ON THE APPLICATION OF THE JACKKNIFE TO THE ESTIMATION OF THE PARAMETERS OF SHORT MULTISINUSOIDAL SIGNALS USING THE DATA-MATRIX FORMULATION

It is demonstrated that the jackknife can be applied to the estimation of the parameters of a single short segment of a noisy, complex multi sinusoid signal where the estimation process itself is based on the da ta-matrix formulation, The parameter of interest are the frequency, am plitude, and initial phase of each sinusoid, and the key role of the j ackknife is to provide an estimate of the standard deviation of the es timates of these parameters from the single record available. The jack knife is shown to be especially appropriate where the primary estimato r is well-behaved and its performance is broadly optimum where the sub -segment length used in creating the data matrix is about one-half of the record length and improves somewhat as the data length itself incr eases. This is inferred from a series of simulations involving three d ifferent algorithms with one, two, and three complex sinusoids in comp lex white noise. The application of the jackknife in the presence of p hase noise and additive colored noise is also briefly examined. Due to the correlation between the columns of the data matrix, the successfu l application of the jackknife to this problem cannot be assumed a pri ori.