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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Evaluation of Anomaly Detection Capability for Ground-Based Pre-Launch Shuttle Operations

This chapter will provide a thorough end-to-end description of the process for evaluation of three different data-driven algorithms for anomaly detection to select the best candidate for deployment as part of a suite of IVHM (Integrated Vehicle Health Management) technologies. These algorithms were deemed to be sufficiently mature enough to be considered viable candidates for deployment in support of the maiden launch of Ares I-X, the successor to the Space Shuttle for NASA's Constellation program. Data-driven algorithms are just one of three different types being deployed. The other two types of algorithms being deployed include a "nile-based" expert system, and a "model-based" system. Within these two categories, the deployable candidates have already been selected based upon qualitative factors such as flight heritage. For the rule-based system, SHINE (Spacecraft High-speed Inference Engine) has been selected for deployment, which is a component of BEAM (Beacon-based Exception Analysis for Multimissions), a patented technology developed at NASA's JPL (Jet Propulsion Laboratory) and serves to aid in the management and identification of operational modes. For the "model-based" system, a commercially available package developed by QSI (Qualtech Systems, Inc.), TEAMS (Testability Engineering and Maintenance System) has been selected for deployment to aid in diagnosis. In the context of this particular deployment, distinctions among the use of the terms "data-driven," "rule-based," and "model-based," can be found in. Although there are three different categories of algorithms that have been selected for deployment, our main focus in this chapter will be on the evaluation of three candidates for data-driven anomaly detection. These algorithms will be evaluated upon their capability for robustly detecting incipient faults or failures in the ground-based phase of pre-launch space shuttle operations, rather than based oil heritage as performed in previous studies. Robust detection will allow for the achievement of pre-specified minimum false alarm and/or missed detection rates in the selection of alert thresholds. All algorithms will also be optimized with respect to an aggregation of these same criteria. Our study relies upon the use of Shuttle data to act as was a proxy for and in preparation for application to Ares I-X data, which uses a very similar hardware platform for the subsystems that are being targeted (TVC - Thrust Vector Control subsystem for the SRB (Solid Rocket Booster)).

Martin, Rodney Alexander↗
NASA NTRS2014

Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

This paper shows how satellite owner/operators may use sequential estimates of collision probability, along with a prior assessment of the base risk of collision, in a compound hypothesis ratio test to inform decisions concerning collision risk mitigation maneuvers. The compound hypothesis test reduces to a simple probability ratio test, which appears to be a novel result. The test satisfies tolerances related to targeted false alarm and missed detection rates. This result is independent of the method one uses to compute the probability density that one integrates to compute collision probability. A well-established test case from the literature shows that this test yields acceptable results within the constraints of a typical operational conjunction assessment decision timeline. Another example illustrates the use of the test in a practical conjunction assessment scenario based on operations of the International Space Station.

Navigation↗
NASA NTRS2022

Deriving Severe Hail Likelihood from Satellite Observations and Model Reanalysis Parameters using a Deep Neural Network

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) series, have been observing severe convection at 15–60-minute intervals for over 40 years. When properly assessed, such a data record can be valuable in efforts of estimating severe storm risk throughout the diurnal cycle based on automated detection of patterns consistently found atop severe storms. Furthermore, environmental conditions favorable for severe weather are well-known and are thought to be represented well by modern reanalysis products. Promoting resilience against such hazards on local and global scales is a chief goal the NASA Disasters program, which seeks to encourage use of satellite observations to mitigate risk. For instance, hail is the costliest severe weather hazard across the globe in terms of insured loss, but reporting inconsistencies for hail events globally make it difficult to develop models that can quantify the risk. Satellite observation and model reanalysis taken together have the potential to, with reasonable skill and specificity, characterize environmental conditions that are favorable for hazardous weather, and thereby enable creation of hazard climatologie. Such climatologies are particularly useful over regions without extensive radar networks or storm reporting. By mapping the multivariate combination of observed cloud features and reanalysis environmental parameters/indices to United States Next Generation Weather Radar (NEXRAD) radar-estimated Maximum Expected Size of Hail (MESH) by way of a deep neural network (DNN), estimates of likelihood for potentially severe hail can be produced. Such estimates are of greater complexity and efficiency than could be performed with previous multivariate or logistic regression analyses for observed points within convective systems. Statistical distributions of convective parameters from satellite and reanalysis are shown to highlight non-severe/severe class separation for well-known hailstorm predictors, e.g., overshooting cloud top characteristics, deep-layer wind shear, mid-level stability, helicity, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN, which can efficiently produce a quantitative hail risk metric with better than 70% detection rate and under 30% false alarms. These hail classifications can then be aggregated across the satellite record to yield a hazard climatology for hail frequency and severity – knowledge of which is of particular interest to those who manage risk (e.g., insurers) and are seeking opportunities to identify hail-prone regions, particularly in developing nations. This NASA study uses satellite observations and model parameters in a DNN to perform climatological hailstorm analysis in support of catastrophe model development, with the hope of promoting risk resilience particularly in regions without adequate weather radar coverage.

Passive Remote Sensing↗
DOE OSTI2024

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collectedunder structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore,their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distanceto the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensembleof trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fittingobserved in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inversephysical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of thesource strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations ofunderlying regression methods.

Rao, Nageswara↗
DOE OSTI2024

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.

Rao, Nageswara↗
NASA NTRS2013

Modeling Weather Impact on Airport Arrival Miles-in-Trail Restrictions

When the demand for either a region of airspace or an airport approaches or exceeds the available capacity, miles-in-trail (MIT) restrictions are the most frequently issued traffic management initiatives (TMIs) that are used to mitigate these imbalances. Miles-intrail operations require aircraft in a traffic stream to meet a specific inter-aircraft separation in exchange for maintaining a safe and orderly flow within the stream. This stream of aircraft can be departing an airport, over a common fix, through a sector, on a specific route or arriving at an airport. This study begins by providing a high-level overview of the distribution and causes of arrival MIT restrictions for the top ten airports in the United States. This is followed by an in-depth analysis of the frequency, duration and cause of MIT restrictions impacting the Hartsfield-Jackson Atlanta International Airport (ATL) from 2009 through 2011. Then, machine-learning methods for predicting (1) situations in which MIT restrictions for ATL arrivals are implemented under low demand scenarios, and (2) days in which a large number of MIT restrictions are required to properly manage and control ATL arrivals are presented. More specifically, these predictions were accomplished by using an ensemble of decision trees with Bootstrap aggregation (BDT) and supervised machine learning was used to train the BDT binary classification models. The models were subsequently validated using data cross validation methods. When predicting the occurrence of arrival MIT restrictions under low demand situations, the model was able to achieve over all accuracy rates ranging from 84% to 90%, with false alarm ratios ranging from 10% to 15%. In the second set of studies designed to predict days on which a high number of MIT restrictions were required, overall accuracy rates of 80% were achieved with false alarm ratios of 20%. Overall, the predictions proposed by the model give better MIT usage information than what has been currently provided under current day operations. Traffic flow managers can use these predictions to identify potential MIT restrictions to eliminate (e.g., those occurring during low arrival demand periods), and to determine the days in which a significant number of restrictions may be required

Operation↗
NASA NTRS2010

Testing of Haar-Like Feature in Region of Interest Detection for Automated Target Recognition (ATR) System

The objectives of this project were to develop a ROI (Region of Interest) detector using Haar-like feature similar to the face detection in Intel's OpenCV library, implement it in Matlab code, and test the performance of the new ROI detector against the existing ROI detector that uses Optimal Trade-off Maximum Average Correlation Height filter (OTMACH). The ROI detector included 3 parts: 1, Automated Haar-like feature selection in finding a small set of the most relevant Haar-like features for detecting ROIs that contained a target. 2, Having the small set of Haar-like features from the last step, a neural network needed to be trained to recognize ROIs with targets by taking the Haar-like features as inputs. 3, using the trained neural network from the last step, a filtering method needed to be developed to process the neural network responses into a small set of regions of interests. This needed to be coded in Matlab. All the 3 parts needed to be coded in Matlab. The parameters in the detector needed to be trained by machine learning and tested with specific datasets. Since OpenCV library and Haar-like feature were not available in Matlab, the Haar-like feature calculation needed to be implemented in Matlab. The codes for Adaptive Boosting and max/min filters in Matlab could to be found from the Internet but needed to be integrated to serve the purpose of this project. The performance of the new detector was tested by comparing the accuracy and the speed of the new detector against the existing OTMACH detector. The speed was referred as the average speed to find the regions of interests in an image. The accuracy was measured by the number of false positives (false alarms) at the same detection rate between the two detectors.

neural network↗
NASA NTRS2010

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

Carpenter, J. Russell↗
NASA NTRS1983

Node Synchronization for the Viterbi Decoder

At very low signal to noise ratios such as those that Voyager 2 will encounter at Uranus, the performance of the Reed-Solomon/Viterbi concatenated coding system could be seriously degraded by loss of node synchronization by the Viterbi decoder. This problem is described and now it can be almost completely avoided with a simple outboard hardware ""node synchronizer''. This device makes statistical decisions about node sync based on the hard quantized undecoded data stream. In a worst case Voyager-like environment, our method will detect and correct a true loss of node sync (thought to be a very rate event) within several hundred bits; many of these false alarms for our technique is on the order several years.

Lorden, G.↗
NASA NTRS1975

Decision-related cortical potentials during an auditory signal detection task with cued observation intervals

Cortical-evoked potentials were recorded from human subjects performing an auditory detection task with confidence rating responses. Unlike earlier studies that used similar procedures, the observation interval during which the auditory signal could occur was clearly marked by a visual cue light. By precisely defining the observation interval and, hence, synchronizing all perceptual decisions to the evoked potential averaging epoch, it was possible to demonstrate that high-confidence false alarms are accompanied by late-positive P3 components equivalent to those for equally confident hits. Moreover the hit and false alarm evoked potentials were found to covary similarly with variations in confidence rating and to have similar amplitude distributions over the scalp. In a second experiment, it was demonstrated that correct rejections can be associated with a P3 component larger than that for hits. Thus it was possible to show, within the signal detection paradigm, how the two major factors of decision confidence and expectancy are reflected in the P3 component of the cortical-evoked potential.

Squires, K. C.↗
NASA NTRS1993

Intelligent neuroprocessors for in-situ launch vehicle propulsion systems health management

Efficacy of existing on-board propulsion systems health management systems (HMS) are severely impacted by computational limitations (e.g., low sampling rates); paradigmatic limitations (e.g., low-fidelity logic/parameter redlining only, false alarms due to noisy/corrupted sensor signatures, preprogrammed diagnostics only); and telemetry bandwidth limitations on space/ground interactions. Ultra-compact/light, adaptive neural networks with massively parallel, asynchronous, fast reconfigurable and fault-tolerant information processing properties have already demonstrated significant potential for inflight diagnostic analyses and resource allocation with reduced ground dependence. In particular, they can automatically exploit correlation effects across multiple sensor streams (plume analyzer, flow meters, vibration detectors, etc.) so as to detect anomaly signatures that cannot be determined from the exploitation of single sensor. Furthermore, neural networks have already demonstrated the potential for impacting real-time fault recovery in vehicle subsystems by adaptively regulating combustion mixture/power subsystems and optimizing resource utilization under degraded conditions. A class of high-performance neuroprocessors, developed at JPL, that have demonstrated potential for next-generation HMS for a family of space transportation vehicles envisioned for the next few decades, including HLLV, NLS, and space shuttle is presented. Of fundamental interest are intelligent neuroprocessors for real-time plume analysis, optimizing combustion mixture-ratio, and feedback to hydraulic, pneumatic control systems. This class includes concurrently asynchronous reprogrammable, nonvolatile, analog neural processors with high speed, high bandwidth electronic/optical I/O interfaced, with special emphasis on NASA's unique requirements in terms of performance, reliability, ultra-high density ultra-compactness, ultra-light weight devices, radiation hardened devices, power stringency, and long life terms.

Gulati, S.↗
DOE OSTI2020

Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations

Integration of Information and Communication Technology (ICT) in modern smart grids (SGs) offers many advantages including the use of renewables and an effective way to protect, control and monitor the energy transmission and distribution. To reach an optimal operation of future energy systems, availability, integrity and confidentiality of data should be guaranteed. Research on the cyber-physical security of electrical substations based on IEC 61850 is still at an early stage. In the present work, we first model the network traffic data in electrical substations, then, we present a statistical Anomaly Detection (AD) method to detect Denial of Service (DoS) attacks against the Generic Object Oriented Substation Event (GOOSE) network communication. According to interpretations on the self-similarity and the Long-Range Dependency (LRD) of the data, an Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model was shown to describe well the GOOSE communication in the substation process network. Based on this ARFIMA-model and in view of cyber-physical security, an effective model-based AD method is developed and analyzed. Two variants of the statistical AD considering statistical hypothesis testing based on the Generalized Likelihood Ratio Test (GLRT) and the cumulative sum (CUSUM) are presented to detect flooding attacks that might affect the availability of the data. Our work presents a novel AD method, with two different variants, tailored to the specific features of the GOOSE traffic in IEC 61850 substations. The statistical AD is capable of detecting anomalies at unknown change times under the realistic assumption of unknown model parameters. The performance of both variants of the AD method is validated and assessed using data collected from a simulation case study. We perform several Monte-Carlo simulations under different noise variances. The detection delay is provided for each detector and it represents the number of discrete time samples after which an anomaly is detected. In fact, our statistical AD method with both variants (CUSUM and GLRT) has around half the false positive rate and a smaller detection delay when compared with two of the closest works found in the literature. Our AD approach based on the GLRT detector has the smallest false positive rate among all considered approaches. Whereas, our AD approach based on the CUSUM test has the lowest false negative rate thus the best detection rate. Depending on the requirements as well as the costs of false alarms or missed anomalies, both variants of our statistical detection method can be used and are further analyzed using composite detection metrics.

IEC 61850 electrical substations↗
DOE OSTI2026

Optimizing Optical Searches for Supermassive Black Hole Binaries in Active Galactic Nuclei Light Curves: Fourier versus Bayesian Periodicity Detection

Simulations predict that supermassive black hole binaries (SMBHBs) will exhibit periodic brightness variations that may exceed the stochastic variability intrinsic to active galactic nuclei (AGN). In this paper, we simulate SMBHBs with damped random walk (DRW) AGN variability and an added sinusoidal signal from the orbital motion, and test three methods—a generalized Lomb–Scargle periodogram (GLSP), a nested Bayesian sampler (NBS), and a weighted wavelet z-transform (or WWZ)—to determine which is best at recovering the periodicity. Our simulated light curves follow the properties of the Catalina Real-Time Transient Survey (or CRTS), Legacy Survey of Space and Time (LSST), and Zwicky Transient Facility (ZTF) to best inform current and future SMBHB searches. We map a broad range of parameter space and identify which DRW-only light curves best mimic periodicity and pass each method’s model selection. The NBS performs best at detecting periodicity and filtering out DRW-only light curves. Combined candidate selection with both the NBS and GLSP significantly reduces false-positive rates (FPRs) with marginal impact on true-positive rates (TPRs). With this joint model selection pipeline, we find the lowest FPRs in ZTF-like simulations and the highest detection rates in LSST-like simulations. Using a modified computation of the false-alarm probability with GLSP, we efficiently triage LSST AGN light curves (∼10 7 light curves in ∼10–30 hr) and achieve TPRs and FPRs of ∼40% and ∼0.5%, respectively.

Banaszak, Sebastian M. [Vanderbilt Univ., Nashvill↗
NASA NTRS2016

Automated Storm Tracking and the Lightning Jump Algorithm Using GOES-R Geostationary Lightning Mapper (GLM) Proxy Data

This study develops a fully automated lightning jump system encompassing objective storm tracking, Geostationary Lightning Mapper proxy data, and the lightning jump algorithm (LJA), which are important elements in the transition of the LJA concept from a research to an operational based algorithm. Storm cluster tracking is based on a product created from the combination of a radar parameter (vertically integrated liquid, VIL), and lightning information (flash rate density). Evaluations showed that the spatial scale of tracked features or storm clusters had a large impact on the lightning jump system performance, where increasing spatial scale size resulted in decreased dynamic range of the system's performance. This framework will also serve as a means to refine the LJA itself to enhance its operational applicability. Parameters within the system are isolated and the system's performance is evaluated with adjustments to parameter sensitivity. The system's performance is evaluated using the probability of detection (POD) and false alarm ratio (FAR) statistics. Of the algorithm parameters tested, sigma-level (metric of lightning jump strength) and flash rate threshold influenced the system's performance the most. Finally, verification methodologies are investigated. It is discovered that minor changes in verification methodology can dramatically impact the evaluation of the lightning jump system.

lightning jump↗
NASA NTRS2009

Optimization of OT-MACH Filter Generation for Target Recognition

An automatic Optimum Trade-off Maximum Average Correlation Height (OT-MACH) filter generator for use in a gray-scale optical correlator (GOC) has been developed for improved target detection at JPL. While the OT-MACH filter has been shown to be an optimal filter for target detection, actually solving for the optimum is too computationally intensive for multiple targets. Instead, an adaptive step gradient descent method was tested to iteratively optimize the three OT-MACH parameters, alpha, beta, and gamma. The feedback for the gradient descent method was a composite of the performance measures, correlation peak height and peak to side lobe ratio. The automated method generated and tested multiple filters in order to approach the optimal filter quicker and more reliably than the current manual method. Initial usage and testing has shown preliminary success at finding an approximation of the optimal filter, in terms of alpha, beta, gamma values. This corresponded to a substantial improvement in detection performance where the true positive rate increased for the same average false positives per image.

false alarm reduction↗
NASA NTRS2010

Ares I-X Ground Diagnostic Prototype

Automating prelaunch diagnostics for launch vehicles offers three potential benefits. First, it potentially improves safety by detecting faults that might otherwise have been missed so that they can be corrected before launch. Second, it potentially reduces launch delays by more quickly diagnosing the cause of anomalies that occur during prelaunch processing. Reducing launch delays will be critical to the success of NASA's planned future missions that require in-orbit rendezvous. Third, it potentially reduces costs by reducing both launch delays and the number of people needed to monitor the prelaunch process. NASA is currently developing the Ares I launch vehicle to bring the Orion capsule and its crew of four astronauts to low-earth orbit on their way to the moon. Ares I-X will be the first unmanned test flight of Ares I. It is scheduled to launch on October 27, 2009. The Ares I-X Ground Diagnostic Prototype is a prototype ground diagnostic system that will provide anomaly detection, fault detection, fault isolation, and diagnostics for the Ares I-X first-stage thrust vector control (TVC) and for the associated ground hydraulics while it is in the Vehicle Assembly Building (VAB) at John F. Kennedy Space Center (KSC) and on the launch pad. It will serve as a prototype for a future operational ground diagnostic system for Ares I. The prototype combines three existing diagnostic tools. The first tool, TEAMS (Testability Engineering and Maintenance System), is a model-based tool that is commercially produced by Qualtech Systems, Inc. It uses a qualitative model of failure propagation to perform fault isolation and diagnostics. We adapted an existing TEAMS model of the TVC to use for diagnostics and developed a TEAMS model of the ground hydraulics. The second tool, Spacecraft Health Inference Engine (SHINE), is a rule-based expert system developed at the NASA Jet Propulsion Laboratory. We developed SHINE rules for fault detection and mode identification. The prototype uses the outputs of SHINE as inputs to TEAMS. The third tool, the Inductive Monitoring System (IMS), is an anomaly detection tool developed at NASA Ames Research Center and is currently used to monitor the International Space Station Control Moment Gyroscopes. IMS automatically "learns" a model of historical nominal data in the form of a set of clusters and signals an alarm when new data fails to match this model. IMS offers the potential to detect faults that have not been modeled. The three tools have been integrated and deployed to Hangar AE at KSC where they interface with live data from the Ares I-X vehicle and from the ground hydraulics. The outputs of the tools are displayed on a console in Hangar AE, one of the locations from which the Ares I-X launch will be monitored. The full paper will describe how the prototype performed before the launch. It will include an analysis of the prototype's accuracy, including false-positive rates, false-negative rates, and receiver operating characteristics (ROC) curves. It will also include a description of the prototype's computational requirements, including CPU usage, main memory usage, and disk usage. If the prototype detects any faults during the prelaunch period then the paper will include a description of those faults. Similarly, if the prototype has any false alarms then the paper will describe them and will attempt to explain their causes.

Schwabacher, Mark↗
DOE OSTI2023

Toward Statistical Real-Time Power Fault Detection

We propose statistical fault detection methodology based on high-frequency data streams that are becoming available in modern power grids. Our approach can be treated as an online (sequential) change point monitoring methodology. However, due to the mostly unexplored and very nonstandard structure of high-frequency power grid streaming data, substantial new statistical development is required to make this methodology practically applicable. The paper includes development of scalar detectors based on multichannel data streams, determination of data-driven alarm thresholds and investigation of the performance and robustness of the new tools. Due to a reasonably large database of faults, we can calculate frequencies of false and correct fault signals, and recommend implementations that optimize these empirical success rates.

bolted faults↗
NASA NTRS1988

Node synchronization of viterbi decoders using state metrics

The concept of node synchronization using state metrics is investigated. The branch metrics are integrated over a fixed time interval and the results are compared to the detection threshold. If the threshold is exceeded, the out-of-sync hypothesis is accepted; otherwise, the in-sync hypothesis is accepted. It is shown that the detection threshold can be chosen independent of any particular convolutional code with fixed code rate and constant length if the code has reasonably good bit error rate performance. Three node synchronization schemes are compared: (1) a scheme using the syndrome; (2) a scheme using the frame-sync patterns; and (3) a scheme using the state metrics. At very low signal to noise ratios (SNR), scheme 2 can be faster than scheme 1. For Voyager's rate 1/2 and constraint length 7 convolutional code, this happens for SNRs of less than 0.7 dB. This result is obtained by assuming that the code frame-sync pattern has good aperiodic autocorrelation properties. For a fixed false alarm probability, the sequential detection scheme based on the syndrome is faster than scheme 3 with fixed integration time. A sequential detection technique is needed to improve the speed of scheme 3.

Cheng, U.↗