A polarization-aware direction-of-arrival (DoA) detection scheme is conceived that leverages the intrinsic vector sensitivity of a single Rydberg atomic vapor cell to achieve quantum-enhanced angle resolution. Our core idea lies in the fact that the vector nature of an electromagnetic wave is uniquely determined by its orthogonal electric and magnetic field components, both of which can be retrieved by a single Rydberg atomic receiver via electromagnetically induced transparency (EIT)- based spectroscopy. To be specific, in the presence of a static magnetic bias field that defines a stable quantization axis, a pair of sequential EIT measurements is carried out in the same vapor cell. Firstly, the electric-field polarization angle is extracted from the Zeeman-resolved EIT spectrum associated with an electricdipole transition driven by the radio frequency (RF) field. Within the same experimental cycle, the RF field is then retuned to a magnetic-dipole resonance, producing Zeeman-resolved EIT peaks for decoding the RF magnetic-field orientation. This scheme exhibits a dual yet independent sensitivity on both angles, allowing for precise DoA reconstruction without the need for spatial diversity or phase referencing. Building on this foundation, we derive the quantum Fisher-information matrix (QFIM) and obtain a closed-form quantum Cramér-Rao bound (QCRB) for the joint estimation of polarization and orientation angles. Finally, simulation results spanning various quantum parameters validate the proposed approach and identify optimal operating regimes. With appropriately chosen polarization and magnetic-field geometries, a single vapor cell is expected to achieve sub-0.1° angle resolution at moderate RF-field driving strengths.

The significant progress of quantum sensing technologies offer numerous radical solutions for measuring a multitude of physical quantities at an unprecedented precision. Among them, Rydberg atomic quantum receivers (RAQRs) emerge as an eminent solution for detecting the electric field of radio frequency (RF) signals, exhibiting great potential in assisting classical wireless communications and sensing. So far, most experimental studies have aimed for the proof of physical concepts to reveal its promise, while the practical signal model of RAQR-aided wireless communications and sensing remained under-explored. Furthermore, the performance of RAQR-based wireless receivers and their advantages over classical RF receivers have not been fully characterized. To fill these gaps, we introduce the RAQR to the wireless community by presenting an end-to-end reception scheme. We then develop a corresponding equivalent baseband signal model relying on a realistic reception flow. Our scheme and model provide explicit design guidance to RAQR-aided wireless systems. We next study the performance of RAQR-aided wireless systems based on our model, and compare them to classical RF receivers. The results show that Doppler broadening-free RAQRs are capable of achieving a substantial received signal-to-noise ratio (SNR) gain of over 27 decibel (dB) and 40 dB in the photon shot limit and standard quantum limit regimes, respectively.

The intrinsic integration of Rydberg atomic receivers into wireless communication systems is proposed, by harnessing the principles of quantum physics in wireless communications. More particularly, we conceive a pair of Rydberg atomic receivers, one incorporates a local oscillator (LO), referred to as an LO-dressed receiver, while the other operates without an LO and is termed an LO-free receiver. The appropriate wireless model is developed for each configuration, elaborating on the receiver's responses to the radio frequency (RF) signal, on the potential noise sources, and on the signal-to-noise ratio (SNR) performance. The developed wireless model conforms to the classical RF framework, facilitating compatibility with established signal processing methodologies. Next, we investigate the associated distortion effects that might occur, specifically identifying the conditions under which distortion arises and demonstrating the boundaries of linear dynamic ranges. This provides critical insights into its practical implementations in wireless systems. Finally, extensive simulation results are provided for characterizing the performance of wireless systems, harnessing this pair of Rydberg atomic receivers. Our results demonstrate that LO-dressed systems achieve a significant SNR gain of approximately 40~50 dB over conventional RF receivers in the standard quantum limit regime. This SNR head-room translates into reduced symbol error rates, enabling efficient and reliable transmission with higher-order constellations.

Rydberg atomic quantum receivers exhibit great potential in assisting classical wireless communications due to their outstanding advantages in detecting radio frequency signals. To realize this potential, we integrate a Rydberg atomic quantum receiver into a classical multi-user multiple-input multiple-output (MIMO) scheme to form a multi-user Rydberg atomic quantum MIMO (RAQ-MIMO) system for the uplink. To study this system, we first construct an equivalent baseband signal model, which facilitates convenient system design, signal processing and optimizations. We then study the ergodic achievable rates under both the maximum ratio combining (MRC) and zero-forcing (ZF) schemes by deriving their tight lower bounds. We next compare the ergodic achievable rates of the RAQ-MIMO and the conventional massive MIMO schemes by offering a closed-form expression for the difference of their ergodic achievable rates, which allows us to directly compare the two systems. Our results show that RAQ-MIMO allows the average transmit power of users to be$>25 \text{d B m}$lower than that of the conventional massive MIMO. Viewed from a different perspective, an extra$\sim 8.8$bits/s/Hz/user rate becomes achievable by ZF RAQ-MIMO.

In this paper, we address the important problem of direction of arrival (DOA) estimation using a single directional antenna under the multipath environment. We address this practically important problem by following a three step approach; i) Restoration, ii) Separation and iii) Estimation. By assuming constant modulus signal similar to earlier works, we employ the constant modulus algorithm (CMA) to restore the constant modularity which gets destroyed due to multipath, in the restoration step. In the subsequent separation step, using the restored signal as the reference, we separate the power profile corresponding to each of the direct and reflected paths. Further, to estimate DOA from these separated power profiles, a compressed sensing based algorithm is also proposed. Both the simulation and experimental results show significantly better multipath mitigation with the proposed approach than those by the existing approaches.

We consider the problem of tracking a receiver using signals-of-opportunity (SOOPs) from beacons and a reference anchor with known positions and velocities, and where all devices have asynchronous local clocks or oscillators. We model the clock drift at individual devices by a two-state model with unknown clock offset and clock skew and analyze the biases introduced by clock asynchronism in the received signals. Based on an extended Kalman filter, we propose a sequential estimator to jointly track the receiver location, velocity, and its clock parameters using altitude information together with time-difference-of-arrival and frequency-difference-of-arrival measurements obtained from the SOOP samples collected by the receiver and a reference anchor. The receiver was implemented on a software-defined radio testbed, and field experiments are carried out using Iridium satellites as the SOOP beacons. The experiment and simulation results demonstrate that our measurement model has a good fit, and our proposed estimator can successfully track both the receiver location, velocity, and the relative clock offset and skew with respect to the reference anchor with good accuracy.

We propose a novel real-time system design for multiband signal blind reconstruction using multi-coset sampling theory. Multi-channel signals are acquired under sub-Nyquist sampling frequency to perfectly reconstruct the original signal spectrum. A novel system design with Field-Programmable Gate Array (FPGA) implementation is presented in this paper. There are two main contributions in this paper. Firstly, the FPGA system uses 32-bit single precision floating point dataflow rather than conventional 16-bit fixed point to recover signals with much lower Signal-Noise Ratio (SNR). Secondly, we introduce a novel Jacobi CORDIC eigenvalue decomposition (EVD) core using parallel pivot-seeking circuit and parallel 3-CORDIC design to improve speed significantly. Hermitian matrices of dimensions from 2 to 10 are tested to compare conventional 2-CORDIC EVD and proposed EVD. The proposed EVD effectively reduces on average 36% of processing time for mesh connection system and over 50% for parallel system.

Spectrum blind reconstruction and direction-of-arrival (DOA) estimation of multiple narrow-band signals spread over wide spectrum sampled at sub-Nyquist sampling rates are considered in this paper. A new sub-Nyquist sampling receiver architecture which requires minimal hardware along with an efficient algorithm for estimation of the parameters and spectrum reconstruction is presented. We further show with the proposed approach, that a minimum average sampling rate of 2(N + 1)B would be sufficient in order to reconstruct the spectrum as well as estimate their corresponding DOA of N narrow-band signals of maximum bandwidth B. Simulation results are also provided which shows the performance very close to the Cramer Rao bound.

Motivated by the existing time-frequency peak filtering (TFPF) algorithm, herein a robust time-varying filtering (RTVF) algorithm is proposed for filtering and separating multicomponent frequency modulation (FM) signals. The performance of the TFPF based on windowed Wigner-Ville distribution is limited by the linear constraint on the waveform of the received signal. The proposed RTVF significantly improves the filtering performance with low complexity by applying a sinusoidal time-frequency distribution, which allows a sinusoidal constraint on the signal's waveform. The RTVF can successfully decompose a multicomponent signal into individual components based on an initial instantaneous frequency (IF) estimate of each component. Unlike existing time-varying filters, the RTVF is much less sensitive to the accuracy of the IF estimate, which can be gradually refined by performing an iterative RTVF procedure.

We consider the problem of localizing two devices using signals of opportunity from beacons with known positions. Beacons and devices have asynchronous local clocks or oscillators with unknown clock skews and offsets. We model clock skews as random, and analyze the biases introduced by clock asynchronism in the received signals. By deriving the equivalent Fisher information matrix for the modified Bayesian Cramér-Rao lower bound (CRLB) of device position and velocity estimation, we quantify the errors caused by clock asynchronism. We propose an algorithm based on differential time-difference-of-arrival (DTDOA) and frequency-difference-of-arrival (FDOA) that mitigates the effects of clock asynchronism to estimate the device positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when clock skews have small standard deviations.

In this paper, a new method based on estimation and line-of-sight (LOS) detection of individual time-of-arrival (TOA) measurement and Kalman filter (KF) is proposed to track a moving target in mixed line-of-sight and non-line-of-sight (LOS/NLOS) environments. In the proposed tracking algorithm, TOA measurements collected by multiple stationary sensors in a wireless sensor network are used. First, a pseudo-measured position is calculated by choosing the point along the circle defined by a given TOA measurement which has the shortest distance to the predicted position of a moving target. The pseudo-measured position is shown to be an approximately unbiased estimate of the true position of the target. Second, each pseudo-measured position calculated is passed to a detector to be identified as either LOS or NLOS. The average of all the selected LOS pseudo-measured positions is then used as a new pseudo-measurement for the KF to track the moving target. Unlike all the existing target tracking algorithms in mixed LOS/NLOS environments, the proposed tracking algorithm is able to perform target tracking even with just one LOS TOA measurement at a given time instance without prior information of the NLOS noise which may be difficult to obtain in practice. Another advantage of the proposed tracking algorithm is its computational efficiency. Simulation results show that the proposed tracking algorithm performs better than some recent tracking algorithms, particularly in severe mixed LOS/NLOS environments.

This paper considers spectrum-blind reconstruction (SBR) of multi-band signals (MBS) which are sampled with multi-coset sampling (MCS) architecture. A new SBR algorithm which we refer to as Khatri-Rao SBR (KR-SBR) is presented. With this new KR-SBR algorithm, the average MCS rate can be reduced by 50% whilst attaining the same performance as that of the existing state-of-art SBR algorithms. Under certain conditions we will also show that the proposed KR-SBR algorithm has the capacity to achieve SBR when the average MCS rate approaches the Landau sampling rate. Simulation results are also presented to demonstrate the advantages of the proposed KR-SBR algorithm.

In this paper, a novel individual angle-of-arrival (AOA) measurement detection method and extended Kalman filter (EKF) based tracking algorithm is proposed. The detection method is used to detect whether an individual AOA measurement is line-of-sight (LOS) or non-line-of-sight (NLOS). After the measurement detection, the selected LOS AOA measurements are then used into an dynamic EKF to track a moving target in mixed LOS/NLOS environments. Different from some traditional NLOS error detection methods, which determine the estimation result of a set of AOA measurements collected at every time step is LOS or not, the proposed method detects each AOA measurement one by one at one time step. This algorithm makes good use of LOS AOA measurements and greatly improves the tracking accuracy of the EKF in mixed LOS/NLOS environments. Simulations implemented under different NLOS percentage scenarios demonstrates the improvement of the classical EKF with the assistance of the proposed measurement detection method for AOA measurement.

The estimation of the mixing matrix as well as the number of sources in blind source separation are two challenging problems. This paper proposes an effective estimation method to solve these two problems for underdetermined blind separation of overlapped sources in short-time Fourier transform (STFT) domain. Our study considers the blind estimation of the mixing matrix based on subspace projection as well as clustering methods, and the number of sources can be therefore estimated by counting the columns of the estimated mixing matrix. The proposed estimation method is noise-robust and suitable for the sources whose spectral contents are highly overlapped in STFT domain. Numerical results on speech sources are presented to illustrate the effectiveness and robustness of the proposed method.

A simple but effective approach based on gating and robust extended Kalman filtering (EKF) is proposed for target tracking in mixed line-of-sight and non-line-of-sight (LOS/NLOS) environments, using time-of-arrival (TOA) measurements. Utilizing a gating based detection method determined by the statistical properties of the TOA measurements, a confidence region is derived. Most of the LOS TOA measurements can be effectively selected from all mixture measurements using the properly defined confidence region. These selected LOS TOA measurements are then passed on to the dynamic robust EKF to do the target tracking. Simulations have shown the proposed tracking approach has outperformed both the classic rEKF as well as a recent target tracking approach. Moreover, the proposed approach does not require any statistical knowledge of the NLOS error and only assumes that the standard deviation of the LOS noise is known.

We consider the problem of localizing two sensors using signals-of-opportunity from beacons with known positions. Beacons and sensors have asynchronous local clocks or oscillators with unknown clock skews and offsets. We analyze the biases introduced by clock asynchronism in the received signals, and derive the Cramér-Rao lower bound (CRLB) for sensor position and velocity estimation errors. We quantify the error caused by beacon clock asynchronism. We also propose an algorithm that mitigates the effects of clock asynchronism to estimate the sensor positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when sensor clock skews have small standard deviations.

This paper consider the problem of relaxing the spatial coverage requirement on the mechanical rotation in the direction finding (DF) approach based on the received power measurements from single antenna pointing to different directions. Under incomplete spatial coverage, we show that the least square (LS) solution used to transform the problem into its spectral form is no longer accurate due to its ill-conditioned system matrix. To overcome this, we propose an approach based on spatial remodeling of the spatial power measurements such that its spatial periodicity can be adjusted according to the spatial coverage. The approach also incorporates the Tikhonov regularization in calculating the LS solution based on the new system matrix. Upon arriving at the new spectral form, the Cadzow-annihilating filter method can then be used to estimate the direction-of-arrival. Both simulation and experimental results are presented to show the efficacy of the proposed method.

In many array processing, the received signals are nonstationary, or in particular, noncircular. Widely linear minimum variance distortionless response (WL MVDR) beamformers can exploit the noncircularity of received signals and improve the performance of the conventional MVDR beamformer. However, in the optimum WL MVDR beamformer, the array steering vector (ASV) and the signal noncircularity coefficient should be known a priori for the signal of interest. This requirement puts strict limitation to the implementation of this beamformer. We therefore in this paper propose a robust approach to the optimal WL MVDR beamformer that can deal with the uncertainties in the ASV and noncircularity coefficient. Two variants of the proposed approach are developed based on the treatment of the uncertainties. By doing so, the requirement on the exact information is relaxed while the performance improvement can still be obtained. Simulation studies are also provided to illustrate the performance of the proposed approach.

This paper proposes an approach to improving the target tracking accuracy in mixed line-of-sight/non-line-of-sight (LOS/NLOS) environments based on individual measurement detection (IMD) and road constraints. Utilizing the IMD algorithm, most LOS time-difference-of-arrival (TDOA) measurements can be correctly selected from mixed LOS/NLOS TDOA measurements. Incorporating the prior knowledge of the road constraint as a pseudo-measurement, the augmented dynamic extended Kalman filter (EKF) is then implemented to track a moving target. Simulation results demonstrate that the road constraint assisted algorithm, in conjunction with the IMD method, performs better than the road constraint assisted algorithm without the IMD method, or tracking algorithm with the IMD method but without the road constraint. The proposed method is especially useful when the number of selected LOS TDOA measurements is less than three.

We consider the problem of localizing two sensors using their TDOA measurements of signals from beacons with known positions. Beacons and sensors have asynchronous local clocks or oscillators with unknown clock skews and offsets. We analyze the effect of the clock skews and offsets on the TDOA estimations, and introduce a novel approach using the difference in TDOA (DTDOA) measurements to mitigate the effects of clock skews and offsets on the location estimates. We propose an algorithm for location and velocity estimation based on DTDOA, and perform simulations to verify the robustness of our algorithm to asynchronous local clocks in the beacons and sensors.

This paper considers the problem of extending the single antenna power measurements based direction finding to the two-dimensional (2D) case, and proposes a method to estimate the azimuth-elevation direction-of-arrival (DOA) from a matrix of received power. Exploiting the fact that the azimuth-elevation antenna pattern is 2D bandlimited, the problem can be transformed into a 2D spectral analysis problem. The proposed method first decomposes the 2D spectral analysis problem into one-dimensional case and then solved them independently. As the solution does not ensure that the estimated azimuth and elevation is in correct order, the solution is subjected to permutation ambiguity. This can then be solved by finding the permutation that best matches the 2D spectral representation. Simulation results demonstrating the high-resolution capability of the proposed method in two-source case and the effectiveness in fivesource case are also presented in this paper.

In this paper, we present an approach to design passive coupling matrix to overcome the performance limitation of direction finding using small aperture array. This approach is inspired by the sound localization acuity of a parasitic fly called Ormia ochracea. Motivated by the requirement from practical implementation that each element of the coupling matrix is realized as a passive analog phase shifter and attenuator in a similar fashion as that of conventional analog beamforming, in the proposed approach we confine the magnitude of each element to being no larger than 1. By taking the advantage of the coupling mechanism, this approach can design compact aperture antenna array yet with much improved direction finding performance. Furthermore, the proposed design is applicable to arbitrary array geometry. Numerical examples illustrate the effectiveness of the proposed approach and show a performance gain of 30 over the uncoupled array of the same aperture of 10 cm diameter at 40 MHz.

Non-line-of-sight (NLOS) error is one of the most important factors affecting the accuracy of positioning or tracking especially in urban or indoor environments. This paper concentrates on alleviating the influence of the NLOS error. A position detection approach utilizing the circle error probability (CEP) in conjunction with the least square (LS) method and Kaiman Filter (KF) tracking algorithms is proposed. The LS is used to estimate the positions of a moving target from time-of-arrival (TOA) measurements and the KF is used to smooth the tracking trajectory. Simulation results show that this approach can effectively identify line-of-sight (LOS) estimated positions, leading to higher tracking accuracy than that by other tracking methods without using position detection.

Two new approaches to adaptive beamforming in sparse subarray-based sensor arrays are proposed. Each subarray is assumed to be well calibrated but the intersubarray gain and/or phase mismatches are assumed to remain unknown or imperfectly known. Our first approach is based on a worst-case beamformer design that, unlike the existing worst-case designs, exploits a structured ellipsoidal uncertainty model for the signal steering vector. Our second approach exploits the idea of estimating the signal steering vector by maximizing the output power of the minimum variance beamformer. Several modifications of our second approach are developed for the cases of gain-and-phase and phase-only intersubarray distortions.

This paper proposes an iterative robust capon beamformer (IRCB) with adaptive uncertainty level. The approach iteratively estimates the actual steering vector based on conventional RCB formulation. Instead of using a fixed uncertainty level, we adaptively update the uncertainty level at each iteration. The uncertainty is updated based on the projection of the presumed steering vector onto the noise subspace. The iteration converges when the noise subspace projection is zero. We additionally impose a constraint that restricts the estimated steering vector to be within a spatial sector in order to overcome inappropriate updating of the uncertainty due to subspace swap at low signal-to-noise ratio (SNR) case. Simulation results show that the adaptive uncertainty based IRCB converges faster than the fixed uncertainty based IRCB. Besides alleviating the need to assume any knowledge on the mismatch, the proposed beamformer requires lower computational cost as compared to the convex optimization based beamformer design.

The presence of impulsive noise can severely degrade the accuracy performance of conventional direction of arrival (DOA) estimation algorithms, such as MUSIC and ESPIRIT. We propose a two-stage robust adaptive trimming approach. We first apply Shapiro-Wilk's goodness-of-fitWtest for Gaussianity, as a preprocessing stage. We then robustly estimate the covariance matrix in order to minimize the impact of impulsive noise on conventional DOA estimation algorithms. Numerical simulations are presented to illustrate the efficacy of the proposed approach for high resolution direction finding in highly-impulsive environments.

For bistatic ground moving target indication radar, the clutter Doppler frequency depends on range for all array geometries. This range dependency leads to problems in clutter suppression through STAP techniques. In this paper, we propose a new approach of applying non-linear prediction theory to address the range dependency problem in bistatic airborne radar systems. This technique uses a non-linear function to obtain an estimate of the range-dependent inverse covariance matrix. Simulation results suggest a non-linear fit for the model (nonlinear relationship between the inverse covariance matrices) and show an improvement in processor performance as compared to conventional STAP methods.

Approximate formulations for the 3-dB beamwidth are derived in this letter to measure the spatial resolution of the broadband nonredundant array (NRA) and minimum redundancy array (MRA), which assume the ideal continuous-time, infinite-length filters with the frequency responses obtained by the linearly constrained minimum variance (LCMV) optimization. By these formulations, the beamwidths of NRA and MRA are compared with that of the uniform linear array (ULA). Moreover, the accuracy of the derived formulations is assessed by numerical studies.

In this letter, a new broadband beamformer using infinite impulse response (IIR) filters is proposed. The unique feature of our letter is that by replacing all the delay elements with tap-to-tap IIR filters under some structural restrictions, the Frost processor is naturally extended from the finite impulse response (FIR) beamformer to the IIR beamformer. In the new beamformer, the feedforward and feedback weights are computed with the constrained and unconstrained least-mean-squares algorithms, respectively. The stability of the IIR filters in the proposed beamformer could be monitored easily. Simulation results demonstrate the improved performance of the new IIR beamformer relative to the Frost beamformer.

We consider the problem of source number estimation in the presence of unknown spatially nonuniform noise. Successive array element suppression is applied to isolate the contribution of the noise powers and a likelihood function is derived. When it is combined with the appropriately defined penalty function, a MDL-like criterion is defined. Performance of the new criterion is assessed through simulations and it is shown that the method is powerful in a nonuniform noise environment.

This paper presents an array processing approach that only requires the array outputs to be sampled one at a time by a single channel receiver. We note that the sequential sampling of the array outputs is equivalent to the periodic but non-uniform sampling of the source waveform. The derived array model is structurally similar to the conventional array model. This allows the direct application of most conventional high resolution DOA estimation and beamforming algorithms with the proposed approach. The feasibility of this approach is demonstrated with simulation data.

The problem of direction finding in partly calibrated arrays of an arbitrary geometry is addressed. We assume that an array is composed of multiple calibrated subarrays and consider the cases of unknown (or known with some error) inter-subarray displacements, imperfect synchronization of subarrays in time, as well as unknown channel mismatches between subarrays. Recently, the so-called RAnk Reduction Estimator (RARE) has been proposed as a particular solution to the problem of direction finding in partly calibrated arrays with unknown inter-subarray displacements. However, the application of RARE is restricted by the special case of arrays composed of identically oriented linear subarrays with interelement spacings which are integer multiples of a certain shortest baseline. In this paper, we propose a more general subspacebased approach which further develops the ideas of RARE and is applicable to partly calibrated arrays composed of subarrays of arbitrary geometry. The algorithms proposed enable simple extensions to the two-dimensional (2D) Direction-Of-Arrival (DOA) estimation case.

We develop vector-sensor array processing to estimate the angles-of-arrival (AOAs) and time delays of multipath channels in the space-time-polarization domain. A MUSIC-type algorithm for joint angle and delay estimation with a vector-sensor array is derived. Potential applications include multipath channel estimation and mobile localization. Simulation results show that the space-time-polarization parameterization of the multipath channels results in improved accuracy and resolution performance.

We present an adaptive algorithm for space-time channel identification and equalization. The proposed algorithm performs joint channel estimation and sequence detection by optimizing a least squares cost function iteratively in a forward and backward manner. Simulation results demonstrate the proposed algorithm to be data efficient and fast converging. In addition, a good BER performance is achieved in time-varying channels at relatively low SNR and with an extremely short start-up sequence. These attributes render it suitable for wireless mobile communications using short burst data format.

We propose new methods for fast blind identification and equalization of communication channels based on channel outputs sampled at symbol rate. These methods exploit the FA property of the transmitted sequence as well as the algebraic structures and relationships of the symbol and channel parameter matrices to achieve blind equalization. The block based methods proposed herein are fast converging and data efficient. Simulated studies have illustrated the proposed methods capable of achieving reliable blind equalization with a sequence length as short as 20 samples over a wide-range of SNR.

We present a maximum likelihood approach for calibrating sensor arrays in the presence of mutual coupling, channel gain and phase mismatch and array geometry uncertainties using measured steering vectors of uncertain locations. The estimated perturbation parameters is used to calibrate the array manifold, hence enabling many high resolution array processing algorithms to attain their potential advantages. We present two methods for optimizing the highly nonlinear and multimodal ML cost function. The first method is a linearized local gradient search algorithm. The second method is derived from combining the fast local search of gradient methods with the nonlinear global search ability of the genetic algorithm. The resulting hybrid optimizer is both fast and globally converging. Simulation results are presented to illustrate the usefulness of the proposed approach.