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The KaGE algorithm, a new fast RLS algorithm that has some interesting characteristics is been introduced. Computer simulation suggests that the new algorithm is numerically robust, running successfully for many millions of iterations.

This letter incorporates the adaptive kernel Kalman filter (AKKF) into the belief propagation (BP) algorithm for Multi-target tracking (MTT) in single-sensor systems. The algorithm is capable of tracking an unknown and time-varying number of targets, in the presence of false alarms, clutter and measurement-to-target association uncertainty. Experiment results reveal that the proposed method has a favourable tracking performance using the generalized optimal sub-patten assignment (GOSAP) metrics at substantially less computation cost than the particle filter (PF) based Multi-target tracking (MTT) BP algorithm. [ABSTRACT FROM AUTHOR]

The need is discussed for a conceptual framework for dealing with the computed solution from an algorithm by attending to the distinction between a perturbation analysis of a problem or a method of solution and the stability analysis of an algorithm. A consistent approach to defining concepts facilitates the assessment of the numerical quality of a computed solution.

A systolic array for recursive least squares estimation by inverse updates is derived by means of algorithmic engineering. The derivation of this systolic array is highly non-trivial due to the presence of data contra-flow and feedback loops in the underlying signal flow graph. This would normally prohibit pipelined processing. However, it is shown that suitable delays may be introduced into the signal flow graph by performing a simple algorithmic transformation which compensates for the interference of crossing data flows. The pipelined systolic array is then obtained by retiming the signal flow graph and applying the cut theorem.

In this paper, a generalized signal model is presented to accommodate both narrowband and wideband signals in a multi-input multi-output (MIMO) sensor system scenarios. The derived model is then used to define a MIMO ambiguity function based on the Kullback–Leibler divergence. Moreover, the proposed formulation is parametrized using the signal and channel correlation matrices to account for different waveform and sensor placement designs, thereby allowing a flexible modeling approach. A comparison between the proposed definition and the more conventional approach of summing the squared matched filter outputs is presented for different sensors and waveforms configurations. [ABSTRACT FROM AUTHOR]

The 'standard' minimum variance distortionless response (MVDR) beamforming algorithm of McWhirter and Shepherd [5] is known to suffer from linear roundoff error buildup. An alternative [7] has been developed based on the so-called inverse QR-updating algorithm. It is amenable to pipelined implementation, but unlike the McWhirter and Shepherd algorithm, it is stable numerically. Here, a variant of the latter algorithm that combines (part of) the McWhirter and Shepherd procedure into the inverse QR updating scheme is discussed. This makes the derivation of the algorithm less complex compared to the original [7]. Furthermore, by making use of a residual extraction property of the inverse updating procedure, an interesting correspondence of the new MVDR algorithm with so-called `generalized sideline cancellation' is explicitly revealed.

This paper addresses the extension of the factorization of a Hermitian matrix by an eigenvalue decomposition (EVD) to the case of a parahermitian matrix that is analytic at least on an annulus containing the unit circle. Such parahermitian matrices contain polynomials or rational functions in the complex variable $z$ and arise, e.g., as cross spectral density matrices in broadband array problems. Specifically, conditions for the existence and uniqueness of eigenvalues and eigenvectors of a parahermitian matrix EVD are given, such that these can be represented by a power or Laurent series that is absolutely convergent, at least on the unit circle, permitting a direct realization in the time domain. Based on an analysis of the unit circle, we prove that eigenvalues exist as unique and convergent but likely infinite-length Laurent series. The eigenvectors can have an arbitrary phase response and are shown to exist as convergent Laurent series if eigenvalues are selected as analytic functions on the unit circle, and if the phase response is selected such that the eigenvectors are Hölder continuous with $\alpha >\frac{1}{2}$ on the unit circle. In the case of a discontinuous phase response or if spectral majorisation is enforced for intersecting eigenvalues, an absolutely convergent Laurent series solution for the eigenvectors of a parahermitian EVD does not exist. We provide some examples, comment on the approximation of a parahermitian matrix EVD by Laurent polynomial factors, and compare our findings to the solutions provided by polynomial matrix EVD algorithms. [ABSTRACT FROM AUTHOR]