Joint Estimation of TOA and DOA in IR-UWB System Using a Successive MUSIC Algorithm

Time-of-arrival (TOA) and direction-of-arrival (DOA) are key parameters in the impulse radio ultra wideband (IR-UWB) positioning system with a two-antennas receiver. A two-dimensional (2D) multiple signal classification (MUSIC) algorithm, which requires the 2D spectral peak search, can be used to estimate the parameters, but it has much higher computational complexity. This paper proposes a successive MUSIC algorithm for joint TOA and DOA estimation in IR-UWB system to avoid 2D spectral peak search. The proposed algorithm obtains the initial estimate of TOA corresponding to the first antenna via Root-MUSIC, and simplifies the 2D global search into successive one-dimensional searches to achieve the estimation of TOAs in the two antennas. It then estimates the DOA parameters via the difference of the TOAs between the two antennas. The proposed algorithm can get the parameters paired automatically, and has a much lower complexity than 2D-MUSIC algorithm. In addition, we have derived the mean square error of TOA and DOA estimation of the proposed algorithm and the Cramer–Rao bound of TOA and DOA estimation in the paper. The simulation results show that the parameter estimation performance of the proposed algorithm is better than that of Root-MUSIC, and is almost the same as that of 2D-MUSIC algorithm. Moreover, it has much better performance than matrix pencil algorithm, propagator method and estimation of signal parameters via rotational invariance techniques algorithm.     

IR-UWB 系统中基于 root-MUSIC 算法的 TOA 和 DOA 联合估计简

针对二维多重信号分类算法可以估计出系统的到达时间(TOA, time-of-arrival)和波达方向(DOA, direction- of-arrival)参数,但需要复杂度非常高的二维谱峰搜索这一问题,提出了IR-UWB系统中基于求根MUSIC(root-MUSIC)的TOA和DOA联合估计算法,该算法对接收信号的频域形式建模,先估计出TOA,然后由TOA的差值计算出DOA,从而实现TOA和DOA的联合估计。该算法不需谱峰搜索,可直接给出估计参数的闭式解,还可实现参数配对。还推导了参数估计的误差方差。仿真结果表明,该算法的参数估计性能明显优于矩阵束算法、传播算子算法以及基于旋转不变技术估计信号参数算法,并且非常接近于2D-MUSIC算法,但该算法的复杂度却远远低于2D-MUSIC算法。     

Joint Estimation of TOA and DOA in IR‐UWB System Using Sparse Representation Framework

This paper addresses the problem of joint time of arrival (TOA) and direction of arrival (DOA) estimation in impulse radio ultra‐wideband systems with a two‐antenna receiver and links the joint estimation of TOA and DOA to the sparse representation framework. Exploiting this link, an orthogonal matching pursuit algorithm is used for TOA estimation in the two antennas, and then the DOA parameters are estimated via the difference in the TOAs between the two antennas. The proposed algorithm can work well with a single measurement vector and can pair TOA and DOA parameters. Furthermore, it has better parameter‐estimation performance than traditional propagator methods, such as, estimation of signal parameters via rotational invariance techniques algorithms matrix pencil algorithms, and other new joint‐estimation schemes, with one single snapshot. The simulation results verify the usefulness of the proposed algorithm.     

Efficient 2-D DOA and frequency estimation for L-shaped array via RD-PM

This paper addresses the issue of joint two-dimensional direction of arrival (2-D DOA) and frequency estimation via reduced-dimensional propagator method (RD-PM) with L-shaped array. The proposed algorithm has no need for eigenvalue decomposition of the sample covariance matrix and simplifies three-dimensional global spectral search within the three-dimensional propagator method (3-D PM) to one-dimensional local search, which greatly reduces computational complexity. Furthermore, the proposed algorithm can work under both uniform and non-uniform L-shaped array and can achieve paired 2-D DOA and frequency estimates automatically. In addition, the 2-D DOA and frequency estimation performance for the proposed method is approximate 3-D PM algorithm and parallel factor (PARAFAC) method but exceeds the estimating signal parameters via rotational invariance techniques (ESPRIT) algorithm and improved PM algorithm. The detailed derivation of Cram´er-Rao bound (CRB) is provided and the simulation results demonstrate the effectiveness and superiority of the proposed approach.     

一种基于能量跳跃的脉冲超宽带TOA估计

基于到达时间估计(TOA)的脉冲超宽带(IR-UWB)测距理论上可达到厘米级的精度.当无法估计接收信噪比时,基于门限的TOA估计精度受到门限设置的限制.本文提出了一种基于能量跳跃函数(FEE)的最大能量跳跃(MEL)TOA估计算法.该算法将最大径之前一段时间内FEL取值最大的时刻作为TOA的估计,估计过程中不需要设置门限.本文通过仿真分别在CMl和CM2信道模型中比较了MEL和几种常用算法的绝对平均误差(MAE).仿真结果表明,在多径信道环境尤其是非视距(NLOS)环境中,MEL算法的估计精度比门限比较(TC)算法和最大值回推(MES-SB)算法有较大的提高,而且接收信噪比越高MEL算法的优势越明显,在信噪比高于12dB时估计精度提高约3至4纳秒.     

Two-dimensional DOA estimation for acoustic vector-sensor array using a successive MUSIC

This paper discusses the problem of two-dimensional (2D) direction of arrival (DOA) estimation for acoustic vector-sensor array, and derives a successive multiple signal classification (MUSIC) algorithm therein. The proposed algorithm obtains initial estimations of the azimuth and elevation angles obtained from the signal subspace, and uses successively one-dimensional local searches to achieve the joint estimation of 2D-DOA. The proposed algorithm, which requires the one-dimension local searches, can avoid the high computational cost within 2D-MUSIC algorithm. The proposed algorithm can obtain automatically-paired 2D-DOA estimation for acoustic vector-sensor array, and it has better DOA estimation performance than propagator method, estimation of signal parameters via rotational invariance technique algorithm and trilinear decomposition algorithm. Meanwhile, it has very close angle estimation to 2D-MUSIC algorithm. Furthermore, it is suitable for non-uniform linear arrays, works well for the sources with the same azimuth angle, and imposes less constraint on the sensor spacing, which does not have to be restricted within half-wavelength. We have also derived the mean-square error of DOA estimation of the proposed algorithm and the Cramer-Rao bound of DOA estimation. Simulation results verify the usefulness of the proposed algorithm.     

Novel angle estimation for bistatic MIMO radar using an improved MUSIC

In this article, we study the problem of angle estimation for bistatic multiple-input multiple-output (MIMO) radar and propose an improved multiple signal classification (MUSIC) algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation. The proposed algorithm obtains initial estimations of angles obtained from the signal subspace and uses the local one-dimensional peak searches to achieve the joint estimations of DOD and DOA. The angle estimation performance of the proposed algorithm is better than that of estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, and is almost the same as that of two-dimensional MUSIC. Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired DOD and DOA estimations, and avoid two-dimensional peak searching. The simulation results verify the effectiveness and improvement of the algorithm.     

矢量传感器阵列MIMO雷达高精度二维DOA与极化联合估计

该文采用矢量传感器配置下的十字型阵列MIMO雷达系统,提出一种新的2维高精度DOA与极化参数联合估计算法。首先根据MIMO雷达虚拟阵列导向矢量的特点,通过降维矩阵的设计及回波数据的降维变换,将高维回波数据转换至低维信号空间;然后基于传播算子获得对应信号子空间的估计,利用收、发阵列阵元间长基线对应的旋转不变性和极化矢量中电场矢量和磁场矢量的叉积进行2维高精度DOA估计和解模糊处理,同时利用与阵列结构无关的极化域旋转不变性进行极化辅角和极化相位差的联合估计。该矢量传感器MIMO雷达阵列可同时获取MIMO雷达的波形分集和矢量传感器的极化分集,无需额外增加阵元和硬件开销,能够有效扩展阵列孔径,提高参数估计性能;同时通过降维变换及传播算子,在获取信噪比增益的同时,能够实现2维高精度DOA和2维极化矢量的联合估计及参数的自动配对,有效降低数据处理维数和参数估计的运算复杂度;最后,仿真结果验证了理论分析的正确性和算法的有效性。     

基于双平行线阵的相干分布源二维DOA估计

针对现有相干分布源二维波达方向(DOA)估计算法存在的一些问题,基于双平行均匀线阵提出了一种相干分布源二维DOA估计新算法。利用旋转不变的思想并结合传播算子法来估计相干分布源的二维中心DOA。无需谱搜索和对样本协方差矩阵做特征分解,和传统算法相比,其计算复杂度更低。此外,还给出了详细的参数配对过程,因而能够应用于多源场合。算法在小角度扩展条件下估计性能良好,其性能甚至接近于一维交替搜索算法。算法还是一种对角分布先验知识盲的估计。仿真结果证实了算法的有效性。     

Nested planar array: configuration design,optimal array and DOA estimation

Nested array enables to enhance localisation resolution and achieve under-determined direction of arrival (DOA) estimation. In this paper, we improve the traditional nested planar array to achieve more degrees of freedom (DOFs) and better angle estimation performance. The closed-form expressions for sensor positions of the improved array are given and the optimal array configuration for largest available DOFs is derived. Meanwhile, a computationally efficient DOA estimation algorithm is proposed. Specifically, we utilise two dimensional Discrete Fourier Transform (2D DFT) method to obtain the coarse DOA estimates; Subsequently, we achieve the fine DOA estimates by 2D spatial smoothing multiple signals classification (SS-MUSIC) algorithm. The proposed algorithm enjoys the same estimation accuracy as SS-MUSIC algorithm but with lower complexity because the coarse DOA estimates enable to shrink the range of spectral search. In addition, estimation of the number of signals is not required by 2D DFT method. Extensive simulation results testify the effectiveness of the proposed algorithm.     

Computationally Efficient 2‐D DOA Estimation Using Two Parallel Uniform Linear Arrays

new computationally efficient algorithm‐based propagator method for two‐dimensional (2‐D) direction‐of‐arrival (DOA) estimation is proposed, which uses two parallel uniform linear arrays. The algorithm takes advantage of the special structure of the array which enables 2‐D DOA estimation without pair matching. Simulation results show that the proposed algorithm achieves very accurate estimation at a computational cost 4 dB lower than that of standard methods.     

Blind DOA and polarization estimation for polarization-sensitive array using dimension reduction MUSIC

A novel blind direction-of-arrival (DOA) and polarization estimation algorithm for polarization-sensitive uniform linear array using dimension reduction multiple signal classification (MUSIC) is proposed in this paper. The proposed algorithm utilizes the signal subspace to obtain an initial estimation of DOA, then estimates more accurate DOA through a one-dimensional (1-D) local searching according to the initial estimation of DOA, and finally obtains polarization parameter estimation via the estimated polarization steering vectors. The proposed algorithm, which only requires a one-dimension local searching, can avoid the high computational cost within multi-dimensional MUSIC algorithm. The simulation results reveal that the proposed algorithm has better DOA and polarization estimation performance than both estimation of signal parameters via rotational invariance technique algorithm and trilinear decomposition algorithm. Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired multi-dimensional parameter estimation, and avoid multi-dimensional searching. Simulation results verify the effectiveness of the proposed algorithm.     

基于扩展孔径波达方向矩阵法的高精度二维DOA估计

该文针对扩展孔径会产生估计模糊的现象,提出一种高精度扩展孔径波达方向矩阵算法。算法由个阵列单元组成双平行阵列几何结构,利用阵列传感器沿轴和沿轴的不同间距,分别构造波达方向矩阵,由此计算出高精度模糊的方向余弦估计和低精度无模糊的方向余弦估计,然后利用低精度无模糊的方向余弦估计值对高精度模糊的方向余弦估计值进行解模糊处理,得到高精度无模糊的方向余弦的估计值。该算法无需配对运算和2维搜索,是一种低运算量高精度的算法,计算机仿真实验验证了该算法的性能。     

基于矢量传感器MIMO雷达的DOD DOA和极化联合估计算法

该文研究了一种基于多输入多输出(MIMO)电磁矢量传感器阵列雷达目标波离角(DOD),波达角(DOA)和极化联合估计问题。提出一种新型矢量阵MIMO雷达系统模型,发射阵列采用常规阵元,而接收阵列采用电磁矢量传感器。在此基础上,该文提出4维MUSIC, ESPRIT和迭代1维MUSIC 3种联合参数估计算法。其中迭代1维MUSIC算法首先利用矢量传感器的内在结构特点获得目标DOA预估计,随后采用MUSIC算法对DOD和DOA分别进行1维搜索获得目标角度的高精度估计,最后给出一种基于ESPRIT的目标极化估计算法。迭代1维MUSIC算法可用于不规则阵列,对接收阵列约束较少,无需2维搜索及多维搜索,还可以利用矢量阵特点扩展阵列孔径提高DOA估计精度。此外,论文还推导了DOD, DOA和极化联合估计的CRB。仿真实验表明,与前两种算法相比,迭代1维MUSIC算法具有与CRB更接近的估计精度。     

多径信号到达角和时延高分辨联合估计算法

本文提出了一种新的高分辨高精度的多径信号到达角和时延联合估计算法.该方法通过对多径信号与参考信号进行相关处理,再根据PRO-ESPRIT算法的思想,实现了DOA(Direction-Of-Arrival)估计;并对相关延迟向量进行变换,从互功率谱相位中提取时延信息,完成了高分辨的TOA(Time-Of-Arrival)估计.最后,本文推导了频域模型下到达角和时延联合估计的Cramer-Rao下界.并将通过仿真对本算法的性能进行了评估.     

高斯白噪声下L阵二维波达方向快速估计

针对L型阵列,提出一种在高斯白噪声环境下的二维波达方向( DOA)快速估计方法。首先利用阵列结构特点构建两个互协方差矩阵,同时实现了噪声分量的有效抑制,再依据协方差矩阵的性质构造了波达方向矩阵。对该矩阵进行一次特征分解即可分别得到包含方位角和俯仰角信息的方向矢量和方向元素,实现二维DOA估计。该算法避免了传统算法的谱峰搜索或大矩阵构造及其特征分解过程,计算量小,且参数自动配对。仿真结果表明,该算法在低性噪比和少快拍下的估计精度与2 D ESPRIT算法近似,但计算复杂度大幅降低,适用于实时性高的工程应用背景。     

相干分布式信源二维波达方向估计算法

针对相干分布式信源二维波达方向估计算法多采用谱峰搜索导致计算复杂度较大的问题,该文提出了一种二维波达方向分离估计算法。该算法通过将积分形式的相干分布式信源方向向量化简为点信源方向向量与实向量的Schur-Hadamard积,对子阵X接收的数据构造二阶统计量;利用传播因子最小二乘估计子阵X与Z,X与W之间的旋转不变矩阵。由二阶统计量与旋转不变矩阵分别估计方位角与仰角,对于接近90的仰角也可给出有效的估计。与传统子空间算法相比,无需任何谱峰搜索和特征值分解,降低了计算复杂度。仿真实验表明了所提算法的有效性。     

DOA estimation of noncircular signals for coprime linear array via locally reduced-dimensional Capon

We investigate the issue of direction of arrival (DOA) estimation of noncircular signals for coprime linear array (CLA). The noncircular property enhances the degree of freedom and improves angle estimation performance, but it leads to a more complex angle ambiguity problem. To eliminate ambiguity, we theoretically prove that the actual DOAs of noncircular signals can be uniquely estimated by finding the coincide results from the two decomposed subarrays based on the coprimeness. We propose a locally reduced-dimensional (RD) Capon algorithm for DOA estimation of noncircular signals for CLA. The RD processing is used in the proposed algorithm to avoid two dimensional (2D) spectral peak search, and coprimeness is employed to avoid the global spectral peak search. The proposed algorithm requires one-dimensional locally spectral peak search, and it has very low computational complexity. Furthermore, the proposed algorithm needs no prior knowledge of the number of sources. We also derive the Crámer-Rao bound of DOA estimation of noncircular signals in CLA. Numerical simulation results demonstrate the effectiveness and superiority of the algorithm.     

采用局部搜索的二维DOA估计

针对酉旋转不变估计信号参数(Unitary-ESPRIT)算法估计精度较低的问题,提出了一种采用局部搜索实现的非相干信源二维波达方向(2-D DOA)估计方法.该方法首先利用实特征矢量近似值估计导向矩阵,然后利用矩阵Kronecker积性质以及阵列旋转不变特性获得自动配对的角度估计值,降低了2-D DOA初始估计复杂度,实现了对Unitary-ESPRIT算法的改进;接着,采用一维局部搜索法对该初始估计结果进行优化,提高了低信噪比下的2-D DOA估计精度.仿真实验结果表明,相较于传统的Unitary-ESPRIT算法,所提方法在DOA估计精度和成功率上具有明显的优势,特别是在低信噪比以及快拍数较少条件下,因此该方法能够在计算复杂度和估计性能之间取的较好的折中.     

Unfolded coprime L-shaped arrays for two-dimensional direction of arrival estimation

Generally, a coprime L-shaped array (CLsA) is composed of two uniform L-shaped subarrays with larger spacing among inter-element to accomplish the improved direction of arrival (DOA) estimation performance. In this paper, the two subarrays are unfolded to extend the array aperture and the performance of the unfolded CLsA (UCLsA) for two-dimensional (2D) DOA estimation is investigated. In addition, an all array multiple signals classification (AA-MUSIC) algorithm is proposed for the UCLsA. By stacking the received signals of the two subarrays, the ambiguity problem can be avoided on the basis of the coprime property. Simultaneously, due to the combination of the cross-correlation and auto-correlation, the proposed AA-MUSIC algorithm can achieve the full degrees of freedom (DOFs) and obtain more accurate DOA estimates, nevertheless, the expensive total spectral search is entailed. Consequently, a reduced complexity MUSIC (RC-MUSIC) algorithm is proposed to relieve the computational burden. The Cramer-Rao Bounds (CRBs) are utilised as a theoretical benchmark for the lower bound of unbiased estimate. Furthermore, numerical simulations verify the effectiveness and superiority of the AA-MUSIC algorithm and RC-MUSIC method for the UCLsA.