Subspace Fitting Method Research Articles

Self-Position Determination Based on Array Signal Subspace Fitting under Multipath Environments

A vehicle’s position can be estimated with array receiving signal data without the help of satellite navigation. However, traditional array self-position determination methods are faced with the risk of failure under multipath environments. To deal with this problem, an array signal subspace fitting method is proposed for suppressing the multipath effect. Firstly, all signal incidence angles are estimated with enhanced spatial smoothing and root multiple signal classification (Root-MUSIC). Then, non-line-of-sight (NLOS) components are distinguished from multipath signals using a K-means clustering algorithm. Finally, the signal subspace fitting (SSF) function with a P matrix is established to reduce the NLOS components in multipath signals. Meanwhile, based on the initial clustering estimation, the search area can be significantly reduced, which can lead to less computational complexity. Compared with the C-matrix, oblique projection, initial signal fitting (ISF), multiple signal classification (MUSIC) and signal subspace fitting (SSF), the simulated experiments indicate that the proposed method has better NLOS component suppression performance, less computational complexity and more accurate positioning precision. A numerical analysis shows that the complexity of the proposed method has been reduced by at least 7.64dB. A cumulative distribution function (CDF) analysis demonstrates that the estimation accuracy of the proposed method is increased by 3.10dB compared with the clustering algorithm and 11.77dB compared with MUSIC, ISF and SSF under multipath environments.

Robust DOA Estimation in Satellite Systems in Presence of Coherent Signals Subject to Low SNR

Signal source number detection is an essential issue for the direction of arrival (DOA) estimation in satellite communication systems. The performances of conventional and deep-learning-based signal source number detection methods will deteriorate when the signal-to-noise ratio is low or coherent signals exist. This paper proposes a DOA detection network (DTN) combined with the root weighted subspace fitting (root-WSF) method to tackle this challenge. The DTN uses the constructed deep neural networks (DNN) to denoise the received signals and captures the nonlinear mapping relationship between the received signals and the number of signal sources. The received signals in the complex-valued domain are directly treated as DTN’s input, and the label of DTN is the one-hot encoding of the source number. It solves the issue that the classifier cannot well-handle the coherent signals and extends the values of discrete features to Euclidean space. Accordingly, the trained DTN can detect the signal source numbers with an average detection accuracy of 96.6%, and the root-WSF algorithm is applied as the rear stage of DOA estimation. Compared with the traditional DOA methods, the proposed DTN incorporated with the root-WSF algorithm features superior robustness, high DOA estimation accuracy, and enhanced resolution.

Computationally efficient DOA estimation for coprime linear array: a successive signal subspace fitting algorithm

ABSTRACT In this paper, direction of arrival (DOA) estimation of multiple signals with coprime array is investigated and signal subspace fitting (SSF) method is linked to the coprime array, which achieves a better DOA estimation performance than the traditional uniform array. While the SSF method requires expensive computational cost in the case of multiple signals due to the multidimensional global angular searching, we propose a successive SSF (S-SSF) algorithm from a computationally efficient perspective. In the proposed algorithm, we employ rotational invariance and coprime property to obtain the initial estimates. Then, via a successive scheme, we transform the traditional multidimensional global angular searching problem into one-dimensional partial angular searching one. Consequently, the computational complexity has been significantly reduced. Specifically, the proposed S-SSF algorithm can obtain almost the same DOA estimation performance as SSF but with remarkably lower complexity. Finally, Cramer-Rao Bound (CRB) is provided and numerical simulations demonstrate the effectiveness of the proposed algorithm.

Millimeter Wave Channel Estimation Based on Subspace Fitting

We consider the channel estimation of millimeter wave (mmWave) multiple-input multiple-output systems, where both the transmitter and receiver adopt hybrid beamforming structure. Due to the spatial sparsity of the mmWave channel, it can be reconstructed by estimating the direction and gain of the paths. Leveraging this feature, we propose a channel estimation algorithm based on subspace fitting to estimate the path directions, and the path gains are obtained using the least squares method. However, similar to the most existing mmWave channel estimation schemes, the proposed algorithm requires a two-dimensional search in candidate angle space, which is very complicated. In order to reduce the computational complexity, we develop a low-complexity channel estimation algorithm using the orthogonal matching pursuit (OMP) method, which significantly reduces the computational complexity. However, when the paths are strongly correlated, the channel estimation accuracy will decrease. To overcome this defect, we further develop a low-complexity method based on subspace fitting. This algorithm makes a trade-off between the computational complexity and channel estimation accuracy. Furthermore, the pilot beam pattern for different hybrid beamforming structure is designed using infinitely and quantized phase shifters to improve the signal-to-noise ratio of the pilot signals. In addition, the proposed channel estimation methods can also be used in the multi-user scenario. Simulation results demonstrate that the proposed subspace fitting method outperforms the existing methods when the angular resolution is the same. Meanwhile, the low-complexity OMP and subspace fitting methods have a good performance in single path scenario when compared to subspace fitting method, even if the computation complexity is lower. Moreover, the performance of the low-complexity subspace fitting method is close to the subspace fitting method.

Direct Localization of Multiple Stationary Narrowband Sources Based on Angle and Doppler

Direct position determination (DPD) is a single-step method that directly localizes transmitters from sensor outputs without estimating intermediate parameters. With a moving array, DPDs are usually performed by implicitly using only angle information. This letter proposes a DPD algorithm for multiple stationary transmitters by exploiting location information embedded in angles and Doppler shifts. We fit all signal subspaces with the space-time steering vectors at all positions of the moving array using the weighted subspace fitting method, and then perform an alternating projection procedure to directly localize transmitters. The simulation results corroborate the good localization performance of the proposed algorithm.

Analysis of weighted subspace fitting and subspace-based eigenvector techniques for frequency estimation for the coherent Doppler lidar.

Since the periodogram maximum (PM) algorithm fails to provide consistent estimates, more robust techniques are developed, especially in a low signal-to-noise ratio (SNR) regime. The methods are formulated in a subspace fitting-based framework, such as the eigenvector (EV) method and the proposed weighted subspace fitting (WSF) method by introducing an optimal weighting matrix, which exploits the low-rank properties of the covariance matrix of the coherent Doppler lidar echo data. Simulation results reveal that the number of the reliable estimates by the WSF method is more than the other two methods, and the standard deviation is the smallest. Furthermore, the predicted best-fit Gaussian model for the probability density function of the estimates has a narrower spectral width than that of PM and EV methods. Experimental results also validate the simulation results, which show that the WSF approach outperforms the PM and EV algorithms in the furthest detectable range. The proposed method improves the detection range approximately up to 14.2% and 26.6% when compared to the EV method and the PM method, respectively. In conclusion, the proposed method can reduce the statistical uncertainties and enhance the accuracy in wind estimation specifically for a low SNR regime.

Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the interference parameters. The conventional multidimensional optimization problem reduces, thanks to this relaxation, to a simple spectral search. Following this principle, we propose estimators based on the Deterministic Maximum Likelihood, Weighted Subspace Fitting and covariance fitting methods. To calculate the pseudo-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that the performance of the proposed estimators is superior to the conventional methods especially in the case of low Signal-to-Noise-Ratio and low number of snapshots, irrespectively of any specific structure of the sensor array while maintaining a comparable computational cost as MUSIC.

DOA Estimation of Noncircular Signal Based on Sparse Representation

In this paper, we propose a novel method employing subspace fitting principle for DOA estimation of noncircular signal based on the sparse representation technology. The proposed method combines the signal information contained in both the covariance and elliptic covariance matrix of the received data matrix. We use the eigenvalue decomposition of the extended covariance to obtain the signal eigenvectors, and represent the steering vector on overcomplete basis subject to sparse constraint in subspace fitting method. After casting multiple dimensional optimization problem of the classical subspace fitting method as a sparse reconstruction problem, we use L1-norm penalty for sparsity, and optimization by the second order cone programming framework to obtain the DOA estimates. The proposed method can be used in arbitrary array configuration. Compared with the existing algorithms, the simulation results show that the proposed method has better performance in low SNR. Compared with L1-SVD, the proposed method also own better resolution probability.

Weighted Subspace Fitting DOA Estimation Based on Shuffled Frog Leaping Algorithm

In this paper, shuffled frog leaping algorithm (SFLA) is used to reduce the computation load of weighted subspace fitting (WSF) method for DOA estimation. As a recently proposed meta-heuristic algorithm, SFLA is suitable to solve the nonlinear multimodal optimization problem which WSF method encounters, so it offers an excellent alternative to the conventional methods in WSF-DOA estimation. Thus, the feasibility of SFLA applying to WSF-DOA estimation is analyzed, and its performance is compared with other popular meta-heuristic methods. Simulation results demonstrate that the proposed method is more efficient in computation and statistical performance.

Vibratory diagnosis by finite element model updating and operational modal analysis

In this paper, a subspace fitting method is proposed to update, in the time domain, the finite element model of a rotating machine. The procedure is achieved by minimizing an error norm, leading to the comparison between experimental and theoretical observability matrices. Experimental observability matrix is obtained through a MOESP subspace identification algorithm, by projecting the output signal onto some appropriate subspaces, resulting in a cancellation of input excitations and noises. The theoretical observability matrix is obtained from modal parameters of a finite element model of the structure. The minimization procedure is carried out through a Gauss-Newton algorithm. The method is applied to determine the foundation stiffness of an experimental rotating machine subject to a random noise.

DOA Estimation of Temporally and Spatially Correlated Narrowband Noncircular Sources in Spatially Correlated White Noise

The main contribution of our work consists in developing for the first time a method of estimating the direction of arrival (DOA) parameters assuming noncircular and temporally and spatially correlated signals. This new approach, based on a significant enhancement of the two-sided instrumental variable signal subspace fitting (IV-SSF) method, outperforms its classical version in terms of lower bias and error variance. Moreover, it will be shown that our new method is statistically more efficient than the MODE method especially in the case of partly and fully coherent signals where only the extended and the classical two-sided IV-SSF methods are applicable. We also derive an explicit expression for the stochastic Cramér-Rao bound (CRB) of the DOA estimates from temporally and spatially correlated signals generated from noncircular sources. The new CRB is compared to those of circular temporally correlated and noncircular independent and identically distributed signals to show that the CRB obtained assuming both noncircular sources and temporally correlated signals is lower than the CRBs derived considering only one of these two assumptions. This illustrates the potential gain that both noncircularity and temporal correlation provide when considered together. It will also be proven that the difference between the three CRBs increases with the number of snapshots. However, as the signal-to-noise ratio (SNR) increases, the CRBs merge together and decrease linearly. Moreover, at low SNR values it will be shown that temporal correlation is more informative about the unknown DOA parameters than noncircularity. Finally, the CRB derived assuming noncircular and temporally correlated signals depends on the noncircularity rate, the circularity phase separation, and the DOA separation.

A Simplified Subspace Fitting Method for Estimating Shape of a Towed Array

Although the existing array shape estimation methods using reference sources demonstrate good performance, most of the methods require at least two reference sources 2RS in known locations and the reference sources must be in far field. This communication proposes a simplified subspace fitting method that uses only a single reference source 1RS. In the proposed method, the horizontal and vertical positions of each sensor are modeled by applying fixed intersensor spacing and sensor angles, so that the unknown parameters of the cost function are reduced. Furthermore, the Cramer-Rao lower bound (CRLB) is investigated for the proposed method. The results of the numerical experiments indicate that the proposed method is practical for estimating the shape of a towed array.

Wideband Signal DOA Estimation Based on Modified Quantum Genetic Algorithm

A new wideband signal DOA estimation algorithm based on modified quantum genetic algorithm (MQGA) is proposed in the presence of the errors and the mutual coupling between array elements. In the algorithm, the narrowband signal subspace fitting method is generalized to wideband signal DOA finding according to the character of space spectrum of wideband signal, and so the rule function is constructed. Then, the solutions is encoded onto chromosomes as a string of binary sequence, the variable quantum rotation angle is defined according to the distribution of optimization solutions. Finally, we use the MQGA algorithm to solve the nonlinear global azimuths optimization problem, and get optimization azimuths by fitness values. The computer simulation results illustrated that the new algorithm have good estimation performance.

Computationally Efficient Method of Signal Subspace Fitting for Direction-of-Arrival Estimation

It is interesting to resolve coherent signals impinging upon a linear sensor array with low computational complexity in array signal processing. In this paper, a computationally efficient method of signal subspace fitting (SSF) for direction-of-arrival (DOA) estimation is develped, based on the multi-stage wiener filter (MSWF). To find the new signal subspace, the proposed method only needs to compute the matched filters in the forward recursion of the MSWF, does not involve the estimate of an array covariance matrix or any eigendecomposition, thus implying that the proposed method is computationally efficient. Numerical results show that the proposed method provides the comparable estimation accuracy with the classical weighted subspace fitting (WSP) method for uncorrelated signals at reasonably high SNR and reasonably large samples, and surpasses the latter for coherent signals in the case of low SNR and small samples. When SNR is low and the samples are small, the proposed method is less accurate than the classical WSF method for uncorrelated signals. This drawback is balanced by the computational advantage of the proposed method.

Estimation of Multiple Coherent Source Locations by Using SPM Method Combined with Signal Subspace Fitting Technique

A visualization method of coherent source locations based on the Sampled Pattern Matching (SPM) method is described. Modified SPM method is proposed to improve the S/N, in which the measurement of the electric field distribution is repeated in appropriate time duration and eigenvalue decomposition of the covariance matrix is introduced. A combination of the modified SPM method with the Weighted Subspace Fitting (WSF) method is also proposed to estimate accurate source locations. A calibration technique by using a reference antenna to compensate the complex pattern of the receiving antenna is proposed. Experimental investigation to estimate source location for one dipole antenna and two dipole antennas is also made to demonstrate the validity of the proposed method.

Generalization of the Subspace-Based Array Shape Estimations

This work describes a nonplane wave signal model for array shape estimation in ocean environments. Though existing array shape estimation methods, which utilize reference sources, show good performance in the environment where plane wave assumption is satisfied, their performances are degraded significantly in more realistic nonplane wave situation. The proposed subspace-based array shape estimation method, which generalizes the conventional subspace fitting method, works very well for both plane wave and nonplane wave environments. The Cramer-Rao lower bound is investigated to analyze the theoretical lower bound of the variance of the estimation. The simulation results indicate that the proposed method correctly estimates the shape of perturbed array regardless of reference source location.

Beamspace iterative quadratic WSF for DOA estimation

This article presents a beamspace version of the class of polynomial parameterized weighted subspace fitting (WSF) methods, including the well-known methods iterative quadratic maximum likelihood and method of direction estimation, for direction-of-arrival estimation with a uniform linear array. The difficulty with beamspace operation is that the Vandermonde structure of the array manifold may not preserve during a beamspace transformation. We tackle this obstacle using discrete Fourier transform beams and derive a parameterized polynomial representation of the signal subspace in the beamspace dimension. The resulting beamspace iterative quadratic WSF algorithm is not only computationally attractive, but also enjoys improved resolution threshold over element-space estimation.

A Semidefinite Programming Approach to ARMA Estimation

A method for estimation of scalar ARMA models is proposed. In a first step the AR polynomial is estimated using a novel subspace fitting method. By using the estimated AR polynomial to filter the original data the MA polynomial is determined via an MA-covariance fitting method. Both estimation steps are formulated as quadratic optimization problems with LMI constraints which guarantee valid ARMA solutions and are solved as semidefinite programs.

Performance study of a class of cyclic weighted subspace fitting methods

Based on the idea of weighted subspace fitting and the asymptotic statistic characteristics of cyclic correlation matrices, the performance study of a class of cyclic weighted subspace fitting methods for direction estimation of cyclostationary signals is performed, and the analytic expressions of asymptotic variances of these methods are also given.

Weighted subspace fitting for general array error models

Model error sensitivity is an issue common to all high-resolution direction-of-arrival estimators. Much attention has been directed to the design of algorithms for minimum variance estimation taking only finite sample errors into account. Approaches to reduce the sensitivity due to array calibration errors have also appeared in the literature. Herein, one such approach is adopted that assumes that the errors due to finite samples and model errors are of comparable size. A weighted subspace fitting method for very general array perturbation models is derived. This method provides minimum variance estimates under the assumption that the prior distribution of the perturbation model is known. Interestingly, the method reduces to the WSF (MODE) estimator if no model errors are present. Vice versa, assuming that model errors dominate, the method specializes to the corresponding "model-errors-only subspace fitting method." Unlike previous techniques for model errors, the estimator can be implemented using a two-step procedure if the nominal array is uniform and linear, and it is also consistent even if the signals are fully correlated. The paper also contains a large sample analysis of one of the alternative methods, namely, MAPprox. It is shown that MAPprox also provides minimum variance estimates under reasonable assumptions.