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At least 577 records · Page 32

Generating Real-Time Robotics Control Software from SysML

In this paper, we outline an approach for autogenerating real-time robotics control code from hierarchical state machines and hardware configurations encoded in Systems Modeling Language (SysML). We propose a software architecture that provides an abstract SysML layer with access to device state information and a set of primitive device commands, such as move actuator and release brake, allowing a user to build up a complete functional state machine directly in SysML. The SysML diagram is then exported to a standard SCXML file format and subsequently used to auto-generate hardware control code. Once this architecture is in place, the only explicit code elements that need to be written are the primitive device commands, which can be easily unit tested and reused across different systems. The motivation for this work was the need for a test bed that enables the rapid prototyping of mechanisms and control algorithms for a spacecraft that could ultimately be used for preparing Martian rock samples for their return to Earth. To this end, our software system was also designed to allow for the run-time specification of the hardware layout in SysML, with the hardware-level control functions kept agnostic to the specific parameters or communication bus of any particular device. Further, we outline a system for specifying both the state machine and hardware configuration in the MagicDraw IDE in such a way that the system can be simulated before any code is generated. The resultant software system is easy to debug, understand, and allows users to choose how much information is encoded as a visual or text-based representation.

Godart, Peter↗

Overview of the PLEXIL Plan Execution Technology and its Applications in Autonomous Piloting Projects at NASA

Automated planning is a key Artificial Intelligence technology enabling Unmanned Aerial Systems (UAS) and the eminent reality of Urban Air Mobility (UAM). It produces plans, which formalize procedures often performed by humans. Plans differ from other kinds of computer programs in their ability to react and interact with a dynamically changing environment. Aviation plans must encode the procedural knowledge, reasoning capability, and capacity for multi-tasking held by competent human pilots. Correct execution of these plans (performed by software called an executive) in the dynamic airspace environment is vital to the success of each automated flight, and the safety of the vehicle and all things in its path. In the early 2000s NASA developed a plan representation language and executive called PLEXIL (Plan Execution Interchange Language) that has successfully been applied in several NASA aviation and UAS projects. Autonomy Operating System (AOS), Cockpit Hierarchical Automated Planning and Execution (CHAP-E), and ICAROUS are all projects that have used PLEXIL to help encode and automatically execute flight procedures, some normally performed by human pilots. AOS also automates a subset of pilot/Air Traffic Control communication towards enabling UAS entry into the National Airspace. PLEXIL has been open-source software since 2008 and has seen usage in a wide range of prototypical autonomy applications in academia, government, and industry. In this presentation, we describe PLEXIL and highlight its significant accomplishments in the aviation domain.

Dalal, Michael↗

High-Rate Ka-Band Modulator for the NISAR Mission

In order to meet ever-increasing data return requirements, more satellites are using the near-Earth Ka-band (25.5 – 27.0 GHz) to achieve higher downlink rates. The paper discusses the Universal Space Transponder - Ka-band Modulator (UST-KaM) developed at the NASA Jet Propulsion Laboratory for the NASA-ISRO SAR (NISAR) mission, which is capable of transmitting up to 1.74 Gbps with 7/8 LDPC encoding. The UST-KaM utilizes OQPSK with both baseband and RF filtering to contain the 1 Gsps transmission spectrum within the 1.5 GHz Ka-band, even with the use of an external, saturated amplifier. Due to the high data rates involved, several technical hurdles were overcome in both the digital and RF designs. The UST-KaM is a software defined radio with two digital circuit board assemblies: a low speed housekeeper board for commanding and telemetry, and a high-rate signal processing board known as the Signal Processing Module (SPM). The SPM receives data from the spacecraft via a SERDES interface at up to 2 Gbps, processes and encodes the data using a Xilinx Virtex-5 FPGA, and produces 1 Gsps OQPSK I and Q waveforms via synchronized, multiplexed DACs. The RF Electronics in the UST-KaM employ a heterodyne architecture in which the I/Q digital waveforms are filtered and then up-converted using a sub-harmonic IQ mixer. The LO of the converter, which is included in the exciter assembly, is at 13.125GHz, and the RF output is a 26.25GHz carrier which is modulated with the OQPSK waveforms. The output of the mixer is then filtered using low loss quartz thinfilm edge coupled Chebyshev filters and amplified through a series of low gain Ka-Band amplifiers. The exciter assembly also has a 2GHz, low-phase-noise, PLL synthesizer to supply the clock to the DACs for the high rate digital waveforms.

Spurgers, Carl↗

Exploring Semantic Search Capability of Graph Convolutions Over a Knowledge Graph Built Using Earth Science Corpora

Traditional knowledge graphs tend to be too generic, and often perform poorly on complex scientific queries. Often times, precedence is given to pop culture over scientific knowledge for queries. This is predominantly due to the use of internet sources for building the knowledge graph. With this work, we aim to explore the effectiveness of combining a knowledge graph generated from earth science corpora with a language model and graph convolutions for the purpose of surfacing latent and related sentences given a natural language query. In this model, sentences are conceptualized in the graph as nodes which are connected through entities—words and phrases of interest found in the text—extracted using Google Cloud’s entity extraction model. The language model we used for this is Bidirectional Encoder Representations from Transformers (BERT).The sentences are given a numeric representation by the BERT model. Graph convolutions are then applied to sentence embeddings in order to obtain a vector representation of the sentence as well as the surrounding graph structure, thereby leveraging the power of adjacency inherently encoded in graph structures. With this presentation, we demonstrate the ability of graph convolutions and their improved ability to surface relevant, latent information based on the subject of the input query.

Muthukumaran Ramasubramanian↗

Logical Shadow Tomography: Efficient Estimation of Error-mitigated Observables

In near-term quantum applications, reducing errors and improving device reliability is an essential task. Towards these ends, various techniques have been introduced in recent literature, collectively referred to as quantum error mitigation techniques, for reducing errors in pre-fault-tolerant devices. Here, we introduce logical shadow tomography as a versatile error mitigation method. Our technique uses a stabilizer code to encode information in a logical state. Instead of doing active error correction, quantum states will be measured at the end of computation via shadow tomography and non-logical errors are projected out in the classical post-processing. Relative to quantum subspace expansion which requires O(2(M-1)L) experiments to estimate an logical Pauli observable encoded by an [[M, L, d]] code, our technique only requires 2L experiments, an important practical reduction in resources.

Hong-Ye Hu↗

A Closer Look at Non-Random Patterns Within Chemistry Space for a Smaller, Earlier Amino Acid Alphabet

Recent findings, in vitro and in silico, are strengthening the idea of a simpler, earlier stage of genetically encoded proteins which used amino acids produced by prebiotic chemistry. These findings motivate a re-examination of prior work which has identified unusual properties of the set of twenty amino acids found within the full genetic code, while leaving it unclear whether similar patterns also characterize the subset of prebiotically plausible amino acids. We have suggested previously that this ambiguity may result from the low number of amino acids recognized by the definition of prebiotic plausibility used for the analysis. Here, we test this hypothesis using significantly updated data for organic material detected within meteorites, which contain several coded and non-coded amino acids absent from prior studies. In addition to confirming the well-established idea that “late” arriving amino acids expanded the chemistry space encoded by genetic material, we find that a prebiotically plausible subset of coded amino acids generally emulates the patterns found in the full set of 20, namely an exceptionally broad and even distribution of volumes and an exceptionally even distribution of hydrophobicities (quantified as logP) over a narrow range. However, the strength of this pattern varies depending on both the size and composition the library used to create a background (null model) for a random alphabet, and the precise definition of exactly which amino acids were present in a simpler, earlier code. Findings support the idea that a small sample size of amino acids caused previous ambiguous results, and further improvements in meteorite analysis, and/or prebiotic simulations will further clarify the nature and extent of unusual properties. We discuss the case of sulfur-containing amino acids as a specific and clear example and conclude by reviewing the potential impact of better understanding the chemical “logic” of a smaller forerunner to the standard amino acid alphabet.

Amino acids↗

Mars 2020 Entry, Descent, and Landing as Observed by Radio Science Techniques at UHF and X-band Frequencies

On February 18, 2021, NASA’s Mars 2020 Rover “Perseverance” conducted the Entry, Descent, and Landing (EDL) sequence to land safely on the surface of Mars at Jezero Crater. Due to the criticality of the EDL sequence, redundant telecommunications strategies were utilized to observe the event. The rover transmitted an X-band (8.4 GHz) signal encoded with Multiple Frequency Shift Keying tones direct-to-Earth and a UHF (401.5 MHz) signal with 8 kbps encoded telemetry to orbiters, which relayed the signal back to Earth at X-band. NASA’s Deep Space Network complexes at Goldstone, California and Madrid, Spain received the direct-to-Earth X-band signal. Two of the largest steerable radio telescopes in the world, the 100-meter Green Bank Telescope in West Virginia and the Effelsberg 100-meter Radio Telescope in Germany also received the UHF carrier signal on Earth. During the EDL event, full spectrum recordings of the UHF and X-band signals were captured at these observatories using open-loop receivers. Real-time and post-processing signal analysis to determine power level, received frequency, and Doppler shift allowed determination of the spacecraft’s health and safety state during critical sequences, including event detection such as atmospheric entry, plasma blackouts, and parachute deployment. Simultaneous observations of the UHF and X-band radio links allow for redundancy in the event of a fault and greatly improve confidence in Doppler event detection.

Gladden, Roy↗

Application of Fountain Code to High-Rate Delay Tolerant Networks

Space communication poses several unique challenges that are not always present in typical terrestrial communications. Currently, communication with satellites is based on point-to-point links, and development of an interplanetary internet is an active research area. Delay Tolerant Networking (DTN) has been proposed as a way to mitigate the long delays and disruptions found in deep space. A specialized version of DTN, called High-rate Delay Tolerant Networking (HDTN), has been developed by NASA to support a variety of missions requiring store-and-forward capability. However, there are still several features that are desired for HDTN including data fragmentation, multicast, and anycast. This project proposes the application of fountain code in HDTN as a means of fragmenting, distributing, and reassembling data (in the form of bundles) across multiple nodes (i.e. satellites) to any number of receivers (i.e. ground stations). Fountain code is shown to be a promising encoding method for use with the HDTN protocol suite due to its short runtimes, small encoded file sizes, and loss tolerance.

Noah Douglass↗

Anomaly Detection in Flight Operational Data Using Deep Learning

In this session, we demonstrate two recently developed deep learning models for anomaly detection in flight operational data by the Data Sciences Group at NASA Ames Research Center. The first model is Convolutional Variational Auto-Encoder (CVAE) [1], which is an unsupervised deep encoder-decoder model, designed specifically for finding anomalies in heterogeneous multivariate time series data. We will demonstrate its application to finding anomalies in streaming data from NASA’s Digital Information Platform’s Fuser source. CVAE identifies data instances that are not representative of expected nominal behavior as anomalous. Since it is an unsupervised approach, the flagged anomalies will need to be reviewed by the subject matter experts (SMEs) for validation and labeling and is designed to assist with vulnerability discovery within Safety Monitoring System programs. The second model is Robust and Explainable Semi-supervised Anomaly Detection (RESAD) model [2], which builds on CVAE to allow learning from both minimally labeled data (previously reviewed by the SMEs) as well as majority unlabeled data. RESAD takes advantage of graph theoretic techniques to propagate the labels from the labeled data to the unlabeled data based on a pre-defined similarity metric and structures the learned feature space from flight time-series so that data of the same class would cluster tightly together. This model characteristic is enabled by training with an augmented loss function and allows learning of a more informative feature space for down-stream tasks such as search and active learning. We demonstrate RESAD using data from the NASA DASHlink project [3].

anomaly detection↗

Floquet Codes on Non-Trivalent Lattices

Floquet codes are a novel form of quantum error correcting codes, where the logical degrees of freedom appear in a dynamical form. The first example of such a code was constructed by Hastings and Haah on a honeycomb lattice. Specifically, they showed how to Floquetify the Kitaev honeycomb model, which when viewed as a subsystem code, encodes no logical qubits. However, by choosing a particular measurement schedule of the check operators, this model leads to dynamically encoded logical qubits. Since this initial work, several examples of Floquet codes have been constructed, mainly on trivalent lattices. Here, we report progress on understanding when such codes can be implemented on lattices of different connectivities.

Muhammad Sohaib Alam↗

Towards an Aviation Large Language Model by Fine-tuning and Evaluating Transformers

In the aviation domain, there are many applications for machine learning and artificial intelligence tools that utilize natural language. For example, there is a desire to know the commonalities in written safety reports such as voluntary post incidents reports or aerial wildfire operations reports to better understand the risks present. Another use-case is the possibility of extracting airspace procedures and constraints currently written in documents such as Letters of Agreement. These applications can benefit from the use of state-of-the-art natural language processing techniques when adapted to the language/phraseology specific to the aviation domain. This paper evaluates the viability of adaptation of NLP tools to the aviation domain by fine-tuning transformer based models using aviation data sets. In 2018, a novel language model based on neural units (also called transformers) was created and became known as “Bidirectional Encoder Representations from Transformers” or BERT. This architecture combined with large amounts of English training data and innovative semi-supervised training tasks set the standard for what would later emerge as Large Language Models. The performance of these models was further improved by hyperparameter tuning and refinement of the semi-supervised training task and resulted in “Robustly Optimized BERT Pre-training Approach through hyperparameter tuning” or RoBERTa models. These pre-trained Large Language Models proved to be useful for a wide variety of natural language processing tasks such as text classification and question answering through a process called fine-tuning. The transformer architecture with pre-trained weights served as the basis with the last few layers replaced with layers fine-tuned to perform a new task e.g., a layer that provides a label for the entire input text. This process of fine-tuning can also be used to adapt the models to new domains; e.g., BioBERT started with the pre-trained BERT model and was completed by additional fine-tuning and training on biomedical documents. Transformer-based architectures can also be used to create rich representations of text called embeddings which can serve as the input to other machine learning models. This allows simpler algorithms such as logistic regression to use context-rich representations of the text while still remaining quick to train and evaluate. In the world of aviation, there is a growing demand for natural language processing and understanding but the domain presents unique challenges. Due to the technical content (and specialized language) of most aviation documents, fine-tuning pre-trained Large Language Models to specific tasks has not met the benchmark on natural language processing tasks set by simpler models trained from scratch on the data. To address this deficiency, this paper evaluates the improvements from fine-tuning a Large Language Model on a large set of aviation documents using the original semi-supervised training tasks before performing specific natural language tasks. In fine-tuning, a domain-specific dataset is used on the original training task but with the pre-trained Large Language Model instead of starting from a random initialization. This approach allows the model to be adapted to the specific domain language without discarding the information gained from training on general English data. This paper utilized two major dataset types to train and assess the RoBERTa fine-tuning performance. The first are 7,057 Letters of Agreement which are Federal Aviation Administration (FAA) documents that formalize airspace operations across the national airspace system. They contain many examples of ‘aviation English’ using domain specific terminology and phrasing which serves as a representative basis to perform the semi-supervised fine-tuning. The second type is the 494 document classification labels to be used for evaluation. This down-stream evaluation aims to show the performance of the fine-tuned model, better understand how much data is needed for an effective fine-tuning, and how fine-tuning can be adapted for different applications in-the domain. After semi-supervised training, evaluation begins by encoding the documents for classification using the fine-tuned RoBERTa model. Then a logistic regression classifier is trained to label the document type and compared against our ground truth labels. This currently leads to a 82.8% accuracy on 10-fold cross validation showing improvement over baseline RoBERTa which achieved 81.0%. We plan to measure the improvements on additional tasks and it is expected that these improvements will lead to more robust models that can tackle the natural language processing challenges present in aviation datasets.

ATM↗

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations [1]. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C [2] [3]. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message [2]. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C [3]. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

Philip Dafesh↗

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

LunaNet↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Optimal ranging codes.

Optimum encoding of transmitted signal in ranging system, using boolean functions of component sequences

RANGE MEASUREMENT↗