CHARACTERIZATION AND SIMULATION OF GUNFIRE WITH KARHUNEN-LOEVE EXPANSION

摘要

Gunfire is used as an example to illustrate how the Karhunen-Loeve (K-L) expansion can be used to characterizernand simulate nonstationary random events. The current paper will develop a method to describe the nonstationary randomrnprocess in terms of a K-L expansion. The gunfire record is broken up into a sequence of transient waveforms eachrnrepresenting the response to the firing of a single round. First the mean is estimated and subtracted from each waveform. Thernmean is an estimate of the deterministic part of the gunfire. The autocovariance matrix is estimated from the matrix of thesernsingle round gunfire records. Each column is a realization of the firing of a single round. The gunfire is characterized with thernK-L expansion of the autocovariance matrix. The gunfire is simulated by generating realizations of records of a single roundrnfiring from the expansion and the mean waveform. The individual realizations are then assembled into a realization of a timernhistory of many rounds firing. The method is straightforward, easy to implement, and produces a simulated record very muchrnlike the original measured gunfire record.