Sample covariance based estimation of Capon algorithm error probabilities

Abstract

The method of interval estimation (MIE) provides a strategy for mean squared error (MSE) prediction of algorithm performance at low signal-to-noise ratios (SNR) below estimation threshold where asymptotic predictions fail. MIE interval error probabilities for the Capon algorithm are known and depend on the true data covariance and assumed signal array response. Herein estimation of these error probabilities is considered to improve representative measurement errors for parameter estimates obtained in low SNR scenarios, as this may improve overall target tracking performance. A statistical analysis of Capon error probability estimation based on the data sample covariance matrix is explored herein.

Performance of sample covariance based capon bearing only tracker

“…Reference [4] detailed the impact of estimating P e from R via calculation of the M -th moments. The Capon algorithm evaluated at point θ is given by…”

“…Outlier rejection techniques [2] have been employed with some success for the bearing only tracker problem [3]. Previous work [4] began to explore the potential benefits to tracking of improved measurement errors for bearing estimates obtained from low signal-to-noise ratio (SNR) targets, i.e. those likely to yield erroneous bearing estimates.…”

“…Specifically, use of the method of interval errors (MIE) [5], [6] for obtaining improved measurement errors showed corresponding improvement in the performance of a bearing only Kalman filter (KF) tracker in three ways: MIE (i) reduced the realized root mean squared error (RMSE) of the KF, (ii) improved the tightness of KF prediction of RMSE, and (iii) made KF prediction more conservative in the low SNR regime. While the analysis of [4] is encouraging, the MIE calculations of the measurement error were obtained via use of the true data covariance, and the concomitant bearing estimates provided to the KF were obtained from a * This work was sponsored by Navy under Air Force contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the United States Government.…”

Condition numbers of indefinite rank 2 ghost Wishart matrices

“…Though much is known when Σ is positive definite [5], to the extent of our knowledge, the indefinite case is rarely considered. We work out the distribution of the ratio of the eigenvalues and the condition number of A as it has applications in hypersensitive ground based radars [1,2].…”

“…Note that W ΣW T = QRΣR T Q T and that A is similar to RΣR T . The elements of R may be chosen to be non-negative in which case it is well known that they have independent χ-distributions (1) and that [5]…”