DOA Estimation in Heteroscedastic Noise with sparse Bayesian Learning


  • Peter Gerstoft NoiseLab, UCSD La Jolla, USA
  • Christoph F. Mecklenbrauker Inst. of Telecommunications TU Wien Vienna, Austria
  • Santosh Nannuru IIIT Hyderabad, SPCRC, IIIT Hyderabad Hyderabad, India
  • Geert Leus Dept. of Electrical Eng., Delft Univ. of Technology Delft, Netherlands


Heteroscedastic noise, sparse reconstruction


We consider 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., source powers), leading to stochastic maximum likelihood (ML) DOA estimation. The DOAs are estimated from multisnapshot array data using sparse Bayesian learning (SBL) where the noise is estimated across both sensors and snapshots.


A. Xenaki, P. Gerstoft, and K. Mosegaard, “Compressive beamforming,” J. Acoust. Soc. Am., 136(1):260–271, 2014.

D. P. Wipf and B. D. Rao, “An empirical Bayesian strategy for solving the simultaneous sparse approximation problem,” IEEE Trans. Signal Process., 55(7):3704–3716, 2007.

P. Gerstoft, A. Xenaki, and C. F. Mecklenbrauker. “Multiple and single ¨ snapshot compressive beamforming,” J. Acoust. Soc. Am., 138(4):2003– 2014, 2015.

P. Gerstoft, C. F. Mecklenbrauker, W. Seong, and M. J. Bianco, “In- ¨ troduction to compressive sensing in acoustics,” J. Acoust. Soc. Am., 143:3731–3736, 2018.

P. Gerstoft, C. F. Mecklenbrauker, A. Xenaki, and S. Nannuru, “Mul- ¨ tisnapshot sparse Bayesian learning for DOA’,’ IEEE Signal Process. Lett., 23(10):1469–1473, 2016.

S. Nannuru, K. L Gemba, P. Gerstoft, W. S. Hodgkiss, and C. F. Mecklenbrauker, “Sparse Bayesian learning with multiple dictionaries,” ¨ Signal Processing, 159:159–170, 2019.

P. Gerstoft, S. Nannuru, C. F. Mecklenbrauker, and G. Leus, “DOA ¨ estimation in heteroscedastic noise,” Signal Processing, 161:63–73, 2019.

K. L. Gemba, S. Nannuru, and P. Gerstoft, “Robust ocean acoustic localization with sparse Bayesian learning,” IEEE J Sel. Topics Signal Process., 13:49–60, 2019.

J. F. Bohme. “Source-parameter estimation by approximate maximum ¨ likelihood and nonlinear regression,” IEEE J. Oceanic Eng., 10(3):206– 212, 1985.

P. Stoica and A. Nehorai, “On the concentrated stochastic likelihood function in array processing,” Circuits Syst. Signal Process., 14(5):669– 674, 1995.




How to Cite

Peter Gerstoft, Christoph F. Mecklenbrauker, Santosh Nannuru, & Geert Leus. (2020). DOA Estimation in Heteroscedastic Noise with sparse Bayesian Learning. The Applied Computational Electromagnetics Society Journal (ACES), 35(11), 1439–1440. Retrieved from