Estimation of covariance parameters for an adaptive Kalman filter [thesis]

Jerome Clair Shellenbarger
Signature was redacted for privacy. Signature was redacted for privacy. Signature was redacted for privacy. Pag 1 4 8 12 21 31 36 39 4o 1*1 1*4 45 46 51 52 ii • TABLE OF CONTENTS computations are performed recursively, in the time domain (thereby being well-suited for handling by computers), and are readily applicable to nonstationary and multiple input-output systems. A host of study areas are closely related to, or are sub-categories of, the Kalman-filter theory; some of them treat problems
more » ... em treat problems of stability, sensi tivity, smoothing, prediction, effects of different types of sampling, linear approximations, system identification, and parameter estimation. It is this last topic which is the subject of this dissertation, so further explanation is in order. It is assumed that a Kalman filter is to be developed for use on some linear system about which the following state ments can be made; 1. The system is completely specified, including the "filters" needed to convert Gaussian "white-noise" sources into the actual inputs. The measurement device is specified, 3. The root-mean-square amplitudes of the inputs may or may not be known. The measurement errors have Gaussian, time-independent statistics with zero means and variances which may or may not be known. In order to apply the Kalman filter, the covariances of the measurement errors and the inputs are required. If either, or both, covariance matrices are unknown, due to lack of information as mentioned in parts 3 and k above, then covariance parameter estimation must be employed. Methods are developed in the later sections which enable one to make estimates of the necessary covariance parameters when the measurementerror and/or the input covariances are missing. These estimates cause the Kalman filter to be adaptive to unknown statistics, provided the statistics
doi:10.31274/rtd-180814-4389 fatcat:tnjokkvedvd75j4ysj455budvu