Work

Gaussian Conditionally Markov Sequences: Dynamic Models and Representations of Reciprocal and Other Classes

Year: 2019

Type: article

Abstract: Conditionally Markov (CM) sequences are powerful mathematical tools for modeling problems. One class of CM sequences is the reciprocal sequence. In application, we need not only CM dynamic models, but also know how to design model parameters. Models of two important classes of nonsingular Gaussian (NG) CM sequences, called CMLand CMFmodels, and a model of the NG reciprocal sequence, called reciprocal CML model, were presented in our previous works and their applications were discussed. In this paper, these models are studied in more detail, in particular their parameter design. It is shown that every reciprocal CMLmodel can be induced by a Markov model. Then, parameters of each reciprocal CMLmodel can be obtained from those of the Markov model. Also, it is shown that an NG CML(CMF) sequence can be represented by a sum of an NG Markov sequence and an uncorrelated NG vector. This (necessary and sufficient) representation provides a basis for designing parameters of a CML (CMF) model. From the CM viewpoint, a representation is also obtained for NG reciprocal sequences. This representation is simple and reveals an important property of reciprocal sequences. As a result, the significance of studying reciprocal sequences from the CM viewpoint is demonstrated. A full spectrum of dynamic models from a CMLmodel to a reciprocal CMLmodel is also presented. Some examples are presented for illustration.

Source: IEEE Transactions on Signal Processing

DOI: 10.1109/tsp.2019.2919410

Authors: Reza Rezaie, X. Rong Li

Institution: LSU New Orleans

Language: English

Topic: Control Systems and Identification

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Aeronautics and Space Administration

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.