Tracking multiple targets in MIMO radar via adaptive asymmetric joint diagonalization with deflation

In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.

Online blind source separation based on joint diagonalization

A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation （BSS） for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.

Estimation of 2-D Angles of Arrival Based on Joint Diagonalization of Two Spatio-Temporal Correlation Matrices

In this paper, we propose a two-dimensional （2-D） angles of arrival （AOAs） estimation method based on a joint diagonalization of two spatio-temporal （ST） correlation matrices. The mathematical manipulations proposed in this paper take the structure of the array that enable estimating 2-D AOAs simultaneously without 2-D searching or pairing. The performance comparison shows that the proposed method is better than ST-DOA matrix method.

2-D DOAs estimation in impulsive noise environments using joint diagonalization fractional lower-order spatio-temporal matrices

A novel joint diagonalization fractional lower-order spatio-temporal （ST） moments DOA matrix method is proposed to estimate the 2-D DOAs of uncorrelated narrowband signals in the presence of impulsive noise. The new method retains the advantage of the original ST-DOA matrix method which can estimate 2-D DOAs with neither peak searching nor pair matching. Moreover, it can handle sources with common 1-D angles. Simulation results show that the proposed method yields to better performance to restrain the strong impulsive noise than ST-DOA matrix method, especially for low signal-to-noise ratio case.

Joint diagonalization DOA matrix method

A novel joint diagonalization （DOA） matrix method is proposed to estimate the two-dimensional （2-D） DOAs of uncorrelated narrowband signals. The method constructs three subarrays by exploiting the special structure of the array, thereby obtaining the 2-D DOAs of the array based on joint diagonalization directly with neither peak search nor pair matching. The new method can handle sources with common 1-D angles. Simulation results show the effectiveness of the method.

Gradient Search Non-Orthogonal Approximate Joint Diagonalization Algorithm

The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. This paper describes a relative gradient non-orthogonal approximate joint diagonalization （AJD） algorithm based on a non-least squares AJD criterion and a special AJD using a non-square diagonalizing matrix and an AJD method for ill-conditioned matrices. Simulation results demonstrate the better performance of the relative gradient AJD algorithm compared with the conventional least squares （LS） criteria based gradient-type AJD algorithms. The algorithm is attractive for practical applications since it is simple and efficient.

Descriptors for DNA Sequences Based on Joint Diagonalization of Their Feature Matrices from Dinucleotide Physicochemical Properties

Numerical characterizations of DNA sequence can facilitate analysis of similar sequences. To visualize and compare different DNA sequences in less space, a novel descriptors extraction approach was proposed for numerical characterizations and similarity analysis of sequences. Initially, a transformation method was introduced to represent each DNA sequence with dinucleotide physicochemical property matrix. Then, based on the approximate joint diagonalization theory, an eigenvalue vector was extracted from each DNA sequence,which could be considered as descriptor of the DNA sequence. Moreover, similarity analyses were performed by calculating the pair-wise distances among the obtained eigenvalue vectors. The results show that the proposed approach can capture more sequence information, and can jointly analyze the information contained in all involved multiple sequences, rather than separately, whose effectiveness was demonstrated intuitively by constructing a dendrogram for the 15 beta-globin gene sequences.

Independent component analysis to physical-layer network coding over wireless fading channels

A new combinational technology is proposed,which is feasible to apply physical-layer network coding（PNC） to wireless fading channels by employing the harmful interference strategically.The key step of PNC is that sources broadcast signals simultaneously without orthogonal scheduling.Naturally,the signals overlap in the free space at the receivers.Since the signals from different sources are mutual independent,rooted on this rational assumption,an enhanced joint diagonalization separation named altering row diagonalization（ARD） algorithm is exploited to separate these signals by maximizing the cost function measuring independence among them.This ARD PNC（APNC） methodology provides an innovative way to implement signal-level network coding at the presence of interference and without any priori information about channels in fading environments.In conclusions,the proposed APNC performs well with higher bandwidth utility and lower error rate.

Identification of indoor multi-component pollution gas aliasing peak based on JADE

Monitoring indoor harmful gas can obtain the infrared spectra of mixed harmful gases.Since the absorption bands of mixed gases overlap and their qualitative and quantitative analyses are not easy,feature extraction method based on joint approximative diagonalization of eigenmatrix（JADE）is proposed.By fully mining the hidden information of original data and analyzing higher-order statistics information of the data,each substance spectrum in the mixed gas can be accurately distinguished.In addition,a multi-dimensional data quantitative analysis model of the extracted independent source is established by using support vector machine（SVM）based on regular theory.The experimental results show that the correlation coefficients of the components of mixed gases is above 0.999 1by quantitative analysis,which verifies the accuracy of this feature extraction method.