Philipp Heidenreich

Joint 2-D DOA Estimation and Phase Calibration for Uniform Rectangular Arrays

A precise model of the array response is required to maintain the performance of direction-of-arrival (DOA) estimation. When modeling errors are present or the sensor environment is time-varying, autocalibration becomes necessary. In this paper, the problem of phase autocalibration for uniform rectangular array (URA) geometries is considered. For the case with a single source, a simple and robust least-squares algorithm for joint 2-D DOA estimation and phase calibration is presented. When performing phase autocalibration with a URA, the phase and DOA parameters cannot be identified together without ambiguity. This problem is discussed and a suitable remedy is suggested. An approximate Cramér-Rao bound and analytical expressions for the mean squared error performance of the proposed estimator are presented. The proposed algorithm for phase autocalibration is extended for the case with multiple sources. The results are evaluated using a representative body of simulations.

Morphological image processing for FM source detection and localization

We consider the problem of direction finding for frequency modulated signals impinging on an array of sensors. Making use of a time-frequency representation of the data, we are able to exploit the non-stationary nature of the source signals. We employ morphological image processing to estimate time-frequency signature segments of each source. For the direction finding we apply beamforming techniques on averaged spatial time-frequency distribution matrices. When they occur, overlapping segments are splitted and re-combined after direction finding. The re-combination of segments is based on a bootstrap test, which resamples time-frequency auto-term locations. The proposed method also allows direction finding for the underdetermined case, i.e. when there are more sources than the number of array sensors. Furthermore, it detects the number of sources present, and the detector performance is compared to information based criteria.

Computationally simple DOA estimation of two resolved targets with a single snapshot

Direction-of-arrival (DOA) estimation of two targets with a single snapshot plays an important role in many pulsed radar array applications. We consider the case when the targets are spaced by more than the beamwidth of the array. In this case, the conventional beamformer (BF) is able to resolve them, but results in biased DOA estimation due to the leakage effect. We propose computationally simple strategies to reduce this bias. A novel method is presented, based on the analysis of the noise-free BF spectrum and a local approximation. We comment on computational cost and present simulation results.

Robust direction-of-arrival estimation for FM sources in the presence of impulsive noise

Time-frequency methods can utilize the non-stationarity of signals to enhance the resolution capability and accuracy in direction-of-arrival estimation. In this paper, we consider the problem of non-stationary sources impinging on an array of sensors in an impulsive noise environment. We apply a robust time-frequency method in combination with morphological image processing to estimate the instantaneous frequency of the sources. Then, for the extracted time-frequency points, we employ robust methods to calculate the averaged spatial time-frequency matrix, which is then used for direction-of-arrival estimation.

Direction Finding of Nonstationary Signals using Spatial Time-Frequency Distributions and Morphological Image Processing

We consider the problem of direction finding for nonstationary signals impinging on an array of sensors. Making use of a time-frequency representation of the data, we are able to exploit the non-stationary nature of the source signals. We employ morphological image processing to estimate time-frequency signature segments of each source. Optional overlapping segments are splitted and recombined after direction finding. The proposed method also allows direction finding for the underdetermined case, i.e. when there are more sources than the number of array sensors.

Fast maximum likelihood DOA estimation in the two-target case with applications to automotive radar

Abstract Direction-of-arrival (DOA) estimation of two targets using a single snapshot plays an important role in automotive radar for advanced driver assistance systems. Conventional Fourier methods have a limited resolution and generally yield biased estimates. Subspace methods involve a numerically complex eigendecomposition and require multiple snapshots or a suboptimal pre-processing for reliable estimation. We therefore consider the maximum likelihood (ML) DOA estimator, which is applicable with a single snapshot and shows good statistical properties. To reduce the computational burden, we propose a grid search procedure with a simplified calculation of the objective function. The required projection operators are pre-calculated off-line and stored. To save storage space and computations, we further propose a rotational shift of the field-of-view such that the relevant angular sector, which has to be evaluated, is delimited and centered with respect to broadside. The final estimates are obtained using a quadratic interpolation. The developed method is demonstrated with an example. Simulations are designed to assess the performance of the considered ML estimator with grid search and interpolation, and to compare it among selected representative methods. We further present results obtained with experimental data from a typical application in automotive radar.

Gain and phase autocalibration for uniform rectangular arrays

To maintain the performance of direction-of-arrival (DOA) estimation, an accurate model of the array response is required. In a time-varying sensor environment, this is only possible with autocalibration. For a uniform linear array, there exist algorithms for autocalibration which exploit the Toeplitz structure of the unperturbed spatial covariance matrix. In this paper, we develop an autocalibration method for 2-D DOA estimation with a uniform rectangular array, in which we exploit a Toeplitz-block Toeplitz structure. We present a simple algorithm for gain and phase estimation, discuss ambiguity problems and evaluate the performance using simulations.

High-resolution direction finding of coherent sources in the presence of model errors using alternating projections

Direction finding with coherent source waveforms is of practical importance in radar array processing, e.g. for specular multipath propagation. Furthermore, high-resolution methods require an accurately calibrated array. In this paper, we combine local and global manifold correction with maximum likelihood direction finding using the method of alternating projections. We use simulations to study the effect of array errors and noise. We further apply the combined algorithm to real data recorded using a radar array for an automotive application.

Computational Aspects of Maximum Likelihood DOA Estimation of Two Targets with Applications to Automotive Radar

Direction-of-arrival (DOA) estimation of two targets with a single snapshot plays an important role in many practically relevant scenarios in automotive radar for driver assistance systems. Conventional Fourier-based methods cannot resolve closely spaced targets, and high-resolution methods are required. Thus, we consider the maximum likelihood DOA estimator, which is applicable with a single snapshot. To reduce the computational burden, we propose a grid search procedure with a simplified objective function. The required projection operators are pre-calculated off-line and stored. To save storage space, we further propose a rotational shift of the field of view such that the relevant angular sector, which has to be evaluated, is centered with respect to the broadside. The final estimates are obtained using a quadratic interpolation. An example is presented to demonstrate the proposed method. Also, results obtained with experimental data from a typical application in automotive radar are shown.

Advances in Automotive Radar: A framework on computationally efficient high-resolution frequency estimation

Radar technology is used for many applications of advanced driver assistance systems (ADASs) and is considered as one of the key technologies for highly automated driving (HAD). An overview of conventional automotive radar processing is presented and critical use cases are pointed out in which conventional processing is bound to fail due to limited frequency resolution. Consequently, a flexible framework for computationally efficient high-resolution frequency estimation is presented. This framework is based on decoupled frequency estimation in the Fourier domain, where high-resolution processing can be applied to either the range, relative velocity, or angular dimension. Real data obtained from series-production automotive radar sensor are presented to show the effectiveness of the presented approach.