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NASA NTRS2018

International Space Station Future Correlation Analysis Improvements

Ongoing modal analyses and model correlation are performed on different configurations of the International Space Station (ISS). These analyses utilize on-orbit dynamic measurements collected using four main ISS instrumentation systems: External Wireless Instrumentation System (EWIS), Internal Wireless Instrumentation System (IWIS), Space Acceleration Measurement System (SAMS), and Structural Dynamic Measurement System (SDMS). Remote Sensor Units (RSUs) are network relay stations that acquire flight data from sensors. Measured data is stored in the Remote Sensor Unit (RSU) until it receives a command to download data via RF to the Network Control Unit (NCU). Since each RSU has its own clock, it is necessary to synchronize measurements before analysis. Imprecise synchronization impacts analysis results. A study was performed to evaluate three different synchronization techniques: (i) measurements visually aligned to analytical time-response data using model comparison, (ii) Frequency Domain Decomposition (FDD), and (iii) lag from cross-correlation to align measurements. This paper presents the results of this study.

time synchronization↗

NASA NTRS2008

2008 Year in Review

In February of 2008; NASA Stennis Space Center (SSC), NASA Kennedy Space Center (KSC), and The Applied Research Laboratory at Penn State University demonstrated a pilot implementation of an Integrated System Health Management (ISHM) capability at the Launch Complex 20 of KSC. The following significant accomplishments are associated with this development: (1) implementation of an architecture for ground operations ISHM, based on networked intelligent elements; (2) Use of standards for management of data, information, and knowledge (DIaK) leading to modular ISHM implementation with interoperable elements communicating according to standards (three standards were used: IEEE 1451 family of standards for smart sensors and actuators, Open Systems Architecture for Condition Based Maintenance (OSA-CBM) standard for communicating DIaK describing the condition of elements of a system, and the OPC standard for communicating data); (3) ISHM implementation using interoperable modules addressing health management of subsystems; and (4) use of a physical intelligent sensor node (smart network element or SNE capable of providing data and health) along with classic sensors originally installed in the facility. An operational demonstration included detection of anomalies (sensor failures, leaks, etc.), determination of causes and effects, communication among health nodes, and user interfaces.

Figueroa, Jorge Fernando↗

NASA NTRS1992

Sensor fusion V; Proceedings of the Meeting, Boston, MA, Nov. 15-17, 1992

Topics addressed include 3D object perception, human-machine interface in multisensor systems, sensor fusion architecture, fusion of multiple and distributed sensors, interface and decision models for sensor fusion, computational networks, simple sensing for complex action, multisensor-based control, and metrology and calibration of multisensor systems. Particular attention is given to controlling 3D objects by sketching 2D views, the graphical simulation and animation environment for flexible structure robots, designing robotic systems from sensorimotor modules, cylindrical object reconstruction from a sequence of images, an accurate estimation of surface properties by integrating information using Bayesian networks, an adaptive fusion model for a distributed detection system, multiple concurrent object descriptions in support of autonomous navigation, robot control with multiple sensors and heuristic knowledge, and optical array detectors for image sensors calibration. (No individual items are abstracted in this volume)

Schenker, Paul S.↗

NASA NTRS1990

Integrated Communication and Control Systems. III - Nonidentical sensor and controller sampling

Networking in Integrated Communication and Control Systems (ICCS) introduces randomly varying delays which degrade the system dynamic performance and are a source of potential instability. In Part I of this sequence of papers, a discrete-time, finite-dimensional model of the delayed control system for analysis and design of ICCS was developed where the sensor and controller have identical sampling rates. In Part II, two alternate approaches for ICCS design, namely, identical and nonidentical sampling rates for sensor and controller were proposed. This Part III presents extended modeling of ICCS for nonidentical sensor and controller sampling rates. This model is also suitable for analyzing tracking problems, i.e., control systems with time-dependent reference inputs.

Liou, Luen-Woei↗

NASA NTRS1995

Optical fiber sensors for damage analysis in aerospace materials

Under this grant, fiber optic sensors were investigated for use in the nondestructive evaluation of aging aircraft. Specifically, optical fiber sensors for detection and location of impacts on a surface, and for detection of corrosion in metals were developed. The use of neural networks was investigated for determining impact location by processing the output of a network of fiberoptic strain sensors distributed on a surface. This approach employs triangulation to determine location by comparing the arrival times at several sensors, of the acoustic signal generated by the impact. For this study, a neural network simulator running on a personal computer was used to train a network using a back-propagation algorithm. Fiber optic extrinsic Fabry-Perot interferometer (EFPI) strain sensors are attached to or embedded in the surface, so that stress waves emanating from an impact can be detected. The ability of the network to determine impact location by time-or-arrival of acoustic signals was assessed by comparing network outputs with actual experimental results using impacts on a panel instrumented with optical fiber sensors. Using the neural network to process the sensor outputs, the impact location can be inferred to centimeter range accuracy directly from the arrival time data. In addition, the network can be trained to determine impact location, regardless of material anisotropy. Results demonstrate that a back-propagation network identifies impact location for an anisotropic graphite/bismaleimide plate with the same accuracy as that for an isotropic aluminum plate. Two different approaches were investigated for the development of fiber optic sensors for corrosion detection in metals, both utilizing optical fiber sensors with metal coatings. In the first approach, an extrinsic Fabry-Perot interferometric fiber optic strain sensor was placed under tensile stress, and while in the resulting strained position, a thick coating of metal was applied. Due to an increase in the quantity of material, the sensor does not return to its original position upon removal of the applied stress, and some residual strain is maintained within the sensor element. As the metal thickness decreases due to corrosion, this strain is released, providing the sensing mechanism for corrosion detection. In the second approach, photosensitive optical fibers with long period Bragg gratings in the core were coated with metal. The Bragg gratings serve to couple core modes at discrete wavelengths to cladding modes. Since cladding modes interact with the metal coating surrounding the fiber cladding, the specific wavelengths coupled from core to cladding depend on the refractive index of the metal coating. Therefore, as the metal corrodes, the resulting change in index of the coating may be measured by measuring the change in wavelength of the coupled mode. Results demonstrate that both approaches can be successfully used to track the loss in metal coating on the optical fiber sensors due to corrosion.

Schindler, Paul↗

DOE OSTI2024

Machine Learning Approach for Spatiotemporal Multivariate Optimization of Environmental Monitoring Sensor Locations

Abstract Long-term environmental monitoring is critical for managing the soil and groundwater at contaminated sites. Recent improvements in state-of-the-art sensor technology, communication networks, and artificial intelligence have created opportunities to modernize this monitoring activity for automated, fast, robust, and predictive monitoring. In such modernization, it is required that sensor locations be optimized to capture the spatiotemporal dynamics of all monitoring variables as well as to make it cost-effective. The legacy monitoring datasets of the target area are important to perform this optimization. In this study, we have developed a machine-learning approach to optimize sensor locations for soil and groundwater monitoring based on ensemble supervised learning and majority voting. For spatial optimization, Gaussian process regression (GPR) is used for spatial interpolation, while the majority voting is applied to accommodate the multivariate temporal dimension. Results show that the algorithms significantly outperform the random selection of the sensor locations for predictive spatiotemporal interpolation. While the method has been applied to a four-dimensional dataset (with two-dimensional space, time, and multiple contaminants), we anticipate that it can be generalizable to higher-dimensional datasets for environmental monitoring sensor location optimization.

Siddiquee, Masudur R.↗

NASA NTRS2011

SNE Industrial Fieldbus Interface

Programmable logic controllers (PLCs) have very limited diagnostic and no prognostic capabilities, while current smart sensor designs do not have the capability to communicate over Fieldbus networks. The aim is to interface smart sensors with PLCs so that health and status information, such as failure mode identification and measurement tolerance, can be communicated via an industrial Fieldbus such as ControlNet. The SNE Industrial Fieldbus Interface (SIFI) is an embedded device that acts as a communication module in a networked smart sensor. The purpose is to enable a smart sensor to communicate health and status information to other devices, such as PLCs, via an industrial Fieldbus networking protocol. The SNE (Smart Network Element) is attached to a commercial off-the-shelf Any bus-S interface module through the SIFI. Numerous Anybus-S modules are available, each one designed to interface with a specific Fieldbus. Development of the SIFI focused on communications using the ControlNet protocol, but any of the Anybus-S modules can be used. The SIFI communicates with the Any-bus module via a data buffer and mailbox system on the Anybus module, and supplies power to the module. The Anybus module transmits and receives data on the Fieldbus using the proper protocol. The SIFI is intended to be connected to other existing SNE modules in order to monitor the health and status of a transducer. The SIFI can also monitor aspects of its own health using an onboard watchdog timer and voltage monitors. The SIFI also has the hardware to drive a touchscreen LCD (liquid crystal display) unit for manual configuration and status monitoring.

Lucena, Angel↗

NASA NTRS2012

Application of Artificial Neural Networks to the Development of Improved Multi-Sensor Retrievals of Near-Surface Air Temperature and Humidity Over Ocean

Improved estimates of near-surface air temperature and air humidity are critical to the development of more accurate turbulent surface heat fluxes over the ocean. Recent progress in retrieving these parameters has been made through the application of artificial neural networks (ANN) and the use of multi-sensor passive microwave observations. Details are provided on the development of an improved retrieval algorithm that applies the nonlinear statistical ANN methodology to a set of observations from the Advanced Microwave Scanning Radiometer (AMSR-E) and the Advanced Microwave Sounding Unit (AMSU-A) that are currently available from the NASA AQUA satellite platform. Statistical inversion techniques require an adequate training dataset to properly capture embedded physical relationships. The development of multiple training datasets containing only in-situ observations, only synthetic observations produced using the Community Radiative Transfer Model (CRTM), or a mixture of each is discussed. An intercomparison of results using each training dataset is provided to highlight the relative advantages and disadvantages of each methodology. Particular emphasis will be placed on the development of retrievals in cloudy versus clear-sky conditions. Near-surface air temperature and humidity retrievals using the multi-sensor ANN algorithms are compared to previous linear and non-linear retrieval schemes.

Roberts, J. Brent↗

NASA NTRS1994

QPA-CLIPS: A language and representation for process control

QPA-CLIPS is an extension of CLIPS oriented towards process control applications. Its constructs define a dependency network of process actions driven by sensor information. The language consists of three basic constructs: TASK, SENSOR, and FILTER. TASK's define the dependency network describing alternative state transitions for a process. SENSOR's and FILTER's define sensor information sources used to activate state transitions within the network. Deftemplate's define these constructs and their run-time environment is an interpreter knowledge base, performing pattern matching on sensor information and so activating TASK's in the dependency network. The pattern matching technique is based on the repeatable occurrence of a sensor data pattern. QPA-CIPS has been successfully tested on a SPARCStation providing supervisory control to an Allen-Bradley PLC 5 controller driving molding equipment.

Freund, Thomas G.↗

NASA NTRS2001

Increasing Density and Reducing Costs of Data Acquisition

There are a number of reasons why it is important to increase the density of data acquisition functions. Sensor fusion seeks to integrate large numbers of sensors into a decision network. Addition of health monitoring functions may incur additional sensor requirements. But at the same time, it is important to reduce the per-channel costs of data acquisition systems. Often the most significant cost is the management of data acquisition networks, which incurs substantial costs associated with transducer installation, configuration, calibration, and maintenance. Alternatives that lower the cost of the transducer system and reduce the data acquisition system channel count will directly impact initial system costs. Other techniques that affect maintenance and operating costs will contribute to reducing life cycle costs. This paper describes work undertaken to explore alternative architectures for lowering the cost per transducer function using a MEMS-based accelerometer as the model.

Schmalzel, J. L.↗

DOE OSTI2022

Printed Potentiometric Nitrate Sensors for Use in Soil

Plant-available nitrogen, often in the form of nitrate, is an essential nutrient for plant growth. However, excessive nitrate in the environment and watershed has harmful impacts on natural ecosystems and consequently human health. A distributed network of nitrate sensors could help to quantify and monitor nitrogen in agriculture and the environment. Here, we have developed fully printed potentiometric nitrate sensors and characterized their sensitivity and selectivity to nitrate. Each sensor comprises an ion-selective electrode and a reference electrode that are functionalized with polymeric membranes. The sensitivity of the printed ion-selective electrodes was characterized by measuring their potential with respect to a commercial silver/silver chloride reference electrode in varying concentrations of nitrate solutions. The sensitivity of the printed reference electrodes to nitrate was minimized with a membrane containing polyvinyl butyral (PVB), sodium chloride, and sodium nitrate. Selectivity studies with sulphate, chloride, phosphate, nitrite, ammonium, calcium, potassium, and magnesium showed that high concentrations of calcium can influence sensor behavior. The printed ion-selective and reference electrodes were combined to form a fully printed sensor with sensitivity of −48.0 ± 3.3 mV/dec between 0.62 and 6200 ppm nitrate in solution and −47 ± 4.1 mV/dec in peat soil.

Baumbauer, Carol L. (ORCID:0000000246747551)↗

DOE OSTI2024

Cyber-Secure and Safe Operation of Solar Photovoltaic Power Distribution Systems

Solar photovoltaic (PV)-rich power distribution systems are networked Cyber-Physical Systems (CPS). These are control systems where multiple computing nodes and diverse intelligent agents interact with the physical world in real-time. However, the presence of networked components renders them vulnerable to potential cyber-attacks, cyber-intrusions, and other malicious events. This is because these systems depend on the measurements reported from their heterogeneous sensors. This makes them vulnerable to potential cyber-attacks where malicious agents can compromise the sensors or the communication networks carrying the sensor measurements. This paper proposes a novel methodology for enhancing the cyber-security and cyber-resilient post-attack safe operation of solar PV-rich power distribution systems against potential cyber-attacks through the Dynamic Watermarking (DW), using online system identification. The resiliency of the proposed technique is tested and validated with several attack scenarios on both a lab-scale 3kW grid-connected PV inverter and a Hardware-in-the-Loop (HiL) system. The proposed approach can be applied to other types of power distribution systems to enhance their cyber-secure and cyber-resilient safe operation. This paper thereby contributes to the field of cyber-security of Cyber-Physical Energy Systems (CPES).

Kim, Jaewon↗

NASA NTRS2013

Miniature Trace Gas Detector Based on Microfabricated Optical Resonators

While a variety of techniques exist to monitor trace gases, methods relying on absorption of laser light are the most commonly used in terrestrial applications. Cavity-enhanced absorption techniques typically use high-reflectivity mirrors to form a resonant cavity, inside of which a sample gas can be analyzed. The effective absorption length is augmented by the cavity's high quality factor, or Q, because the light reflects many times between the mirrors. The sensitivity of such mirror-based sensors scales with size, generally making them somewhat bulky in volume. Also, specialized coatings for the high-reflectivity mirrors have limited bandwidth (typically just a few nanometers), and the delicate mirror surfaces can easily be degraded by dust or chemical films. As a highly sensitive and compact alternative, JPL is developing a novel trace gas sensor based on a monolithic optical resonator structure that has been modified such that a gas sample can be directly injected into the cavity. This device concept combines ultra-high Q optical whispering gallery mode resonators (WGMR) with microfabrication technology used in the semiconductor industry. For direct access to the optical mode inside a resonator, material can be precisely milled from its perimeter, creating an open gap within the WGMR. Within this open notch, the full optical mode of the resonator can be accessed. While this modification may limit the obtainable Q, calculations show that the reduction is not significant enough to outweigh its utility for trace gas detection. The notch can be milled from the high- Q crystalline WGMR with a focused ion beam (FIB) instrument with resolution much finer than an optical wavelength, thereby minimizing scattering losses and preserving the optical quality. Initial experimental demonstrations have shown that these opened cavities still support high-Q whispering gallery modes. This technology could provide ultrasensitive detection of a variety of molecular species in an extremely compact and robust package. With this type of modified WGMR, one can inject a gas sample into the open gap, allowing highly sensitive trace molecule detection within a roughly 1-cm volume. Other critical components of the instrument, such as the detector and a semiconductor laser, could be directly packaged with the resonator so as to not significantly increase the size of the device. Besides its low mass, volume, and power consumption, the monolithic design makes these resonators intrinsically robust devices, capable of handling significant temperature excursions, without moving parts to wear out or delicate coatings that can be easily damaged. A sensor could integrate with microfluidics technology for a chip-scale device. It could be mounted to the end of a deployable arm, or inserted into a borehole. Also, a network of individual sensors could be dispersed to monitor conditions over a wide region

Aveline, David C.↗

DOE OSTI2025

Deep Neural Network Assisted Distributed Strain and Temperature Fiber Sensor System for Natural Gas Pipeline Monitoring

Natural gas pipeline integrity monitoring is crucial to detect potential leaks, find structural issues, and prevent environmental damage. This article presents a system of natural gas pipeline monitoring that uses a specialized double Brillouin peak sensing fiber along with the Brillouin optical time domain analysis (BOTDAs) technique. The calibrated sensing fiber coefficients for strain and temperature are 41.8 kHz/ με and 0.9 MHz/°C for peak 1; and 47.2 kHz/ με , and 1.11 MHz/°C for peak 2, respectively. Initially, lab tests were performed by installing a short section of double Brillouin peak fiber (DBPF) on a 1-in steel pipe under pressure up to 1000 per square inch (psi) at elevated temperatures. Simultaneous distributed measurements of temperature and pressure-induced hoop strain were successfully measured. Considering the long processing speed to extract Brillouin frequency shift (BFS), we employ a novel probabilistic deep neural network (PDNN) framework for rapid BFS prediction. Additionally, using the Finite Element Method, the effects of the pipeline pressure on hoop strain were modeled and compared to the experimental hoop strain under the same set of pipeline conditions. Finally, an actual 4-in outer diameter steel natural gas pipeline was used for pilot-scale tests, where hoop strain was measured at various pressure levels. Leaks were simulated to demonstrate accurate pipeline integrity monitoring. At an internal pipe pressure of 1000 psi, hoop strain of approximately 300 με was observed, and the sensitivity was calculated as 0.28 με /psi. The results of this pilot-scale study demonstrated that the system is capable of performing distributed monitoring sufficient to detect pipeline pressure and the presence of leaks to ensure the safe operation of gas pipelines in the field.

03 NATURAL GAS↗

DOE OSTI2020

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf’s ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2015

Cloud-to-Ground Lightning Estimates Derived from SSMI Microwave Remote Sensing and NLDN

Lightning observations are collected using ground-based and satellite-based sensors. The National Lightning Detection Network (NLDN) in the United States uses multiple ground sensors to triangulate the electromagnetic signals created when lightning strikes the Earth's surface. Satellite-based lightning observations have been made from 1998 to present using the Lightning Imaging Sensor (LIS) on the NASA Tropical Rainfall Measuring Mission (TRMM) satellite, and from 1995 to 2000 using the Optical Transient Detector (OTD) on the Microlab-1 satellite. Both LIS and OTD are staring imagers that detect lightning as momentary changes in an optical scene. Passive microwave remote sensing (85 and 37 GHz brightness temperatures) from the TRMM Microwave Imager (TMI) has also been used to quantify characteristics of thunderstorms related to lightning. Each lightning detection system has fundamental limitations. TRMM satellite coverage is limited to the tropics and subtropics between 38 deg N and 38 deg S, so lightning at the higher latitudes of the northern and southern hemispheres is not observed. The detection efficiency of NLDN sensors exceeds 95%, but the sensors are only located in the USA. Even if data from other ground-based lightning sensors (World Wide Lightning Location Network, the European Cooperation for Lightning Detection, and Canadian Lightning Detection Network) were combined with TRMM and NLDN, there would be enormous spatial gaps in present-day coverage of lightning. In addition, a globally-complete time history of observed lightning activity is currently not available either, with network coverage and detection efficiencies varying through the years. Previous research using the TRMM LIS and Microwave Imager (TMI) showed that there is a statistically significant correlation between lightning flash rates and passive microwave brightness temperatures. The physical basis for this correlation emerges because lightning in a thunderstorm occurs where ice is first present in the cloud and electric charge separation occurs. These ice particles efficiently scatter the microwave radiation at the 85 and 37 GHz frequencies, thus leading to large brightness temperature depressions. Lightning flash rate is related to the total amount of ice passing through the convective updraft regions of thunderstorms. Confirmation of this relationship using TRMM LIS and TMI data, however, remains constrained to TRMM observational limits of the tropics and subtropics. Satellites from the Defense Meteorology Satellite Program (DMSP) have global coverage and are equipped with passive microwave imagers that, like TMI, observe brightness temperatures at 85 and 37 GHz. Unlike the TRMM satellite, however, DMSP satellites do not have a lightning sensor, and the DMSP microwave data has never been used to derive global lightning. In this presentation, a relationship between DMSP Special Sensor Microwave Imager (SSMI) data and ground-based cloud-to-ground (CG) lightning data from NLDN is investigated to derive a spatially complete time history of CG lightning for the USA study area. This relationship is analogous to the established using TRMM LIS and TMI data. NLDN has the most spatially and temporally complete CG lightning data for the USA, and therefore provides the best opportunity to find geospatially coincident observations with SSMI sensors. The strongest thunderstorms generally have minimum 85 GHz Polarized Corrected brightness Temperatures (PCT) less than 150 K. Archived radar data was used to resolve the spatial extent of the individual storms. NLDN data for that storm spatial extent defined by radar data was used to calculate the CG flash rate for the storm. Similar to results using TRMM sensors, a linear model best explained the relationship between storm-specific CG flash rates and minimum 85 GHz PCT. However, the results in this study apply only to CG lightning. To extend the results to weaker storms, the probability of CG lightning (instead of the flash rate) was calculated for storms having 85 GHz PCT greater than 150 K. NLDN data was used to determine if a CG strike occurred for a storm. This probability of CG lightning was plotted as a function of minimum 85 GHz PCT and minimum 37 GHz PCT. These probabilities were used in conjunction with the linear model to estimate the CG flash rate for weaker storms with minimum 85 GHz PCTs greater than 150 K. Results from the investigation of CG lightning and passive microwave radiation signals agree with the previous research investigating total lightning and brightness temperature. Future work will take the established relationships and apply them to the decades of available DMSP data for the USA to derive a map of CG lightning flash rates. Validation of this method and uncertainty analysis will be done by comparing the derived maps of CG lightning flash rates against existing NLDN maps of CG lightning flash rates.

Winesett, Thomas↗

NASA NTRS1980

Evolution of snow sensors and the potential of microwave devices in operational telemetry networks

Both manually collected snow-course data and telemetered information from SNOTEL sites throughout the western United States are used to make forecasts of streamflow. Although these conventional methods have proven highly reliable over the years, they still exhibit some shortcomings. Active and passive microwave remote sensing systems recently developed and tests present the potential to eliminate some negative aspects associated with other types of sensors currently in use. Because of their ability to see through the snowpack they offer a unique opportunity to improve snowpack measurement techniques. As yet neither the active nor passive system is developed sufficiently to supplant existing methods in operational telemetry networks. Active microwave sensors are the most promising for the near future and are being used in research and development programs to study snow pillow performance in the SNOTEL system.

Shafer, B. A.↗

NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

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. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it 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 of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗