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Singularity in CM Sequences

Year: 2019
Type: preprint
Abstract: Most existing results about modeling and characterizing Gaussian Markov, reciprocal, and conditionally Markov (CM) processes assume nonsingularity of the processes. This assumption makes the analysis easier, but restricts application of these processes. This paper studies, models, and characterizes the general (singular/nonsingular) Gaussian CM (including reciprocal and Markov) sequence. For example, to our knowledge, there is no dynamic model for the general (singular/nonsingular) Gaussian reciprocal sequence in the literature. We obtain two such models from the CM viewpoint. As a result, the significance of studying reciprocal sequences from the CM viewpoint is demonstrated. The results of this paper unify singular and nonsingular Gaussian CM (including reciprocal and Markov) sequences and provide tools for their application. An application of CM sequences in trajectory modeling with a destination is discussed and illustrative examples are presented.
DOI: 10.48550/arxiv.1910.12373
Institution: LSU New Orleans
Language: English
Open Access status: green
Award: AIR TRAFFIC DEMAND IN THE NATIONAL AIRSPACE SYSTEMS (NAS) HAS BEEN FORECAST TO DOUBLE BY THE YEAR 2025. UNFORTUNATELY THE PRESENT AIR TRAFFIC CONTROL (ATC) SYSTEM IS ALREADY STRAINED AND CANNOT SCALE TO MEET THIS DEMAND. MOREOVER WITH THE ADVENT OF UNMANNED AERIAL SYSTEMS SHARING NAS THE SITUATION MAY DETERIORATE EVEN MORE RAPIDLY. TO RESTRUCTURE THE ATC SYSTEM NASA IS COOPERATINGWITH THE FEDERAL AVIATION ADMINISTRATION AS WELL AS OTHER GOVERNMENT AGENCIES TO DEVELOP NEXTGEN DESIGNED TO GREATLY INCREASE THE NAS CAPACITY EFFICIENCY SAFETY FLEXIBILITY AND ENVIRONMENTAL PROTECTION. HOWEVER WHAT IS NEEDED IS A TRANSFORMATION FROM ATC TO AIR TRAFFIC MANAGEMENT (ATM) ALLOWING AIRCRAFT MORE AUTONOMY. DEVELOPING MAJOR COMPONENTS OF THAT TRANSFORMATIONAL SYSTEM IS THE OVERALL GOAL OF THIS PROJECT WHICH IS COORDINATED BY SCIENCE PI X. RONG LI UNIVERSITY OF NEW ORLEANS. THE TEAM INVOLVES RESEARCHERS AT LSU AND SU AS WELL AS SUPPORT FROM AMES LARC SIX BUSINESS/INDUSTRY CONCERNS PLUS THE U.S. AIR FORCEAND THE DEPARTMENT OF ENERGY. AN ATM SYSTEM IS CENTERED ON TRAJECTORY-BASED OPERATIONS WHICH RELY CRITICALLY ON RELIABLE AND ACCURATE INFORMATION PROCESSING AND NETWORK-CENTRIC MANAGEMENT. THIS INCLUDES 4D TRAJECTORY PREDICTION (TP) INTENT INFERENCE AND VERIFICATION (IIV) CONFLICT DETECTION AND RESOLUTION (CDR) SEPARATION ASSURANCE (SA) CONFORMANCE MONITORING (CM) AND AIRCRAFT HEALTH MANAGEMENT. EACH OF THESE REPRESENTS A SEPARATE OPERATIONAL PROBLEM FOR WHICH WE PROPOSE INNOVATIVE AND SOLID FORMULATIONS OF THE PROBLEM SYSTEMATIC AND PROMISING SOLUTION APPROACHES AND WELL-THOUGHT-OUT RESEARCH TASKS. FOR EXAMPLE ACCURATE AND RELIABLE LONG-TERM TP AND IIV CAN ONLY COME HAND IN HAND SINCE THEY INVOLVE AIRCRAFT INTENT WEATHER CONDITIONS NAVIGATION ACCURACY ETC. OURAPPROACH IS BASED ON JOINT DECISION AND ESTIMATION A FRAMEWORK WE DEVELOPED RECENTLY ALONG WITH ITS OPTIMAL SOLUTION. SIMILARLY OUR PROPOSED STATISTICAL CDR REPRESENTS A NOVEL APPROACH OFFERING CONFLICT ALERTS AT DIFFERENT LEVELS BASED ON A DIRECT STATISTICAL HYPOTHESISTESTING FORMULATION WHICH WILL BE MORE CONVENIENT TO USE THAN MOST EXISTING MODELS. A PRIMARY TASK IS TO COMBINE THE SOLUTIONS INTO A MULTI-AGENT SYSTEM (MAS) APPROACH TO ATM. WE PROPOSE TO FULLY ACCOUNT FOR THE HETEROGENEITY OF THE INDIVIDUAL SYSTEMS AND CONTROLLERS AND TO TAKE INTO ACCOUNT THE PRACTICAL COMMUNICATION CONSTRAINTS. THE MERIT OF THIS PROJECT IS FOURFOLD. FIRST THE RESEARCHTOPICS HAVE GREAT IMPORTANCE FOR NEXTGEN; SECOND THE RESEARCH PLANS ARE WELL DEVELOPED; THIRD THE TEAM IS UNIQUELY QUALIFIED FOR THE WORK; AND FOURTH THE RESULTS WILL BOOST LOUISIANA S INVESTMENT IN THIS FIELD AND MAKE A MAJOR CONTRIBUTION TO NASA AERONAUTICS.
OpenAlex ID: W3032923933
Cites: 28
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Related to: 20