Adaptive Arrays and Tracking
Abstract
Adaptive arrays and tracking share many concepts mathematical tools, practical issues, and algorithms. For example, ill-conditioning of the sample covariance matrix for adaptive arrays and ill-conditioning of the covariance matrix in a Kalman filter are both serious problems that can be mitigated by the same set of about a dozen methods, including Tychonoff regularization (called "diagonal loading" in adaptive arrays), factorization of the covariance matrix, using principal coordinates or approximately principal coordinates, etc. The basic mathematics of Kalman filters and adaptive arrays includes linear algebra and probability Theory, but more specifically, Kalman filters and adaptive arrays use essentially the same matrix inversion formula. Multiple hypothesis tracking is the method of choice nowadays in tracking, and it could be applied to adaptive arrays and STAP for different types of jamming, clutter, and targets. In particular, there is no reason these days to settle for only one adaptive antenna pattern, but rather we could have a bank of ten or more such adaptive antenna patterns for the same batch of data combined adaptively using standard Bayesian methods. Sample covariance matrix estimation in adaptive arrays could benefit from robust multiple hypothesis algorithms developed for tracking. Adaptive array design and STAP can be viewed as nonlinear estimation problems, which suggest that adaptive arrays could profit by using the powerful and elegant exponential family of probability densities, which includes the multivariate Gaussian density as a special case. In particular, exact nonlinear filters, which generalize the Kalman filter, have been developed using the exponential family over the last two decades Markov random fields, which are relevant to adaptive arrays, also correspond to the exponential family, according to the Hammersley-Clifford Theorem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 20, 2004
- Accession Number
- ADA432577
Entities
People
- Frederick E. Daum