Maximum Likelihood Direction Of Arrival Estimation Research Articles

Neural-Network-Based DOA Estimation in the Presence of Non-Gaussian Interference

This work addresses the problem of direction-of-arrival (DOA) estimation in the presence of non-Gaussian, heavy-tailed, and spatially-colored interference. Conventionally, the interference is considered to be Gaussian-distributed and spatially white. However, in practice, this assumption is not guaranteed, which results in degraded DOA estimation performance. Maximum likelihood DOA estimation in the presence of non-Gaussian and spatially colored interference is computationally complex and not practical. Therefore, this work proposes a neural network (NN) based DOA estimation approach for spatial spectrum estimation in multi-source scenarios with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> unknown number of sources in the presence of non-Gaussian spatially-colored interference. The proposed approach utilizes a single NN instance for simultaneous source enumeration and DOA estimation. It is shown via simulations that the proposed approach significantly outperforms conventional and NN-based approaches in terms of probability of resolution, estimation accuracy, and source enumeration accuracy in conditions of low SIR, small sample support, and when the angular separation between the source DOAs and the spatially-colored interference is small.

Maximum likelihood DOA estimation based on improved invasive weed optimization algorithm and application of MEMS vector hydrophone array

&lt;abstract&gt;&lt;p&gt;Direction of arrival (DOA) estimation based on Maximum Likelihood is a common method in array signal processing, with many practical applications, but the huge amount of calculation limits the practical application. To deal with such an Maximum Likelihood (ML) DOA estimation problem, firstly, the DOA estimation model with ML for acoustic vector sensor array is developed, where the optimization standard in various cases can be unified by converting the maximum of objective function to the minimum. Secondly, based on the Invasive Weed Optimization (IWO) method which is a novel biological evolutionary algorithm, a new Improved IWO (IIWO) algorithm for DOA estimation of the acoustic vector sensor array is proposed by using ML estimation. This algorithm simulates weed invasion process for DOA estimation by adjusting the non-linear harmonic exponent of IWO algorithm adaptively. The DOA estimation accuracy has been improved, and the computation of multidimensional nonlinear optimization for the ML method has been greatly reduced in the IIWO algorithm. Finally, compared with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE) method and Tuna Swarm Optimization(TSO) algorithm, numerical simulations show that the proposed algorithm has faster convergence rate, improved accuracy in terms of Root Mean Square Error (RMSE), lower computational complexity and more robust estimation performance for ML DOA estimation. The experiment with tracking the orientation of the motorboat by Microelectronic mechanical systems (MEMS) vector hydrophone array shows the superior performance of proposed IIWO algorithm in engineering application. Therefore, the proposed ML-DOA estimation with IIWO algorithm can take into account both resolution and computation. which can meet the requirements of real-time calculation and estimation accuracy in the actual environment.&lt;/p&gt;&lt;/abstract&gt;

An improved atomic search algorithm for optimization and application in ML DOA estimation of vector hydrophone array

&lt;abstract&gt;&lt;p&gt;The atom search optimization (ASO) algorithm has the characteristics of fewer parameters and better performance than the traditional intelligent optimization algorithms, but it is found that ASO may easily fall into local optimum and its accuracy is not higher. Therefore, based on the idea of speed update in particle swarm optimization (PSO), an improved atomic search optimization (IASO) algorithm is proposed in this paper. Compared with traditional ASO, IASO has a faster convergence speed and higher precision for 23 benchmark functions. IASO algorithm has been successfully applied to maximum likelihood (ML) estimator for the direction of arrival (DOA), under the conditions of the different number of signal sources, different signal-to-noise ratio (SNR) and different population size, the simulation results show that ML estimator with IASO algorithum has faster convergence speed, fewer iterations and lower root mean square error (RMSE) than ML estimator with ASO, sine cosine algorithm (SCA), genetic algorithm (GA) and particle swarm optimization (PSO). Therefore, the proposed algorithm holds great potential for not only guaranteeing the estimation accuracy but also greatly reducing the computational complexity of multidimensional nonlinear optimization of ML estimator.&lt;/p&gt;&lt;/abstract&gt;

Maximum-likelihood direction of arrival estimation under intermittent jamming

Multiple-snapshot maximum-likelihood (ML) direction of arrival (DOA) estimation problem is studied for the intermittent jamming scenario. The intermittent jamming modality is based on the assumption that only a subset of the collected snapshots are contaminated by the jammer while the others are jammer-free; but the receiver does not know which is which. This type of jamming is frequently encountered in practice either inadvertently, say due to the sporadic activity of a non-hostile system; or intentionally, say due to the activity of an adversary sweeping the operational bandwidth of the receiver. Exact maximum likelihood solution for the problem is analytically intractable and an expectation maximization (EM) method based solution is developed for coherent and non-coherent signal models. Coherent signal model assumes that the phase difference between the coefficients of two consecutive snapshots are known a-priori which is an assumption compatible with the Swerling-1/3 target models in the radar signal processing literature. Non-coherent signal model does not have such an assumption and it is suitable for Swerling-2/4 targets. The suggested EM based solution is shown to yield an important estimation accuracy improvement over conventional maximum-likelihood solution which ignores the intermittency of jammer and also over the atomic norm based high resolution estimation techniques. Cramer-Rao type performance lower bounds for the problem is also provided to illustrate the efficacy of the suggested estimator.

DOA Estimation in Heteroscedastic Noise with sparse Bayesian Learning

We consider direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e., source powers), leading to stochastic maximum likelihood (ML) DOA estimation. The DOAs are estimated from multi-snapshot array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots.

High-Order Maximum Likelihood Methods for Direction of Arrival Estimation

It is shown that using high-order statistics (higher than two) is beneficial in subspace-based Direction Of Arrival (DOA) estimation methods. Particularly, the high-order MUltiple SIgnal Classification (MUSIC) method, also known as 2q-MUSIC method, presents more robustness to both modeling error and strong colored background noise, has better resolution, and makes it possible to process more sources with a given array, compared to the second-order MUSIC. Moreover, when the sources are uncorrelated and the number of snapshots is large, MUSIC algorithm is a realization of Maximum Likelihood (ML) DOA estimation method, with much less complexity. However, when the sources are correlated, this less complexity costs a degradation in performance compared to ML method. Besides that, there are several methods including Alternating Projection (AP), gradient ascent, Newton, and Method Of Direction Estimation (MODE), which are used to reduce the complexity of ML method, and keep its good performance. In this paper, we propose a high-order ML DOA estimation method and develop high-order extensions for the reduced complexity ML-based DOA estimation methods. The idea of using higher-order statistics in ML-based methods is novel. This can be a basis for other ML-based high-order methods. Moreover, deriving the required formulas in this paper is different from the related second-order works. Furthermore, the performance of the proposed methods are evaluated and compared. The results are also compared with 2q-MUSIC method through computer simulations. The simulation results show the good performances of the proposed methods, which are obviously better than 2q-MUSIC when the sources are correlated.

2-D DOA Estimation in a Cuboid Array Based on Metaheuristic Algorithms and Maximum Likelihood

This paper proposes to apply the genetic algorithm and the firefly algorithm to enhance the estimation of the direction of arrival (DOA) angle of electromagnetic signals of a smart antenna array. This estimation is essential for beamforming, where the antenna array radiating pattern is steered to provide faster and reliable data transmission with increased coverage. This work proposes using metaheuristics to improve a maximum likelihood DOA estimator for an antenna array arranged in a uniform cuboidal geometry. The DOA estimation performance of the proposed algorithm was compared to that of MUSIC on different two dimensions scenarios. The metaheuristic algorithms present better performance than the well-known MUSIC algorithm.

On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima.

Threshold Region Performance of Multicarrier Maximum Likelihood Direction of Arrival Estimator

This paper addresses the performance characterization of a direction of arrival (DoA) estimator in the low signal-to-noise-ratio (SNR) region. The case of a sensor array simultaneously collecting signals emitted at multiple carrier frequencies by a single source is considered. A maximum likelihood (ML) approach is used as a reference method for DoA estimation and its accuracy is characterized in terms of mean square error (MSE). It is well known that for SNR values included in the so-called threshold region, the DoA estimation accuracy decreases rapidly, due to the presence of outliers. This effect can be possibly mitigated when multiple frequency channels are jointly exploited. However, the capability to predict this performance degradation is fundamental either for assessing the robustness of an existing sensor or for supporting its design. Therefore, the scope of this paper is to introduce appropriate approximations to the MSE of a multifrequency ML DoA estimator in order to provide a reliable characterization of its performance in the threshold region. Two models for the source signals are considered and separately discussed, namely the deterministic (or conditional) and stochastic (or unconditional). An extensive simulated analysis is reported to prove the tightness of the approximations and to characterize the benefits steming from the exploitation of signals emitted at multiple carriers.

Robust estimation of DOA from array data at low SNR

We consider direction of arrival (DOA) estimation for a plane wave hidden in additive circularly symmetric noise at low signal to noise ratio. Starting point is the maximum-likelihood DOA estimator for a deterministic signal carried by a plane wave in noise with a Laplace-like distribution. This leads to the formulation of a DOA estimator based on the Least Absolute Deviation (LAD) criterion. The phase-only beamformer (which ignores the magnitude of the observed array data) turns out to be an approximation to the LAD-based DOA estimator. We show that the phase-only beamformer is a well performing DOA estimator at low SNR for additive homoscedastic and heteroscedastic Gaussian noise, as well as Laplace-like noise. We compare the root mean squared error of several different DOA estimators versus SNR in a simulation study: the conventional beamformer, the phase-only beamformer, and the weighted phase-only beamformer. The simulations indicate that the phase-only DOA estimator has desirable properties when the additive noise deviates from the Laplace-like assumption. The qualitative robustness of these DOA estimators is investigated by comparing the empirical influence functions. Finally, the estimators are applied to passive sonar measurements acquired with a horizontal array in the Baltic Sea.

DOA Estimation in heteroscedastic noise

The paper considers direction of arrival (DOA) estimation from long-term observations in a very noisy environment. The concern is to derive methods obtaining reasonable DOAs at very low SNR. The noise is assumed zero-mean Gaussian and its variance varies in time and space, causing stationary data models to fit poorly over long observation times. Therefore a heteroscedastic Gaussian noise model is introduced where the variance varies across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood (ML) DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. This SBL approach is more flexible and performs better than other high-resolution methods since they cannot estimate the heteroscedastic noise process. An alternative to SBL is simple data normalization, whereby only the phase across the array is utilized. Simulations in noisy environments demonstrate that taking the heteroscedastic noise into account causes the DOA estimation to fail at lower SNR, often at 20 dB lower SNR.

Distributed Maximum Likelihood DOA Estimation Algorithm for Correlated Signals in Wireless Sensor Network

The performance of the existing direction of arrival (DOA) estimation algorithms for source localization in the wireless sensor networks (WSN) degrades when the sources are correlated. The degradation is due to the rank deficiency of the source covariance matrix which is reflected in the high cramer-Rao lower bound (CRLB) for correlated sources. Unlike subspace based techniques, maximum likelihood (ML) based technique does not require any preprocessing technique for DOA estimation of correlated signals. Hence ML technique can be directly applied for WSN with arbitrary array geometry. The DOA estimation accuracy for correlated signals is improved by employing distributed ML approach in this paper. The subarray formed at a particular node which is experiencing highest CRLB can improve its estimation accuracy by receiving better DOA estimates from its neighbors. The corresponding distributed CRLB is derived and found a substantial improvement in the distributed scenario. The distributed CRLB lies between that of local CRLB for the subarray formed at the node and global CRLB for the array formed by all sensors in the WSN. Diffusion quantum particle swarm optimization is used to optimize ML estimator for fully correlated signals as it has only a single parameter for tuning. Simulation results show that the estimation accuracy improves at a node even for correlated signals yielding highest CRLB using distributed approach. The root mean square error at a specific node using distributed algorithm approaches to the derived distributed CRLB.

Application of Bee Evolutionary Genetic Algorithm to Maximum Likelihood Direction-of-Arrival Estimation

The maximum likelihood (ML) method achieves an excellent performance for DOA estimation. However, its computational complexity is too high for a multidimensional nonlinear solution search. To address this issue, an improved bee evolutionary genetic algorithm (IBEGA) is applied to maximize the likelihood function for DOA estimation. First, an opposition-based reinforcement learning method is utilized to achieve a better initial population for the BEGA. Second, an improved arithmetic crossover operator is proposed to improve the global searching performance. The experimental results show that the proposed algorithm can reduce the computational complexity of ML DOA estimation significantly without sacrificing the estimation accuracy.

An Improved Squirrel Search Algorithm for Maximum Likelihood DOA Estimation and Application for MEMS Vector Hydrophone Array

Maximum likelihood (ML) method for direction of arrival (DOA) estimation achieves an excellent performance in array signal processing, but the complexity and computational load of searching the multidimensional nonlinear function prevented it from practical application. Based on squirrel search algorithm (SSA), an improved SSA (ISSA) for ML DOA estimation is proposed in this paper, which can reduces the computational complexity. The idea of spatial variation and diffuse inspired by the invasive weed optimization(IWO) algorithm is applied to ISSA. The simulation experiments compared ISSA with SSA, IWO, seeker optimization algorithm(SOA), sine cosine algorithm (SCA), genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE) method for ML DOA estimator show that the proposed algorithm has faster convergence speed, fewer iterations and lower root mean square error(RMSE) under different number of signal sources, different signal to noise ratio(SNR) and different population size. Therefor the proposed algorithm does not only ensure the estimation accuracy, but also greatly reduce the computation complexity of multidimensional nonlinear optimization for the ML method. Finally, the test experiment using Micro Electronic Mechanical Systems(MEMS) vector hydrophone array in Fenhe lake show the engineering practicability of proposed ML DOA estimator with ISSA.The results obtained will be valuable in the application of engineering.

Iterative marginal maximum likelihood DOD and DOA estimation for MIMO radar in the presence of SIRP clutter

Abstract The spherically invariant random process (SIRP) clutter model is commonly used in scenarios where the radar clutter cannot be correctly modeled as a Gaussian process. In this short communication, we devise a novel Maximum-Likelihood (ML)-based iterative estimator for direction-of-departure and direction-of-arrival estimation in the Multiple-input multiple-output (MIMO) radar context in the presence of SIRP clutter. The proposed estimator employs a stepwise numerical concentration approach w.r.t. the objective function related to the marginal likelihood of the observation data. Our estimator leads to superior performance, as our simulations show, w.r.t. to the existing likelihood based methods, namely, the conventional, the conditional and the joint likelihood based estimators, and w.r.t. the robust subspace decomposition based methods. Finally, interconnections and comparison between the Iterative Marginal ML Estimator (IMMLE), Iterative Joint ML Estimator (IJMLE) and Iterative Conditional ML Estimator (ICdMLE) are provided.

DOA estimation in heteroscedastic noise

The paper considers direction of arrival (DOA) estimation from long-term observations in a noisy environment. In such an environment the noise source might evolve, causing the stationary models to fail. Therefore a heteroscedastic Gaussian noise model is introduced where the variance can vary across observations and sensors. The source amplitudes are assumed independent zero-mean complex Gaussian distributed with unknown variances (i.e. the source powers), inspiring stochastic maximum likelihood DOA estimation. The DOAs of plane waves are estimated from multi-snapshot sensor array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots. This SBL approach is more flexible and performs better than high-resolution methods since they cannot estimate the heteroscedastic noise process. An alternative to SBL is simple data normalization, whereby only the phase across the array is utilized. Simulations demonstrate that taking the heteroscedastic noise into account improves DOA estimation.

A novel ML DOA estimation algorithm for array signal processing

A novel algorithm for finding the optimal solution of nonlinear function in maximum likelihood DOA estimation is proposed to reduce the calculation in multi-dimensional nonlinear search of the estimation. In the proposed method, firstly, the mode of population initialization mode is modified to improve the stability of population evolution. Secondly, the crossover operator is also improved to enlarge the range of new generated individual. Thirdly, parameters adaptive adjustment strategy is designed to accelerate convergence. The simulation shows that the proposed algorithm can greatly reduce the calculation time.

Robust DoA estimation in case of multipath environment for a sense and avoid airborne radar

This paper deals with the sense and avoid problem for an helicopter. The objective of such a system is to early detect collision targets (typically high voltage wires). The Direction of Arrival (DoA) of the target is then a crucial information. In severe multipath environments (flight over a river, for instance) classical DoA estimation schemes dramatically degrade. In this paper, we make use of a method based on the Maximum Likelihood (ML) principle that can resolve two highly correlated and close targets. The major drawback of ML algorithms, namely the computational burden, is removed using an approximation for closely space targets. The contribution of this paper is twofold. We first extend the approximated ML DoA estimation to the case of Non Uniform Linear Antennas (NULA) and we complete the procedure by a detection scheme. Second, we attest the validity of this new processing on real radar data. Hence, we show that the proposed procedure is able to detect a high voltage wire, over a river, at ranges up to 1 km, where a capon beamformer cannot.

Spatial Filtering Based on Differential Spectrum for Improving ML DOA Estimation Performance

Recently, maximum spatial eigenfiltering allowed significant improvements on the estimation performance of maximum likelihood direction-of-arrival (DOA) estimators for closely spaced sources. However, that eigenfilter may greatly attenuate widely spaced sources as SNR decreases, leading to severe performance degradation. Since the differential spectrum shows prominent spectral peaks around the true DOA angles even at very low SNR, we originally propose using it to derive two eigenvalue-based finite-impulse response spatial filters to overcome that problem. The first one employs the frequency sampling approach, whereas the second one includes moving average modeling, to fit the frequency response to the differential spectrum. Both the amount of spectral samples and the filter orders were carefully chosen to control aliasing in time domain and reduce the overall computational effort. The simulation results showed that the proposed filters preserved signal passbands of DOA sources, even where the maximum spatial eigenfilter failed. Compared with that filter, our propositions significantly reduced the threshold SNR for widely spaced sources while performing very similarly for closely spaced sources, at the expense of an small increase in runtime. To the best of our knowledge, the proposed filters are the first to allow spatial filtering in maximum likelihood DOA estimation independently of source separation.

Application of comprehensive learning particle swarm optimisation algorithm for maximum likelihood DOA estimation in wireless sensor networks

Direction of arrival (DOA) estimation is one of the challenging problem in wireless sensor networks. Several methods based on maximum likelihood (ML) criteria have been established in literature. But, the multimodal nature of ML cost function is one of the inherent limitations in ML-DOA estimation technique. Generally, to obtain the likelihood solutions, the DOAs must be estimated by optimising a complicated function over a high-dimensional problem space. Recently particle swarm optimisation (PSO) algorithm is used in MLDOA estimation. To overcome the drawback of premature convergence in PSO, a learning strategy is introduced, and this approach called comprehensive learning particle swarm optimisation (CLPSO), which is applied to this problem and a comparison of results is made between these two. Simulation results confirms that the ML-CLPSO estimator is significantly giving better performance at low signal-to-noise ratio compared to conventional methods like multiple signal classification (MUSIC) and ML-PSO in various scenarios at less computational costs.