Direction finding for two-dimensional incoherently distributed sources with Hadamard shift invariance in non-uniform orthogonal arrays

This paper proposes a novel algorithm for Two-Dimensional (2D) central Direction-of-Arrival (DOA) estimation of incoherently distributed sources. In particular, an orthogonal array structure consisting of two Non-uniform Linear Arrays (NLAs) is considered. Based on first-order Taylor series approximation, the Generalized Array Manifold (GAM) model can first be established to separate the central DOAs from the original array manifold. Then, the Hadamard rotational invariance relationships inside the GAMs of two NLAs are identified. With the aid of such relationships, the central elevation and azimuth DOAs can be estimated through a search-free polynomial rooting method. Additionally, a simple parameter pairing of the estimated 2D angular parameters is also accomplished via the Hadamard rotational invariance relationship inside the GAM of the whole array. A secondary but important result is a derivation of closed-form expressions of the Cramer-Rao lower bound. The simulation results show that the proposed algorithm can achieve a remarkably higher precision at less complexity increment compared with the existing low-complexity methods, which benefits from the larger array aperture of the NLAs. Moreover, it requires no priori information about the angular distributed function.     

Azimuth/elevation direction finding using regular array geometries

The authors consider the problem of extending the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm for multiple source, cochannel direction finding to the two-dimensional case (e.g., azimuth and elevation angle estimation). Two algorithms are presented, one based on the optimal (minimal variance) subspace fitting formulation of ESPRIT, and the other based on an approximation to it. The algorithms are applicable to antenna arrays composed of identical subarrays displaced in two dimensions, such as uniform rectangular phased arrays. Simulation results illustrating the relative performance of the algorithms are also presented     

Sensitivity analysis of DOA estimation algorithms to sensor errors

A unified statistical performance analysis using subspace perturbation expansions is applied to subspace-based algorithms for direction-of-arrival (DOA) estimation in the presence of sensor errors. In particular, the multiple signal classification (MUSIC), min-norm, state-space realization (TAM and DDA) and estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithms are analyzed. This analysis assumes that only a finite amount of data is available. An analytical expression for the mean-squared error of the DOA estimates is developed for theoretical comparison in a simple and self-contained fashion. The tractable formulas provide insight into the algorithms. Simulation results verify the analysis     

A simple fixed-lag algorithm for tracking frequency rate-of-change

A family of simple fixed-lag frequency smoothing algorithms which provide good estimates of both frequency and frequency rate-of-change is reported. The smoothers were developed from a fixed-gain αβ tracker by replacing the recursive derivative estimator with a finite-impulse-response (FIR) differentiator. Simulation results are presented which show that the smoothing algorithms provide frequency estimates with a similar variance to those produced by the αβ filter but with greatly improved frequency-rate estimates. The smoothing algorithms and the αβ filter are also compared on the basis of the bias and delay introduced in the frequency-rate estimates. Although the results presented are for frequency estimation, the smoothing algorithms can be used in any single-input tracking application where some lag in the estimates is allowable     

2-D spatial smoothing for multipath coherent signal separation

The use of two-dimensional spatial smoothing (SS) to increase channel capacity of wireless communications system is discussed, The necessary and sufficient conditions on array configuration for applying SS to multiple signal classification (MUSIC), and adaptive beamforming algorithms are defined and proved, This array must have an orientational invariance structure with an ambiguity free center array, and the number of subarrays must be larger than or equal to the size of the largest group of coherent signals. We also studied the cause of ambiguities in a multipath environment. We found the necessary and sufficient conditions for a three-sensor array manifold to be ambiguity free and identified several higher order ambiguity situations, If an array is also central symmetric, the forward/backward SS (FBSS) can be used to improve the resolution. Finally, we extended our results to the estimation of signal parameters via rotational invariance techniques (ESPRIT). All the predicted results are verified by simulations     

一种基于高斯混合模型粒子滤波的故障预测算法

针对一类故障预测问题提出了一种基于粒子滤波的故障预测算法。在算法的状态估计阶段,采用联合估计和粒子滤波同时估计对象系统故障演化模型状态和未知参数的后验分布。在算法的状态预测阶段,采用了两种不同的计算方法：一种方法是对状态变量当前时刻的后验分布进行迭代采样,从而获得未来时刻的状态变量的先验分布;另一种方法是采用数据驱动的方法预测未来一段时间内对象系统的量测信息,从而将未来时刻状态变量的先验分布的预测问题转化为一个求解后验分布的估计问题。采用高斯混合模型近似随机变量分布密度,从而将两种方法的计算结果在一个统一的预测框架之下进行有效交互,进一步提高了预测的准确性和可靠性。在算法的决策阶段,在获取的故障演化模型状态变量分布基础上,结合一定的故障判据近似计算出对象系统剩余寿命分布。故障预测仿真实验结果证明了所提算法的有效性。     

A Fault-Tolerant Multisensor Navigation System Design

The problem of soft-failure tolerant estimation in navigationsystems composed of multiple inertial measurement clusters and oneor more reference sensors is addressed. A new approach ispresented that achieves containment of failed sensor data, andisolates the historic good data provided by the unfailed sensors.Multiple (local) estimates are computed where the estimates areconditioned on different subsets of the sensors. A statistical overlaptest is used to determine the validity of the local estimates, and afailed sensor can be identified from analysis of the invalid localestimates. After the time of detection the most accurate estimatebased on all but the failed sensor is identified. The results areapplied to a dual-inertial/Doppler radar navigation system andsimulation results are presented.     

Instrumental variable adaptive array processing

An instrumental variable (IV) approach is presented for estimating the weights of an adaptive antenna array. Theoretical analysis of the IV method shows that the antenna gain weights are independent of finitely correlated noise, so that unbiased estimation of signal arrival angles is possible. Only matrix inversions are required to compute the weight estimates. In this sense, the IV method provides performance comparable with eigenvector techniques but with lower computational burden. Both minimal and overdetermined IV estimators are derived. The overdetermined estimators give the same theoretical array weights as minimal estimators, but yield more accurate weight estimates in real data situations. Simulation results are presented to compare these IV methods with one another and with conventional matrix inversion weight estimators. In these examples it is seen that IV methods are able to resolve closely spaced interference sources when conventional matrix inversion techniques cannot. It is also shown that overdetermined methods are capable of providing weight estimates with lower variances than those of minimal methods     

Improving ESPRIT via beamforming

Beamforming techniques are presented that improve the performance of the ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm for solving the narrowband multiple source location problem with uniform linear arrays. Using ESPRIT with these beamforming approaches maintains the computational advantage of the original ESPRIT while further exploiting the special structure of uniform linear arrays. Simulation results show that the use of ESPRIT with beamforming yields significantly improved performance compared with the original ESPRIT     

Decentralized linear estimation in correlated measurement noise

Some results and perspectives are provided on the problem of optimally combining estimates from different sensors when the measurement noise processes are correlated. The authors consider only the static estimation problem and limit the discussion to fusion with two sensors. A necessary and sufficient condition for optimality of the decentralized estimator in the presence of correlated measurement noise processes is presented. The result ties together previously reported work, and yields additional insights.<>     

Performance analysis of bearing-only target location algorithms

The performance of two well-known bearing-only location techniques, the maximum likelihood (ML) and the Stansfield estimators, is examined. Analytical expressions are obtained for the bias and the covariance matrix of the estimation error, which permit performance comparison for any case of interest. It is shown that the Stansfield algorithm provides biased estimates even for large numbers of measurements, in contrast with the ML method. The RMS error of the Stansfield technique is not necessarily larger than the RMS of the ML technique. However, it is shown that the ML technique is superior to the Stansfield method when the number of measurements is large enough. Simulation results verify the predicted theoretical performance     

一种MIMO雷达幅相误差估计方法

 针对单基地相关多输入多输出(MIMO)雷达中存在的阵列幅相误差问题进行了研究。给出了单基地相关MIMO雷达的阵列模型,并提出了一种MIMO雷达幅相误差估计方法。利用发射正交信号对阵列接收信号进行匹配滤波,可分离得到类似传统阵列的"虚拟阵列",利用分时信源数据将该阵列中真实导向矢量中信源波达方向(DOA)引起的相位与幅相误差分离开,通过构造代价函数得到波达方向估计值,进而分别得到发射阵与接收阵的幅相误差的估计值,同时给出了误差引入量分析。最后通过仿真验证了该方法的有效性。本文介绍的方法简单可行,适用于任意构型MIMO雷达的幅相误差估计。     

An experimental investigation of three eigen DF techniques

The comparative direction-finding (DF) performance of multiple signal classification (MUSIC), ROOT-MUSIC, and estimation of signal parameters via rotational invariance techniques (ESPRIT) is considered. Data were collected from two target transmitters operating simultaneously. The objective of the experiment was to evaluate multipath resolution capability using measurement precision equivalent to that found in modern radio direction-finding systems     

Angle of arrival estimation of coherent signals using an arraydoublet in motion

Shown here is how the estimation of signal parameters via relational invariance techniques (ESPRIT) algorithm may be used with a single pair of antennas in motion to estimate angles of arrival (AOA) for coherent signals. The approach exploits the Doppler frequency shifts caused by the doubler in motion. With this estimator, the number of signals that can be handled is not limited by the size of the array, as in the usual ESPRIT application, but by an adjustable parameter. A theoretical performance analysis of the estimator and typical examples showing the use of this estimator are given     

Error estimation of INS ground alignment through observabilityanalysis

A systematic analysis of the observability of an inertial navigation system (INS) in ground alignment with Bar-Itzhack and Berman's error model is presented. It is shown that the unobservable states are separately contained in two decoupled subspaces. The constraints on the selection of unobservable states are discussed. An estimation algorithm which is derived fully from the horizontal velocity outputs for computing the misalignment angles is provided. It reveals that the azimuth error can be entirely estimated from the estimates of leveling error and leveling error rate, without using gyro output signals explicitly     

Doppler ambiguity resolution using multiple PRF

An algorithm for velocity ambiguity resolution in coherent pulsed Doppler radar using multiple pulse repetition frequencies (PRF) is presented. It relies on the choice of particular values for the PRFs. The folded frequency of the target signal is obtained by averaging the folded frequency estimates for each PRF, and a quasi maximum likelihood criterion is maximized for ambiguity order estimation. The fast implementation of this nonambiguous estimation procedure is based on the fast Fourier transform (FFT), The proposed waveform allows full exploitation of any (even) number of PRFs, which appears to be important for estimation improvement. The effects of the waveform parameters and the folded frequency estimation variance on the performance of the ambiguity order estimation procedure are evaluated theoretically and through computer simulations. Mean square error (MSE) curves are given to assess the Doppler frequency estimation accuracy. Finally, the new method is compared with a classical technique and the implementation of the algorithm in a clutter environment is addressed.     

Performance analysis for DOA estimation algorithms: unification,simplification, and observations

Subspace based direction-of-arrival (DOA) estimation has motivated many performance studies, but limitations such as the assumption of an infinite amount of data and analysis of individual algorithms generally exist in these performance studies. The authors have previously proposed a unified performance analysis based on a finite amount of data and achieved a tractable expression for the mean-squared DOA estimation error for the multiple signal classification (MUSIC). Min-Norm, estimation of signal parameters using rotational invariance techniques (ESPRIT), and state-space realization algorithms. However, this expression uses the singular values and vectors of a data matrix, which are obtained by the highly nonlinear transformation of the singular value decomposition (SVD). Thus the effects of the original data parameters such as numbers of sensors and snapshots, source coherence and separations were not explicitly analyzed. The authors unify and simplify this previous result and derive a unified expression based on the original data parameters. They analytically observe the effects of these parameters on the estimation error     

Attitude Determination from Vector Observations: Quaternion Estimation

Two recursive estimation algorithms, which use pairs of measured vectors to yield minimum variance estimates of the quaternion of rotation, are presented. The nonlinear relations between the direction cosine matrix and the quaternion are linearized, and a variant of the extended Kalman filter is used to estimate the difference between the quaternion and its estimate. With each measurement this estimate is updated and added to the whole quaternion estimate. This operation constitutes a full state reset in the estimation process. Filter tuning is needed to obtain a converging filter. The second algorithm presented uses the normality property of the quaternion of rotation to obtain, in a straightforward design, a filter which converges, with a smaller error, to a normal quaternion. This algorithm changes the state but not the covariance computation of the original algorithm and implies only a partial reset. Results of Monte-Carlo simulation runs are presented which demonstrate the superiority of the normalized quaternion.     

A non-Bayesian segmenting tracker for highly maneuvering targets

The segmenting track identifier (STI) is introduced as a new methodology for tracking highly maneuvering targets. This nonBayesian approach dynamically partitions a target track into a sequence of track segments, making hard estimates of when the target's maneuvering mode transitions occur, and then estimates the parameters of the target model for each segment. STI is compared with two variable structures interacting multiple model (VS-IMM) algorithms through simulations, where it is shown to have a three fold performance advantage in median absolute turn rate estimation errors, as well as better position estimation for very highly maneuvering targets. STI is also shown to outperform a Rauch-Tung-Striebel (RTS) fixed-interval smoother when estimates are retrospectively derived, and STI accurately characterize the temporal pattern of maneuvers.     

受地效影响飞机起飞着陆运动模型的参数辨识

利用基于最小模型误差法和线性不连续跳跃多重打靶法建立的非线性辨识法，辨识了飞机起飞着陆过程的非线性动态模型。对于包含复杂非线性项的动态系统，本方法可以从实际试验测量的系统非线性数据，确定飞机处于地面效应影响运动过程的系统模型，而不需要预先详细描述系统的非线性形式。算例表明该方法对于原始近似动态系统的状态估计是足够精确的。