Five methods of direction-of-arrival (DOA) estimation which can be derived from the maximum-likelihood (ML) principle are considered. The ML method (MLM) results from the application of the ML principle to the statistics of the observed raw data. The standard multiple signal classification (MUSIC) procedure, called MUSIC-1, is obtained as a brute-force approximation of the MLM. An improved MUSIC procedure, named MUSIC-2, is obtained by applying the ML principle to the statistics of certain linear combinations of the sample noise space eigenvectors. A procedure which compromises between the good performance of the MLM and the computational simplicity of MUSIC is a method of direction estimation (MODE-1) which is derived as a large sample realization of the MLM. A fifth method, called MODE-2, is obtained by using the ML principle on the statistics of certain linear combinations of the sample eigenvectors. MODE-2 is computationally less demanding than the MLM (it is of the same complexity as MODE-1) and statistically more efficient. A numerical comparison of these five DOA estimation methods is presented. It confirms the analytic results on their theoretical performance levels. >

Maximum likelihood methods for direction-of-arrival estimation

Problems associated with the use of intersecting hyperboloids for passive source localization from time-of-arrival difference signals are discussed. A closed-form solution for source location is presented given time-of-arrival difference measurements when the distance from the source to any arbitrary reference is unknown.

Passive source localization employing intersecting spherical surfaces from time-of-arrival differences

This paper attempts to demonstrate that a modem optimization methodology known as semidefinite programming (SDP) can serve as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator IIR filters Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for IIR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity

/pdf/a-unified-approach-for-the-design-of-2-d-digital-filters-via-30nxee7iq9.pdf

A unified approach for the design of 2-D digital filters via semidefinite programming

Singular-value decomposition (SVD) is applied to the design of two-dimensional (2-D) FIR (finite-impulse-response) digital filters. It is shown that three realizations are possible, namely, a direct realization, a modified version of direct realization, and a realization based on the combined application of SV and LU decomposition. Each of the realizations consists of a parallel arrangement of cascaded pairs of 1-D filters; hence extensive parallel processing and pipelining can be applied. The 1-D FIR filters can be designed using standard methods, and linear-phase causal 2-D filters that are suitable for real-time or quasi-real-time applications can also be designed. The three realizations are compared, and it is shown that the realization based on combined SV and LU decomposition leads to the lowest approximation error and involves the smallest number of multiplications. SVD, the McClellan transformation, and 2-D window design methods are used to design a bandpass and a fan filter, and the results are compared. >

Design of two-dimensional FIR digital filters by using the singular-value decomposition

The Levinson algorithm has been shown recently to be redundant in complexity. It can be broken down into two simpler algorithms; either of these "split Levinson algorithms" needs only to be processed. In the present paper it is shown that the Schur algorithm, the lattice algorithm, and the normalized lattice algorithm for computing reflection coefficients can be broken down in a similar manner. The number of multiplications in each of the resulting split algorithms is reduced, with respect to the classical version, by a factor lying between 1.5 and 2.

On the splitting of classical algorithms in linear prediction theory

The design of two-dimensional (2-D) circularly-symmetric low-pass digital filters by cascading several rotated filters (a rotated filter is defined to be one produced by rotating a one-dimensional (1-D) continuous filter into a two-dimensional continuous filter which is in turn bilinearly transformed into a two-dimensional digital filter) is a well-known and useful technique. An alternate approach which is an extension of the above technique is presented. This new method is based on a spectral transformation from the one-dimensional discrete domain into the two-dimensional discrete domain. This approach retains most of the advantages of the original technique while permitting design entirely in the discrete domain, yielding filters with better stability characteristics, and facilitating frequency response optimization via nonlinear programming.

A design technique for circularly symmetric low-pass filters

It is shown that the problem of minimizing the prediction error under the constraint that the zeros of the predictor polynomial be on the unit circle can be solved by using a modification of the Levinson algorithm. Consequences of this result are discussed.

https://ieeexplore.ieee.org/iel6/29/26170/01163893.pdf

D. Goodman

Papers

A design technique for circularly symmetric low-pass filters

A note on minimizing the prediction error when the zeros are restricted to the unit circle