Elsevier

Signal Processing

Volume 161, August 2019, Pages 203-213
Signal Processing

Direct position determination of multiple coherent sources using an iterative adaptive approach

https://doi.org/10.1016/j.sigpro.2019.03.023Get rights and content

Highlights

  • The direct localization algorithm combining with the iterative approach is proposed for coherent sources.

  • The connected domain separation method can efficiently isolate and extract the domains containing different sources.

  • The proposed algorithm outperforms the existing methods in accuracy and robustness for locating coherent sources.

  • Increasing antennas can obtain better localization performance from energy gain and spatial filtering effect.

Abstract

The direct position determination (DPD) approach is known to outperform the two-step localization at low signal to noise ratio, however, and it encounters many difficulties when locating multiple coherent sources. In this paper, we combine the DPD with the iterative adaptive approach (IAA) to address the localization problem of coherent sources without knowing the transmitted signals. The frequency-domain coherent signal model is established to obtain snapshot samples for jointly processing signals received by all distributed arrays. To avoid the covariance matrix becoming rank-deficient, we propose to use the IAA to compute it and the intercepted signals, instead of the traditional methods directly based on the snapshots. Once estimating the intercepted signals, the closed-form spatial power function is derived to determine the positions of multiple coherent sources. Additionally, the method based on connected domain separation is also proposed to extract the position of each source from the spatial power map. Numerical experiments show that the proposed algorithm is superior to the existing DPD algorithms in accuracy and robustness for coherent sources, and can obtain the same great performance with the existing ones for noncoherent sources.

Introduction

Localization of sources is a crucial fundamental task in many application fields such as radar, sonar, navigation system and wireless sensor network, and recently attracts much interest of many researchers [1], [2], [3], [4], [5], [6], [7], [8], [9]. Generally, localization methods are mainly categorized as two-step localization and one-step localization. In the two-step localization method, the estimation of a source position is implemented by two processing steps, where sensors firstly measure angles or ranges of the source from received signals, such as angle of arrival (AOA), time of arrival (TOA) and time difference of arrival (TDOA), and then estimate the source position by utilizing the previous measurements according to the geometric relationship between the source and sensors [6], [10], [11], [12], [13], [14], [15]. In the one-step localization method, the position is determined by directly handling the raw received signals without estimating the intermediate measurements like TDOA, etc. On the basis of knowing a received signal model, the one-step localization is generally accomplished by adopting the maximum likelihood (ML) estimation [8], [9], [16], the least square (LS) approach [17], [18], [19] or the sparsity recovery method [20], [21].

The one-step localization method can directly estimate the source position from the raw received signals, and obtain processing gain, so it has an advantage of high-accurate and robust localization over the two-step approach, especially in strong noise environment. In [17], the direct position determination (DPD) approach, belonging to the one-step localization, has shown better accuracy than the two-step localization based on AOA or TOA at low signal to noise ratio (SNR) for a single emitter. Additionally, the DPD approach has also natural superiority in application of multi-target localization, since it needn’t match these AOAs, TOAs or TDOAs to the corresponding targets as the two-step approach does.

Having the advantages over the two-step localization, the DPD approach has been applied in the scene of multiple sources [18], [19], [22]. The DPD approach based on the multiple signal classification (MUSIC) [23], called as DPD-MUSIC, is proposed to locate multiple sources on the condition of knowing the number of sources [18]. DPD-MUSIC only requires two-dimensional spectrum peak search in a planar geometry to determine the positions of all sources without high computational cost. In [19], the high-accurate DPD combined with the minimum variance distortionless response (MVDR) [24], called as DPD-MVDR, is developed to deal with the case where the number of sources are unknown. Similar with DPD-MUSIC, DPD-MVDR can also locate the source positions only by two-dimensional search. But, only when the transmitted signals are uncorrelated or partially correlated, can both DPD-MUSIC and DPD-MVDR obtain high localization accuracy for each source.

In practice, many perfectly correlated (coherent) signals appear in some cases, such as coherent interference, multipath propagation and coherent radiation sources. In the coherent case, many techniques based on eigenstructure and beamforming, like MUSIC and MVDR approaches, fail to work [25]. Due to the property of MUSIC and MVDR, DPD-MUSIC and DPD-MVDR will encounter a serious performance deterioration for coherent signals. Although many algorithms based on the spatial smoothing preprocessing scheme and the iterative approach have been proposed to settle the coherent signal problems [26], [27], [28], [29], [30], [31], they can only provide the intermediate measurements AOAs to determine the source positions by the two-step localization [32], [33], [34], [35]. As mentioned above, the two-step localization methods based AOA confront unstable performance at low SNR, and also have to match measurement parameters in multiple sources scene.

The focus of this paper is to solve the direct localization problem of multiple coherent sources. Our proposed method combines the DPD technique with the iterative adaptive approach (IAA) [30] to estimate the positions of coherent sources. In this paper, we quantitatively analyze the reasons of invalidity of DPD-MUSIC and DPD-MVDR for coherent signals. To avoid the covariance matrix becoming rank-deficient, we propose to employ the IAA to compute it, instead of the traditional array processing. Meanwhile, the received signals are also estimated iteratively. Based on these signals, a spatial power function is derived to compute the intercepted power from which the source positions can be determined by grid search. In addition, an extraction method based on connected domain separation is proposed to obtain the position of each source. Similar with DPD-MUSIC and DPD-MVDR method, the proposed algorithm also requires only two-dimensional search for planar geometry to locate all sources. Unlike the two-step methods, the proposed algorithm is direct without estimating the intermediate measurements. The simulation results are shown to demonstrate the efficiency of the proposed algorithm for coherent sources.

The contributions of our paper are summarized as follow. (1) We propose to employ the IAA to address the direct localization problem of multiple coherent sources. The IAA is developed to apply in the one-step localization without estimating intermediate measurements AOAs. (2) For the position extraction problem that the multi-target localization always encounters, we propose a method based on connected domain separation to obtain the position of each source.

The paper is organized as follows: Sections 2 and 3 state the signal model and the DPD problem formulated for coherent sources at distributed receivers, respectively. Section Sections 4 presents the proposed algorithm in detail, followed by numerical examples in Sections 5. Finally, a conclusion is drawn in Sections 6.

Section snippets

Signal model

Consider a localization system consisting of L widely distributed receivers, each of which equips a M-element antenna array. It is required that K emitters (or sources) transmitting unknown coherent signals are located by the L receivers, shown in Fig. 1. The receivers and emitters are located in a two-dimensional plane. The coordinates of L receivers and K emitters are denoted by ql=(xl,yl), l=1,,L and pk=(xk,yk), k=1,,K, respectively. The transmitted signals from K emitters, represented by s

Problem formulation about direct position determination of coherent sources

As denoted in (6), the position parameters of the emitters only appear at the equivalent array response a˜l(pk,ωi), so many spectral methods can be employed to estimate the positions [18], [19]. For brevity, (6) is rewritten as the vector formrl(ωi,n)=Al(θ,ωi)s(ωi,n)+el(ωi,n),whereAl(θ,ωi)=[αl1a˜l(p1,ωi),,αlKa˜l(pK,ωi)],s(ωi,n)=[s1(ωi,n),,sK(ωi,n)],and “⊤” is the transpose notation. Considering the coherency defined in (1), the correlation matrix of the transmitted signals in frequency

Direct position determination algorithm of multiple coherent sources

In this section, the DPD based on the IAA is derived to solve the localization problem for the coherent sources, called as DPD-IAA below for brevity. DPD-IAA utilizes signal power to estimate the source positions essentially. We first employ the weighted least square (WLS) to estimate the intercepted signals, and then further compute the covariance matrix and the spatial power iteratively by the estimated signals. After determining the convergent spatial power function, the positions of each

Numerical examples

In this section, we investigate the proposed DPD-IAA, DPD-MUSIC and DPD-MVDR algorithms for multiple sources in the two situations of transmitting coherent and noncoherent signals. The Monte Carlo simulation experiments are conducted to examine the performance of three algorithms. In each of the experiments, three sources are distributed randomly at three different rectangular regions respectively with their centers located at coordinates (8,12) km, (0,18) km and (8,12) km while four receivers

Conclusion

In this paper, we propose the localization algorithm combining the IAA method with the DPD concept to locate multiple coherent sources with distributed receivers. The paper derives the spatial power function to estimate the source positions. The proposed algorithm can still work effectively even though the signals are perfectly correlated. The method based on connected domain separation is also proposed to extract the position of each source. Simulation experiments compare the performance of

Conflict of interest

None.

Acknowledgments

This work was supported in part by the Chang Jiang Scholars Program, in part by the 111 Project No. B17008, in part by the National Natural Science Foundation of China under Grant 61771110, in part by the Fundamental Research Funds of Central Universities under Grant ZYGX2016J031, and in part by the Chinese Postdoctoral Science Foundation under Grant 2014M550465 and Special Grant 2016T90845.

References (38)

  • A.J. Weiss

    Direct position determination of narrowband radio frequency emitters

    IEEE Signal Process. Lett.

    (2004)
  • R. Schmidt

    Multiple emitter location and signal parameter estimation

    IEEE Trans. Antennas Propag.

    (1986)
  • T. Yardibi et al.

    Source localization and sensing: a nonparametric iterative adaptive approach based on weighted least squares

    IEEE Trans. Aerosp. Electron. Syst.

    (2010)
  • N. Patwari et al.

    Locating the nodes: cooperative localization in wireless sensor networks

    IEEE Signal Process. Mag.

    (2005)
  • K. Witrisal et al.

    High-accuracy localization for assisted living: 5g systems will turn multipath channels from foe to friend

    IEEE Signal Process. Mag.

    (2016)
  • H. Godrich et al.

    Target localization accuracy gain in MIMO radar-based systems

    IEEE Trans. Inf. Theory

    (2010)
  • M.Z. Win et al.

    Network localization and navigation via cooperation

    IEEE Commun. Mag.

    (2011)
  • Y. Han et al.

    Performance limits and geometric properties of array localization

    IEEE Trans. Inf. Theory

    (2016)
  • K.W.K. Lui et al.

    Semi-definite programming algorithms for sensor network node localization with uncertainties in anchor positions and/or propagation speed

    IEEE Trans. Signal Process.

    (2009)
  • T. Le et al.

    Closed-form and near closed-form solutions for TDOA-based joint source and sensor localization

    IEEE Trans. Signal Process.

    (2017)
  • R. Niu et al.

    Target localization and tracking in noncoherent multiple-input multiple-output radar systems

    IEEE Trans. Aerosp. Electron. Syst.

    (2012)
  • Q. He et al.

    Noncoherent MIMO radar for location and velocity estimation: more antennas means better performance

    IEEE Trans. Signal Process.

    (2010)
  • K.C. Ho et al.

    Source localization using TDOA and FDOA measurements in the presence of receiver location errors: analysis and solution

    IEEE Trans. Signal Process.

    (2007)
  • Y. Wang et al.

    TDOA source localization in the presence of synchronization clock bias and sensor position errors

    IEEE Trans. Signal Process.

    (2013)
  • J. Shen et al.

    Accurate passive location estimation using TOA measurements

    IEEE Trans. Wireless Commun.

    (2012)
  • J. Liang et al.

    Lagrange programming neural network approach for target localization in distributed MIMO radar

    IEEE Trans. Signal Process.

    (2016)
  • A. Guerra et al.

    Single-anchor localization and orientation performance limits using massive arrays: MIMO vs. beamforming

    IEEE Trans. Wirel. Commun.

    (2018)
  • A. Shahmansoori et al.

    5G position and orientation estimation through millimeter wave MIMO

    Proc. IEEE Globecom Workshops (GC Wkshps)

    (2015)
  • W. Yi et al.

    Joint estimation of location and signal parameters for an LFM emitter

    Signal Process.

    (2017)
  • Cited by (0)

    View full text