**1. Introduction**

Multi-target Direction of Arrival (DOA) estimation is an essential issue in array processing and has a wide range of applications in source location, radar, sonar, and wireless communications [1,2]. Sparse representation and compressive sensing methods are used for DOA estimation of coprime array [3–6], while these methods are only applied in the case where the sources are stationary. In addition, difficulties also arise from the uncertainties of the source dynamics: the source may be moving or static. Thus, it is significant to extend the static DOA estimation algorithm to the dynamic DOA tracking algorithm.

The representative dynamic DOA tracking algorithms include the subspace tracking algorithm and the particle filter (PF) algorithm. The subspace tracking algorithm includes Projection Approximation Subspace Tracking (PAST) [7] and the Projection Approximation Subspace Tracking with Deflation (PASTD) [8]. In essence, these algorithms transform the determination of the eigensubspace into solving an unconstrained optimization problem, and combine the recursive least squares (RLS) theory to achieve effective tracking of the eigensubspace of time-varying sources. However, the RLS method is very sensitive to impulse noise, and the PAST algorithm's subspace tracking performance will degrade sharply in the impulse noise environment [9–11]. In an army of acoustic applications, such as underwater and room acoustic signal processing, the noise environment is non-Gaussian and is impulsive in nature [12,13]. Under investigation, it was found that α stable distribution (0 < α ≤ 2) is a suitable noise model to describe this type of noise [14]. In recent years, DOA estimation technology in impulse noise environment has developed rapidly [15–17]. The PF algorithm based on Bayesian recursive estimation can solve the target tracking problem by utilizing a priori DOA and current measurement information [18]. In [19], the author considers the particle filtering method to estimate the single target DOA by using the spatial spectral function based on FLOM matrix as the likelihood function in the impulse noise environment. However, those algorithms needs to know the number of targets in advance and cannot deal with the estimation problem of the time-varying sources DOA.

In practical applications, such as submarine tracking and sonar positioning, the number of the sources are dynamic. Mahler introduced the concept of random finite set (RFS) in [20]. A tutorial on Bernoulli filters is introduced in [21]. A track-before-detect (TBD) Bernoulli filter based on RFS is proposed for DOA tracking in single dynamic system in [22], but it cannot solve the DOA tracking in multiple target dynamic system. The Multi-target Multi-Bernoulli (MeMBer) filtering [23] is a filter developed under the RFS framework. The advantage is that it operates on the dimensions of a single target space, thus avoiding the computational complexity and data association problems of the joint filter. Choppala P B et al. studied the Bayesian multi-target tracking problem based on phased array sensor, and proposed the MUSIC spatial spectral as a pseudo-likelihood in the Multi-Bernoulli filter in [24]. However, the shortcoming of this algorithm is that impulse noise is not considered, and Gaussian noise model is not appropriate in practical applications.

Based on the above analysis, a particle filter algorithm of DOA tracking for Unscented Transform MeMBer (UT-MeMBer) in an impulse noise environment is proposed. UT is used to construct a new important density function, which makes the estimation accuracy higher when the particle degenerates. Since particles close to the real state are more likely to output a larger spatial spectral response, the magnitude of the spatial spectral response is used as a feature of pseudo-likelihood. Based on the FLOM matrix, this paper uses FLOM matrix to substitute the covariance matrix to obtain the corresponding MUSIC spatial spectrum as the particle likelihood function. Further exponential weighting can increase the weight of the particles, making resampling more efficient. The main advantage of the tracking algorithm is that the number and state of the target can be accurately tracked when the number and state of the sources are unknown in impulse noise environment.

The rest of the paper is organized as follows. In Section 2, the problem of the DOA tracking in impulsive noise environment is described. In Section 3, we outline the Multi-Bernoulli's Bayesian theory of DOA tracking. An improved algorithm for likelihood functions is introduced in Section 4. The UT-MeMBer DOA particle filter tracking algorithm is given in Section 5. We then show our simulation results in Section 6 and conclusion in Section 7.
