Underdetermined DOA Estimation of Quasi-Stationary Signals Using a Partly-Calibrated Array

Abstract

Quasi-stationary signals have been widely found in practical applications, which have time-varying second-order statistics while staying static within local time frames. In this paper, we develop a robust direction-of-arrival (DOA) estimation algorithm for quasi-stationary signals based on the Khatri–Rao (KR) subspace approach. A partly-calibrated array is considered, in which some of the sensors have an inaccurate knowledge of the gain and phase. In detail, we first develop a closed-form solution to estimate the unknown sensor gains and phases. The array is then calibrated using the estimated sensor gains and phases which enables the improved DOA estimation. To reduce the computational complexity, we also proposed a reduced-dimensional method for DOA estimation. The exploitation of the KR subspace approach enables the proposed method to achieve a larger number of degrees-of-freedom, i.e., more sources than sensors can be estimated. The unique identification condition for the proposed method is also derived. Simulation results demonstrate the effectiveness of the proposed underdetermined DOA estimation algorithm for quasi-stationary signals.

Doa Estimation of Quasi-Stationary Signals Using a Partly-Calibrated Uniform Linear Array With Fewer Sensors Than Sources

“…Fig. 3 shows the RMSE of DOA estimation under different SNRs, with the proposed method, an KR-ESPRIT-like method [8] and its reduced-dimension (RD) version. It is observed that the proposed method renders lower RMSE than the other two methods, under all SNRs of consideration.…”

“…Next, by stacking the quasi-stationary signalsȳ q over all Q time frames, we haveȲ ( 8 ) up which the singular value decomposition (SVD) technique is applied to obtain…”

“…The KR-ESPRIT-like algorithm can detect up to 2N − 3 source signals with a partly-calibrated uniform linear array (PC-ULA) of N sensors, two of which are calibrated [8]. In this work, a two-step KR-MUSIC algorithm is proposed to first estimate the uncertainties in gain and phase of some sensors, then to estimate the DOAs of source signals.…”

“…However, the performance of KR-MUSIC algorithm significantly deteriorates when uncertainties exist in gain and phase of sensors. Motivated by [3] and [7], a KR-ESPRIT-like method [8] was proposed to jointly estimate the uncertainties of sensors and the DOAs of source signals. The noise-removal in [7] were adopted before applying the subspace processing.…”

Joint DOA and DOD Estimation Based on Tensor Subspace with Partially Calibrated Bistatic MIMO Radar

“…Therefore, the above algorithms will suffer from performance degradation or even fail to achieve accurate DOD and DOA estimation in many scenarios. A number of algorithms have been proposed to deal with the array calibration problem [13][14][15][16][17]. An iterative algorithm based on the MUSIC technique is proposed in [13], which can simultaneously achieve the angle and gain-phase uncertainties estimation.…”