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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Developing capacitated p-median location-allocation model in the spopt library to allow UCL student teacher placements using public transport

Location-allocation is a key tool within the GIS and network analysis toolbox. In this paper we discuss the real world application of a location-allocation case study (approx 800 students, 500 schools) from UCL using public transport. The use of public transportation is key for this case study, as many location-allocation approaches only make use of drive-time or walking-time distances, but the location of UCL in Greater London, UK makes the inclusion of public transport vital for this case study. The location-allocation is implemented as a capacitated p-median location-allocation model, using the spopt library, part of the Python Spatial Analysis Library (PySAL). The capacitated variation of the p-median location-allocation problem is a new addition to the spopt library, which this work will present. The results from the initial version of the capacitated p-median location-allocation problem has shown a marked improvement on public transport travel time, with public transport travel time reduced by 891 minutes overall for an initial sample of 93 students (9.58 minutes per student). Results will be presented below and plans for further improvement shared.

Bearman, Nick↗
NASA NTRS2000

Confirmation of NLDN Long Range Strike Locations with LIS Observations

This study compares the lightning locations reported by the National Lightning Detection Network (NLDN) with the lightning locations determined by the Lightning Imaging Sensor (LIS). The NLDN system identifies the rf signature of cloud-to-ground lightning. The LIS data is the top level of a hierarchy of optical data objects. The centroid and timing of each LIS lightning activity center are compared with each flash in a subset of the NLDN long range lightning location data in a portion of the Atlantic Ocean and the Caribbean Sea consisting of those locations more than 625 km from any sensor. This subset is produced by analyzing each reported NLDN location to determine if that location is within the LIS field of view at the time of the reported flash. The Tropical Rainfall Measuring Mission Satellite (TRMM) orbit limits the cross-sensor comparison to tropical and sub-tropical regions. Because the rf-detection system depends on ionospheric propagation conditions, a separate analysis was made for daylight conditions at both source and sensor as well as nighttime at both places. A full year of data is compared to provide an adequate sample of each data set. Confirmation of lightning in the general location of the NLDN report is established when LIS detected one or more centers of lightning activity within a 2 degree radius from the NLDN location.

Boeck, William↗
NASA NTRS2001

Preliminary Design of a Lightning Optical Camera and ThundEr (LOCATE) Sensor

The preliminary design of an optical/acoustical instrument is described for making highly accurate real-time determinations of the location of cloud-to-ground (CG) lightning. The instrument, named the Lightning Optical Camera And ThundEr (LOCATE) sensor, will also image the clear and cloud-obscured lightning channel produced from CGs and cloud flashes, and will record the transient optical waveforms produced from these discharges. The LOCATE sensor will consist of a full (360 degrees) field-of-view optical camera for obtaining CG channel image and azimuth, a sensitive thunder microphone for obtaining CG range, and a fast photodiode system for time-resolving the lightning optical waveform. The optical waveform data will be used to discriminate CGs from cloud flashes. Together, the optical azimuth and thunder range is used to locate CGs and it is anticipated that a network of LOCATE sensors would determine CG source location to well within 100 meters. All of this would be accomplished for a relatively inexpensive cost compared to present RF lightning location technologies, but of course the range detection is limited and will be quantified in the future. The LOCATE sensor technology would have practical applications for electric power utility companies, government (e.g. NASA Kennedy Space Center lightning safety and warning), golf resort lightning safety, telecommunications, and other industries.

Phanord, Dieudonne D.↗
NASA NTRS1996

Adjustment of Sensor Locations During Thermal Property Parameter Estimation

The temperature dependent thermal properties of a material may be evaluated from transient temperature histories using nonlinear parameter estimation techniques. The usual approach is to minimize the sum of the squared errors between measured and calculated temperatures at specific locations in the body. Temperature measurements are usually made with thermocouples and it is customary to take thermocouple locations as known and fixed during parameter estimation computations. In fact, thermocouple locations are never known exactly. Location errors on the order of the thermocouple wire diameter are intrinsic to most common instrumentation procedures (e.g., inserting a thermocouple into a drilled hole) and additional errors can be expected for delicate materials, difficult installations, large thermocouple beads, etc.. Thermocouple location errors are especially significant when estimating thermal properties of low diffusively materials which can sustain large temperature gradients during testing. In the present work, a parameter estimation formulation is presented which allows for the direct inclusion of thermocouple positions into the primary parameter estimation procedure. It is straightforward to set bounds on thermocouple locations which exclude non-physical locations and are consistent with installation tolerances. Furthermore, bounds may be tightened to an extent consistent with any independent verification of thermocouple location, such as x-raying, and so the procedure is entirely consonant with experimental information. A mathematical outline of the procedure is given and its implementation is illustrated through numerical examples characteristic of light-weight, high-temperature ceramic insulation during transient heating. The efficacy and the errors associated with the procedure are discussed.

Milos, Frank S.↗
NASA NTRS1990

Close binding of identity and location in visual feature perception

The binding of identity and location information in disjunctive feature search was studied. Ss searched a heterogeneous display for a color or a form target, and reported both target identity and location. To avoid better than chance guessing of target identity (by choosing the target less likely to have been seen), the difficulty of the two targets was equalized adaptively; a mathematical model was used to quantify residual effects. A spatial layout was used that minimized postperceptual errors in reporting location. Results showed strong binding of identity and location perception. After correction for guessing, no perception of identity without location was found. A weak trend was found for accurate perception of target location without identity. We propose that activated features generate attention-calling "interrupt" signals, specifying only location; attention then retrieves the properties at that location.

Orientation↗
NASA NTRS2004

A Preliminary ZEUS Lightning Location Error Analysis Using a Modified Retrieval Theory

The ZEUS long-range VLF arrival time difference lightning detection network now covers both Europe and Africa, and there are plans for further expansion into the western hemisphere. In order to fully optimize and assess ZEUS lightning location retrieval errors and to determine the best placement of future receivers expected to be added to the network, a software package is being developed jointly between the NASA Marshall Space Flight Center (MSFC) and the University of Nevada Las Vegas (UNLV). The software package, called the ZEUS Error Analysis for Lightning (ZEAL), will be used to obtain global scale lightning location retrieval error maps using both a Monte Carlo approach and chi-squared curvature matrix theory. At the core of ZEAL will be an implementation of an Iterative Oblate (IO) lightning location retrieval method recently developed at MSFC. The IO method will be appropriately modified to account for variable wave propagation speed, and the new retrieval results will be compared with the current ZEUS retrieval algorithm to assess potential improvements. In this preliminary ZEAL work effort, we defined 5000 source locations evenly distributed across the Earth. We then used the existing (as well as potential future ZEUS sites) to simulate arrival time data between source and ZEUS site. A total of 100 sources were considered at each of the 5000 locations, and timing errors were selected from a normal distribution having a mean of 0 seconds and a standard deviation of 20 microseconds. This simulated "noisy" dataset was analyzed using the IO algorithm to estimate source locations. The exact locations were compared with the retrieved locations, and the results are summarized via several color-coded "error maps."

Elander, Valjean↗
NASA NTRS2022

Phase II and III Solid Waste Management Unit Assessment and Confirmatory Sampling Report for Per- and Polyfluorinated Alkyl Substances, Potential Release Location 237, Kennedy Space Center, Florida

Per- and polyfluoroalkyl substances (PFAS) Phase II and III Solid Waste Management Unit (SWMU) Assessment (SA) and Confirmatory Sampling (CS) were conducted at the John F. Kennedy Space Center (KSC), Potential Release Location (PRL) 237, located in Merritt Island, Brevard County, Florida for the National Aeronautics and Space Administration (NASA) under Contract 80KSC019D0010/80KSC019F0289. A Phase I SA and CS Report was previously submitted that identified 33 locations of concern (LOCs) at KSC associated with the storage, use, or release of materials containing PFAS. The objectives of the Phase II and III SA and CS were to: - Complete site and source characterization of identified LOCs; - Identify areas of potential concern (AOPCs) where past or present activities may have resulted in a release of PFAS to the environment; - Qualitatively characterize migration potential of released PFAS to environmental media (primarily soil, groundwater, surface water, and sediment); and - Identify potential receptors for exposure to PFAS-impacted environmental media. Surface water samples were collected from LOCs/AOPCs and locations on the KSC periphery during PFAS CS Phases I, II and III. Including duplicate samples, 143 environmental samples were analyzed for 14 PFAS compounds and 104 environmental samples were analyzed for 18 PFAS compounds. Ten of the analytes on the 14 compound list were detected at least once in surface water at KSC, with a wide range in magnitude of detections. The State of Florida has surface water screening levels (SWSLs) for perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS) in surface water, both for human and ecological receptors. The human health screening levels are lower than the ecological ones and are used in this report. PFOA was not detected in surface water at concentrations exceeding the SWSL at any LOC or Area of Potential Concern (AOPC). PFOS was detected in surface water at concentrations exceeding the SWSL at 28 LOCs/AOPCs, plus 42 locations on the KSC periphery. The data suggest a wide distribution of PFAS, particularly PFOS, in surface water but the sources of surface water contamination are not yet adequately understood. Sediment samples were collected during Phases II and III but not Phase I. Including duplicate samples, 104 environmental samples were analyzed for 14 PFAS compounds and 10 environmental samples were analyzed for 18 PFAS compounds. Twelve compounds were detected in sediment at KSC, with a wide range in magnitude of detections. There are currently no screening levels or cleanup target levels (CTLs) for sediment. The need to delineate and further characterize PFAS in sediment will be evaluated for those sites that move forward into Site Assessment. Groundwater samples were collected via DPT from LOCs/AOPCs and locations on the KSC periphery during PFAS CS Phases I, II and III. Including duplicate samples, 812 environmental DPT groundwater samples were analyzed for 14 PFAS compounds and 247 environmental samples were analyzed for 18 PFAS compounds. Twelve of the 14 compounds were detected in groundwater at KSC, with a wide range in magnitude of detections. The State of Florida has provisional groundwater cleanup target levels (GCTLs) for PFOA, PFOS and the additive concentration of PFOA+PFOS. PFOA was detected in groundwater at concentrations exceeding its provisional GCTL at 16 LOCs/AOPCs, with no exceedances on the KSC periphery. PFOS was detected in groundwater at concentrations exceeding its provisional GCTL at 30 LOCs/AOPCs, plus two locations on the KSC periphery. PFOA+PFOS was detected in groundwater at concentrations exceeding the provisional GCTL at 31 LOCs/AOPCs, plus two locations on the KSC periphery. Soil samples were collected during Phases II and III but not Phase I. Including duplicate samples, 292 environmental samples were analyzed for 14 PFAS compounds and 80 environmental samples were analyzed for 18 PFAS compounds. Fourteen compounds were detected in soil at KSC, with a wide range in magnitude of detections. The State of Florida has provisional soil cleanup target levels (SCTLs) for PFOA and PFOS. There were no PFOA results above its provisional SCTL. There was one LOC with a result above the provisional SCTL for residential settings. Recommendations are presented for each LOC and AOPC.

PFAS↗
DOE OSTI2020

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Using Wi-Fi Location-Based Services (LBS) for Commercial Building Occupancy Sensing

From May 2019 through October 2022, this DOE-funded project investigated and demonstrated the use of Wi-Fi Location-Based Services (LBS) to perform occupancy sensing in commercial buildings. Wi-Fi LBS can be used to detect the presence of Wi-Fi enabled mobile devices and laptops that accompany occupants as they move through the building. These signals can be used to determine occupant presence, head count, and location. When integrated with the building automation system, this emerging technology approach can be used to manage other connected systems such as lighting and HVAC to reduce energy usage in the building and improve occupant comfort. An open source location detection algorithm was developed, which uses data collected from three or more Wi-Fi access points to determine the presence and estimate the location of mobile devices and laptops. Access points can detect Wi-Fi enabled devices even if they are not connected to the existing Wi-Fi network. Building occupancy is determined based on the presence, location, and movement of these devices through the space. From lab and small-scale in-situ testing, the Location Detection Algorithm (LDA) was found to be accurate to within 10 feet and could be further refined by tuning the algorithm for the specific space characteristics such as layout and obstructions (walls, furniture, etc.). An open source method to integrate the occupancy data with existing building automations systems was investigated. The Wi-Fi occupancy sensing approach was then demonstrated and validated at two commercial buildings located in Minnesota and Wisconsin.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Comparison of source-location algorithms for atmospheric samplers

Numerous algorithms have been developed to determine the source characteristics for an atmospheric release, e.g., (Bieringer et al., 2017). This study compares three models that have been applied to the data collected by the International Monitoring System operated by the Comprehensive Nuclear-Test-Ban Treaty Preparatory Commission to estimate source event parameters. Each model uses a different approach to estimate the parameters. A deterministic model uses a possible source region (PSR) approach (Ringbom et al., 2014) that is based on the correlation between predicted and measured sample values. An unnamed model developed at Pacific Northwest National Laboratory (herein called BAYEST) uses a Bayesian formulation (Eslinger et al., 2019; Eslinger et al., 2020; Eslinger and Schrom, 2016). The FREAR model uses a different Bayesian formulation (De Meutter and Hoffman, 2020; De Meutter et al., 2021; Pieter De Meutter, 2021). The performance of the three source-location models is evaluated with 100 synthetic release cases for the single xenon isotope, 133 Xe. The release cases resulted in detections in a fictitious network with 120 noble gas samplers. All three source-location models use the same sampling data. The two Bayesian models yield more accurate location estimates than the deterministic PSR model, with FREAR having slightly better location performance than BAYEST. Samplers with collection periods of 3, 6, 8, 12, and 24-h were used. Results from BAYEST show that location accuracy improves with each reduction in sample collection length. The BAYEST model is slightly better for estimating the start time of the release. The PSR model has about the same spread in start times as the FREAR model, but the PSR results have a better average start time. The Bayesian source-location algorithms give more accurate results than the PSR approach, and provide release magnitude estimates, while the base PSR model does not estimate the release magnitude. This investigation demonstrates that a reasonably dense sampling grid will sometimes yield poor location and time estimates regardless of the model. The poor estimates generally coincide with cases where there is a much larger distance between the release point and the first detecting sampler than the average sampler spacing.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

A Generalizable Evaluated Approach, Applying Advanced Geospatial Statistical Methods, to Identify High Lead Exposure Locations at Census Tract Scale: Michigan Case Study

BACKGROUND: Despite great progress in reducing environmental lead (Pb) levels, many children in the United States are still being exposed. OBJECTIVE: Our aim was to develop a generalizable approach for systematically identifying, verifying, and analyzing locations with high prevalence of children’s elevated blood Pb levels (EBLLs) and to assess available Pb models/indices as surrogates, using a Michigan case study. METHODS: We obtained ~1:9 million BLL test results of children <6 years of age in Michigan from 2006–2016; we then evaluated them for data representativeness by comparing two percentage EBLL (%EBLL) rates (number of children tested with EBLL divided by both number of children tested and total population). We analyzed %EBLLs across census tracts over three time periods and between two EBLL reference values (≥5 vs. ≥10 μg/dL) to evaluate consistency. Locations with high %EBLLs were identified by a top 20 percentile method and a Getis-Ord Gi* geospatial cluster “hotspot” analysis. For the locations identified, we analyzed convergences with three available Pb exposure models/indices based on old housing and sociodemographics. RESULTS: Analyses of 2014–2016 %EBLL data identified 11 Michigan locations via cluster analysis and 80 additional locations via the top 20 percentile method and their associated census tracts. Data representativeness and consistency were supported by a 0.93 correlation coefficient between the two EBLL rates over 11 y, and a Kappa score of ~0:8 of %EBLL hotspots across the time periods (2014–2016) and reference values. Many EBLL hotspot locations converge with current Pb exposure models/indices; others diverge, suggesting additional Pb sources for targeted interventions. DISCUSSION: This analysis confirmed known Pb hotspot locations and revealed new ones at a finer geographic resolution than previously available, using advanced geospatial statistical methods and mapping/visualization. It also assessed the utility of surrogates in the absence of blood Pb data. This approach could be applied to other states to inform Pb mitigation and prevention efforts. https://doi.org/10.1289/EHP9705

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Event Location using Arrival Times from Seismic and Acoustic Phenomena

Accurately locating seismoacoustic sources with geophysical observations helps to monitor natural and anthropogenic phenomena. Sparsely deployed infrasound arrays can readily locate large sources thousands of kms away, but small events typically produce signals observable at only local to regional distances. At such distances, accurate location efforts rely on observations across smaller regional or temporary deployments which often consist of single-channel infrasound sensors that cannot record direction of arrival. Event locations can also be aided by inclusion of ground coupled airwaves (GCA). This study demonstrates how we can robustly locate a catalog of seismoacoustic events using infrasound, GCA, and seismic arrival times at local to near-regional distances. We employ a probabilistic location framework using simplified forward models. Our results indicate that both single-channel infrasound and GCA arrival times can provide accurate estimates of event location in the absence of array-based observations even when using simple models. However, one must carefully choose model uncertainty bounds to avoid underestimation of confidence intervals.

58 GEOSCIENCES↗
NASA NTRS1985

Theoretical and experimental investigations of sensor location for optimal aeroelastic system state estimation

One of the major concerns in the design of an active control system is obtaining the information needed for effective feedback. This involves the combination of sensing and estimation. A sensor location index is defined as the weighted sum of the mean square estimation errors in which the sensor locations can be regarded as estimator design parameters. The design goal is to choose these locations to minimize the sensor location index. The choice of the number of sensors is a tradeoff between the estimation quality based upon the same performance index and the total costs of installing and maintaining extra sensors. An experimental study for choosing the sensor location was conducted on an aeroelastic system. The system modeling which includes the unsteady aerodynamics model developed by Stephen Rock was improved. Experimental results verify the trend of the theoretical predictions of the sensor location index for different sensor locations at various wind speeds.

Liu, G.↗
NASA NTRS1991

Experiments for locating damaged truss members in a truss structure

Locating damaged truss members in large space structures will involve a combination of sensing and diagnostic techniques. Methods developed for damage location require experimental verification prior to on-orbit applications. To this end, a series of experiments for locating damaged members using a generic, ten bay truss structure were conducted. A 'damaged' member is a member which has been removed entirely. Previously developed identification methods are used in conjunction with the experimental data to locate damage. Preliminary results to date are included, and indicate that mode selection and sensor location are important issues for location performance. A number of experimental data sets representing various damage configurations were compiled using the ten bay truss. The experimental data and the corresponding finite element analysis models are available to researchers for verification of various methods of structure identification and damage location.

Mcgowan, Paul E.↗
NASA NTRS1934

Effect of retractable-spoiler location on rolling- and yawing-moment coefficients

In this report are presented the results of wind-tunnel tests of retractable spoilers on the upper surface of a Clark Y wing, which have been made as part of an investigation of lateral control devices being conducted by the National Advisory Committee for Aeronautics. Spoilers with chords up to 15.0 percent of the wing chord were tested in several locations on a plain rectangular wing and in two locations on the same wing equipped with a 20.0 percent chord split flap down 60 degrees. Charts are given for four representative angles of attack from which values of rolling- and yawing-moment coefficients may be obtained for spoilers up to 15.0 percent chord located on the upper surface of a Clark Y wing. The tests showed that at low angles of attack practically the same rolling moments can be obtained with a given spoiler at any location back of 30.0 percent of the wing chord, while at high angles of attack there is a definite advantage in locating the spoiler at least as far forward as 30.0 percent of the chord. The yawing moments accompanying a given rolling moment increase positively as the spoiler location is moved forward from the trailing edge of the wing. It is concluded that the 30.0 percent chord location is probably the optimum provided that instantaneous response of the airplane to a control movement can be obtained.

Shortal, J A↗
NASA NTRS1998

The Error Distribution of BATSE GRB Location

We develop empirical probability models for BATSE GRB location errors by a Bayesian analysis of the separations between BATSE GRB locations and locations obtained with the InterPlanetary Network (IPN). Models are compared and their parameters estimated using 394 GRBs with single IPN annuli and 20 GRBs with intersecting IPN annuli. Most of the analysis is for the 4B (rev) BATSE catalog; earlier catalogs are also analyzed. The simplest model that provides a good representation of the error distribution has 78% of the locations in a 'core' term with a systematic error of 1.85 degrees and the remainder in an extended tail with a systematic error of 5.36 degrees, implying a 68% confidence region for bursts with negligible statistical errors of 2.3 degrees. There is some evidence for a more complicated model in which the error distribution depends on the BATSE datatype that was used to obtain the location. Bright bursts are typically located using the CONT datatype, and according to the more complicated model, the 68% confidence region for CONT-located bursts with negligible statistical errors is 2.0 degrees.

Briggs, Michael S.↗
NASA NTRS2001

Source Identification and Location Techniques

Mr. Weir presented source location results obtained from an engine test as part of the Engine Validation of Noise Reduction Concepts program. Two types of microphone arrays were used in this program to determine the jet noise source distribution for the exhaust from a 4.3 bypass ratio turbofan engine. One was a linear array of 16 microphones located on a 25 ft. sideline and the other was a 103 microphone 3-D "cage" array in the near field of the jet. Data were obtained from a baseline nozzle and from numerous nozzle configuration using chevrons and/or tabs to reduce the jet noise. Mr. Weir presented data from two configurations: the baseline nozzle and a nozzle configuration with chevrons on both the core and bypass nozzles. This chevron configuration had achieved a jet noise reduction of 4 EPNdB in small scale tests conducted at the Glenn Research Center. IR imaging showed that the chevrons produced significant improvements in mixing and greatly reduced the length of the jet potential core. Comparison of source location data from the 1-D phased array showed a shift of the noise sources towards the nozzle and clear reductions of the sources due to the noise reduction devices. Data from the 3-D array showed a single source at a frequency of 125 Hz. located several diameters downstream from the nozzle exit. At 250 and 400 Hz., multiple sources, periodically spaced, appeared to exist downstream of the nozzle. The trend of source location moving toward the nozzle exit with increasing frequency was also observed. The 3-D array data also showed a reduction in source strength with the addition of chevrons. The overall trend of source location with frequency was compared for the two arrays and with classical experience. Similar trends were observed. Although overall trends with frequency and addition of suppression devices were consistent between the data from the 1-D and the 3-D arrays, a comparison of the details of the inferred source locations did show differences. A flight test is planned to determine if the hardware tested statically will achieve similar reductions in flight.

Weir, Donald↗
NASA NTRS2012

Monitoring Location and Angular Orientation of a Pill

A mobile pill transmitter system moves through, or adjacent to, one or more organs in an animal or human body, while transmitting signals from its present location and/or present angular orientation. The system also provides signals from which the present roll angle of the pill, about a selected axis, can be determined. When the location coordinates angular orientation and the roll angle of the pill are within selected ranges, an aperture on the pill container releases a selected chemical into, or onto, the body. Optionally, the pill, as it moves, provides a sequence of visually perceptible images. The times for image formation may correspond to times at which the pill transmitter system location or image satisfies one of at least four criteria. This invention provides and supplies an algorithm for exact determination of location coordinates and angular orientation coordinates for a mobile pill transmitter (PT), or other similar device that is introduced into, and moves within, a GI tract of a human or animal body. A set of as many as eight nonlinear equations has been developed and applied, relating propagation of a wireless signal between either two, three, or more transmitting antennas located on the PT, to four or more non-coplanar receiving antennas located on a signal receiver appliance worn by the user. The equations are solved exactly, without approximations or iterations, and are applied in several environments: (1) association of a visual image, transmitted by the PT at each of a second sequence of times, with a PT location and PT angular orientation at that time; (2) determination of a position within the body at which a drug or chemical substance or other treatment is to be delivered to a selected portion of the body; (3) monitoring, after delivery, of the effect(s) of administration of the treatment; and (4) determination of one or more positions within the body where provision and examination of a finer-scale image is warranted.

Schipper, John F.↗