as 1) input to qualification calculations, 2) validates current conditions remain bounded by qualification calculations, and 3) documents a record of change over time. This data is vital for the effective evaluation of the tunnel structure and aids with predicting the life cycle service life safety envelope to protect the public, environment, and facility worker. The goal of the 2019 deployment was to use a more robust vehicle to ensure travel over obstacles, perform the inspection with higher resolution cameras, and have the ability to elevate the cameras to view surfaces previously obscured by abandon-in-place ducts in the tunnel. The inspection information will serve to strengthen the input basis for qualification calculations, versus using excessive conservative calculation assumptions. This 2019 inspection was compared with previous crawler visual evidence to identify change over time to project remaining service life and confirm field conditions remain bounded by qualification calculations. The results of the 2019 Exhaust Tunnel inspection continue to improve and provide a firm basis to make sound engineering judgements regarding tunnel capability and approaches in projecting remaining service life with an aging system and component. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Macrovoid resolved simulations of transport through HPRO relevant membrane geometries

Modeling the transport properties such as diffusivity and permeability of high pressure reverse osmosis (HPRO) membranes is critical for the selection and manufacture of membranes suitable for operation under high pressure. These properties can be significantly affected by the changes in heterogeneous pore structures due to compaction. Here, the modeling platform presented in this work resolves the two scale porosity in HPRO relevant membranes. A synthetic membrane geometry is constructed based on available experimental visualizations of pore structures. The simulations directly capture the flow channeling that results from a combination of material properties and geometric features of the macrovoids. A parametric study is presented to account for the transition of flow characteristics from a material governed regime to a macrovoid governed regime. Permeability of the membrane is evaluated using the simulation data and compared with an existing model that scales with the square of tortuosity over a range of material properties. The model is found to perform well under a narrow range of tortuosity while deviating from the calculated permeabilities at extreme conditions. The effective permeability of the membrane is found to vary by at least two orders of magnitude between the two flow regimes. It is also observed that tortuosity is a bounded property with its upper limit determined by the macrovoid geometry. Consequently, the tortuosity based correlations fail near a flow regime that is mainly governed by the macrovoids. The modeled permeability can be more than an order of magnitude smaller than the simulation result. A new model based on flux-weighted porosity of a membrane is introduced and its correlation with tortuosity is studied. The model agrees with the simulated data as, in addition to tortuosity, it also accounts for the flux partition within and outside the flow channels. Such correlations enable extending the existing understanding of flow characteristics to enhance predictability of porous media models.

42 ENGINEERING↗

NASA NTRS2019

ASPIRE Aerodynamic Models and Flight Performance

The Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) project waslaunched to develop the capability for testing supersonic parachutes at Mars-relevant conditions.Three initial parachute tests, targeted as a risk-reduction activity for NASA's upcomingMars2020 mission, successfully tested two candidate parachute designs and provided valuabledata on parachute inflation, forces, and aerodynamic behavior. Design of the flight tests dependedon flight mechanics simulations which in turn required aerodynamic models for the payload, andthe parachute. Computational Fluid Dynamics (CFD) was used to generate these models preflightand are compared against the flight data after the tests. For the payload, the reconstructedaerodynamic behavior is close to the pre-flight predictions, but the uncertainties in thereconstructed data are high due to the low dynamic pressures and accelerations during the flightperiod of comparison. For the parachute, the predicted time to inflation agrees well with the preflightmodel; the peak aerodynamic force and the steady state drag on the parachute are withinthe bounds of the pre-flight models, even as the models over-predict the parachute drag atsupersonic Mach numbers. Notably, the flight data does not show the transonic drag decreasepredicted by the pre-flight model. The ASPIRE flight tests provide previously unavailablevaluable data on the performance of a large full-scale parachute behind a slender leading bodyat Mars-relevant Mach number, dynamic pressure and parachute loads. This data is used topropose a new model for the parachute drag behind slender bodies to aid future experiments.

Muppidi, Suman↗

DOE OSTI2022

Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU(N c ) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation, and is different from the correlator for the heavy quark diffusion coefficient. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the R ξ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The renormalization group equation of this electric field correlator is determined by that of the strong coupling constant. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

The Gross-Neveu-Yukawa archipelago

We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Measurement and Modeling of the effects of exhaust composition and hydrothermal aging on the ammonia storage capacity of a commercial Cu-SSZ-13 catalyst

Copper exchanged chabazites are among the state-of-the-art catalyst materials being studied for selective catalytic reduction of NOx, however, there is still a need to understand how these materials store ammonia after aging. In this work, studies are performed to assess the ammonia storage capacity of Cu-SSZ-13 as a function of concentration, temperature, and extent of hydrothermal aging. Ammonia binds at three difference sites: (i) a Cu site bound at 1 framework Al (Z 1 Cu site), (ii) a Cu site bound at 2 framework Al (Z 2 Cu site), and (iii) a Brønsted acid site (ZH site). Results show that a 3-site model can accurately capture ammonia storage across all conditions. Impacts for hydrothermal aging are considered via 3 aging reactions that change the site densities of each identified adsorption site. Model assessment shows that during aging there is a significant loss in Brønsted acid sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Regioselective Hydrosilylation Catalysis with Supported Well-Defined Pt(0) Complexes: Effects of Surface Anions and Phosphenium Ligands

Achieving stable, selective single-atom catalysts is challenging because localsurface-site structures are difficult to control. Surface organometallic chemistry and organic−inorganic hybrid materials offer partial solutions, but applications to supporting zero-valent metals are limited. We demonstrate that well-defined, ionically bound N-heterocyclic phosphenium ([NHP] + ) ligands can be generated on silylium-functionalized sulfated zirconia ([ i Pr 3 Si][SZO]). These surface-bound [NHP][SZO] ligands coordinate Pt(0) centers, forming [(NHP)Pt(0)L][SZO] precatalysts that are highly active for alkyne hydrosilylation. Systematic studies reveal that sterically bulky aromatic ligands enhance regioselectivity, achieving performances comparable to molecular Pt catalysts. Further, more-coordinating anions support more-regioselective precatalysts; therefore, SZO supports more-selective species than weaker-coordinating Al(OC(CF 3 ) 3 ) 3 - functionalized silica, a trend confirmed by molecular analogues. These results demonstrate that both the ligand and support control catalytic behavior and enable solid-state structure− activity relationships.

Catalysts↗

DOE OSTI2021

Scalable Polymeric Few-Nanometer Organosilica Membranes with Hydrothermal Stability for Selective Hydrogen Separation

Nanoporous silica membranes exhibit excellent H 2 /CO 2 separation properties for sustainable H 2 production and CO 2 capture but are prepared via complicated thermal processes above 400 °C, which prevent their scalable production at a low cost. Here, we demonstrate the rapid fabrication (within 2 min) of ultrathin silica-like membranes (~3 nm) via an oxygen plasma treatment of polydimethylsiloxane-based thin-film composite membranes at 20 °C. The resulting organosilica membranes unexpectedly exhibit H2 permeance of 280-930 GPU (1 GPU = 3.347 x 10 -10 mol m -2 s -1 Pa -1 ) and H2/CO2 selectivity of 93-32 at 200 °C, far surpassing state-of-the-art membranes and Robeson’s upper bound for H 2 /CO 2 separation. When challenged with a 3 d simulated syngas test containing water vapor at 200 °C and a 340 d stability test, the membrane shows durable separation performance and excellent hydrothermal stability. The robust H 2 /CO 2 separation properties coupled with excellent scalability demonstrate the great potential of these organosilica membranes for economic H 2 production with minimal carbon emissions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Short-depth circuits for efficient expectation-value estimation

The evaluation of expectation values Tr[$\rho \mathcal{O}$] for some pure state $\rho$ and Hermitian operator $\mathcal{O}$ is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements N approaching the Heisenberg limit N = O(1/ ε) as a function of target accuracy ε. The use of quantum phase estimation (QPE) requires, however, long circuit depths C = O(1/ ε) making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using N = O(1/ε 2 ) measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ε r . Further, we propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth C = O (ε μ ) (with μ ≥ 0) and to a number of measurements N = O (1/ε 2 + ν ) for 0 < ν ≤ 1 and a much smaller prefactor. We provide detailed descriptions of two implementations of our strategy for ν = 1 and ν ≈ 0.5 and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Emulating ab initio computations of infinite nucleonic matter

We construct efficient emulators for the computation of the infinite nuclear matter equation of state. These emulators are based on the subspace-projected coupled-cluster method for which we here develop a new algorithm called small-batch voting to eliminate spurious states that might appear when emulating quantum many-body methods based on a non-Hermitian Hamiltonian. The efficiency and accuracy of these emulators facilitate a rigorous statistical analysis within which we explore nuclear matter predictions for > 10 6 different parametrizations of a chiral interaction model with explicit Δ -isobars at next-to-next-to leading order. Constrained by nucleon-nucleon scattering phase shifts and bound-state observables of light nuclei up to He 4 , we use history matching to identify nonimplausible domains for the low-energy coupling constants of the chiral interaction. Within these domains we perform a Bayesian analysis using sampling and importance resampling with different likelihood calibrations and study correlations between interaction parameters, calibration observables in light nuclei, and nuclear matter saturation properties. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Prospects for detecting heavy WIMP dark matter with the Cherenkov Telescope Array: The Wino and Higgsino

TeV-scale particles that couple to the standard model through the weak force represent a compelling class of dark matter candidates. The search for such weakly interacting massive particles has already spanned multiple decades, and whilst it has yet to provide any definitive evidence for their existence, viable parameter space remains. In this paper, we show that the upcoming Cherenkov Telescope Array (CTA) has significant sensitivity to uncharted parameter space at the TeV mass scale. To do so, we focus on two prototypical dark matter candidates, the Wino and Higgsino. Additionally, sensitivity forecasts for both models are performed including the irreducible background from misidentified cosmic rays, as well as a range of estimates for the Galactic emissions at TeV energies. For each candidate, we find substantial expected improvements over existing bounds from current imaging atmospheric Cherenkov telescopes. In detail, for the Wino we find a sensitivity improvement of roughly an order of magnitude in <σ v>, whereas for the Higgsino we demonstrate that CTA has the potential to become the first experiment that has sensitivity to the thermal candidate. Taken together, these enhanced sensitivities demonstrate the discovery potential for dark matter at CTA in the 1–100 TeV mass range.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Review and Assessment of Available Data Regarding the Behavior of Sodium Aerosols

Recently, there has been a resurgence of interest in advanced (non-light water) reactor designs, including sodium fast reactors (SFRs). In parallel, multiple efforts are underway to develop risk informed, performance-based licensing pathways for advanced reactors. However, such licensing approaches depend on the accuracy of the associated safety assessments, including mechanistic source term (MST) analyses. Unlike historical source term assessments, which utilizes bounding estimates of radionuclide release, MSTs attempt to realistically estimate the transport and retention of radionuclides for specific transient scenarios. For SFR MST analyses, the behavior of radionuclide aerosols is a key factor, as noted in recent studies. Due to the use of sodium as the primary coolant, many potential transient scenarios involve the release of radionuclide aerosols in conjunction with sodium aerosols. For such scenarios, sodium may be the dominant aerosol species, compared to that of released radionuclides. Therefore, understanding the behavior of sodium aerosols is particularly important to an accurate assessment of aerosol transport. Although many approaches to aerosol modeling exist, it is vital to establish their capabilities in evaluating sodium aerosol behavior for SFR analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗

DOE OSTI2021

Data accompanying the publication "Sensitivity of grass fires burning in marginal conditions to atmospheric turbulence" in the Journal of Geophysical Research-Atmospheres

Data accompanying Jonko, Yedinak, Conley, and Linn (2021): "Sensitivity of grass fires burning in marginal conditions to atmospheric turbulence", JGR-Atmospheres. LA-UR-21-24832. The following files were generated from simulations performed with Los Alamos National Laboratory coupled atmosphere-fire behavior model FIRETEC v1.3: -area_burned.csv contains the area burned per second in m^2 for 45 CORE simulations, 20 INIT simulations and 20 BOUND simulations (85 columns), and 600 seconds of simulation (600 rows). -fire_perimeter.csv containing the fire perimeters in m for 45 CORE simulations, 20 INIT simulations and 20 BOUND simulations (85 columns), and 600 seconds of simulation (600 rows). -consumption_per_second.csv containing consumption in kg/s for 45 CORE simulations, 20 INIT simulations and 20 BOUND simulations (85 columns), and 600 seconds of simulation (600 rows). -rate_of_spread.csv containing the distance of the fire front from the ignition line in m for 45 CORE simulations, 20 INIT simulations and 20 BOUND simulations (85 columns), and 600 seconds of simulation (600 rows). -CORE1_u_10m_300_sec.hdf, INIT3_u_10m_300_sec.hdf, and BOUND3_u_10m_300_sec.hdf contain u wind speeds at 10 m height for 300 seconds (3D: time, x, y) of simulation for simulations CORE1, INIT3, and BOUND3, respectively. -CORE.final.fuel.density.hdf contains final fuel densities in the surface layer of the model (3D: ensemble member, x, y) for all 45 CORE simulations. -CORE{1-45}_3D_u_120_sec.hdf: 45 files containing vertically and horizontally resolved u winds for 120 seconds of simulation (4D: time, x, y, z) for the 45 CORE ensemble members. For additional information about this data, please contact the corresponding author at ajonko@lanl.gov.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1971

Bounding filters in the presence of inexactly known parameters.

Optimum bounding filters are derived for a specific version (steady state time-invariant with scalar observations) of the Kalman-Bucy filtering problem with inexactly known system parameters and for the Wiener filtering problem with inexactly known spectral densities. The designed filter obtains a bound on the actual error covariance which is not known, and it also prevents apparent divergence. Conditions are derived for the design of the optimum bounding filter within a permissible class of solutions; this turns out to be the min-max mean-square error filter for an extended class of solutions. The bounding filter can be of lower order than the original system, and a technique is devised for reducing the order of the filtering system and concurrently obtaining a figure of merit for its performance.

Nahi, N. E.↗