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For the first time, alternating trilinear decomposition-assisted multivariate curve resolution (ATLD-MCR) was applied to analyse complex gas chromatography–mass spectrometric (GC-MS) data with severe baseline drifts, serious co-elution peaks and slight retention time shifts for the simultaneous identification and quantification of polycyclic aromatic hydrocarbons (PAHs) in aerosols. It was also compared with the classic multivariate curve resolution-alternating least-squares (MCR-ALS) and the GC-MS-based external standard method. In validation samples, average recoveries of five PAHs were within the range from (96.2 ± 6.8)% to (106.5 ± 4.1)% for ATLD-MCR, near to the results of MCR-ALS ((98.0 ± 1.5)% to (106.7 ± 4.3)%). In aerosol samples, the concentrations of pyrene provided by ATLD-MCR were not significantly different from those of MCR-ALS. The other four PAHs including chrysene, benzo[a]anthracene, fluoranthene and benzo[b]fluoranthene were not detected by ATLD-MCR and the GC-MS-based external standard method. The results of figures of merit further demonstrated that ATLD-MCR achieved high sensitivities (8.9 × 10 4 to 1.7 × 10 6 mAU ml µg −1 ) and low limits of detection (0.003 to 0.087 µg ml −1 ), which were better than or similar to MCR-ALS, presenting a great choice to deal with complex GC-MS data for the simultaneous determination of targeted PAHs in aerosols.

We investigate the topic of two-dimensional direction of arrival (2D-DOA) estimation for rectangular array. This paper links angle estimation problem to compressive sensing trilinear model and derives a compressive sensing trilinear model-based angle estimation algorithm which can obtain the paired 2D-DOA estimation. The proposed algorithm not only requires no spectral peak searching but also has better angle estimation performance than estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. Furthermore, the proposed algorithm has close angle estimation performance to trilinear decomposition. The proposed algorithm can be regarded as a combination of trilinear model and compressive sensing theory, and it brings much lower computational complexity and much smaller demand for storage capacity. Numerical simulations present the effectiveness of our approach.

A new receptor model based on the alternating trilinear decomposition followed by a score matrix reconstruction (ATLD-SMR) was developed for the source apportionment of urban PM10 for the first time. First, simulated three-way data arrays of gas chromatography-mass spectrometry (GC-MS) were used to verify the feasibility of the ATLD-SMR method. Then, PM10 samples (receptor) at five locations and TSP samples of ten pollution sources were collected during July and August, 2018 in Loudi City, China. The collected samples were measured by GC-MS. PAHs were used as tracers and their concentrations were accurately obtained by the ATLD-SMR analysis of GC-MS data of these samples after the problems of GC-MS including baseline drift, retention-time shift and unexpected peaks overlapping were successfully resolved. The highest concentrations of individual PAH in these samples were for phenanthrene and benzo [a] pyrene (40.76 ng m-3 and 39.63 ng m-3 in Liangang steel-making workshop, respectively). Last, a relative contribution matrix of the source to the receptor was estimated by the ATLD-SMR method. The proposed method was employed to apportion the source contributions to PM10 particles at five locations and reasonable results were obtained, thus presenting a promising tool for source apportionment of complex ambient particulate matter.

This paper discusses the blind carrier frequency offset (CFO) estimation for orthogonal frequency division multiplexing (OFDM) systems by utilizing trilinear decomposition and generalized precoding. Firstly, the generalized precoding is employed to obtain multiple covariance matrices which are requisite for the trilinear model, and then a novel CFO estimation algorithm is proposed for the OFDM system. Compared with both the joint diagonalizer and estimation of signal parameters via rotational invariant technique (ESPRIT), the proposed algorithm enjoys a better CFO estimation performance. Furthermore, the proposed algorithm can work well without virtual carriers. Simulation results illustrate the performance of this algorithm.

This paper links the constrained trilinear tensor model into array signal processing. The structure properties of baseband signal, such as the Constant-Modulus (CM) and Finite Alphabet (FA) structures which are already known in the receiving array, are exploited in trilinear decomposition. Two novel algorithms for constrained trilinear decomposition are proposed and applied to array signal processing. The distinguishing features of the proposed model and algorithms compared to the traditional trilinear signal processing methods are: (i) the proposed model has a better performance and lower computation complexity. (ii) it can still work well even if degeneracy of factors are involved in the data model, which is not valid in traditional algorithms. Simulation results are presented to illustrate the application of the constrained trilinear decomposition to array signal processing and evaluate the performance of the proposed algorithms in DOAs estimation.

Indole-3-acetic acid (IAA) is a phytohormone of the auxin group and is capable of coordinating the overall processes of plant growth and development. IAA is active in the very low concentration range. Therefore, it is important to quantify IAA in the low concentration range in complex system. In this work, a new spectrofluorometric method for the direct determination of IAA in soil is proposed and discussed. It combines the fluorescence excitation-emission matrices (EEMs) with second-order calibration methods based on the alternating trilinear decomposition (ATLD) algorithm and the self-weighed alternating trilinear decomposition (SWATLD) algorithm. These methodologies fully exploit the second-order advantage of the three-way fluorescence data, allowing the analyte concentrations to be quantified even in the presence of unknown fluorescent interferents. IAA recoveries in soil were determined as 100.6 +/- 3.0 and 96.9 +/- 1.1% with ATLD and SWATLD, respectively. The limits of detection obtained were 17.6 and 4.6 ng mL(-1), and the limits of quantification were 52.9 and 13.9 ng mL(-1) with ATLD and SWATLD, respectively.

This paper links the two-dimension-spread-spectrum-system source separation problem to the trilinear model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a blind source separation algorithm. The proposed algorithm capitalizes on time-domain spread, frequency-domain spread and temporal diversity-combining. The simulation results reveal that the performance of the blind source separation algorithm for two-dimension spread spectrum system is very close to nonblind minimum mean-squared error method, and this algorithm works well for small sample size. The blind source separation algorithm does not require channel fading information and spread codes, so it has blind and robust characteristics.

This paper links the polarization-sensitive-array signal detection problem to quadrilinear decomposition model. Exploiting this link, it generates a deterministic blind quadrilinear decomposition- based signal detection algorithm, which doesn't require DOA (direction of arrival) and polarization information and has blind and robust characteristics. The proposed algorithm fully utilizes the polarization, spatial and temporal diversity. The simulation results reveal that the performance of blind quadrilinear decomposition-based signal detection algorithm for polarization sensitive uniform square array is close to nonblind MMSE method, and even works better than trilinear decomposition algorithm.

A novel blind Direction of arrival (DOA) and polarization estimation method for polarization-sensitive uniform circular array is investigated in this paper. An analysis of the received signal of the polarization-sensitive uniform circular array shows that the received signal has trilinear model characteristics, and hence trilinear decomposition-based blind DOA and polarization estimation for polarization sensitive uniform circular array is proposed in this paper. Our proposed algorithm has better DOA and polarization estimation performance. Our proposed algorithm can be thought of as a generalization of ESPRIT, and has wider application than ESPRIT method. The useful behavior of the proposed algorithm is verified by simulations.

In this study a new spectrofluorimetric method for the direct determination of metoprolol in human plasma is presented and discussed. It is based on the use of fluorescence excitation-emission matrices (EEMs) and second-order calibration performed with parallel factor analysis (PARAFAC) or alternating trilinear decomposition (ATLD). This methodology enables accurate and reliable discrimination of the analyte signal, even in the presence of unknown and uncalibrated fluorescent component(s), which is often referred to as the second-order advantage. No separation or sample pretreatment steps were required. Satisfactory results were obtained. Metoprolol recoveries in plasma were determined as 87+/-2% and 90+/-4% with PARAFAC and ATLD, respectively. All RSD values of intra- and interday assays were below 5%.

A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. Kruskal has previously shown that the three component matrices involved are essentially unique when the sum of their k-ranks is at least twice the rank of the decomposition plus 2. It was proved that Kruskal's sufficient condition is also necessary when the rank of the decomposition is 2 or 3. If the rank is 4 or higher, the condition is not necessary for uniqueness. However, when the k-ranks of the component matrices equal their ranks, necessity of Kruskal's condition still holds in the rank-4 case. Ten Berge and Sidiropoulos conjectured that Kruskal's condition is necessary for all cases of rank 4 and higher where ranks and k-ranks coincide. In the present paper we show that this conjecture is false. (c) 2004 Elsevier B.V. All rights reserved.

First- and second-order multivariate calibration of fluorescence data have been compared as regards the determination of anti-inflammatories and metabolites in the biological fluids serum and urine. The simultaneous resolution of naproxen-salicylic acid mixtures in serum and naproxen-salicylic acid-salicyluric acid mixtures in urine was accomplished and employed for a discussion of the relative advantages of the applied chemometric tools. The analysis of second-order fluorescence excitation-emission matrices was performed using iteratively reweighted generalized rank annihilation method (IRGRAM), parallel factor analysis (PARAFAC), and self-weighted alternating trilinear decomposition (SWATLD). The results were compared with first-order fluorescence emission data analyzed with partial least-squares regression (PLS). In all cases, the performance of the methods was improved through the formation of inclusion complexes of the analytes with beta-cyclodextrin. The concentration ranges in which the analytes could be determined were as follows: naproxen, 0-250 ng mL(-1) in serum and 0-200 ng mL(-1) in urine; salicylic acid, 0-500 ng mL(-1) in serum and 0-300 ng mL(-1) in urine, and salicyluric acid, 0-300 ng mL(-1) in urine.

Quantitative analysis of p-chlorotoluene in the presence of o-chlorotoluene as an interferent was attempted by using HPLC with diode array detection and second-order calibration methods. An emphasis was placed on a further comparison between two methods, i.e., the traditional parallel factor analysis (PARAFAC) and the alternating trilinear decomposition (ATLD) methods. The following conclusions have been confirmed for the calibration examples tested. PARAFAC does not always converge to chemical meaningful solutions and its convergence rate is slow for the . This seems to be owing to the deficiency of a real trilinear sense in PARAFAC. The convergence rate of the ATLD algorithm is extremely fast. The ATLD-based calibration not only retains the advantage of second-order calibration but can give satisfactory concentration predictions.

A low complexity monostatic cross multiple-in multiple-out (MIMO) radar scheme is proposed in this paper. The minimum-redundancy linear array (MRLA) is introduced in the cross radar to improve the efficiency of the array elements. The two-dimensional direction-of-arrival (DOA) estimation problem links to the trilinear model, which automatically pairs the estimated two-dimensional angles, requiring neither eigenvalue decomposition of received signal covariance matrix nor spectral peak searching. The proposed scheme performs better than the uniform linear arrays (ULA) configuration under the same conditions, and the proposed algorithm has less computational complexity than that of multiple signal classification (MUSIC) algorithm. Simulation results show the effectiveness of our scheme.

A simple, rapid, and sensitive method for the simultaneous determination of vancomycin and cephalexin in human plasma was developed by using HPLC-DAD with second-order calibration algorithms. Instead of a completely chromatographic separation, mathematical separation was performed by using two trilinear decomposition algorithms, that is, PARAFAC-alternative least squares (PARAFAC-ALSs) and self-weight-alternative-trilinear-decomposition- (SWATLD-) coupled high-performance liquid chromatography with DAD detection. The average recoveries attained from PARAFAC-ALS and SWATLD with the factor number of 4 (N=4) were101±5% and102±4% for vancomycin, and96±3% and97±3% for cephalexininde in real human samples, respectively. The statistical comparison between PARAFAC-ALS and SWATLD is demonstrated to be similar. The results indicated that the combination of HPLC-DAD detection with second-order calibration algorithms is a powerful tool to quantify the analytes of interest from overlapped chromatographic profiles for complex analysis of drugs in plasma.

An improved trilinear decomposition algorithm based on a Lagrange operator (LO) is developed in this paper, which introduces a Lagrange operator and penalty terms in the loss function to improve the performance of the algorithm. Compared to the traditional parallel factor (PARAFAC) algorithm, the algorithm not only may converge much faster, but also overcome the sensibility to estimate the number of components. A set of simulated and measured excitation/emission fluorescence data were treated by both the proposed and traditional PARAFAC algorithm to compare their efficiencies. The analytical results obtained with real chemical system containing aspirin and its metabolic products show that the trilinear decomposition methodology is a promising tool to obtain spectral and composition information from mixtures without chemical separation.

In this study, the authors address the problem of angle estimation in a bistatic multiple-input multiple-output (MIMO) radar. This study links the problem to the trilinear model, and then we derive a trilinear decomposition-based angle estimation algorithm, which can obtain automatically paired 2D angle estimation. The proposed algorithm requires no spectral peak searching or pair matching, and it has better angle estimation performance than conventional algorithms such as the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm and the root multiple signal classification (MUSIC) algorithm. Simulation results illustrate performance of the proposed algorithm.

A novel algorithm has been proposed for joint time delay and frequency estimation of sinusoidal signals received at multiple separated sensors. The joint time delay and frequency estimation problem is linked to a trilinear model. Exploiting this link, it derives a trilinear decomposition-based joint time delay and frequency method algorithm. The simulation results reveal that the algorithm performance is close to that of the Cramer-Rao lower bound, and the proposed algorithm even supports small sample sizes.