Time delay estimation at high signal-to-noise ratio

The estimation of the delay between two signals is examined in the limit of high signal-to-noise ratio (SNR). It is shown that for the case of white noise, cross correlation with no prefiltering approaches the optimal maximum-likelihood (ML) estimator as the SNR grows to infinity. In simulation experiments with SNRs greater than 1, it outperforms the approximate ML estimator, which is based on estimated spectra. Other algorithms, such as generalized cross correlation or parameter estimation algorithms, are shown to be suboptimal at high SNRs     

Adaptive Maximum Likelihood Receiver for Direct-Ranging Applications

Recent interest in direct-ranging navigation methods has prompted new research into practical receiver structures which provide improved signal processing. Maximum likelihood receivers are compared with conventional phase-locked receivers by theoretical and simulation methods as phase estimators based on signal measurements only. Signal-to-noise ratio (SNR) enhancement is examined and filter recommendations made. An adaptive maximum likelihood receiver is then developed which uses both signal measurements and a priori data to improve phase estimation accuracy. Simulation results indicate a 33.3 dB processing gain yielding a ranging error standard deviation of ±15 feet for zero dB received SNR. Nonadaptive and adaptive receivers are fabricated, flight tested, and experimental results reported.     

The split symbol moments SNR estimator in narrow-band channels

The split symbol moments estimator (SSME) is an algorithm that is designed to estimate symbol signal-to-noise ratio (SNR) in the presence of additive white Gaussian noise (AWGN). The performance of the SSME algorithm in bandlimited channels is examined, and the effects of the resulting intersymbol interference (ISI) are quantified. All results obtained are in closed form and can be easily evaluated numerically for performance-prediction purposes. The results are also validated through digital simulations     

Performance of a Square Law Pseudonoise Ranging Time-of-Arrival Estimator

The performance of a square law time-of-arrival (TOA) estimator that has been proposed for use in ASTRO-DABS, part of a possible satellite-based fourth generation air traffic control system is considered. The transmitted message consists of a pulse amplitude modulated (PAM) ranging sequence that, due to transmitter characteristics, is corrupted by an unknown frequency offset. The optimum TOA estimator, for the case of no frequency uncertainty, is first presented, together with a lower bound on the variance of the estimate generated. This is followed by the consideration of a suboptimum TOA estimator for which a high signal-to-noise ratio (SNR) performance analysis is carried out; here, the effects of frequency uncertainty are included. Next, the zero-crossing properties of the derivative of the (suboptimum) estimation statistic are presented and the results used to derive an upper bound to the TOA estimate variance that is valid for all SNR values. This latter result is significant because it displays the system threshold effect and complements performance lower bounds that may be derived via other methods. In addition, the method presented here may be applied to other optimum and suboptimum systems where a discrete set of parameters is to be estimated.     

Radar power multiplier for acquisition of low observables using anESA radar

In this paper the acquisition of a low observable (LO) incoming tactical ballistic missile using the measurements from a surface based electronically scanned array (ESA) radar is presented. We present a batch maximum likelihood (ML) estimator to acquire the missile while it is exo-atmospheric. The proposed estimator, which combines ML estimation with the probabilistic data association (PDA) approach resulting in the ML-PDA algorithm to handle false alarms, also uses target features. The use of features facilitates target acquisition under low signal-to-noise ratio (SNR) conditions. Typically, ESA radars operate at 13-20 dB, whereas the new estimator is shown to be effective even at 4 dB SNR (in a resolution cell, at the end of the signal processing chain) for a Swerling III fluctuating target, which represents a significant counter-stealth capability. That is, this algorithm acts as an effective “power multiplier” for the radar by about an order of magnitude. An approximate Cramer-Rao lower bound (CRLB), quantifying the attainable estimation accuracies and shown to be met by the proposed estimator, is derived as well     

Multiple radar targets estimation by exploiting induced amplitude modulation

This work deals with the problem of estimating complex amplitudes, Doppler frequencies, and directions of arrival (DOA) of multiple targets present in the same range-azimuth resolution cell of a surveillance radar. The maximum likelihood (ML) and the asymptotic (large sample size) ML (AML) estimators are derived. To reduce the computational complexity of the maximization of the nonlinear two-dimensional criterion function of the AML estimator, we propose a computationally efficient algorithm based on the RELAXation method. It allows decoupling the problem of jointly estimating the parameters of the signal components into a sequence of simpler problems, where the parameters of each component are separately and iteratively estimated. The proposed method overcomes the resolution limitation of the classical monopulse technique and resolves multiple targets exhibiting an arbitrarily small difference in azimuth as long as their Doppler frequencies differ at least by the inverse of the number of integrated pulses, provided that enough signal-to-noise ratio (SNR) per pulse is available. The performance of the proposed AML-RELAX estimator is numerically investigated through Monte Carlo simulation and Cramer-Rao lower bound (CRLB) calculation.     

Spacecraft formation-containment flying control with time-varying translational velocity

This paper investigates the problem of Spacecraft Formation-Containment Flying Control (SFCFC) when the desired translational velocity is time-varying. In SFCFC problem, there are multiple leader spacecraft and multiple follower spacecraft and SFCFC can be divided into leader spacecraft’s formation control and follower spacecraft’s containment control. First, under the condition that only a part of leader spacecraft can have access to the desired time-varying translational velocity, a velocity estimator is designed for each leader spacecraft. Secondly, based on the estimated translational velocity, a distributed formation control algorithm is designed for leader spacecraft to achieve the desired formation and move with the desired translational velocity simultaneously. Then, to ensure all follower spacecraft converge to the convex hull formed by the leader spacecraft, a distributed containment control algorithm is designed for follower spacecraft. Moreover, to reduce the dependence of the designed control algorithms on the graph information and increase system robustness, the control gains are changing adaptively and the parametric uncertainties are handled, respectively. Finally, simulation results are provided to illustrate the effectiveness of the theoretical results.     

圆形轨迹导引下的无人机事件触发抗干扰环绕控制

针对内部不确定性以及外部环境摄动的目标环绕控制问题,在基于反步法的双层制导框架下,利用级联控制思想,提出了一种圆形轨迹导引下的四旋翼无人机事件触发抗扰环绕控制方法。在轨迹回路中,构建了可满足持续激励条件的目标位置估计器,保证仅通过视线方位角就能获取可满足最终一致有界条件的目标估计项。随后,基于目标的位置估计结果,设计了目标环绕控制律生成线速度指令,并通过方向向量场验证了该环绕制导律的有效性,消除了现有李雅普诺夫向量场制导(LVFG)对相对位置和目标速度的依赖。在姿态回路中,通过采用扩张状态观测器(ESO)补偿系统的集总不确定性,设计了基于相对阈值事件触发控制的姿态控制器,在有效降低控制器到执行机构之间信号传输频率的同时,实现了四旋翼无人机对静止/移动目标环绕。然后,借助输入状态稳定性定理证明了系统的稳定性。仿真结果表明,所提控制方案能够实现圆形轨迹导引下四旋翼无人机对静止/移动目标的环绕监视。     

Angular Tracking of Two Closely Spaced Radar Targets

Bounds on the accuracy of unbiased estimates of the angular coordinates of a target, in the presence of a nearby interfering target, have previously been determined. These bounds allow for the angular resolution of two CW targets to an extent limited only by the signal-to-noise ratio (SNR). An SNR of 40 dB will allow two targets to be resolved at less than one-fifth beamwidth (?/2 X) separation, for most values of target relative phase angles. The maximum-likelihood estimator for this problem, based on the outputs of a plane circular array of receiving elements, is found and simplified. An analog realization of the two-target maximum-likeli-hood processor is presented. This realization has the simple form of two single-target trackers each tracking one of the targets, linked by a decoupling network which accounts for the interference produced in each by the presence of a second target, when the targets are separated by less than a beamwidth. Results of an analog-computer simulation of the system are given and discussed. Finally an application to the finite-size single-target problem is given.     

Constrained bandwidth waveforms with minimal dilation sensitivity

Bandpass waveforms which have envelopes which are insensitive to this velocity-induced time dilation can be efficiently processed by narrowband receivers in which envelope correlation is fixed and Doppler tested using fast Fourier transform (FFT) processing. The peak level of the waveform ambiguity function (AF) can be used to gauge the distortion of the waveform induced by dilation. The degree of AF attenuation is shown to be proportional to the dilation parameter or velocity, waveform traveling wave (TW) product, and a sensitivity parameter which depends on the envelope function utilized. Classes of symmetric, constrained bandwidth, phase modulated envelope functions which are minimally dilation sensitive (Doppler tolerant) are derived. When the resulting waveforms are used with a simple correlation receiver structure and the echo data is derived from slowly fluctuating point scattering in white Gaussian noise, the receiver becomes an uncoupled joint estimator of delay and dilation (Doppler). In the case of the bandpass waveforms, only odd symmetry of the phase modulation (PM) yields an uncoupled estimator     

A Study on Particle Filters for Single-Tone Frequency Tracking

In this paper, we present an online approach for frequency tracking of a noisy sinusoid using sequential Monte Carlo (SMC) methods, also known as particle filters (PFs). In addition, apart from employing the classical Cartesian formulation model, we also develop two alternative dynamical models, namely, nearly constant frequency (NCF) and Singer, which are adapted from the maneuvering target tracking discipline, to describe the evolution of time-varying frequencies, and investigate their fitness to the frequency tracking application. When compared with conventional techniques whose performance is restricted to linear Gaussian models and/or to slowly varying frequencies, PFs are more flexible to handle situations where these conditions are violated. Extensive evaluations on the proposed new models and PF tracking algorithms are conducted with different sets of frequency inputs and levels of signal-to-noise ratio (SNR). According to the computer simulation results, it is found that PFs under all investigated models consistently outperform and are less sensitive to SNR levels than the extended Kalman filter (EKF). Furthermore, the results suggest that while none of the models perfectly fits all types of frequency inputs, NCF model is more suitable for moderately varying frequencies, whereas the Singer is more suitable for rapidly changing frequencies.     

Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

Likelihood-ratio detection of frequency-hopped signals

The optimum system for intercepting frequency-hopped signals uses a channelized receiver and a likelihood-ratio test (LRT). Previous results on the performance of the optimum system have been based on Gaussian assumptions, which are generally valid for transmissions having large time-bandwidth areas. Results, obtained by Monte Carlo simulation, for relatively small time-bandwidth transmissions are given here. The signal model is a simple one known as “pure frequency hopping.” Comparisons with the LRT show that energy detection loss increases when the time-bandwidth product of the transmission is increased by increasing the number of frequencies, even when the number of pulses is also increased. The loss decreases when only the number of pulses is increased. Over the parameter range observed, binary detection loss tends to increase with the number of pulses and decrease with the number of frequencies. Results are included for a moving-window version of the LRT. A parameter of the LRT is the signal-to-noise ratio (SNR). The effect of using a design value not equal to the true SNR is shown     

Coordinated target localization base on pseudo measurement for clustered space robot

This paper presents a coordinated target localization method for clustered space robot.According to the different measuring capabilities of cluster members,the master-slave coordinated relative navigation strategy for target localization with respect to slavery space robots is proposed;then the basic mathematical models,including coordinated relative measurement model and cluster centralized dynamics,are established respectively.By employing the linear Kalman flter theorem,the centralized estimator based on truth measurements is developed and analyzed frstly,and with an intention to inhabit the initial uncertainties related to target localization,the globally stabilized estimator is designed through introduction of pseudo measurements.Furthermore,the observability and controllability of stochastic system are also analyzed to qualitatively evaluate the convergence performance of pseudo measurement estimator.Finally,on-orbit target approaching scenario is simulated by using semi-physical simulation system,which is used to verify the convergence performance of proposed estimator.During the simulation,both the known and unknown maneuvering acceleration cases are considered to demonstrate the robustness of coordinated localization strategy.     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

Maximun Posterion Probability Demodulation of Angle-Modulated Signals

An algorithm is presented for maximum posterior probability (MPP) demodulation of angle-modulated signals. A sampled data version of the problem is considered, in which additive Gaussian noise and Gaussian modulating signal are assumed. The algorithm is a numerical method for solving the nonlinear equations which are necessary conditions for MPP estimation. Results of a simulation of the algorithm are presented and discussed. Improvements in performance with respect to a phaselocked loop appear to stem from use of data before and after the time position of a phase estimate and from optimization of performance at low signal-to-noise ratio (SNR) as well as at high SNR.     

A new approach to robust fault detection and identification

A methodology for instrument fault detection and identification (FDI) in linear dynamical systems subject to plant parameter variations or uncertainties is presented. At the heart of this approach is a robust estimator for which the necessary and sufficient conditions to its existence are outlined. The robust estimator can simultaneously estimate the unmeasurable state variables of the system for the purpose of control and provide necessary information for FDI purposes. A novel feature of this approach is that it can actually identify the shape and magnitude of the failures. The scheme allows for fast and accurate FDI, and can account for structural uncertainties and variations in the parameters of the dynamical model of the system. The overall fault tolerant control system strategy proposed is verified through simulation studies performed on the control of a vertical takeoff and landing (VTOL) aircraft in the vertical plane     

On-line Vehicle Motion Estimation from Visual Terrain Information Part II: Ground Velocity and Position Estimation

An algorithm, combining velocity/height estimates, obtained from an airborne body fixed image shift estimator with auxiliary on-board measurements and sparsely stored terrain profile information constitutes an entirely passive autonomous navigation system suitable for moderate-g flight missions. Two versions are addressed. The "naive estimator," in which altitude estimates are multiplied by velocity/height estimaters, yields ground velocity. Position, obtained by integration, diverges with time. The "extended Kalman filter" (EKF) version, in which velocity and position are defined as state space components, locks on the stored terrain profile and does not diverge with time. It degenerates into the "naive estimator" if the terrain is completely flat. Numerical examples indicate excellent performance potential of the EKF estimator.     

遗传算法在低信噪比图象点目标检测中的应用

将遗传算法用于图象中低信噪比点目标的检测。在分析了点目标及背景特点的基础上,设计了编码方案及遗传操作算子,提出了合格个体保留法。仿真结果表明应用此算法,可实现信噪比为2dB的点目标的检测与跟踪。