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NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗
NASA NTRS2000

A Comparison of Center/TRACON Automation System and Airline Time of Arrival Predictions

Benefits from information sharing between an air traffic service provider and a major air carrier are evaluated. Aircraft arrival time schedules generated by the NASA/FAA Center/TRACON Automation System (CTAS) were provided to the American Airlines System Operations Control Center in Fort Worth, Texas, during a field trial of a specialized CTAS display. A statistical analysis indicates that the CTAS schedules, based on aircraft trajectories predicted from real-time radar and weather data, are substantially more accurate than the traditional airline arrival time estimates, constructed from flight plans and en route crew updates. The improvement offered by CTAS is especially advantageous during periods of heavy traffic and substantial terminal area delay, allowing the airline to avoid large predictive errors with serious impact on the efficiency and profitability of flight operations.

Heere, Karen R.↗
NASA NTRS1987

Estimating the arrival times of photon-limited laser pulses in the presence of shot and speckle noise

Maximum-likelihood (ML) receivers are frequently used to optimize the timing performance of laser-ranging and laser-altimetry systems in the presence of shot and speckle noise. Monte Carlo method was used to examine ML-receiver performance with return signals in the 10-5000-photoelectron (pe) range. The simulations were performed for shot noise only and for shot and speckle noise. The results agree with previous theory for signal strengths greater than about 100 pe's but show that the theory can significantly underestimate timing errors for weaker received signals. Sharp high-bandwidth features in the detected signals are shown to improve timing performance only if their signal levels are greater than 4-5 pe's.

Abshire, James B.↗
NASA NTRS1988

Predicting the arrival times of solar particles

A procedure has been developed to generate a computerized time-intensity profile of the solar proton intensity expected at the earth after the occurrence of a significant solar flare on the sun. This procedure is a combination of many pieces of independent research and theoretical results. Many of the concepts used were first reported by Smart and Shea (1979) and are summarized by Smart and Shea (1985). Extracts from the general procedure that relate to predicting the expected onset time and time of maximum at the earth after the occurrence of a solar flare are presented.

Smart, D. F.↗
NASA NTRS1975

Flight experience with time-of-arrival control for STOL aircraft in the terminal area

A research program on STOL operating systems is underway at the Ames Research Center. One investigation is concerned with design, analysis, and flight test of promising four-dimensional RNAV systems. One promising system generates a capture flight path from the present aircraft position to a waypoint on a selected fixed STOL approach route. It predicts arrival time at the runway and controls time and position along the path. The system was flight tested using a digital avionics system on a Convair 340 and on an experimental powered-lift STOL airplane. Flight tests in the flight director mode show that the pilot can choose and change the desired time of arrival, and meet this time within a few seconds, in spite of navigation errors and varying winds. Initial tests of the automatic mode using a flight simulator and the NASA Augmentor Wing Jet STOL Research Aircraft (AWJSRA) show that good time control was achieved at the cost of excess throttle activity. This fault was later corrected.

Neuman, F.↗
NASA NTRS2013

X-Ray Detection and Processing Models for Spacecraft Navigation and Timing

The current primary method of deepspace navigation is the NASA Deep Space Network (DSN). High-performance navigation is achieved using Delta Differential One-Way Range techniques that utilize simultaneous observations from multiple DSN sites, and incorporate observations of quasars near the line-of-sight to a spacecraft in order to improve the range and angle measurement accuracies. Over the past four decades, x-ray astronomers have identified a number of xray pulsars with pulsed emissions having stabilities comparable to atomic clocks. The x-ray pulsar-based navigation and time determination (XNAV) system uses phase measurements from these sources to establish autonomously the position of the detector, and thus the spacecraft, relative to a known reference frame, much as the Global Positioning System (GPS) uses phase measurements from radio signals from several satellites to establish the position of the user relative to an Earth-centered fixed frame of reference. While a GPS receiver uses an antenna to detect the radio signals, XNAV uses a detector array to capture the individual xray photons from the x-ray pulsars. The navigation solution relies on detailed xray source models, signal processing, navigation and timing algorithms, and analytical tools that form the basis of an autonomous XNAV system. Through previous XNAV development efforts, some techniques have been established to utilize a pulsar pulse time-of-arrival (TOA) measurement to correct a position estimate. One well-studied approach, based upon Kalman filter methods, optimally adjusts a dynamic orbit propagation solution based upon the offset in measured and predicted pulse TOA. In this delta position estimator scheme, previously estimated values of spacecraft position and velocity are utilized from an onboard orbit propagator. Using these estimated values, the detected arrival times at the spacecraft of pulses from a pulsar are compared to the predicted arrival times defined by the pulsar s pulse timing model. A discrepancy provides an estimate of the spacecraft position offset, since an error in position will relate to the measured time offset of a pulse along the line of sight to the pulsar. XNAV researchers have been developing additional enhanced approaches to process the photon TOAs to arrive at an estimate of spacecraft position, including those using maximum-likelihood estimation, digital phase locked loops, and "single photon processing" schemes that utilize all available time data associated with each photon. Using pulsars from separate, non-coplanar locations provides range and range-rate measurements in each pulsar s direction. Combining these different pulsar measurements solves for offsets in position and velocity in three dimensions, and provides accurate overall navigation for deep space vehicles.

Sheikh, Suneel↗
NASA NTRS2012

The Influence of Pickup Protons, from Interstellar Neutral Hydrogen, on the Propagation of Interplanetary Shocks from the Halloween 2003 Solar Events to ACE and Ulysses: A 3-D MHD Modeling Study

We describe our 3-D, time ]dependent, MHD solar wind model that we recently modified to include the physics of pickup protons from interstellar neutral hydrogen. The model has a time-dependent lower boundary condition, at 0.1 AU, that is driven by source surface map files through an empirical interface module. We describe the empirical interface and its parameter tuning to maximize model agreement with background (quiet) solar wind observations at ACE. We then give results of a simulation study of the famous Halloween 2003 series of solar events. We began with shock inputs from the Fearless Forecast real ]time shock arrival prediction study, and then we iteratively adjusted input shock speeds to obtain agreement between observed and simulated shock arrival times at ACE. We then extended the model grid to 5.5 AU and compared those simulation results with Ulysses observations at 5.2 AU. Next we undertook the more difficult tuning of shock speeds and locations to get matching shock arrival times at both ACE and Ulysses. Then we ran this last case again with neutral hydrogen density set to zero, to identify the effect of pickup ions. We show that the speed of interplanetary shocks propagating from the Sun to Ulysses is reduced by the effects of pickup protons. We plan to make further improvements to the model as we continue our benchmarking process to 10 AU, comparing our results with Cassini observations, and eventually on to 100 AU, comparing our results with Voyager 1 and 2 observations.

Detman, T. R.↗
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↗
NASA NTRS1999

Flight Test Results: CTAS Cruise/Descent Trajectory Prediction Accuracy for En route ATC Advisories

The Center/TRACON Automation System (CTAS), under development at NASA Ames Research Center, is designed to assist controllers with the management and control of air traffic transitioning to/from congested airspace. This paper focuses on the transition from the en route environment, to high-density terminal airspace, under a time-based arrival-metering constraint. Two flight tests were conducted at the Denver Air Route Traffic Control Center (ARTCC) to study trajectory-prediction accuracy, the key to accurate Decision Support Tool advisories such as conflict detection/resolution and fuel-efficient metering conformance. In collaboration with NASA Langley Research Center, these test were part of an overall effort to research systems and procedures for the integration of CTAS and flight management systems (FMS). The Langley Transport Systems Research Vehicle Boeing 737 airplane flew a combined total of 58 cruise-arrival trajectory runs while following CTAS clearance advisories. Actual trajectories of the airplane were compared to CTAS and FMS predictions to measure trajectory-prediction accuracy and identify the primary sources of error for both. The research airplane was used to evaluate several levels of cockpit automation ranging from conventional avionics to a performance-based vertical navigation (VNAV) FMS. Trajectory prediction accuracy was analyzed with respect to both ARTCC radar tracking and GPS-based aircraft measurements. This paper presents detailed results describing the trajectory accuracy and error sources. Although differences were found in both accuracy and error sources, CTAS accuracy was comparable to the FMS in terms of both meter-fix arrival-time performance (in support of metering) and 4D-trajectory prediction (key to conflict prediction). Overall arrival time errors (mean plus standard deviation) were measured to be approximately 24 seconds during the first flight test (23 runs) and 15 seconds during the second flight test (25 runs). The major source of error during these tests was found to be the predicted winds aloft used by CTAS. Position and velocity estimates of the airplane provided to CTAS by the ATC Host radar tracker were found to be a relatively insignificant error source for the trajectory conditions evaluated. Airplane performance modeling errors within CTAS were found to not significantly affect arrival time errors when the constrained descent procedures were used. The most significant effect related to the flight guidance was observed to be the cross-track and turn-overshoot errors associated with conventional VOR guidance. Lateral navigation (LNAV) guidance significantly reduced both the cross-track and turn-overshoot error. Pilot procedures and VNAV guidance were found to significantly reduce the vertical profile errors associated with atmospheric and aircraft performance model errors.

Green, S.↗
NASA NTRS1974

Kilometer-wave type III burst - Harmonic emission revealed by direction and time of arrival

A type III solar burst was observed at seven frequencies between 3.5 MHz and 80 kHz by the Michigan experiment aboard the IMP-6 satellite. From the data burst direction of arrival as well as time of arrival can be determined. These quantities are predicted, using simple models whose parameters are varied to obtain a good fit to the observations. It is found that between 3.5 MHz and 230 kHz the observed radiation was emitted at the fundamental of the local plasma frequency, while below 230 kHz it was emitted at the second harmonic. The exciter particles that produced the burst onset and burst peak have velocities of 0.27 and 0.12, respectively, in units of the velocity of light.

Alvarez, H.↗
NASA NTRS1991

Perturbation analysis of queueing systems with a time-varying arrival rate

The authors consider an M/G/1 queuing with a time-varying arrival rate. The objective is to obtain infinitesimal perturbation analysis (IPA) gradient estimates for various performance measures of interest with respect to certain system parameters. In particular, the authors consider the mean system time over n arrivals and an arrival rate alternating between two values. By choosing a convenient sample path representation of this system, they derive an unbiased IPA gradient estimator which, however, is not consistent, and investigate the nature of this problem.

Cassandras, Christos G.↗
NASA NTRS1999

A Comparison of CTAS and Airline Time of Arrival Predictions

A statistically-based comparison of aircraft times of arrival between Center/TRACON Automation System (CTAS) air traffic control scheduling and airline predictions is presented. CTAS is found to provide much improved values, forming the foundation for airline operational improvements, as observed during an airline field trial of a CTAS display.

Heere, Karen R.↗