Deterministic Maximum Likelihood Estimator Research Articles

Expectation-maximization type algorithms for direction of arrival estimation in unknown nonuniform noise

The expectation–maximization (EM) algorithm updates all of the parameter estimates simultaneously, which is not applicable to direction of arrival (DOA) estimation in unknown nonuniform noise. In this work, we present several computationally efficient EM-type algorithms, which update the parameter estimates sequentially, for solving both the deterministic and stochastic maximum–likelihood (ML) direction finding problems in unknown nonuniform noise. Specifically, we design a generalized EM (GEM) algorithm and a space-alternating generalized EM (SAGE) algorithm for computing the deterministic ML estimator. Simulation results show that the SAGE algorithm outperforms the GEM algorithm. Moreover, we design two SAGE algorithms for computing the stochastic ML estimator, in which the first updates the DOA estimates simultaneously while the second updates the DOA estimates sequentially. Simulation results show that the second SAGE algorithm outperforms the first one.

A method of Robust low-angle target height and compound reflection coefficient joint estimation

It is always a challenging issue for radar systems to estimate the height of a low-angle target in the multipath propagation environment. The highly deterministic maximum likelihood estimator has a high accuracy, but the errors of the ground reflection coefficient and the reflecting surface height have serious influence on the method. In this paper, a robust estimation method with less computation burden is proposed based on the compound reflection coefficient multipath model for low-angle targets. The compound reflection coefficient is estimated from the received data of the array and then a one-dimension generalized steering vector is constructed to estimate the target height. The algorithm is robust to the reflecting surface height error and the ground reflection coefficient error. Finally, the experiment and simulation results demonstrate the validity of the proposed method.

Direction-of-Arrival Estimation With ULA: A Spatial Annihilating Filter Reconstruction Perspective

Direction-of-arrival (DOA) estimation under low signal-to-noise ratio (SNR) and snapshot deficient scenarios has practical application value. Since the array output of the uniform linear array (ULA) can be viewed as a linear combination of the equal interval sampling complex exponentials, it can be annihilated by a spatial annihilating filter and the DOAs are able to be obtained from the filter coefficients. To reconstruct the spatial annihilating filter, a multiple measurement vectors structured total least norm approach is used under the structured total least squares framework, along with a spatial fast Fourier transform based initialization method. It is proved that the new method is equivalent to the deterministic maximum likelihood estimator of DOA. It can resolve up to $M-1$ sources using $M$ -element ULA and is capable of both incoherent and coherent signals. Numerical results show that the proposed method surpasses the representative methods largely in resolution and estimation performance under the low SNR, snapshot deficient, and closely spaced signals scenarios.

Low-complexity DOA estimation from short data snapshots for ULA systems using the annihilating filter technique

This paper addresses the problem of DOA estimation using uniform linear array (ULA) antenna configurations. We propose a new low-cost method of multiple DOA estimation from very short data snapshots. The new estimator is based on the annihilating filter (AF) technique. It is non-data-aided (NDA) and does not impinge therefore on the whole throughput of the system. The noise components are assumed temporally and spatially white across the receiving antenna elements. The transmitted signals are also temporally and spatially white across the transmitting sources. The new method is compared in performance to the Cramér-Rao lower bound (CRLB), the root-MUSIC algorithm, the deterministic maximum likelihood estimator and another Bayesian method developed precisely for the single snapshot case. Simulations show that the new estimator performs well over a wide SNR range. Prominently, the main advantage of the new AF-based method is that it succeeds in accurately estimating the DOAs from short data snapshots and even from a single snapshot outperforming by far the state-of-the-art techniques both in DOA estimation accuracy and computational cost.

Bayesian approach to the inverse problem in a light scattering application

In this article, static light scattering (SLS) measurements are processed to estimate the particle size distribution of particle systems incorporating prior information obtained from an alternative experimental technique: scanning electron microscopy (SEM). For this purpose we propose two Bayesian schemes (one parametric and another non-parametric) to solve the stated light scattering problem and take advantage of the obtained results to summarize some features of the Bayesian approach within the context of inverse problems. The features presented in this article include the improvement of the results when some useful prior information from an alternative experiment is considered instead of a non-informative prior as it occurs in a deterministic maximum likelihood estimation. This improvement will be shown in terms of accuracy and precision in the corresponding results and also in terms of minimizing the effect of multiple minima by including significant information in the optimization. Both Bayesian schemes are implemented using Markov Chain Monte Carlo methods. They have been developed on the basis of the Metropolis–Hastings (MH) algorithm using Matlab® and are tested with the analysis of simulated and experimental examples of concentrated and semi-concentrated particles. In the simulated examples, SLS measurements were generated using a rigorous model, while the inversion stage was solved using an approximate model in both schemes and also using the rigorous model in the parametric scheme. Priors from SEM micrographs were also simulated and experimented, where the simulated ones were obtained using a Monte Carlo routine. In addition to the presentation of these features of the Bayesian approach, some other topics will be discussed, such as regularization and some implementation issues of the proposed schemes, among which we remark the selection of the parameters used in the MH algorithm.

InSAR 고도계의 높이 및 각도 추정에 대한 모의실험

본 논문에선 Interferometric Synthetic Aperture Radar(InSAR) 고도계의 측정값인 거리와 도래각(Angle of Arrival: AOA)을 실제 수치 표고 자료(Degital Elevation Model: DEM)상에서 모의실험하여 얻었다. 이 때 거리 측정값을 얻기 위해서 필요한 원시 데이터 및 압축 데이터의 결과도 나타냈다. 도래각은 안테나 간의 위상 차이로부터 Deterministic Maximum Likelihood Estimator(DMLE)를 사용하여 구했다. 거리 빈(range bin)의 크기와 펄스 반복 주기(PRI: Pulse Repetition Interval)가 실제 수치 표고 자료의 셀 크기에 비해 작기 때문에 모의실험에 적합하지 않다. 따라서 본 논문에서는 선형 보간법을 이용하여 해상도가 높은 수치 표고 자료를 생성하여 모의실험하였다. 서론 부분에서 InSAR 고도계를 소개하였고, 고도와 각도를 구하는 방법에 대해서 설명하였으며, 모의실험 부분에서 위에 소개된 방법의 성능을 보였다. We present a simulation study of an algorithm for the range and angle of arrival(AOA) estimation with an interferometric synthetic aperture radar(InSAR) altimeter using a real digital elevation model(DEM). We also illustrate a step-by-step procedure of generating raw InSAR data, as well as their range and azimuth compressed data, which is to be used for the subsequent altitude and angle estimation. The AOA is estimated using a deterministic maximum likelihood estimator(DMLE) applied to the first arrived point for each pulse in the compressed data obtained with three antennas. The range bin size and the pulse repetition interval(PRI) are much smaller than the cell size of the DEM used in this study. To make the DEM compatible to the radar parameters, we first generate a higher resolution DEM by linearly interpolating the given DEM. After a brief description of the principle of the InSAR altimeter, the algorithms for altitude and angle estimation are presented, and their performance is assessed through simulation.

Single snapshot DOA estimation

Abstract. In array signal processing, direction of arrival (DOA) estimation has been studied for decades. Many algorithms have been proposed and their performance has been studied thoroughly. Yet, most of these works are focused on the asymptotic case of a large number of snapshots. In automotive radar applications like driver assistance systems, however, only a small number of snapshots of the radar sensor array or, in the worst case, a single snapshot is available for DOA estimation. In this paper, we investigate and compare different DOA estimators with respect to their single snapshot performance. The main focus is on the estimation accuracy and the angular resolution in multi-target scenarios including difficult situations like correlated targets and large target power differences. We will show that some algorithms lose their ability to resolve targets or do not work properly at all. Other sophisticated algorithms do not show a superior performance as expected. It turns out that the deterministic maximum likelihood estimator is a good choice under these hard conditions.

Optimization of array geometry for direction-of-arrival estimation using a priori information

Abstract. This paper focuses on the estimation of the direction-of-arrival (DOA) of signals impinging on a sensor array. A novel method of array geometry optimization is presented that improves the DOA estimation performance compared to the standard uniform linear array (ULA) with half wavelength element spacing. Typically, array optimization only affects the beam pattern of a specific steering direction. In this work, the proposed objective function incorporates, on the one hand, a priori knowledge about the signal's DOA in terms of a probability density function. By this means, the array can be adjusted to external conditions. On the other hand, a modified beam pattern expression that is valid for all possible signal directions is taken into account. By controlling the side lobe level and the beam width of this new function, DOA ambiguities, which lead to large DOA estimation errors, can be avoided. In addition, the DOA fine error variance is minimized. Using a globally convergent evolution strategy, the geometry optimization provides array geometries that significantly outperform the standard ULA with respect to DOA estimation performance. To show the quality of the algorithm, four optimum geometries are presented. Their DOA mean squared error is evaluated using the well known deterministic Maximum Likelihood estimator and compared to the standard ULA and theoretical lower bounds.

Complexity reduction in the parametric estimation of superimposed signal replicas

The estimation of the delays and angles of arrival of several superimposed signal replicas requires a high computational burden, which is reduced in practice by employing sub-optimal estimators or by exploiting a specific structure of the problem. In this paper, we propose to reduce the computational burden by looking beforehand for a data representation of small size, which is obtained from an a priori distribution of the parameters. This distribution, being different to the distribution of the parameters in the estimation problem itself, summarises the information about their range of variation. The data reduction can be regarded as the result of applying a Karhunen–Loève expansion. Focusing on the delay parameterisation, we show how this data reduction can be performed efficiently. We present the adaptation of the TLS-ESPRIT algorithm for delay estimation, and of the deterministic Maximum Likelihood estimator to this data reduction. In order to calculate the latter estimator, we discuss the application of Newton-type methods.

Spatial filtering of superimposed convolutional coded signals

In this paper, a method for simultaneously demodulating and estimating the parameters of a number of convolutional coded communication signals incident on an antenna array is presented. The method has the potential to increase the throughput of current multiple-access channel systems, e.g., satellite communications and digital mobile cellular phones, by using an antenna array. The contribution of this paper is the use of sequence estimation combined jointly with parameter estimation in array processing problems. A hidden Markov-model-based technique, the segmental k-means algorithm, is applied to the problem. This algorithm is an iterative procedure with two steps per iteration. The first step involves computing the most likely state sequence for each of the signals (demodulating the signals) given estimates of the signals' parameters. The second step refines the parameter estimates using the signals' mostly likely state sequence estimates. In the simulations presented, it is shown that a significant improvement in the accuracy of the demodulated signals and in the estimation of the signals' angle of arrivals is obtained when compared to a deterministic maximum likelihood estimation method.

Efficient joint space-time maximum-likelihood estimator

A new formulation of the deterministic maximum-likelihood estimator is derived which uniquely enables two-dimensional FFTs to be employed in the parameter estimation, hence reducing the computation required by several orders of magnitude.