A dynamic programming algorithm for the maximum likelihood localization of multiple sources

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.

Based on TLS-ESPRIT algorithm, this paper proposes a weighted spatial smoothing DOA estimation algorithm to address the problem that the conventional TLS-ESPRIT algorithm will be disabled to estimate the direction of arrival (DOA) in the scenario of coherent sources. The proposed method divides the received signal array into several subarrays with special structural feature. Then, utilizing these subarrays, this paper constructs the new weighted covariance matrix to estimate the DOA based on TLS-ESPRIT. The auto-correlation and cross-correlation information of subarrays in the proposed algorithm is extracted sufficiently, improving the orthogonality between the signal subspace and the noise subspace so that the DOA of coherent sources could be estimated accurately. The simulations show that the proposed algorithm is superior to the conventional spatial smoothing algorithms under different signal to noise ratio (SNR) and snapshot numbers with coherent sources.

We introduce a new conceptually simple and computationally effective solution to the maximum likelihood (ML) direction of arrival (DOA) estimation problem that consists of maximizing the likelihood function (LF) over a set of points derived from the data. Two different data-supported optimization (DSO) based techniques are formulated which use the data-supported grid points obtained by means of ESPRIT-like and root-MUSIC-like methods, respectively. The first technique is shown to be the method of choice in the short sample size case, whereas the second technique is applicable to situations where the number of snapshots is large. We show that the data-supported grid search of the LF provides the performance similar to that achieved by the genetic algorithm (GA), but at a significantly lower computational cost.

An approximate maximum likelihood (ML) method for joint estimation of time delays and directions-of-arrivals (DOAs) for the direct-sequence code-division multiple-access (DS-CDMA) systems over the multipath Rayleigh fading channels is developed. The proposed estimation scheme is developed by modeling the known training sequence of the desired user as the desired signal and the multiple access interference (MAI)-plus-AWGN as unknown colored Gaussian noise uncorrelated with the desired signal. An efficient iterative algorithm for estimating channel parameters (the time delays and DOAs of multipath signals) is proposed to reduce the computational complexity. The algorithm transforms the multi-dimensional maximization problem into two simple one-dimensional (1-D) maximization problems based on an iterative scheme. Analytical and simulation results are presented to illustrate the performance in comparison with the Cramer-Rao bounds (CRBs). It is shown that the proposed algorithm is near-far resistant for both time delay and DOA estimation and little performance loss is observed in comparison with the CRBs at reasonable SNRs.

DOA (direction of arrival) estimation plays a key role in radar and sonar signal processing. Compared with one-dimensional spectral analysis, DOA is more difficult because spatial information is mixed up with temporal information. Temporal coherence between sources usually lowers the performance of high-resolution DOA estimators. To overcome difficulties caused by coherence, some cost in computation or array aperture is often involved. In this paper, a method is presented to reduce the two-dimensional DOA estimation to a problem of one-dimensional frequency analysis. Results of a 15-transducer air sonar experiment demonstrate that the presented approach can resolve both incoherent and coherent signal sources, with resolution and precision equivalent to maximum likelihood and weighted subspace fitting methods.

In this paper, a dynamic programming (DP) algorithm is proposed to compute the maximum a posteriori probability (MAP) estimate of the random location of multiple sources by passive sensor array. Based on the principle of optimality, the multivariate MAP decision problem can be transformed into a multistage one‐dimensional maximization problem. By a recursive computation and backward optimum searching technique, the MAP solution can be obtained. The computational complexity is much less than that of the direct MAP searching method, especially when the number of sensors and/or the number of sources is large. In addition, the DP computation technique is equally applicable both in the case of correlated sources and the case of uncorrelated sources.

This paper addresses the issue of adaptive optimal beamspace transformation in sensor array processing. Assuming a deterministic, parameterized signal model, and spatially colored, but temporally white Gaussian noise and interference, an optimality condition on how to choose the beamspace transformation is derived. This condition ensures that the Cramer-Rao bounds of the parameter estimates are preserved by the transformation. The optimal transformation depends on the unknown array correlation matrix and the directions of arrival. In view of this fact, practical procedures for approximating the optimal transformation are discussed. Simulations that support the theoretical results are included for the case where the source signals are sinusoidal.

ABSTRACTGenetic algorithm (GA)-based direction of arrival (DOA) estimation is proposed using fourth-order cumulants (FOC) and ESPRIT principle which results in Multiple Invariance Cumulant ESPRIT algorithm. In the existing FOC ESPRIT formulations, only one invariance is utilised to estimate DOAs. The unused multiple invariances (MIs) must be exploited simultaneously in order to improve the estimation accuracy. In this paper, a fitness function based on a carefully designed cumulant matrix is developed which incorporates MIs present in the sensor array. Better DOA estimation can be achieved by minimising this fitness function. Moreover, the effectiveness of Newton’s method as well as GA for this optimisation problem has been illustrated. Simulation results show that the proposed algorithm provides improved estimation accuracy compared to existing algorithms, especially in the case of low SNR, less number of snapshots, closely spaced sources and high signal and noise correlation. Moreover, it is observed that the optimisation using Newton’s method is more likely to converge to false local optima resulting in erroneous results. However, GA-based optimisation has been found attractive due to its global optimisation capability.

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.

In this paper, the direction of arrival (DOA) and adaptive antenna array beamforming for the smart antenna applications are realized by using Minimum Variance Distortionless Response (MVDR) algorithm of DOA estimation. The MVDR supported by joint approximate diagonalization of eigenmatrices (JADE) algorithm is used to estimate the direction of arrivals of coherent signals in non-coherent groups. The generalized steering vectors using JADE algorithm are first estimated, and then the spectrum methods are realized to estimate the DOA of each signal. Root mean square error (RMSE) values are computed in different scenarios for the proposed method as well as JADE-MUSIC and the corresponding results are compared. Although both methods resolved the signals correctly, simulation results show that JADE based MVDR has better performances in the cases of low number of antenna elements and snapshots. The DOAs obtained are then processed using LMS adaptive beamforming algorithm to steer the main lobe of the radiation pattern to desired angles (signals) and the nulls to undesired angles (signals). The simulation results also reveal that adaptive beamforming is successfully done by annihilating the effects of undesired signals significantly.

This paper investigates the localization of multiple near-field narrowband sources with a symmetric uniform linear array, and a new linear prediction approach based on the truncated singular value decomposition (LPATS) is proposed by taking an advantage of the anti-diagonal elements of the noiseless array covariance matrix. However, when the number of array snapshots is not sufficiently large enough, the “saturation behavior” is usually encountered in most of the existing localization methods for the near-field sources, where the estimation errors of the estimated directions-of-arrival (DOAs) and ranges cannot decrease with the signal-to-noise ratio. In this paper, an oblique projection based alternating iterative scheme is presented to improve the accuracy of the estimated location parameters. Furthermore, the statistical analysis of the proposed LPATS is studied, and the asymptotic mean-square-error expressions of the estimation errors are derived for the DOAs and ranges. The effectiveness and the theoretical analysis of the proposed LPATS are verified through numerical examples, and the simulation results show that the LPATS provides good estimation performance for both the DOAs and ranges compared to some existing methods.

Functional delay and sum beamforming for three-dimensional acoustic source identification with solid spherical arrays

Source direction of arrival (DOA) estimation is one of the challenging problems in many applications. Such applications can be seen in wireless communications, radar, radio astronomy, sonar and navigation. The resolution of a source direction of arrival estimation can be enhanced by an array antenna system with innovative signal processing. Super resolution techniques take the advantage of array antenna structures to better process the incoming waves. These techniques also have the capability to identify the direction of multiple targets. This paper investigates performance of the DOA estimation algorithms namely; MUSIC and ESPRIT on the uniform linear array (ULA) in the presence of white noise. The performance of these DOA algorithms for a set of input parameters such as number of snapshots, number of array elements, signal-to-noise ratio are investigated. The simulation results showed that the resolution of the DOA techniques MUSIC and ESPRIT improves as number of snapshots, number of array elements, signal-to-noise ratio and separation angle between the two sources are increased.

The localization of multiple near-field sources in a spatially white Gaussian noise environment is studied. A modified two-dimensional (2-D) version of the multiple signal classification (MUSIC) algorithm is used to localize the signal sources; range and bearing. A global-optimum maximum likelihood searching approach to localize these sources is discussed. It is shown that in the single source situation, the covariances of both the 2-D MUSIC estimator and the maximum likelihood estimator (MLE) approach the Cramer-Rao lower bound as the number of snapshots increases to infinity. In the multiple source situation, it is observed that for a high signal-to-noise ratio (SNR) and a large number of snapshots, the root mean square errors (RMSEs) of both localization techniques are relatively small. However, for low SNR and/or small number of snapshots, the performance of the MLE is much superior that of the modified 2-D MUSIC.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An array antenna system with innovative advanced signal processing can reduce the direction of arrival (DOA) estimation variance. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> This paper presents the DOA estimation by estimation of signal parameters via rotational invariant technique (ESPRIT). Two different array antennas are used in this simulation study. The DOA performance as a function of signal to noise ratio (SNR), number of snapshots and effect of spatial smoothing are discussed in this paper. The position of array antenna elements may deviate from the ideal location. The imprecise element position will increase the DOA estimation variance. Sensitivity analysis due to non-ideal element position is also discussed in this paper.