This paper focuses on improving 3D sound mapping using acoustic simultaneous localization and mapping (SLAM), angle of arrival (AOA), and time difference of arrival (TDOA). We use quaternion for orientation tracking. Through simulations involving a drone equipped with microphone arrays and an inertial measurement unit (IMU), the paper shows the effective localization of a drone moving in a room and mapping multiple stationary sources in a dynamic environment.

A log-likelihood gridless sparse direction-of-arrival (DOA) estimation is presented. The likelihood fit is optimized using the sample covariance matrix and a reconstructed covariance matrix constrained to a few atoms. This approach enables using Wirtinger gradients for DOA. The sensitivity to local minima is mitigated by initializing with the best DOAs from a gridded DOA method. In simulations, the method achieves the Cramer-Rao bound and offers superior resolution compared to conventional gridless DOA methods.

We propose a data-driven method for direction-of-arrival (DOA) trajectory estimation. We use a deep complex architecture which leverages complex-valued representations to capture both magnitude and phase information in the received sensor array data. The network is designed to output the DOA trajectory parameters and amplitudes of the strongest source. Deviating from conventional methods, which attempt to estimate parameters for all sources simultaneously – leading to assignment ambiguity and the problem of uncertain output dimensions, we adopt a sequential approach. The estimated source signal contribution is subtracted from the input to obtain a residual signal. This residual signal is then fed back into the network to identify the next strongest source and so on, making the proposed network reusable. We evaluate our network on simulated data of varying complexity. Results demonstrate the feasibility of such a reusable network and potential improvements can be explored in future.

This study investigates adversarial attacks on deep learning (DL)-enabled Wi-Fi sensing systems using channel state information (CSI) for privacy. This paper presents a technique to disturb the signal used for channel estimation transmitted from the user device when the classifier is located at the router. We employ generative adversarial imitation learning (GAIL), a deep reinforcement learning method to build adversarial attacks using estimated CSI data without explicit reward function feedback. Our approach does not require the adversary to know the structure or the weights of the network. Our proposed method lowers classifier accuracy to 50% using perturbation signals with an amplitude 1.0 dB lower than those used in the attack scheme based on impractical assumptions.

Representing variable-length and continuous-indexed signals through a linear combination of basis functions poses a fundamental challenge in science and engineering. Current approaches resort to preprocessing steps, such as interpolation and extrapolation, to handle irregular and off-grid measurements, which compromise the physical nature of signals and degrade the representation performance. To address this challenge, rather than utilizing discrete vectors, we introduce a Bayesian functional representation model that capitalizes on the continuous nature and rich expressiveness of Gaussian processes to facilitate interpretable and effective basis function learning. Moreover, an analytical and efficient algorithm based on the variational inference framework is developed. Experimental results using real-life datasets demonstrate the superior performance of our proposed method.

Predicting ocean acoustic fields in shallow water is challenging due to high spatial variability, with depth scales of 100 m and range scales of 1 km. Limited acoustic data further complicates this task. We propose a physics-informed neural network (PINN) with the Helmholtz equation as a physics constraint, enhancing prediction accuracy with scarce data. A preprocessing step using an envelope smoothing technique is introduced. This reduces the spatial field variability, enabling more accurate training of the PINN than purely data-driven approaches. Our method is validated through ocean data, demonstrating substantial improvements in PINN performance for complex ocean acoustic predictions.

We present a sample-efficient Bayesian optimization (BO) method to estimate underwater source localization robust to unknown tilt in a vertical line array. Rather than conducting exhaustive search of parameter space to estimate localization and tilt, BO uses a Gaussian process (GP) surrogate model of the Bartlett power objective function to guide sampling of the parameter space. Samples are suggested using a heuristic acquisition function that uses the GP to balance exploitation and exploration of parameter space. Using experimental data, we show that BO obtains better localization estimates than conventional grid search and quasi-random sampling strategies, and that robustness to array tilt comes with little additional computational cost.

We consider uncertainty quantification (UQ) for multiple DOAs in an acoustic environment. The performance of DOA estimation is affected due to external uncertainty and yet the methods provide no UQ for the DOAs. Conformal prediction obtains statistically valid prediction intervals from an estimation model. First, we assume that a Gaussian mixture model can parameterize the conditional multi-source DOA distribution. Next, we demonstrate the effectiveness of conformal prediction to generate statistical uncertainty intervals from the mixture model outputs. The performance is validated on plane wave data with different sources of uncertainty using statistical metrics.

Gridless direction-of-arrival (DOA) estimation with multiple frequencies can be applied to acoustic source localization. We formulate this as an atomic norm minimization (ANM) problem and derive a regularization-free semi-definite program (SDP) avoiding regularization bias. We also propose a fast SDP program to deal with non-uniform frequency spacing. The DOA is retrieved via irregular Vandermonde decomposition (IVD), and we theoretically guarantee the existence of the IVD. We extend ANM to the multiple measurement vector setting and derive its equivalent regularization-free SDP. For a uniform linear array using multiple frequencies, we can resolve more sources than the sensors. The effectiveness of the proposed framework is demonstrated via numerical experiments.

We propose an approach to fuse multiresolution seismic tomography models with physics-informed probability graphical models (PIPGMs), which consider the physical information (ray-path density). To evaluate the efficacy of the PIPGM fusion method, we use both synthetic checkerboard models and real fault zone structures imaged from 2019 Ridgecrest, CA, earthquake sequence. The proposed method improves the combined models in terms of travel time residual, image quality, and peak signal-to-noise ratio, compared to those obtained by multiple conventional methods. The proposed fusion method can merge any type of gridded multi-resolution velocity model, a valuable tool for computational imaging.

In this study, the modulation of symbols on OFDM subcarriers is classified for transmissions following Wi-Fi 6 and 5G downlink specifications. First, our approach estimates the OFDM symbol duration and cyclic prefix length based on the cyclic autocorrelation function. We propose a feature extraction algorithm characterizing the modulation of OFDM signals, which includes removing the effects of a synchronization error. The obtained feature is converted into a 2D histogram of phase and amplitude and this histogram is taken as input to a convolutional neural network (CNN)-based classifier. The classifier does not require prior knowledge of protocol-specific information such as Wi-Fi preamble or resource allocation of 5G physical channels. The classifier’s performance, evaluated using synthetic and real-world measured over-the-air (OTA) datasets, achieves a minimum accuracy of 97% accuracy with OTA data when SNR is above the value required for data transmission.

In a spoofing attack, an attacker impersonates a legitimate user to access or modify data belonging to the latter. Typical approaches for spoofing detection in the physical layer declare an attack when a change is observed in certain channel features, such as the received signal strength (RSS) measured by spatially distributed receivers. However, since channels change over time, for example due to user movement, such approaches are impractical. To sidestep this limitation, this paper proposes a scheme that combines the decisions of a position-change detector based on a deep neural network to distinguish spoofing from movement. Building upon community detection on graphs, the sequence of received frames is partitioned into subsequences to detect concurrent transmissions from distinct locations. The scheme can be easily deployed in practice since it just involves collecting a small dataset of measurements at a few tens of locations that need not even be computed or recorded. The scheme is evaluated on real data collected for this purpose.

A robust and sparse Direction of Arrival (DOA) estimator is derived for array data that follows a Complex Elliptically Symmetric (CES) distribution with zero-mean and finite second-order moments. The derivation allows to choose the loss function and four loss functions are discussed in detail: the Gauss loss which is the Maximum-Likelihood (ML) loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate t-distribution (MVT) with ν degrees of freedom, as well as Huber and Tyler loss functions. For Gauss loss, the method reduces to Sparse Bayesian Learning (SBL). The root mean square DOA error of the derived estimators is discussed for Gaussian, MVT, and ϵ-contaminated data. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian array data.

Gaussian processes (GP’s) have been used to predict acoustic fields by interpolating under-sampled field observations. Using GP interpolation to predict fields is advantageous because of its ability to denoise measurements and for its prediction of likely field outcomes given a certain field coherence, or in GP terminology, a kernel. While there are many design options for a coherence function, in this study we focus on the radial basis function kernel for estimating the direction-of-arrival (DOA) of a plane wave impinging on a uniform linear array. We demonstrate that an array sampled with spacing larger than a half wavelength can benefit from GP interpolation, providing a smaller root mean squared error in comparison to the error of conventional beamforming for DOA estimation.

The physics-informed neural network (PINN) is able to identify partial differential equation (PDE) coefficients which are constant across the space directly from physical measurements. In this paper, we propose a modification of PINN, named as SD-PINN, which can recover the coefficients in spatially-dependent PDEs using only one neural network without the requirement of domain-specific physical knowledge. The network structure is a simple fully connected neural network, and multiple physical information like the time-invariance and spatial-smoothness of the PDE coefficients is incorporated as loss functions. The method is robust to noise due to introduced physical constraints, which is verified by experiments.

Classification of modulation of Wi-Fi~6 and 5G downlink (DL) user data signals for spectrum sensing is studied. First, the orthogonal frequency division multiplexing (OFDM) symbol duration and cyclic prefix (CP) length are estimated based on the cyclic autocorrelation function (CAF). We propose a feature extraction algorithm characterizing the modulation of OFDM signals based on the estimated parameters. The algorithm includes removing the effects of a synchronization error and converting the obtained feature into a 2D histogram of phase and amplitude. This histogram is input to a convolutional neural network (CNN)-based classifier. Our system works without knowledge of a carrier frequency, Wi-Fi preamble, or resource allocation of 5G physical channels. We evaluate the classifier's performance with data with various protocol-compliant configurations. Our classifier achieves at least 98% accuracy when SNR is above the value required for data transmission.

Application of Deep learning (DL) to modulation classification has shown significant performance improvements. The focus has been model centric, where newer architectures are attempted on benchmark dataset RADIOML.2016.10A (RML16). RML16 is a high impact effort that laid the foundation for generating a synthetic dataset for applying DL models to wireless problems. This encouraged development of newer architectures to RML16. We use a data centric DL approach where focus moves from model architectures to data quality. RML16 has shortcomings such as errors and ad-hoc choices of parameters. We build upon RML16 and provide realistic and correct methodology of generating dataset. A new benchmark dataset RML22 is generated. Going forward, we envision researchers to improve model quality on RML22. We attempt to improve data quality by studying the impact of information sources. Further, the choices of artifacts and signal model parameterization are analyzed carefully. The Python source code used to generate RML22 is shared to enable researchers to further improve dataset quality.

Machine learning (ML) approaches to source localization have demonstrated promising results in addressing reverberation. Even with large data volumes, the number of labels available for supervised learning in such environments is usually small. This challenge has recently been addressed using semi-supervised learning (SSL) based on deep generative modeling with variational autoencoders. A problem with ML approaches is they often ignore the intuitions from conventional signal processing approaches. We present a hybrid approach to ML-based source localization, which uses both SSL and conventional, analytic signal processing approaches to obtain source location estimates. An SSL approach is developed which accounts for the residual between analytic source location estimates true locations. Thus, the approach can exploit both labelled and unlabeled data, as well as analytic source location intuition, to provide better localization than either approach in isolation.1

We propose a data-driven partial differential equation (PDE) identification scheme based on ℓ1-norm minimization which can identify spatially-dependent PDEs from measurements. Spatially-dependent PDEs refers to that the terms in the PDEs vary across space. In reality a physical system is often governed by spatially-dependent PDEs because the properties of the medium can be various across space, and the proposed method is the first data-driven spatially-dependent PDEs identification scheme. In addition, our method is efficient owing to its non-iterative nature and efficient implementation by coordinate descent.1

Recent investigations indicate that Sparse Bayesian Learning (SBL) is lacking in robustness. We derive a robust and sparse Direction of Arrival (DOA) estimation framework based on the assumption that the array data has a centered (zero-mean) complex elliptically symmetric (ES) distribution with finite second-order moments. In the derivation, the loss function can be quite general. We consider three specific choices: the ML-loss for the circularly symmetric complex Gaussian distribution, the ML-loss for the complex multivariate t-distribution (MVT) with ν degrees of freedom, and the loss for Huber’s M-estimator. For Gaussian loss, the method reduces to the classic SBL method. The root mean square DOA performance of the derived estimators is discussed for Gaussian, MVT, and ϵ- contaminated noise. The robust SBL estimators perform well for all cases and nearly identical with classical SBL for Gaussian noise.

We present a sparsity-promoting method for the detection and estimation of the directions of arrival (DOAs) of source signals. The proposed method is based on the recently introduced variational Bayesian line spectral estimation (VALSE) approach, which is gridless. However, the performance of VALSE is sensitive to an initial guess of the measurement noise variance and potential DOAs. Thus, we propose a sparse Bayesian learning-aided initialization. Simulation results show that this learning-aided VALSE outperforms state-of-the-art DOA estimation methods as well as the conventional VALSE. We also evaluate the proposed method using acoustic data from an ocean acoustics experiment.

Echo State Networks (ESNs) are a variant of recurrent neural networks (RNNs). ESNs perform as nonlinear fading memory filters and excel in prediction of "chaotic" signals. Predictions are made using a forced nonlinear dynamical system called the "reservoir" which incorporates past information into new states. The length of memory is critical to a task effective ESN. We examine the rank behavior of minimal task-effective ESNs predicting the chaotic Lorenz 1963 system for single and multi-variable input/output. Relationships are observed between the rank of the controllability matrix, memory length, and attractor features. We find that reservoir memory varies dependent on input forcing and location in state space. Knowledge of controllability matrix rank indicates a signal specific range for memory length. This variability corresponds to the reservoir varying between stable and unstable. The controllability matrix rank can facilitate efficient use of data and ESN construction.

Direction of Arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this work, we solve the continuous (gridless) line spectrum estimation problem by incorporating the multi-frequency model into an atomic norm minimization (ANM) framework. We show that our ANM problem is equivalent to a semi-definite program (SDP) which can be solved by an off-the-shelf SDP solver. We also provide the dual certificate that can certify the optimality of the SDP solution, and we localize the sources by finding the peaks of the norm of the dual polynomial. Numerical results support our theoretical findings and demonstrate the effectiveness of the method.

We present a system for localizing sound sources in a room with severalad hocmicrophone arrays. Each circular array performs direction of arrival (DOA) estimation independently using commercial software. The DOAs are fed to a fusion center, concatenated, and used to perform the localization based on two proposed methods, which require only a few labeled source locations (anchor points) for training. The first proposed method is based on principal component analysis (PCA) of the observed DOA and does not require any knowledge of anchor points. The array cluster can then perform localization on a manifold defined by the PCA of concatenated DOAs over time. The second proposed method performs localization using an affine transformation between the DOA vectors and the room manifold. The PCA has fewer requirements on the training sequence, but is less robust to missing DOAs from one of the arrays. The methods are demonstrated with five IoT 8-microphone circular arrays, placed at unspecified fixed locations in an office. Both the PCA and the affine method can easily map out a rectangle based on a few anchor points with similar accuracy. The proposed methods provide a step toward monitoring activities in a smart home and require little installation effort as the array locations are not needed.

The direction-of-arrivals (DOAs) of plane waves in a high-frequency region are estimated without spatial aliasing using multi-frequency processing. The method exploits the difference frequency (DF), the difference between two high frequencies. This enables processing data in a feasible region without spatial aliasing. We analyze DOA characteristics upon DF processing and propose a MUSIC-based method dealing with multi-DF and multi-snapshot. Multiple DFs having the same frequency difference allow processing multi-DF equivalently to multi-snapshot. We propose a method that considers all DFs and snapshots jointly and a joint DF method providing a single snapshot DF-MUSIC that does not require stationary DOAs. Numerical examples validate the effectiveness of the proposed method and its DOA performance is discussed.

We present a gridless sparse iterative covariance-based estimation method based on alternating projections for direction-of-arrival (DOA) estimation. The gridless DOA estimation is formulated in the reconstruction of Toeplitz-structured low rank matrix, and is solved efficiently with alternating projections. The method improves resolution by achieving sparsity, deals with single-snapshot data and coherent arrivals, and, with co-prime arrays, estimates more DOAs than the number of sensors. We evaluate the proposed method using simulation results focusing on co-prime arrays.

Reservoir computers are a fast training variant of recurrent neural networks, excelling at approximation of nonlinear dynamical systems and time series prediction. These machine learning models act as self-organizing nonlinear fading memory filters. While these models benefit from low overall complexity, the matrix computations are a complexity bottleneck. This work applies the controllability matrix of control theory to quickly identify a reduced size replacement reservoir. Given a large, task-effective reservoir matrix, we calculate the rank of the associated controllability matrix. This simple calculation identifies the required rank for a reduced size replacement, resulting in time speed-ups to an already fast deep learning model. Additionally, this rank calculation speaks to the state space reachable set required to model the input data.

This paper presents SSLIDE, Sound Source Localization for Indoors using DEep learning, which applies deep neural networks (DNNs) with encoder-decoder structure to localize sound sources with random positions in a continuous space. The spatial features of sound signals received by each microphone are extracted and represented as likelihood surfaces for the sound source locations in each point. Our DNN consists of an encoder network followed by two decoders. The encoder obtains a compressed representation of the input likelihoods. One decoder resolves the multipath caused by reverberation, and the other decoder estimates the source location. Experiments based on both the simulated and experimental data show that our method can not only outperform multiple signal classification (MUSIC), steered response power with phase transform (SRP-PHAT), sparse Bayesian learning (SBL), and a competing convolutional neural network (CNN) approach in the reverberant environment but also achieve a good generalization performance.

We present a Bayesian method for sequential direction finding based on variational line spectral estimation (VALSE). The proposed method promotes sparse solutions by means of a Bernoulli-Gaussian amplitude model, is grid-less, and provides marginal posterior distributions from which DOA estimates and their uncertainties can be extracted. Simulation results demonstrate performance improvements in the considered scenario. We also evaluate the proposed method using acoustic data from an underwater source localization experiment.

This paper introduces compressive sensing (CS) based two-dimensional (2-D) off-grid direction-of-arrival (DOA) estimation approach which can output the azimuths and elevations of radiating sources for propeller tip vortex cavitation localization. With a discretized angular search-grid of the conventional CS based approach, grid mismatch deteriorates the DOA estimation performance. To obtain the off-grid estimation performance, we formulate the 2-D off-grid DOA estimation problem into a block-sparse CS framework. In addition, the presented method can be applied to arrays of arbitrary geometry with no array configuration constraint. The approach is illustrated by numerical simulations and experimental data (cavitation tunnel experiment).

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.

Sparse arrays such as co-prime and nested arrays can identify more sources than the number of sensors. This is because their difference co-arrays contain a uniformly spaced virtual array with more elements than the number of sensors in the array. In this paper we demonstrate this using two dimensional co-prime and nested sparse arrays combined with sparse Bayesian learning (SBL) for 2D beamforming in azimuth and elevation. SBL can directly process the sparse array data and significantly outperform conventional beam-forming and MUSIC as seen from simulations.

An alternative method for solving the gridless direction-of-arrival (DOA) estimation problem is presented. Gridless DOA estimation involves solving the semi-definite characterization of a rank minimization problem. We show that the original non-convex formulation of the gridless DOA estimation problem can be solved efficiently using the method of alternating projections (AP). We deem our solution `alternating projections based gridless DOA estimation,' or APG. Using insight from the derivation of APG we present a reduced dimension variation of APG, (RD-APG). The presented algorithms are compared in speed and accuracy to gridless DOA estimation solved using the current state of the art SDP solver.

We develop a 2D travel time tomography method which regularizes the inversion by modeling sparsely patches of slowness pixels from discrete slowness map, and adapts sparse dictionaries to the slowness data. This locally-sparse travel time tomography (LST) approach considers global and local behavior of slowness, whereas conventional regularization methods consider only global covariance of pixels. We develop a maximum a posteriori formulation of LST, and further exploit the sparsity of patches using dictionary learning. We demonstrate the LST method on densely, but irregularly sampled synthetic slowness maps.

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), leading to 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. Simulations demonstrate that taking the heteroscedastic noise into account improves DOA estimation.

Densely sampled dynamic geophysical data are often modeled using principal components analysis (PCA, a.k.a. empirical orthogonal function or EOF analysis) to provide constraints for their inversion with remote sensing techniques. We show that overcomplete sparsifying dictionaries, generated using dictionary learning, provide a more informative basis for geophysical signal representation. Relative to EOFs, all the vectors in learned dictionaries represent significant variance in the geophysical signals. Since many geophysical inverse problems are ill-posed, this behavior makes learned dictionaries ideal for both minimizing the solution dimension and improving the resolution of parameter estimates. The K-SVD algorithm is applied to ocean sound speed profile (SSP) data. It is shown that learned dictionaries improves SSP inversion resolution.

Sparse Bayesian learning is a sparse processing method used for solving high-dimensional, underdetermined linear equations. Often the sensing matrix in the system of equations is assumed known and in presence of perturbations in this matrix performance of sparse processing degrades. We develop a sparse Bayesian learning method that accounts for perturbations in the sensing matrix. We derive an iterative weight update by performing evidence maximization. Beamforming simulations are used to demonstrate the advantages of the proposed method.

The directions of arrival (DOA) of plane waves are estimated from multisnapshot sensor array data using sparse Bayesian learning (SBL). The prior for the source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters, the unknown variances (i.e., the source powers). For a complex Gaussian likelihood with hyperparameter, the unknown noise variance, the corresponding Gaussian posterior distribution is derived. The hyperparameters are automatically selected by maximizing the evidence and promoting sparse DOA estimates. The SBL scheme for DOA estimation is discussed and evaluated competitively against LASSO (ℓ1-regularization), conventional beamforming, and MUSIC.

Covariance matrices of noise models are used in signal and array processing to study the effect of various noise fields and array configurations on signals and their detectability. Here, the asymptotic eigenvalues of noise covariance matrices in 2-D and 3-D attenuating media are derived. The asymptotic eigenvalues are given by a continuous function, which is the Fourier transform of the infinite sequence formed by sampling the spatial coherence function. The presence of attenuation decreases the value of the large eigenvalues and raises the value of the smaller eigenvalues (compared to the attenuation free case). The eigenvalue density of the sample covariance matrix also shows variation in shape depending on the attenuation, which potentially could be used to retrieve medium attenuation properties from observations of noise.

Decentralized physics-based field estimation in clustered sensor networks requires the exchange of state vectors between neighboring clusters. We reduce the communication overhead between clusters by using a differential encoding of state vectors that exploits the spatio-temporal field dependencies. This encoding involves a Kalman prediction step that builds on the state-space equations governing the field's spatio-temporal evolution. The Kalman step keeps the computational complexity low. Simulation results for an acoustic field demonstrate the approach.

Modern signal and array processing methods now incorporate the physics of wave propagation as an integral part of the processing. Matched field processing (MFP) refers to signal and array processing techniques in which, rather than a plane wave arrival model, complex-valued (amplitude and phase) field predictions for propagating signals are used. Matched field processing has been successfully applied in ocean acoustics and electromagnetics. In this paper, source localization performance via MFP is examined in the electromagnetics domain. Specifically, the impact of uncertainty in the a priori knowledge of the underlying physical parameters, atmospheric refractivity vs. height, on source localization performance is examined.

Matched field processing (MFP) refers to signal and array processing techniques in which, rather than a planewave arrival model, complex-valued (amplitude and phase) field predictions for propagating signals are used. Matched field processing has been successfully applied in ocean acoustics. In this paper the extension of MFP to the electromagnetic domain, i.e., electromagnetic (EM) MFP (EM-MFP) is described. Simulations of EM-MFP in the tropospheric setting suggest that, under suitable conditions, EM-MFP methods can enable EM sources to be both detected/localized and used as sources of opportunity for estimating the environmental parameters that determine EM propagation.

A generalized likelihood ratio test is considered for testing acoustic environmental models with application to parameter inversion using an acoustic propagation code. In the following, we use the term "hierarchy of models" to denote a sequence of model structures M/sub 1/, M/sub 2/, ... in which each particular model structure M/sub m/ contains all previous ones as special cases. We propose a combined parameter estimation and multiple sequential test for simultaneously determining the model order and its parameters: given the observed data, how many parameters should be included in the model? The last question is important for the order selection problem in hierarchies of models with increasing number of parameters where the observations are corrupted by additive noise. Monte Carlo simulations show the behaviour of the sequential test for selecting a model order as a function of the SNR. Finally, the test is applied to broadband data measured using a vertical array near the island of Elba in the Mediterranean Sea and compared with Akaike's information criterion.