ResearchSpace :: Browsing by Author "McDonald, Andre M"

Browsing by Author "McDonald, Andre M"

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Algebraic analysis of Toeplitz decorrelation techniques for direction-of-arrival estimation
(2019-11) Shafuda, F; McDonald, Andre M; Van Wyk, MA; Versfeld, J
In this paper, we investigate the correlation Toeplitz (CTOP) and averaging Toeplitz (AVTOP) decorrelation techniques, as applied towards direction of arrival (DOA) estimation of coherent narrowband sources with the multiple signals classi cation (MUSIC) algorithm. Numerical studies suggest that CTOP leads towards more accurate DOA estimation than AVTOP; however, no theoretical motivation for this performance gap has yet been presented. In this paper, we derive expressions for the Toeplitz matrices produced by the CTOP and AVTOP techniques, for a scenario involving a three-element uniform linear array and two coherent source signals in additive white Gaussian noise. These expressions lead to the claim that the accuracy of the CTOP technique can be attributed to its retention of source DOA information as independent sums (i.e. in a superposition form) in the Toeplitz matrix. The claim is supported by an investigation of the MUSIC spectra corresponding to the distinct Toeplitz matrices.
Arta process model of maritime clutter and targets
(IEEE Xplore, 2012-10) McDonald, Andre M; Cilliers, Jacques E
A coherent autoregressive–to–anything (ARTA) stationary stochastic process for modelling maritime clutter and targets is presented in this paper. The ARTA stochastic process model is an improvement over previous models in the sense that it is complex–valued, has a magnitude with an arbitrary, nonnegative distribution and an arbitrary autocorrelation function. A rapidly converging algorithm for finding appropriate filter coefficients to realize a specified autocorrelation function is presented. The validity and practicality of the ARTA process model is demonstrated by deriving models for a maritime target and for sea clutter, both from measurements and without any prior assumption regarding the distribution of measurements. This ability to generate additional data samples with the same statistics as a set of measurements is a prerequisite for the verification of system specifications in situations where only a few data measurements are available for each mode of operation and / or environmental condition.
Automatic detection of emerging threats to computer networks
(CSIR, 2015-10) McDonald, Andre M
South Africa is growing increasingly reliant on information and communications technology (ICT) to provide access to information and services. In making progress towards bridging the digital divide, our country now faces a host of increasingly sophisticated threats against personal, financial and confidential information of both organisations and individuals. The potential impact of these threats is amplified due to the penetration of ICT systems into critical infrastructure such as the electricity grid, banks, the stock exchange and others. Conventional network security mechanisms are no longer able to protect computing resources from emerging threats due to the growing complexity of computer networks and technology. The purpose of network intrusion detection technology is to detect threats to networked information systems and networking infrastructure in an automated fashion, thereby providing an opportunity to deploy countermeasures. This presentation showcases the research and development of this technology at the CSIR, with emphasis on novel techniques for detecting emerging threats.
A condition for unbiased direction-of-arrival estimation with Toeplitz decorrelation techniques
(IEEE, 2019-11) McDonald, Andre M; Van Wyk, MN
Toeplitz decorrelation techniques, as applied towards direction-of-arrival estimation of coherent narrowband signals using a sensor array, significantly improve the accuracy of subspace methods without reducing the effective array aperture. The novel contribution of this paper is a necessary and sufficient condition that any jointly Toeplitz and Hermitian matrix produced by these techniques must satisfy in order to facilitate unbiased estimation via a subspace method. The condition is derived for a uniform linear array and additive white Gaussian noise model. The row-selection and diagonal-averaging strategies for generating Toeplitz matrices are evaluated against the condition, for the case where all sources are coherent. It is proved that row selection accommodates unbiased estimation if and only if the first row of the deficient covariance matrix is selected, whereas diagonal averaging invariably leads to bias.
Construction of semi-Markov ergodic maps with selectable spectral characteristics via the solution of the inverse eigenvalue problem
(2017-12) McDonald, Andre M; Van Wyk, A
This paper presents a novel technique for constructing semi–Markov ergodic maps that harnesses a new solution of the inverse eigenvalue problem for 3–by–3 doubly stochastic matrices. The proposed solution facilitates the selection of the spectral characteristics of the trajectories generated by these ergodic maps through the selection of appropriate eigenvalues for the Frobenius–Perron matrices associated with the maps. It is proved that the proposed solution is able to realise all possible eigenvalue triples for the matrices of interest, thereby providing greater freedom in selecting the power spectral density than existing techniques. The novel technique is demonstrated by constructing several semi–Markov ergodic maps with distinct power spectra. It is concluded that the flexibility and versatility of the technique holds potential for the purpose of system modelling in various contexts.
Distribution analysis of segmented wave sea clutter in littoral environments
(IEEE, 2015-10) Strempel, MD; De Villiers, JP; Cilliers, Jacques E; McDonald, Andre M
This paper investigates the littoral sea clutter amplitude distributions associated with individual segments within a periodic wave. Low grazing angle, X-Band sea clutter data, obtained from the CSIR online database was utilised for this study. The dataset contains fixed frequency pulsed radar returns of low grazing angle sea clutter with a pulse repetition frequency (PRF) of 2.5kHz. The processing involves correcting the data by means of rotation such that the periodic wave phase structures within the data align over time and are parallel to the longtime axis. Thereafter, the data and thus the wave structures, are segmented into multiple partitions, where each partition represents a section of the wave phase in the range dimension. These segments are then fitted against the K-distribution. It is shown that the approach can accurately describe specific sections of the wave with a reduced error between actual and estimated distributions. The improved probability density function (PDF) representation will allow for more accurate data analysis and data generation in littoral environments, which can be used for the development of new detectors, as well as the simulation of their performance.
Efficient generation of random signals with prescribed probability distribution and spectral bandwidth via ergodic transformations
(2018-09) McDonald, Andre M; Van Wyk, MA
A novel random signal generator design that accommodates the specification of both the sample probability distribution as well as the signal bandwidth is presented in this paper. The generator achieves a high degree of computational efficiency through the nonlinear transformation of trajectories produced by a discrete–time dynamical system which has an ergodic map as evolution rule. The ergodic map is designed using a recently proposed solution of the inverse Frobenius–Perron problem that allows for the selection of the map’s invariant distribution as well as its spectral characteristics. The nonlinear transformation is obtained via a novel piecewise polynomial fitting algorithm, which facilitates the approximation of absolutely continuous probability distributions over compact support with greater accuracy than existing techniques. Numerical experiments indicate that the proposed design achieves a reduction in signal generation time of up to 22% compared to a conventional generator, while at the same time using a smaller lookup table, maintaining a comparable level of accuracy, and offering flexibility in the selection of the signal bandwidth. It is concluded that the proposed approach is suitable for signal generation in applications where low computational complexity is a critical requirement.
Efficient sorting of Bessel beams
(Optical Society of America, 2013-01) Dudley, Angela L; Mhlanga, T; Lavery, M; McDonald, Andre M; Roux, FS; Padget, M; Forbes, A
We demonstrate the efficient sorter of Bessel beams separating both the azimuthal and radial components. This is based upon the recently reported transformation of angular to transverse momentum states. We separately identify over forty azimuthal and radial components, with a radial spacing of 1588 m-1, and outline how the device could be used to identify the two spatial dimensions simultaneously.
Efficient sorting of Bessel beams [Conference paper]
(SPIE Digital llibrary, 2013-02) Mhlanga, T; Dudley, Angela L; McDonald, Andre M; Roux, FS; Lavery, M; Padgett, M; Forbes, A
A procedure to efficiently sort orbital angular momentum (OAM) states of light, by performing a Cartesian to log-polar coordinate transformation which translates helically phased beams into a transverse phase gradient, currently exists1. We implement this mode transformer, which comprises of two custom refractive optical elements2, to efficiently sort Bessel beams carrying OAM. Introducing two cylindrical lenses, allows the focusing of each of the input OAM Bessel states to a different lateral position in the Fourier plane and separates the radial wave-vectors in the image-plane. We demonstrate the concept by separating over forty OAM states and radial wave-vectors.
Evaluation of the information content of wideband and ultra-wideband radar returns from an F14, F15 and F16 using asymptotic electromagnetic techniques
(IEEE Xplore, 2012-10) Cilliers, Jacques E; Smit, JC; McDonald, Andre M; Baker, CJ; Woodbridge, K
This paper addresses the prediction of the maximum recognition performance of a radar for a predetermined set of targets and radar waveforms. Use is made of the information theoretic concept of mutual information (MI) to perform this analysis. Returns from an F14, F15 and F16 were simulated using an asymptotic RCS prediction code. The information content of the three targets is evaluated for four sets of radar waveforms.
Feature selection for anomaly–based network intrusion detection using cluster validity indices
(2015-09) Naidoo, T; Tapamo, JR; McDonald, Andre M
A feature selection algorithm that is novel in the context of anomaly–based network intrusion detection is proposed in this paper. The distinguishing factor of the proposed feature selection algorithm is its complete lack of dependency on labelled data, which is rarely available in operational networks. It uses normalized cluster validity indices as an objective function that is optimized over the search space of candidate feature subsets via a genetic algorithm. Feature sets produced by the algorithm are shown to improve the classification performance of an anomaly–based network intrusion detection system over the NSL-KDD dataset. The system approaches the performance attained by using feature sets derived from labelled training data via existing wrapper and filter–based feature selection algorithms.
Feature selection for anomaly–based network intrusion detection using cluster validity indices
(http://www.satnac.org.za, 2015-09) Naidoo, Tyrone; McDonald, Andre M; Tapamo, J-R
A feature selection algorithm that is novel in the context of anomaly–based network intrusion detection is proposed in this paper. The distinguishing factor of the proposed feature selection algorithm is its complete lack of dependency on labelled data, which is rarely available in operational networks. It uses normalized cluster validity indices as an objective function that is optimized over the search space of candidate feature subsets via a genetic algorithm. Feature sets produced by the algorithm are shown to improve the classification performance of an anomaly–based network intrusion detection system over the NSL-KDD dataset. The system approaches the performance attained by using feature sets derived from labelled training data via existing wrapper and filter–based feature selection algorithms.
Hardware in the loop testing and evaluation of seaborne search radars
(2012-09) Strydom, JJ; Cilliers, Jacques E; McDonald, Andre M; Olivier, K
This presentation gives an overview of the testing and evaluation of seaborne search radars and the advances in DRFM technology.
Implementation of anomaly detection algorithms for detecting transmission control protocol synchronized flooding attacks
(IEEE, 2015-08) Mkuzangwe, Nenekazi NP; McDonald, Andre M; Nelwamondo, Fulufhelo V
This work implements two anomaly detection algorithms for detecting Transmission Control Protocol Synchronized (TCP SYN) flooding attack. The two algorithms are an adaptive threshold algorithm and a cumulative sum (CUSUM) based algorithm. Furthermore, we fused the outcomes of the two algorithms using the logic OR operator at different thresholds of the two algorithms to obtain improved detection accuracy. Indeed, the results indicated that the OR operator performs better than the two algorithms in detecting SYN flooding attack and detection delay.
The inverse Frobenius-Perron problem: A survey of solutions to the original problem formulation
(2021-08) McDonald, Andre M; Van Wyk, M; Chen, G
The inverse Frobenius-Perron problem (IFPP) is a collective term for a family of problems that requires the construction of an ergodic dynamical system model with prescribed statistical characteristics. Solutions to this problem draw upon concepts from ergodic theory and are scattered throughout the literature across domains such as physics, engineering, biology and economics. This paper presents a survey of the original formulation of the IFPP, wherein the invariant probability density function of the system state is prescribed. The paper also reviews different strategies for solving this problem and demonstrates several of the techniques using examples. The purpose of this survey is to provide a unified source of information on the original formulation of the IFPP and its solutions, thereby improving accessibility to the associated modeling techniques and promoting their practical application. The paper is concluded by discussing possible avenues for future work.
Linear least squares parameter inference for the SIR epidemiology model
(2025-11) Van Wyk, MA; McDonald, Andre M; Ngwako, MT; Nyandoro OT, OT; Zhang, F, MA McDonald
Accurate and early estimation of Susceptible-Infected-Recovered (SIR) epidemiology model parameters in infectious epidemics can enhance planning and resource allocation, thereby mitigating the adverse impacts on affected populations. Focusing on the basic SIR epidemiology model, in this paper we examine the scenario of known incidence rate (e.g., cases per day). Even though the SIR model is nonlinear, we obtain an exact least squares solution that is linear in simple algebraic functions of the SIR model’s parameters, the infection rate, recovery rate and total population. Linear least squares solutions lend themselves to be applied to only a selected time period, to the censoring of unreliable measurements such as obvious outliers as well as to enable iterative update of the parameter estimates as new data (i.e., measurements) become available. We present numerical results for both simulated and real-world COVID-19 data to demonstrate the practical utility and accuracy of the proposed method. The proposed method demonstrates advantages over state-of-the-art approaches while also providing reliable parameter estimates.
A novel approach to solving the generalized inverse Frobenius-Perron problem
(2020-10) McDonald, Andre M; Van Wyk, M
A new approach to solving a more general formulation of the inverse Frobenius-Perron problem, which requires the construction of a one-dimensional ergodic map with prescribed invariant probability density function and power spectral density, is presented. The proposed approach relies on a novel technique for generating distinct maps with the same invariant density, and which facilitates selection of the structural characteristics of each map in advance. We consider a new class of maps constructed with this technique, the piecewise monotonic hat maps, and present an algorithm for selecting the map parameters to achieve simultaneous and independent prescription of the invariant density and multimodal power spectrum characteristics. This approach to solving the generalized inverse FrobeniusPerron problem is demonstrated by constructing several ergodic maps with the beta invariant density as well as unimodal and bimodal power spectra with distinct mode center frequencies and bandwidths. We conclude that the proposed approach provides a means for generating more realistic models of systems and processes as compared to existing methods.
Novel estimators for the number of susceptible individuals in SIR models of infectious epidemics
(2024-12) Van Wyk, MA; McDonald, Andre M; Rubin, DM; Zhang, F
Accurate estimation of model parameters early in infectious epidemics may improve planning and resource allocation in mitigating the adverse consequences on affected populations. By applying the Peano-Baker series formula and the Cauchy repeated integral formula, we present the development of three novel estimators which facilitate the estimation of the number of susceptible people as a function of time S(t) for an SIR model of an infectious epidemic. Association of these three estimators by combining them produces new estimators. We present the case for the new estimator, ˆ S1,3, derived from the association of two of the original estimators, ˆ S1 and ˆ S3, to estimate S(0). This produces an estimate based on the history of net infection rate, I′(t), from time 0 to t. By assuming parameters from the literature for the spread of COVID-19 in Wuhan, we run numerical simulations starting with an infection rate I′(t) and adding filtered Gaussian noise. Discretization produces inaccuracy in bias and variance, however ˆ S1 and ˆ S3 yield accurate figures for S(t), despite noise contamination. ˆ S1,3 also yields accurate figures for S(0), with improvements as more observations are accumulated. We plan to investigate other novel estimators and further study their performance with real-world data.
On the zero-trust intranet certification problem
(2024-03) Badenhorst, Danielle P; Barbour, Graham D; McDonald, Andre M; Gertenbach, Wian P; Buckinjohn, Ethan
Securing corporate networks and ensuring the trustworthiness of network resources are critical security concerns for organisations in today's interconnected digital landscape. The zero-trust security model is an approach to designing and implementing ICT systems which prescribes that clients and servers cannot be trusted automatically, even when connected to networks traditionally considered trusted. The implementation of the zero-trust model within the corporate intranet requires a secure method to verify the identity of local servers. On the Internet, trust in the identity of public servers is established by well-known public Certificate Authorities (CAs), which issue digital certificates to securely identify servers. However, local intranet servers exist within the internal address space of the network. Consequently, it is impossible to naturally obtain digital certificates for these servers, validly signed by a public CA, without publicly disclosing sensitive information such as intranet server Domain Name System (DNS) records. This leaves organisations with the option of relying on endpoint management systems to install custom CA root certificates on all corporatre browsers or, in some cases, ignoring the problem altogether. In this paper, we draw on practical experience in the deployment of cybersecurity devices in corporate intranets to formally define the intranet certification problem. We specify five requirements that a solution to this problem must satisfy. We then conduct a comprehensive review of existing candidate solutions and academic research relevant to the intranet certification problem. Specifically, existing ICT systems for public key infrastructure and endpoint management are identified and evaluated with respect to their ability to meet the stated requirements for solving the intranet certification problem, as well as their cost. Our study reveals that solutions that meet the technical and security requirements of the intranet certification problem are beyond the reach of smaller private sector companies and public sector organisations in underdeveloped and emerging economies. The high cost and technical expertise required for their implementation and management render these solutions impractical. Consequently, by relying on servers with self-signed certificates, these entities inadvertently leave their servers susceptible to impersonation, information theft, and unauthorised resource access, thus violating the fundamental principles of the zero-trust model. We conclude that a gap exists for a simple, cost-effective, and easily managed solution to the intranet certification problem.
Practical measurement of Parkinson’s patients gait using simple walker based motion sensing and data analysis
(American Society of Mechanical Engineers (ASME), 2018-02) Aharonson, V; Schlesinger, I; McDonald, Andre M; Dubowsky, S; Korczyn, AD
We present PAMM II, the Personal Aid for Mobility and Monitoring II, an instrumented walker for Parkinson’s Disease (PD) patients’ gait monitoring. The objective of the walker is to aid in the diagnosis and monitoring of PD progression as well as the effects of clinical treatment and rehabilitation. In contrast to existing devices, the walker is a low cost solution that is simple to operate and maintain, requiring no adjustments, special usage instructions or infrastructure. This preliminary study reports on the efficiency, reliability and accuracy of PAMM II when used to evaluate 22 PD patients and 20 control individuals. All subjects walked two prescribed paths while pushing the walker, and their kinematic motion signals were automatically collected by the walker. Feature derivation from the walker’s signals was followed by combinations of two classical feature selection methods and two learning algorithms, with the objective of discriminating PD patients from control subjects. Sensitivity and specificity scores of 91% and 95% were achieved for the first walking protocol, whereas discrimination over the second walking protocol produced sensitivity and specificity scores of 96% and 100%. These preliminary results provide insight as to the usefulness of PAMM II and its data processing algorithms for the assessment of PD patients’ condition.

Browsing by Author "McDonald, Andre M"

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