This paper proposes a novel approach to handle the singularity problem in the Homotopy algorithm. Following a state-of-art ridge-adding-based method, the authors introduce a random ridge term to each element of the measure matrix to avoid the occurrence of singularities. Then, the authors give the sufficient condition of avoiding singularities, and prove that adding random ridge is greatly useful to deal with the singularity problem, even the random ridge tends to zero. Although the main procedures in the method coincide with the state-of-art method, all the derivations and theoretical analyses are different because of distinct forms of optimisation problems. Thus, this work is by no means a trivial task. Moreover, the authors note that the most computationally expensive step in the proposed method is the inversion of active matrices, whose time complexity relative to that of other required operations is proportional to the active set's cardinality. This motivates us to develop an efficient QR update algorithm based on the new ridge-adding-based method, which is incorporated in Givens QR factorisation and Gaussian elimination. It turns out that, with such new QR update algorithm, the previous ratio of time complexities can be reduced to a constant order. As a consequence, the new method can eliminate the bottleneck of matrix inversion in the improved Homotopy algorithm.

Target detection, tracking and classification are three essential and closely coupled subjects for most surveillance systems. In the finite set statistics (FISST) framework, this paper presents a Bayesian and recursive solution to joint detection, tracking and classification (JDTC) of a manoeuvring target in a cluttered environment, which is inspired by previous work on joint target tracking and classification in the classical Bayesian filter framework. The derived JDTC algorithm exploits the dependence of target state on target class by using class-dependent dynamical model sets. The relative merits of this JDTC algorithm are demonstrated via a two-dimensional example using a sequential Monte Carlo implementation. It is shown that handling those three closely coupled subjects jointly can achieve comparable detection and tracking performance to that of the exact filter in the FISST framework with a prior known class. The classification results are consistent with the previous work.

Snore related signals (SRS) have been found to carry important information about the snore source and obstruction site in the upper airway of an Obstructive Sleep Apnea/Hypopnea Syndrome (OSAHS) patient. An overnight audio recording of an individual subject is the preliminary and essential material for further study and diagnosis. Automatic detection, segmentation and classification of SRS from overnight audio recordings are significant in establishing a personal health database and in researching the area on a large scale. In this study, the authors focused on how to implement this intelligent method by combining acoustic signal processing with machine learning techniques. The authors proposed a systematic solution includes SRS events detection, classifier training, automatic segmentation and classification. An overnight audio recording of a severe OSAHS patient is taken as an example to demonstrate the feasibility of their method. Both the experimental data testing and subjective testing of 25 volunteers (17 males and 8 females) demonstrated that their method could be effective in automatic detection, segmentation and classification of the SRS from original audio recordings.

In this paper, an entropy-constrained vector quantiser (ECVQ) scheme with finite memory, called finite-state ECVQ (FS-ECVQ), is presented. This scheme consists of a finite-state vector quantiser (FSVQ) and multiple component ECVQs. By utilising the FSVQ, the inter-frame dependencies within source sequence can be effectively exploited and no side information needs to be transmitted. By employing the ECVQs, the total memory requirements of FS-ECVQ can be efficiently decreased while the coding performance is improved. An FS-ECVQ, designed for the modified discrete cosine transform coefficients coding, was implemented and evaluated based on the unified speech and audio coding (USAC) scheme. Results showed that the FS-ECVQ achieved reduction of the total memory requirements by 92.3%, compared with the encoder in USAC working draft 6 (WD6), and over 10%, compared with the encoder in USAC final version (FINAL), while maintaining coding performance similar to FINAL, which was about 4% better than that of WD6.

This study addresses the sensor scheduling problem of selecting and assigning sensors dynamically for multi-target tracking. The authors goal is to trade off the tracking accuracy and the interception risk in a period of time. The interception risk is incurred by the fact that the emission energy originating from a sensor can be intercepted by the target during the tracking mission. To react to sensor emission, the targets are able to switch between dynamic models. This non-myopic sensor scheduling problem is formulated as a partially observable Markov decision process, where the one-step reward is constructed by combining the tracking error with the interception probability and the information state is tracked by the interacting multiple model extended Kalman filtering. A novel sampling approach using the unscented transformation is proposed for long-term reward approximation. Numerical simulations illustrate the validity of the proposed scheduling scheme.

The aim of this paper is to present a non-linear statistical model to fit and forecast the signal-to-interference plus noise ratio (SINR) in two-tier heterogeneous cellular networks which consist of macrocells and femtocells. Since in these networks the number and locations of femtocell base stations (FBS) are variable, SINR forecasting can be useful in some areas such as power control and handover management. So far, linear autoregressive (AR) models have commonly been used in forecasting the received signal strength (rss) in macrocellular networks. However, AR modelling results in high mean square error (MSE) when data are non-linear. This paper focuses on SINR which takes into account signal strength, interference and noise effects. Moreover, macro-femto cellular network is considered. The F-test results show that the SINR data are non-linear, leading to use non-linear models instead of AR model. A non-linear logistic smooth threshold AR (LSTAR) model is utilised to model and forecast the SINR data. Kolmogorov–Smirnov (K-S) test demonstrates that LSTAR provides good fitness to the SINR samples. The results indicate that LSTAR model achieves much better performance in modelling and forecasting of SINR data than the AR model.

In this paper, a distributed estimation algorithm using Bayesian-based forward backward Kalman filter (KF) is proposed for stochastic singular linear systems. The method incorporates generalised versions of KF for bounded cases with complete and incomplete prior information, followed by estimation fusion of these cases. The incorporated filters remain optimal given the cross-covariance of the local estimates. The proposed approach is validated on a coupled-tank system.

In this paper, the authors propose a widely-linear (WL) receiver structure for multiple access interference (MAI) and jamming signal (JS) suppression in direct-sequence code-division multiple-access systems. A vector space projection (VSP) scheme is also considered to cancel the JS before detecting the desired signals. They develop a novel multiple-candidate successive interference cancellation (MC-SIC) scheme which processes two consecutive user symbols at one time to process the unreliable estimates and a number of selected points serve as the feedback candidates for interference cancellation, which is effective for alleviating the effect of error propagation in the successive interference cancellation (SIC) algorithm. WL signal processing is then used to enhance the performance of the receiver in non-circular modulation scheme. By bringing together the techniques mentioned above, a novel interference suppression scheme is proposed which combines the WL MC-SIC minimum-mean-squared error (MMSE) algorithm with the VSP scheme to suppress MAI and JS simultaneously. Simulations for binary phase shift keying modulation scenarios show that the proposed structure achieves a better MAI suppression performance compared with previously reported SIC MMSE receivers at lower complexity and a superior JS suppression performance.

A new method to estimate the Teager energy (TE) is presented here which uses an instantaneous energy expression and the Hilbert–Huang transform (HHT). The energy expression depends on the square of the instantaneous amplitude and digital frequency of the signal. This energy of the signal is estimated from the instantaneous energies of the intrinsic mode functions (IMFs), obtained from the HHT. The energy expression used for the TE ensures that the energy is always positive, and it is in agreement with the energy required to generate a sinusoid. It avoids the limitations in the use of the discrete TE operator (TEO), where for the output of the TEO to be positive and to give energies which match the energy required to generate a sinusoid, the signal must satisfy certain conditions. Numerical study on a data set of neuro-signals shows that these problems persist even when TEO is applied to the IMFs obtained from the empirical mode decomposition of the signal. Such a procedure is used in the Teager–Huang transform. There is a sharp drop in the number of negative values when IMFs are used, but the number is still not zero.

Electrocardiogram (ECG) signals are usually corrupted by baseline wander, power-line interference, muscle noise etc. Numerous methods have been proposed to remove these noises. However, in case of wireless recording of the ECG signal it gets corrupted by the additive white Gaussian noise (AWGN). For the correct diagnosis, removal of AWGN from ECG signals becomes necessary as it affects the diagnostic features. The natural signals exhibit correlation among their samples and this property has been exploited in various signal restoration tasks. Motivated by that, in this study we propose a non-local wavelet transform domain ECG signal denoising method which exploits the correlations among both local and non-local samples of the signal. In the proposed method, the similar blocks of the samples are grouped in a matrix and then denoising is achieved by the shrinkage of its two-dimensional discrete wavelet transform coefficients. The experiments performed on a number of ECG signals show significant quantitative and qualitative improvements in denoising performance over the existing ECG signal denoising methods.

In this paper, the authors provide an analytical expression of the mean square error (MSE) and the bit error rate (BER) lower bound of an orthogonal frequency division multiplexing signal transmission over a multipath Rayleigh channel considering estimation errors. For some pilot arrangements, an interpolation is required to perform the channel estimation. Owing to their low complexity, polynomial based interpolations are usually applied at the receiver, which induces estimation and signal errors. Based on a statistical analysis of these errors, the exact MSE expression of the channel estimation is provided. Furthermore, with a geometrical study of the constellation, an analytical BER limit is derived. For a given channel, it is shown that the errors are perfectly characterised by the interpolation method and the frequency gap between the pilot tones. All the steps of the analytical developments are validated through simulations. The proposed analysis then predicts the performance of the receiver, thus enabling the latter to a priori select the interpolation method with minimum complexity, according to a given channel and a BER target.