Multiple delays estimation for chirp signals using structured total least squares

Objectives To solve the problem that the coefficient matrix and the observation vector have structured characteristics for many practical applications in the field of surveying and mapping, that is, the coefficient matrix and the observation vector contain fixed quantities (or even fixed columns) and random quantities, and the random quantities at different positions are linearly related. Methods Starting from the errors-in-variables (EIV) function model, the augmented matrix composed of the coefficient matrix and the observation vector is expressed as an affine function form, and the function model is reconstructed by the variable projection method. Then, a structured total least squares (STLS) estimation algorithm is derived by the Lagrange method. Results The example results show that the proposed algorithm is consistent with the existing weighted or structured total least squares estimation algorithms that can solve structured problem in the coefficient matrix and the observation vector. Compared with the weighted total least squares (WTLS) estimation algorithms, the proposed algorithm only needs to establish a positive definite weight matrix of independent random variables and reduces the number of estimates. Compared with other STLS estimation algorithms, the proposed algorithm takes into account the overall structure of the coefficient matrix and the observation vector. Conclusions This shows the effectiveness of the proposed algorithm. The STLS estimation and the WTLS estimation ensure the statistical optimality from the perspective of the function model and the stochastic model, respectively.

Linear inverse problems with uncertain measurement matrices appear in many different applications. One of the standard techniques for solving such problems is the total least squares (TLS) method. Recently, an alternative approach has been suggested, based on maximizing an appropriate likelihood function assuming that the measurement matrix consists of random Gaussian variables. We refer to this technique as the total maximum likelihood (TML) method. Here we extend this strategy to the case in which the measurement matrix is structured so that the perturbations are not arbitrary but rather follow a fixed pattern. The resulting estimate is referred to as the structured TML (STML). As we show, the STML can be viewed as a regularized version of the structured TLS (STLS) approach in which the regularization consists of a logarithmic penalty. In contrast to the STLS solution, the STML always exists. Furthermore, its performance in practice tends to be superior to that of the STLS and competitive to other regularized solvers, as we illustrate via several examples. We also consider a few interesting special cases in which the STML can be computed efficiently either by reducing it into a one-dimensional problem regardless of the problem size or by a decomposition via a discrete Fourier transform.

ABSTRACTThe present work deals with the optimal placement of piezoelectric actuators on a thin plate using modified control matrix and singular value decomposition (MCSVD) approach. The MCSVD is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with MHGA (modified heuristic genetic algorithm). Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions to suppress first specified modes using LQR (linear quadratic regulator) controller. It is observed that the positions of patches obtained with this approach give greater vibration suppression, reduced computational requirements, and provide global optimum solution only.

Parameter estimation of chirp signals based on fractional Fourier transform

Time delay estimation of a noise-like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar/sonar applications. A new method is presented to analyze the mean-square error performance of delay estimation schemes based on a modified (improved) version of the Ziv-Zakai lower bound (ZZLB). This technique is shown to yield the tightest results on the attainable system performance for a wide range of signal-to-noise ratio (SNR) conditions. For delay estimation using narrow-band (ambiguity-prone) signals, the fundamental result of this study is illustrated in Fig. 3. The entire domain of SNR is divided into several disjoint segments indicating several distinct modes of operation. If the available SNR does not exceed SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation. As a result, the attainable mean-square error <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{\epsilon}^{2}</tex> is bounded only by the a priori parameter domain. If SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> < SNR < SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> , the modified ZZLB coincides with the Barankin bound. In this regime differential delay observations are subject to ambiguities. If SNR > SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> the modified ZZLB coincides with the Cramer-Rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved. The transition from the ambiguity-dominated mode of operation to the ambiguity-free mode of operation starts at SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and ends at SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> . This is the threshold phenomenon in time delay estimation. The various deflection points SNR <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> and the various segments of the bound (Fig. 3) are given as functions of such important system parameters as time-bandwidth product (WT), signal bandwidth to center frequency ratio (W/ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> ) and the number of half wavelengths of the signal center frequency contained in the spacing between receivers. With this information the composite bound illustrated in Fig. 3 provides the most complete characterization of the attainable system performance under any prespecified SNR conditions.

The intake system in an automotive engine has a short duct compared with that of the exhaust system. The filtered-x LMS (FX-LMS) algorithm has been applied to the active noise control (ANC) system in a short acoustic duct. This algorithm design is based on the FIR (finite impulse response) filter; however, it has a slow convergence issue due to a large number of zero coefficients. To improve the convergence performance, the step size of the LMS algorithm was modified from fixed to variable. However, this algorithm is still not suitable for the ANC system of a short acoustic duct because the reference signal is affected by the backward acoustic wave propagated from a secondary source. Therefore, the recursive filtered-u LMS algorithm (FU-LMS) based on the infinite impulse response (IIR) is developed to consider backward acoustic propagation. Generally, this algorithm has a stability problem. The stability issue was improved using an error-smoothing filter. In this paper, the recursive LMS algorithm with a variable step size and smoothing error filter is designed. This recursive LMS algorithm, the FU-VSSLMS algorithm, uses an IIR filter. With fast convergence and good stability, this algorithm is suitable for the ANC system in a short acoustic duct, such as the intake system of an automotive engine. This algorithm is applied to the ANC system of a short acoustic duct. The disturbance signals used as primary noise source are a sinusoidal signal embedded in white noise and the chirp signal, which has a variable instantaneous frequency. The test results demonstrate that the FU-VSSLMS algorithm has a superior convergence performance when compared with the FX-LMS and FX-LMS algorithms. The algorithm can be successfully applied to the ANC system in a short duct, such as the intake duct.

Positron emission tomography (PET) imaging studies have shown that amyloid beta (Aβ) is significantly correlated with glucose metabolism in mild cognitive impairment independently of the apolipoprotein E (APOE) ε4 genotype. We used a singular value decomposition (SVD) approach to pairwise cross-correlation among tau, Aβ, and fluorodeoxyglucose PET images. The resulting SVD-based tau and Aβ scores as well as the APOE ε4 genotype, were entered as predictors in a voxelwise general linear model for statistical assessment of their effect on FDG. We found cortical regions where a reduced glucose metabolism was maximally correlated with distributed patterns of tau, accounting for the effect of Aβ and APOE ε4 genotype. By highlighting the more significant role of tau, rather than Aβ, in the reduction of glucose metabolism, our results provide a better understanding of their combined effect in the development and progression of Alzheimer's disease. This study uses a data-driven singular value decomposition approach to the cross-correlation matrix between tau and fluorodeoxyglucose (FDG) images, as well as between FDG and amyloid beta (Aβ) positron emission tomography (PET) images. From a population of mild cognitive impairment subjects, we found that spatially distributed scores of tau PET are associated with an even stronger reduction of glucose metabolism, independent of the apolipoprotein E ε4 genotype and confounded by Aβ. By highlighting the more significant role of tau, rather than Aβ, on the reduction of glucose metabolism, our results provide a better understanding of their combined effects in the development of Alzheimer's disease.

Image enhancement and reconstruction is an important field of research in digital image analysis. To increase the quality of low-contrast images, a variety of image-enhancing technologies are available. Among these image enhancement techniques, singular value decomposition and discrete wavelet transform are the popular approaches for enhancing low-quality images. In this study, we have developed a modified singular value decomposition approach to enhance low-contrast and low-resolution close-circuit television images. Low-quality and low-resolution images with singular values near zero are used as input in the proposed approach. On the selected data, a threshold value was determined in the singular values of the diagonal matrix. Finally, the proposed modified singular value decomposition technique was applied to enhance the value of images with low quality and resolution. The datasets include 90 facial images of different individuals with low quality and resolution from a university database. The performance of the proposed approach is assessed using image entropy, peak signal to noise ratio, mean square error, contrast measurement and time computation. During the experiments performed on the obtained dataset, it was found that the proposed modified singular value decomposition approach outperformed the existing singular value decomposition, discrete wavelet transform-singular value decomposition and stationary wavelet transform methods.

Pure normal mode test, a routine ground vibration test (GVT) for large aircrafts, needs many shakers. When conducting such test for a pure mode, two major problems remain unsolved: One is how to determine the best shaker number; another is how to determine the best distribution of the shakers after shaker number is determined. This paper will answer these two important questions. When one mode is to be excited, the number of the shakers and the corresponding locations of shakers can be determined by a singular value decomposition approach, an algorithm proposed in this paper. The force appropriation can also be solved by SVD method with FRF matrix. The force appropriation effect is quantified by two indexes, the pure index and effective index. And the complete FRF matrix can be constructed by modal parameters of initial modal test or FEM. At the first section of this paper, the pure normal mode test theory development is reviewed. At the end, a simulation example is given to help understanding the new theory.

The Fractional Fourier Transform (FrFT) is a useful tool that has many applications, such as interference mitigation for communications and radar target echo separation. In this paper, we present a new use, which is estimating an unknown multipath channel, by sending a short chirp signal through the channel. The multiple received chirps in multipath are rotated to the proper FrFT dimension where they become high power tones, whose amplitudes and delays are easily estimated by determining which values in the rotated spectrum exceed a given threshold $\gamma$, which is also easily computed. These are then mapped back to the original time domain. This method is enabled because of the nature of the FrFT and its ability to pull signals, especially chirp signals, out of noise. We present the signal and multipath model, and then describe how the FrFT is used to obtain the channel estimates. Through simulations, we show that this is a very accurate method, providing root mean-square error (RMSE) estimates of both channel coefficients and delays at least an order magnitude below that of existing methods, even at signal-to-noise ratios (SNRs) as low as 0dB. It is also very low in complexity, because all coefficient amplitude and delays are estimated simultaneously with few computations; it therefore offers a promising channel estimation solution for existing and future terrestrial communications systems, including 4G/5G cellular systems requiring high data rate applications.

In most of biomedical signal processing applications the presence of interference signals is inevitable. Processing of lung sounds is not an exemption. In this case the heart sounds are unavoidable and sometimes a severe disturbing noise source. Previous studies indicated that the performance of any interference cancellation scheme relies strongly on an adequate time delay estimation between the reference and the primary signals. Here, a new procedure for time delay estimation using the multi-resolution framework is presented. The proposed methodology possesses such key benefits as the multiple looks information of a signal at different bands, robustness in presence of noise and a validation procedure for the delay estimates. The procedure is applicable to a broad range of problems where time delay estimation is required. Results obtained with lung sounds show the promise of the scheme for the time delay estimation and subsequent interference cancellation.

High-speed skip gliding targets have become a new threat to national defense due to its high speed and large maneuverability. The trajectories of these targets have skip gliding characteristics, which cause serious model mismatch and reduce the trajectory estimation accuracy. Considering the trajectory estimation of skip gliding targets, an aerodynamic parameter recognition method is proposed based on LSTM to solve the model mismatch problem in trajectory estimation. First, the dynamic model of the targets is given, and the aerodynamic labels are defined by analyzing the recognition requirements. Then, considering the skip gliding characteristics of the targets, LSTM-based aerodynamic recognition networks are designed and trained by the available trajectory data. Finally, the aerodynamic recognition results and effect on trajectory estimation are analyzed in typical scenarios. Simulation results show that the proposed method can accurately recognize aerodynamic parameters and suppress the model mismatch, which improve the accuracy and dynamic performance of trajectory estimation.

The use of non-invasive skin accelerometers placed over the extrathoracic trachea has been proposed in the literature for measuring vocal function. Glottal airflow is estimated using inverse filtering or Bayesian techniques based on a subglottal impedance-based model when utilizing these sensors. However, deviations in glottal airflow estimates can arise due to sensor positioning and model mismatch, and addressing them requires a significant computational load. In this paper, we utilize system identification techniques to obtain a low order state-space representation of the subglottal impedance-based model. We then employ the resulting low order model in a Kalman smoother to estimate the glottal airflow. Our proposed approach reduces the model order by 94% and requires only 1.5% of the computing time compared to previous Bayesian methods in the literature, while achieving slightly better accuracy when correcting for glottal airflow deviations. Additionally, our Kalman smoother approach provides a measure of uncertainty in the airflow estimate, which is valuable when measurements are taken under different conditions. With its comparable accuracy in signal estimation and reduced computational load, the proposed approach has the potential for real-time estimation of glottal airflow and its associated uncertainty in wearable voice ambulatory monitors using neck-surface acceleration.

Microwave interferometer is one of the devices for measuring the movement travel– –varying or time-varying velocity of projectile in bore. Microwave interferometer first obtains the Doppler echo signal including the motion information of the projectile in bore, then the velocity is measured based on instantaneous frequency estimation (IFE) of the processed and transformed signal. The parametric time-frequency analysis method can make spectral energy of nonlinear frequency modulation (FM) signal concentrate at some range in the new transform domain. As the motion echo signal of projectile in bore (MSPB) is a nonlinear FM signal, it could be described by polynomial chirplet, one of polynomial FM signal modes, which is used to construct transform kernel for the signal. In this paper, Polynomial chirplet transform (PCT) method is proposed to analyze the simulation and experiment echo signals of projectile in bore. The estimation error and Renyi entropy are used to measure quantify of the time-frequency distribution. Compared with short-time Fourier transform (STFT) method and Wigner-Ville distribution (WVD) method, our results show that the PCT method has most powerful anti-interference performance and highest accuracy of instantaneous frequency estimation for the simulation signal, and lowest Renyi entropy of the instantaneous frequency estimation for the experiment signal. In general, the PCT method has powerful anti-interference performance and high time-frequency concentration and accuracy of instantaneous frequency estimation for the motion echo signal of projectile in bore.

The paper addresses the problem of estimating the chirp signals embedded in Gaussian noise. The proposed method is based on a model of the signal phase as a polynomial. This approach offers the opportunity to represent these signals by an adequate state space model and to apply standard Kalman filtering procedures in view to estimate the parameters of chirp signals. Procedure simulations were made on linear chirp sinusoids with time-varying amplitude and are consistent with the theoretical approach. The paper presents the most important results.