Multidim Syst Sign Process https://doi.org/10.1007/s11045-017-0539-z Two-dimensional noisy autoregressive estimation with application to joint frequency and direction of arrival estimation Alireza Amanat 1 · Alimorad Mahmoudi 1 · Majid Hatam 2 Received: 18 June 2017 / Revised: 20 November 2017 / Accepted: 22 November 2017 © Springer Science+Business Media, LLC, part of Springer Nature 2017 Abstract The present study addresses the problem of two-dimensional autoregressive esti- mation in the presence of additive white noise. The estimation method is based on combining the low-order and high-order Yule-Walker equations. The noise-compensated YW equations are solved using an iterative algorithm. The proposed method is also applied to joint fre- quency and direction of arrival estimation in uniform linear arrays. Using simulation study, the performance of the proposed algorithm is evaluated and compared with other methods. Keywords Two-dimensional noisy autoregressive model · Yule-Walker equations · Least-squares estimation · Spatial spectrum 1 Introduction Two-dimensional (2-D) autoregressive (AR) estimation has many applications in radar (Kay et al. 1993), sonar, and communications. In radars, for instance, we can assume that the received signals are 2-D signals in terms of range and Doppler (Liu 2013; Jingyu et al. 2015). The clutter and noise can be modeled by a two-dimensional AR process and an additive white process respectively. The whole AR clutter and white noise can be modeled by a noisy AR model. As another example, in array signal processing, the received source signal can be modeled by a 2-D noisy AR in terms of sensor number and snapshot number. By estimating the model parameters, a joint temporal and spatial signal spectrum can be provided. Using the spectrum the source parameters, including the frequency and the direction of arrival (DOA) can simultaneously be estimated. B Alimorad Mahmoudi a.mahmoudi@scu.ac.ir 1 Electrical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran 2 Iranian Space Research Center, Mechanic Institute, Shiraz, Iran 123