Spatial Time-frequency Distributions Research Articles

Polarization Direction of Arrival Estimation Using Dual Algorithms Based on Time-Frequency Cross Terms

In radar array signal processing, weak nonstationary polarization signal direction of arrival (DOA) estimation is a challenging and significant issue when both strong and weak nonstationary signals coexist. Time-frequency (T-F) analysis is an effective method to deal with nonstationary signals. In the last decade, spatial time-frequency distributions (STFDs) have been proposed for multiple dual-polarization antenna arrays and efficaciously used for nonstationary signal DOA estimation. In this article, we introduced a novelty means for estimating weak nonstationary polarization signal DOA by utilizing spatial polarimetric time-frequency distributions (SPTFDs) of cross terms when there are strong nonstationary polarization interference signals and additive Gaussian white noise. The cross terms’ SPTFDs are considered via a replaceability matrix for data covariance in multiple signal classification (MUSIC) and the estimation of signal parameters using the rotational invariance technique (ESPRIT). Combining the STFDs of cross terms with polarization information about weak nonstationary signals improves signal DOA estimation accuracy. The combined MUSIC and ESPRIT are used in the algorithm to further ensure the success probability and accuracy of DOA estimation. Through simulation analyses, the proposed algorithm is more suitable for the required application scenarios than other algorithms and is superior to other algorithms.

Parameter Estimation of Frequency-Hopping Signal in UCA Based on Deep Learning and Spatial Time–Frequency Distribution

The parameter estimation and sorting of frequency-hopping (FH) signals are of great importance in both civilian and military applications. In this article, the estimation of hopping time, hopping period, hopping frequency, instantaneous bandwidth, and 2-D direction of arrival (2-D-DOA) of multiple FH signals in the uniform circular array (UCA) is studied. First, a novel lightweight model based on You Only Look Once (YOLO), named FH-GYOLO, is proposed to detect FH signals and estimate their time–frequency (TF) parameters. The proposed FH-GYOLO takes advantage of the ghost module, which can significantly reduce the computational cost and, simultaneously, achieve an efficient detection with high performance. Then, the 2-D-DOA estimation method of FH signals in UCA is proposed with the spatial TF distribution (STFD). In the proposed method, the steering vector of UCA and the STFD matrix are transformed into beamspace by beamspace transformation, and the closed-form solution is derived for the estimation of autopaired elevation and azimuth angles without the computationally expensive spatial–spectral search. Furthermore, in the proposed method, an iterative compensation process is developed, which can greatly improve the accuracy of DOA estimation without significantly increasing the computational complexity. Extensive simulation results and analysis demonstrated that the proposed algorithms exhibit better or similar performance than the other benchmark methods, and most importantly, the computational cost is substantially reduced.

Polarimetric Direction of Arrival Estimations Based on Adaptive Linear Time-Frequency Transforms

A spatially polarized time-frequency distribution (SPTFD) based on dual-polarized double-fed antenna arrays is adapted to deal with polarization-unstable signals. A linear time-frequency (TF) representation was used for an instantaneous frequency (IF) estimate, primarily due to its simplicity and immunity to cross-interference. Using a set of linear TF transformations using Gaussian windows and Fourier oscillation kernels, the IF estimated window widths of multiple unstable signals are obtained. This paper introduces a new method for estimating the direction of arrival (DOA) of polarized waves using adaptive linear time-frequency transforms. In this paper, a narrowband far-field point source on the receiving array is analyzed. The source signal is split into two orthogonally polarized components. The optimal window is determined by the first derivative of the IF; for this purpose, we take a simple algorithm for solving the derivative and optimize it. In developing TF-adaptive and fully automatic TF display technology, the first method is to use the time-adaptive window for minimizing the IF estimate mean square error (MSE) sum at each moment, while the second procedure is to adjust according to time and frequency and minimize estimate MSE sum at each position in the TF region. Due to its combination with signal polarization, the spatial time-frequency distribution (STFD) gains more freedom and thus perfects the phonon space estimation of noise and signal. On the SPTFD platform, polarized time-frequency multiple signal classification (PTF-MUSIC) is used for the estimation of signal direction of arrival, which outperforms conventional time-frequency MUSIC. Using the example of a synthesized signal, this method outperforms conventional techniques in DOA estimation.

Direction of Arrival Estimation by Combining Robust Spatial Time–Frequency Distributions and Spatial Filtering

Direction of Arrival Estimation by Combining Robust Spatial Time–Frequency Distributions and Spatial Filtering

DOA estimation of LFM signal based on Krylov subspace method

Direction of arrival estimation of LFM signal is an essential task in radar, sonar, acoustics and biomedical. In this paper, a short time Fourier transform multi-step knowledge aided iterative generalized minimum residual (STFT-MS-KAI-GMRES) approach is presented to amend the angle measurement of this signal. A three stage algorithm is proposed. First, the process is initiated with formulating an estimation algorithm for the carrier frequency and chirp rate, followed by calculation of STFT of the output of array element; this yields a spatial time–frequency distribution matrix. Next, the Krylov subspace-based estimation algorithm is formulated in the presence of MS-KAI-ESPRIT algorithm. If the number of antennas increases, the accuracy of the algorithm will increase, but we will incur more communication costs. Results are presented showing attainment of the CRLB by STFT-MS-KAI-GMRES the for an adequately large signal to noise ratio. An important feature of the method presented in the current study is the low computational complexity that has higher suitability for practical applications.

Multi-condition identification in milling Ti-6Al-4V thin-walled parts based on sensor fusion

Chatter and tool wear always coexist during the milling of Ti-6Al-4V thin-walled parts, while the boundary characteristics, time-varying, modal coupling, and position dependence characteristics in milling thin-walled parts lead to the variable spatial time–frequency distribution of the signal features related to milling conditions. As a result, the existing milling monitoring methods can only identify single chatter or tool wear while ignoring another condition. Therefore, in order to identify the chatter and tool wear simultaneously, a multi-condition identification method based on sensor fusion is proposed by fusing multi-source heterogeneous data with different spatial time–frequency distributions. Multi-sensor features of the milling process are extracted from sound, acceleration, and cutting bending moment signals. To reduce the complexity of the original feature dataset, an upgraded principal component analysis (UPCA) algorithm is proposed by screening sensor features in specific frequency bands. Moreover, a new signal feature considering energy proportion is extracted to improve the identification accuracy of multiple conditions. The process parameters are designed according to the stability lobe diagram (SLD) to improve the experimental efficiency. The experimental results show that the proposed method can identify the multi-milling condition composed of chatter and tool wear failure. With the help of UPCA and energy proportion, the computational efficiency is also improved, and the identification accuracy of the proposed method reaches 93.75%, which is much higher than the accuracy of classifiers with traditional data processing methods.

A Passive DOA Estimation Algorithm of Underwater Multipath Signals via Spatial Time-Frequency Distributions

Direction of arrival (DOA) estimation of underwater multipath signals has become an indispensable part of many military and civil applications in the oceanic field. However, DOAs of different paths of the multipath signals may be the same or too close to be separated in space, which brings a great challenge to the DOA estimation of multipath signals. Besides, the number of multipath is generally unknown and time-varying in passive scenarios which generally lead to an underdetermined case. Therefore, it is essential to study an efficient algorithm to realize the underdetermined DOA estimation of underwater multipath signals in passive scenarios. This paper proposes a passive DOA estimation algorithm of underwater multipath signals via spatial time-frequency distributions (STFDs). Firstly, we establish a multipath signals model and utilize the quadratic time-frequency (TF) analysis method to reduce cross-terms while keeping a good resolution. Then, we estimate the number of multipath and introduce a novel multi-ridge detection technique to extract the TF trajectories of multipath signals, which adopts the idea of smoothing forward and backward, and the edge TF point detection strategy. Lastly, we estimate the DOA of each path of the multipath signals separately and realize source association based on the clustering-based method. Simulation results and analysis demonstrate that this algorithm can effectively improve the estimation accuracy of instantaneous frequency (IF) and DOA estimation of underwater multipath signals in underdetermined cases and passive situations.

Time-frequency DOA estimation of chirp signals based on multi-subarray

Spatial time-frequency distribution (STFD) utilizes the spatial time-frequency characteristics of chirp signals and effectively improves the direction of arrival (DOA) estimation performance. However, the existing methods based on the STFD matrix assumed that each source has good time-frequency point selection performance. In practice, the time-frequency point selection accuracy of chirp signals suffers from the signal-to-noise ratio (SNR). Especially in the case of low SNR, the time-frequency point selection error increased, leading to the reduction of the SNR and degradation of the DOA estimation performance in the time-frequency domain. To solve the above problems, we propose a time-frequency DOA estimation method based on multiple subarrays. The array is firstly divided into several overlapping subarrays, and the data received by the array is transformed from the element space into beamspace by using beamforming, which improves the source separation and the SNR. Then, chirp signals possess the ideal energy collection features in the time-frequency domain so that the time-frequency analysis tools are used for separated sources in beamspace to further improve the source separation and the SNR in the time-frequency domain. This results in better time-frequency point selection accuracy of chirp signals at a low SNR regime. Finally, the averaged STFD matrix can be obtained through averaging over multiple single-source time-frequency points in the time-frequency domain, and the DOAs can be obtained by combining with the subspace-based method. The theoretical analysis and simulation results indicate that compared with the existing STFD-based methods, the proposed method in this paper provides good performance on estimation and resolution in cases with low input SNRs due to beamspace processing. Furthermore, in cases where the DOAs between the coherent sources are closely spaced and the snapshot number is low, our proposed method significantly improves the performance of the DOA estimation.

Spatially Smoothed TF-Root-MUSIC for DOA Estimation of Coherent and Non-Stationary Sources Under Noisy Conditions

This paper proposes a method for efficient Direction-of-Arrival (DOA) estimation of coherent and non-stationary sources under adverse noise conditions. The method consists of three main parts: 1) derivation of Spatial Time-Frequency Distribution (STFD) matrix; 2) application of the forward-backward spatial smoothing technique; 3) estimating the angles of arrival by solving for the roots of the polynomial. The key significance of the proposed method is that the combination of existing methods and techniques allows an estimation of DOA angles for both coherent and non-stationary source signals under noise. Whereas the individual use of the existing methods does not show adequate performance under these conditions. The experiments allow studying the performance of the proposed method for 1) both coherent and non-coherent clean sinusoidal signals; 2) noisy non-stationary chirp signals; 3) coherent and non-stationary signals under noise. Furthermore, extensive simulations have been carried out to compute the root mean square error (RMSE) performance of the proposed method in comparison with the existing ones. The experiments have been designed for varying number of microphones, level of noise, and value of the time-frequency threshold. As a result of the experiments, we observe the efficacy of the proposed method in comparison with the conventional Root-MUSIC and Time-Frequency MUSIC (TF-MUSIC) methods.

Robust spatial time-frequency distributions for DOA estimation using spatial averaging and directional smoothing

A new method of computing robust spatial time-frequency distributions (STFDs) for signals received in a uniform linear array is presented. The proposed method adopts a two step procedure to improve the robustness of STFDs. In the first step, improved spatial averaging is performed to suppress cross-terms and noise. In the second step, the adaptive directional smoothing using signal dependent kernel is performed to further improve the robustness of STFDs. Experimental results indicate that the proposed STFD outperforms the conventional STFDs for direction of arrival estimation.

Blind modal estimation using smoothed pseudo Wigner–Ville distribution and density peaks clustering

The determination of the number of active modes is always an obstacle to the identification of dynamic systems. To tackle this issue, a new blind modal estimation method is proposed through which the number of active modes does not need to be presupposed, even in underdetermined blind source separation cases. Firstly, the spatial time–frequency distribution matrices are constituted from the smoothed pseudo Wigner–Ville distribution of acceleration signals. The auto-source time–frequency points that contain modal information about only one mode are selected and then the density peaks clustering algorithm is introduced to identify the mode shape vectors. Finally, one can reconstruct the time–frequency distributions of modal coordinates and estimate the natural frequencies and damping ratios. The method is verified by a numerical study and a vibration experiment. The anti-noise study demonstrates that the method performs well.

Linear Chirp Signal DOA Estimation Using Sparse Time–Frequency Dictionary

This paper is concerned with the estimation of the directions-of-arrival (DOA) of multiple linear chirp signals. We construct a novel time-frequency dictionary based on the properties of chirp signals in the fractional Fourier domain, and a sparse reconstruction algorithm is proposed to achieve high performance. Then, the errors resulting from the off-grid model mismatch is considered, and the dictionary matrix is reformulated into a multiplication of a fixed matrix and a sparse matrix. Further, an iterative alternating approach is proposed to improve the accuracy of the DOA estimates. The proposed algorithm provides better estimation, anti-correlation performances and increased resolution than Multiple Signal Classification (MUSIC) and the time–frequency MUSIC (TF-MUSIC) based on the spatial time–frequency distributions. Simulation results demonstrate the effectiveness of the proposed approach.

DOA estimation of spectrally overlapped LFM signals based on STFT and Hough transform

Traditional subspace methods which are based on the spatial time-frequency distribution (STFD) matrix have been investigated for direction-of-arrival (DOA) estimation of linear frequency modulation (LFM) signals. However, the DOA estimation performance may degrade substantially when multiple LFM signals are spectrally overlapped in time-frequency (TF) domain. In order to solve this problem, this paper proposes single-source TF points selection algorithm based on Hough transform and short-time Fourier transform (STFT). Firstly, the signal intersections in TF domain can be solved based on the Hough transform, and multiple-source TF points around the intersections are removed, so that the single-source TF points set is reserved. Then, based on the Euclidean distance operator, the single-source TF points set belonging to each signal can be obtained according to the property that TF points of the same signal have same eigenvector. Finally, the averaged STFD matrix is constructed for each signal, and DOA estimation is achieved based on multiple signal classification (MUSIC) algorithm. In this way, the proposed algorithm exhibit remarkable superiority in estimation accuracy and angular resolution over the state-of-the-art schemes and can achieve DOA estimation in the underdetermined cases. In addition, the proposed algorithm can still perform DOA estimation when multiple LFM signals intersect at one point. Numerical simulations demonstrate the validity of the proposed method.

Spatial time-frequency distribution of cross term-based direction-of-arrival estimation for weak non-stationary signal

In the radar array signal processing direction of arrival (DOA), the estimation of weak non-stationary signal is an important and difficult problem when both strong and weak signals are coexisting particularly because the weak non-stationary signals are often submerged in noise. In this paper, we proposed a novelty method to estimate the direction of arrival (DOA) of weak non-stationary signal in scenario for strong non-stationary interference signals and Gaussian white noise. The method utilizes spatial time-frequency distribution (STFD) of cross terms rather than suppressing cross terms in time-frequency analysis. The STFD of cross terms are introduced as an alternative matrix, which is similar to data covariance matrix in multiple signal classification (MUSIC), for the DOA estimation of a weak non-stationary signal. The cross-term amplitude of the strong and weak signals is usually above the noise and is easier to use than the auto-term of the weak signal. In the cross term, the information of the weak signal is included, and the auto-term of these weak signals is difficult to extract directly. The ability to incorporate the STFD of cross terms empowers information about a weak non-stationary signal for DOA estimation, leading to improved signal estimates for direction finding. The method based on the STFD of cross terms for DOA estimation of the weak non-stationary signal is revealed to outperform the time-frequency MUSIC and traditional MUSIC algorithm by simulation, respectively. This method has the advantages of the time-frequency direction finding method and also deals with the situation of weak signals. When the strong and weak signals exist at the same time and the two angles are similar, the cross-terms can be used to perform DOA estimation on the weak signal.

Novel direction of arrival estimation using Adaptive Directional Spatial Time-Frequency Distribution

Novel spatial time-frequency distributions and instantaneous frequency estimation scheme are developed for the proposed direction of arrival estimation scheme. A new class of spatial adaptive time-frequency distributions is proposed that are obtained by local optimization of the smoothing kernel for obtaining spatial time-frequency distributions. The instantaneous frequencies of the source signals are estimated using modified Viterbi algorithm that exploits both the spatial diversity (estimated through spatial time-frequency distributions) and continuity of the instantaneous frequency curves for accurate estimation at low Signal-to-Noise-Ratio (SNR) scenarios when the signal components intersect each other in time-frequency domain. In the proposed scheme the estimated instantaneous frequencies are used for the direction of arrival estimation of each source separately, thus results in accurate estimates even in low SNR regime. Experimental results are given that indicate that the proposed direction of arrival estimation algorithm outperforms the traditional directional of arrival estimation schemes.

Robust adaptive beam forming against random calibration error via interference-plus-noise covariance matrix reconstruction

Abstract Adaptive beamformers based on interference-plus-noise covariance matrix reconstruction can extract the signal of interest (SOI) effectively in the condition of precise array manifold, but suffer performance degradation in the presence of array calibration error. In this paper, a novel interference-plus-noise covariance matrix reconstruction and steering vector estimation method is proposed, which is robust against random mismatches. By transforming the received signal into the time-frequency (TF) domain, the proposed method reconstructs the interference-plus-noise covariance matrix and estimates the steering vector of the SOI using the spatial time-frequency distribution (STFD) matrices. Neither the imprecise prior information about the array manifold nor the sample covariance matrix is utilized in the whole procedure, guaranteeing high estimation accuracy and excellent output performance. Simulation results demonstrate that the proposed method outperforms existing adaptive beamformers, and achieves high output signal-to-interference-plus-noise ratio (SINR) close to the optimal one even in the case of large calibration error.

The Algorithm Research of Blind Source Separation Based on Spatial Time-frequency Distribution for FSK Signal

Track circuit is an important guarantees of the railway security, a large number of non-stationary interference and noise induce from the electrified railway block in the process of the FSK signal transmission in the track circuit, seriously affect its testing accuracy and reliability. Aiming at the problem, this paper propose a algorithm of blind source separation (BSS) based on the spatial time-frequency distribution (STFD) and singular value decomposition(SVD). First using SVD on mixed signal to remove noise, then reassign spectrum and pre-white in STFD domain, improve the selection function of single autoterm in STFD matrix, the get unitary matrix by joint diagonal, last estimated out the mixed matrix. The algorithm is not limited with Gaussian source signal, so it has strong applicability. Computer simulation results indicate that the algorithm to effectively separate the non-stationary signals and improve its BSS performance in a low signal-to-noise (SNR) environment.

DOA estimation of LFM signals based on STFT and multiple invariance ESPRIT

In order to improve the angle measurement precision of LFM signals with a low computational complexity, a direction of arrival (DOA) estimation algorithm STFT-MI-ESPRIT is proposed in this paper. The algorithm is based on short time Fourier transform (STFT) and multiple invariance estimation of signal parameters via rotational invariance techniques (MI-ESPRIT). Firstly, the STFT of the array element’s output is calculated and the signals are transformed to the time-frequency domain. Then the spatial time-frequency distribution matrix can be obtained through selecting multiple single-source time-frequency points in the time-frequency plane and the signal subspace can also be obtained using Eigen decomposition. Finally, the multiple rotational invariant equation of the array based on STFT is obtained and the closed-form solution is obtained using the multi-least-squares (MLS) criterion. The simulation results show that the proposed algorithm can improve the estimation precision greatly compared with the traditional ESPRIT-like algorithms and its computational complexity remains the same in general. This paper also proposes that the STFT-MI-ESPRIT algorithm can use partial rotational invariances of the array instead of all the rotational invariances, which can reduce the computational complexity on the basis of ensuring the estimation precision basically. The simulation results verify the effectiveness of the conclusion.

Spatial time-frequency DOA estimation based on joint diagonalization using Jacobi rotation

Direction-of-arrival (DOA) estimation consists of locating closely spaced sources impinging from different directions in the presence of considerable noise or interference. Recently, this problem has been solved using spatial time-frequency distribution (STFD) information that is available in the array signals. In this work, a new joint diagonalization approach based on Jacobi rotation, which can efficiently combine all of the relevant STFD points, is proposed to achieve superior DOA resolutions and suppressed sidelobes in the spatial spectrum. It is discovered that our proposed Jacobi technique leads to a non-orthogonal joint diagonalization structure and can avoid pre-whitening the signal component of the observation. In addition, we further adopt the minimum variance distortionless response (MVDR) processor instead of the MUltiple SIgnal Classification (MUSIC) algorithm to avoid the estimation of the signal subspace and noise subspace in the time-frequency DOA domain. Finally, computer simulations of several frequently encountered types of challenging scenarios (such as low SNR and coherent arrivals) show that significant improvements are achieved by our proposed approach in comparison to the existing techniques.

DOA estimation of closely-spaced and spectrally-overlapped sources using a STFT-based MUSIC algorithm

The multiple signal classification (MUSIC) algorithm based on spatial time-frequency distribution (STFD) has been investigated for direction of arrival (DOA) estimation of closely-spaced sources. However, the limitations of the bilinear time-frequency based MUSIC (TF-MUSIC) algorithm lie in that it suffers from heavy implementation complexity, and its performance strongly depends on appropriate selection of auto-term location of the sources in time-frequency (TF) domain for the formulation of a group of STFD matrices, which is practically difficult especially when the sources are spectrally-overlapped. In order to relax these limitations, this paper aims to develop a novel DOA estimation algorithm. Specifically, we build a MUSIC algorithm based on spatial short-time Fourier transform (STFT), which effectively reduces implementation cost. More importantly, we propose an efficient method to precisely select single-source auto-term location for constructing the STFD matrices of each source. In addition to low complexity, the main advantage of the proposed STFT-MUSIC algorithm compared to some existing ones is that it can better deal with closely-spaced sources whose spectral contents are highly overlapped in TF domain.