AUTOREGRESSIVE MOVING-AVERAGE (ARMA) MODEL IDENTIFICATION FOR DEGENERATE TIME SERIES WITH APPLICATION TO MANEUVERING TARGET TRACKING (STOCHASTIC MODELING, KALMAN FILTER).

摘要

Research was conducted in the general areas of time series analysis and stochastic realization. Results were then applied to the specific problem of tracking a highly maneuverable aircraft target.; An algorithm was developed to identify the order and parameters of the minimum order autoregressive moving-average (ARMA) model of a multi-variable system given the output autocorrelation sequence. Studies were also conducted in the area of degenerate time series modeling. It was found that degeneracy in vector-valued time series is caused by the presence of one or more deterministic relationships in the time series. ARMA models for degenerate time series can be identified by finding and extracting the deterministic relationships from the time series. The result is a reduced dimension stochastic model of the system. The model found will have fewer white noise inputs than outputs. An ARMA identification algorithm for use with degenerate times series was developed.; The equivalence between the ARMA model found and the Kalman filter innovations representation was discussed. A thorough numerical example demonstrating this equivalence as well as degenerate time series modeling was presented.; Application of the ARMA model identification procedure to the target tracking problem was investigated. It was discovered that the time series formed from target inertial velocity vectors is degenerate. This fact has physical significance and allows one to determine the orientation of the maneuver plane (the plane containing all the target motion) in inertial space. The ARMA modeling technique was used to develop an adaptive modeling and tracking algorithm. Operation of the algorithm was demonstrated using a target trajectory simulation.