Distributed processing of a fractal array beamformer

Fractals have been proven as potential candidates for satellite flying formations, where its different elements represent a thinned array. The distributed and low power nature of the nodes in this network motivates distributed processing when using such an array as a beamformer. This paper proposes such initial idea, and demonstrates that benefits such as strictly limited local processing capability independent of the array’s dimension and local calibration can be bought at the expense of a slightly increased overall cost

On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix

This paper addresses the extension of the factorisation 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 realisation in the time domain. Based on an analysis on 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 α>½ 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

Ambiguity function for distributed MIMO radar systems

In this paper a multi-static ambiguity function (AF) based on the Kullback directed divergence (KDD) and a distributed multiple-input and multiple-output radar system (DMRS) framework is introduced. Additionally a mathematical analysis is used to derive the AF in terms of signal-to-noise ratios (SNRs) and matched filter outputs. This method manages to extract an upper bound and properly define an AF bounded from 0 to 1. Moreover, this method leads in avoidance of large matrices inversions allowing less complex and more accurate computations. Finally the performance of the proposed method in localisation problems is assessed by comparing the proposed AF with the squared summation of the matched filter outputs at each receiver at different SNR scenarios

Analysing the performance of divide-and-conquer sequential matrix diagonalisation for large broadband sensor arrays

A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations. Inspired by recent work towards a low complexity divide-and-conquer PEVD algorithm, this paper analyses the performance of this algorithm - named divide-and-conquer sequential matrix diagonalisation (DC-SMD) - for applications involving broadband sensor arrays of various dimensionalities. We demonstrate that by using the DC-SMD algorithm instead of a traditional alternative, PEVD complexity and execution time can be significantly reduced. This reduction is shown to be especially impactful for broadband multichannel problems involving large arrays

Impact of fast-converging PEVD algorithms on broadband AoA estimation

Polynomial matrix eigenvalue decomposition (PEVD) algorithms have been shown to enable a solution to the broadband angle of arrival (AoA) estimation problem. A parahermitian cross-spectral density (CSD) matrix can be generated from samples gathered by multiple array elements. The application of the PEVD to this CSD matrix leads to a paraunitary matrix which can be used within the spatio-spectral polynomial multiple signal classification (SSP-MUSIC) AoA estimation algorithm. Here, we demonstrate that the recent low-complexity divide-and-conquer sequential matrix diagonalisation (DC-SMD) algorithm, when paired with SSP-MUSIC, is able to provide superior AoA estimation versus traditional PEVD methods for the same algorithm execution time. We also provide results that quantify the performance trade-offs that DC-SMD offers for various algorithm parameters, and show that algorithm convergence speed can be increased at the expense of increased decomposition error and poorer AoA estimation performance

Performance Evaluation of Simultaneous Sensor Registration and Object Tracking Algorithm

Reliable object tracking with multiple sensors requires that sensors are registered correctly with respect to each other. When an environment is Global Navigation Satellite System (GNSS) denied or limited – such as underwater, or in hostile regions – this task is more challenging. This paper performs uncertainty quantification on a simultaneous tracking and registration algorithm for sensor networks that does not require access to a GNSS. The method uses a particle filter combined with a bank of augmented state extended Kalman filters (EKFs). The particles represent hypotheses of registration errors between sensors, with associated weights. The EKFs are responsible for the tracking procedure and for contributing to particle state and weight updates. This is achieved through the evaluation of a likelihood. Registration errors in this paper are spatial, orientation, and temporal biases: seven distinct sensor errors are estimated alongside the tracking procedure. Monte Carlo trials are conducted for the uncertainty quantification. Since performance of particle filters is dependent on initialisation, a comparison is made between more and less favourable particle (hypothesis) initialisation. The results demonstrate the importance of initialisation, and the method is shown to perform well in tracking a fast (marginally sub-sonic) object following a bow-like trajectory (mimicking a representative scenario). Final results show the algorithm is capable of achieving angular bias estimation error of 0.0034 o , temporal bias estimation error of 0.0067 s, and spatial error of 0.021m

Extension of power method to para-Hermitian matrices : polynomial power method

This document extends the idea of the power method to polynomial para-Hermitian matrices for the extraction of the principal analytic eigenpair. The proposed extension repeatedly multiplies a polynomial vector with a para-Hermitian matrix followed by an appropriate normalization in each iteration. To limit the order growth of the product vector, truncation is performed post-normalization in each iteration. The method is validated through simulation results over an ensemble of randomized para-Hermitian matrices and is shown to perform significantly better than state-of-the-art algorithms

A Gaussian Process Regression based Dynamical Models Learning Algorithm for Target Tracking

Maneuvering target tracking is a challenging problem for sensor systems because of the unpredictability of the targets' motions. This paper proposes a novel data-driven method for learning the dynamical motion model of a target. Non-parametric Gaussian process regression (GPR) is used to learn a target's naturally shift invariant motion (NSIM) behavior, which is translationally invariant and does not need to be constantly updated as the target moves. The learned Gaussian processes (GPs) can be applied to track targets within different surveillance regions from the surveillance region of the training data by being incorporated into the particle filter (PF) implementation. The performance of our proposed approach is evaluated over different maneuvering scenarios by being compared with commonly used interacting multiple model (IMM)-PF methods and provides around $90\%$ performance improvement for a multi-target tracking (MTT) highly maneuvering scenario.Comment: 11 pages, 10 figure

Maximum energy sequential matrix diagonalisation for parahermitian matrices

Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step