Multipath mitigation method based on Gaussian mixture model in RF relative measurement

Radio Frequency (RF) technology represents a high-precision relative navigation solution that has significant potential for application to earth-orbiting satellites. In precision applications, multipath errors dominate the total error because observables, which are used to estimate carrier-phase integer ambiguity, are not always subject to a Gaussian distribution when dual-frequency ambiguity estimation methods are used in the presence of multipath. As it has been shown that ranging observables obey a Gaussian mixture distribution, this study proposes improvements to the accuracy of estimation based on multipath mitigation founded on the Gaussian mixture model. To this end, such a model is created for integer ambiguity resolution in the presence of multipath, using which the theoretical error in dual-frequency ambiguity estimation is derived. Expectation Maximization (EM), which aids dual-frequency ambiguity estimation, is subsequently proposed to reduce the effect of multipath errors. Finally, two experimental scenarios are implemented to test the performance of the proposed method. The results show that EM-aided dual-frequency ambiguity estimation reduces the range error to approximately 20% in comparison with simple dual-frequency ambiguity estimation. Therefore the proposed technique is effective for multipath mitigation in RF relative measurement.     

多径效应对GPS载波相位观测量的影响

推导了ＧＰＳ接收机中多径效应引入的最大载波相位跟踪误差的闭合形式。得到以下结论：当直达信号跟踪误差不超过１码片时,最大载波测相多径误差为１／４周,该值出现在测码伪距多径误差最小的情况下;当直达信号跟踪误差超过或等于１码片时,接收机跟踪多径信号,信号误检发生。     

An LMS Adaptive Array for Multipath Fading Reduction

Multipath fading often poses a serious hindrance in radiocommunication. The application of a least-mean-square (LMS)adaptive array to the problem of multipath fading reduction is discussed. However, it is known that multipath components are in general correlated with one another. We examine the effect of the correlation on the performance of the LMS adaptive array. When the correlation coefficient does not equal or approximate 1, the LMS adaptive array suppresses the multipath signals significantly by nulling. On the other hand, when the correlation coefficient nearly equals 1, the LMS adaptive array prevents the output signalpower from decreasing. Therefore, the LMS adaptive array mayreduce the multipath fading effectively for any correlation coefficient value. A reference signal in the LMS adaptive array is also discussed. It is shown that synchronization in the referencesignal generation must be extremely accurate. Moreover, aprocessor configuration is proposed which may generate thereference signal with the required accuracy.     

GPS code and carrier multipath mitigation using a multiantennasystem

Multipath is a major source of error in high precision Global Positioning System (GPS) static and kinematic differential positioning. Multipath accounts for most of the total error budget in carrier phase measurements in a spacecraft attitude determination system. It is a major concern in reference stations, such as in Local Area Augmentation Systems (LAAS), whereby corrections generated by a reference station, which are based on multipath corrupted measurements, can significantly influence the position accuracy of differential users. Code range, carrier phase, and signal-to-noise (SNR) measurements are all affected by multipath, and the effect is spatially correlated within a small area. In order to estimate and remove code and carrier phase multipath, a system comprising a cluster of five GPS receivers and antennas is used at a reference station location. The spatial correlation of the receiver data, and the known geometry among the antennas, are exploited to estimate multipath for each satellite in each antenna in the system. Generic receiver code and carrier tracking loop discriminator functions are analyzed, and relationships between receiver data, such as code range, carrier phase, and SNR measurements, are formulated and related to various multipath parameters. A Kalman filter is described which uses a combination of the available information from the antennas (receivers) in the multiantenna cluster to estimate various multipath parameters. From the multipath parameters, the code range and carrier phase multipath is estimated and compensated. The technique is first tested on simulated data in a controlled multipath environment. Results are then presented using field data and show a significant reduction in multipath error     

Receiver-channel based adaptive blind equalization approach for GPS dynamic multipath mitigation

Aiming at mitigating multipath effect in dynamic global positioning system (GPS) satellite navigation applications, an approach based on channel blind equalization and real-time recursive least square (RLS) algorithm is proposed, which is an application of the wireless communication channel equalization theory to GPS receiver tracking loops. The blind equalization mechanism builds upon the detection of the correlation distortion due to multipath channels; therefore an increase in the number of correlator channels is required compared with conventional GPS receivers. An adaptive estimator based on the real-time RLS algorithm is designed for dynamic estimation of multipath channel response. Then, the code and carrier phase receiver tracking errors are compensated by removing the estimated multipath components from the correlators’ outputs. To demonstrate the capabilities of the proposed approach, this technique is integrated into a GPS software receiver connected to a navigation satellite signal simulator, thus simulations under controlled dynamic multipath scenarios can be carried out. Simulation results show that in a dynamic and fairly severe multipath environment, the proposed approach achieves simultaneously instantaneous accurate multipath channel estimation and significant multipath tracking errors reduction in both code delay and carrier phase.     

A model for target detection with over-the-horizon radar

The effects of including Faraday rotation and multipath on the probability of detecting low-flying, distant, fluctuating and nonfluctuating targets immersed in Rayleigh noise plus clutter are studied. The effect of ionospheric fluctuations is also considered. It is found that both multipath and Faraday rotation strongly influence the detection statistics, with the effect being greatest for linearly polarized targets and less marked for symmetric targets     

Antenna Performance in the Presence of Diffuse Multipath

Diffuse multipath is a random phenomenon that arises out of the diffraction of waves from rough surfaces. This form of multipath can in turn affect the angle estimation performance of monopulse antenna systems. In order to evaluate its effect, it is necessary to obtain the channel spread function that results. This function is basically the wave number spectrum of the resulting random field generated by the scattering. To do this, use is made of the Kodis-Barrick arrick scattering cross section and Wagner's shadowing function. The evaluation is performed for the specific geometry of a spherical earth. Evaluation of the system performance degradation is made for various angle estimation system configurations.     

On Optimizing Array Reception of Multipath

This paper reviews system configuration requirements and analyzes detectability performance characteristics for maximum likelihood array reception of multipath. Performance is analyzed to determine the effects of channel multipath structure (multipath delay and signal power division among the paths), space-time correlation properties of the incident processes, and the array spacing. It is shown by a series of case studies, that for single element coupling, as well as array coupling, an increased multipath delay factor results in decreased system detectability for fixed signal and noise intensity levels. The performance capacity is degraded as the available signal power tends to distribute more uniformly between the paths. These effects are attributed to the loss of effective signal energy concentration, resulting in a lower effective pre-detection signal-to-noise ratio. An investigation of the effects upon system performance, due to array element spacing, shows that performance is enhanced by increasing the spacing relative to the multipath delay factor and the reciprocal signal bandwidth. The former is the result of a more directive detectability (beam) pattern arising from the increased spacing. In effect, with increased spacing, the main lobe of the pattern is narrowed, while the side lobes are optimally suppressed by the required noise related array element link, frequency filters (weights).     

Assessment and improvement of the capabilities of a window correlator to model GPS multipath phase errors

The potential of output from a window correlator to mitigate GPS phase multipath is reviewed and assessed based on the analysis of data collected in controlled multipath environments under both static and kinematic conditions. Previous findings that the method is suboptimal for reflectors leading to additional path lengths of less than about 7m are confirmed, and methods for combining this output with two other multipath indicators: time series of signal-to-noise ratios (SNRs) and estimates of code multipath from dual frequency code and phase combinations, are investigated. A new method to combine all three indicators has been found and its application is shown to improve the quality of GPS static phase data by between 10% and 20% depending on the length of the additional path travelled by the reflected signal. The method can be applied completely automatically as it uses just the three multipath indicators; no knowledge of the surrounding environment is required. The paper concludes with some suggested practical applications.     

北斗二号中AS信号多径抑制方法及性能分析

针对北斗二号系统中AS（Authorized Service,授权服务）采用的BPSK（10）、BOC（14,2）、BOC（15,2.5）信号,研究如何抑制多径效应对AS信号跟踪的影响,提高定位精度.对3种信号的自相关特性及功率谱密度进行比对,并在对基于码跟踪环的EML（Early Minus Late,早减迟）和HRC（High Resolution Correlator,高精度相关器）技术进行分析的基础上,将这2种技术用于北斗二号AS信号的多径抑制.仿真表明：EML和HRC均适用于北斗二号AS信号,采用EML时,对BOC（14,2）、BOC（15,2.5）的多径抑制性能优于对BPSK（10）的;采用HRC时,对BPSK（10）的多径抑制性能优于对BOC（14,2）、BOC（15,2.5）的;对于BPSK（10）,HRC较EML在误差包络面积上多径抑制性能提高约89.7％;对于BOC（14,2）、BOC（15,2.5）,HRC和EML多径抑制性能相当,而EML的计算量相对较小因而整体性能更优;通过减小相关器间隔和增大带宽,可提高多径抑制性能,对BPSK（10）的效果比对BOC（14,2）、BOC（15,2.5）的更为明显.     

Multipath-adaptive GPS/INS receiver

Multipath interference is one of the contributing sources of errors in precise global positioning system (GPS) position determination. This paper identifies key parameters of a multipath signal, focusing on estimating them accurately in order to mitigate multipath effects. Multiple model adaptive estimation (MMAE) techniques are applied to an inertial navigation system (INS)-coupled GPS receiver, based on a federated (distributed) Kalman filter design, to estimate the desired multipath parameters. The system configuration is one in which a GPS receiver and an INS are integrated together at the level of the in-phase and quadrature phase (I and Q) signals, rather than at the level of pseudo-range signals or navigation solutions. The system model of the MMAE is presented and the elemental Kalman filter design is examined. Different parameter search spaces are examined for accurate multipath parameter identification. The resulting GPS/INS receiver designs are validated through computer simulation of a user receiving signals from GPS satellites with multipath signal interference present The designed adaptive receiver provides pseudo-range estimates that are corrected for the effects of multipath interference, resulting in an integrated system that performs well with or without multipath interference present.     

非合作无源探测中的假设检验弱目标检测方法

在非合作无源探测系统中,弱目标回波不仅会受到强直达波、强多径的干扰,还会受到强目标的掩盖干扰,因此很难对其进行有效检测。为了解决这一问题,提出了一种基于多择复合假设检验的弱目标检测方法。首先将接收信号投影到多径干扰的正交补子空间内,以消除强直达波和强多径干扰,然后将目标检测看作一个多择复合假设检验问题,建立了与之相应的基本框架模型,利用最大后验估计方法对目标时延、多普勒频移及信号幅度等参数进行估计,构造检验统计量,设置相应的门限,根据假设检验结果,逐个消除强目标干扰从而达到检测弱目标的目的。仿真结果表明,本方法可以有效抑制强直达波、强多径及强目标干扰,有效检测出弱目标,且虚警率低。     

Adaptive SNR-based carrier phase multipath mitigation technique

An improved technique that mitigates specular multipath in Global Positioning System (GPS) differential carrier phase measurements is described. It adaptively estimates the spectral parameters (frequency, amplitude, phase offset) of multipath in the associated signal-to-noise ratio (SNR), and then constructs a profile of the multipath error in the carrier phase. A multipath correction is subsequently made by subtracting the profile from the actual phase measurement data. The technique is demonstrated on ground based experimental data, as well as flight data from the atmospheric research satellite CRISTA-SPAS. Ground experiments were conducted on static platforms in severe multipath environments. Multipath was deliberately introduced by either strategic placement of reflectors or electronic injection. This allowed for some control over the strength and frequency of the multipath. Averaging the results from 43 ground and 18 flight data sets, the differential carrier phase multipath was reduced by 47%. The complete results for both ground and flight tests are presented and are accompanied by discussions of individual cases     

Evaluation and reduction of multipath-induced bias on GPS time-of-arrival

New expressions are presented for the multipath-induced pseudorange error (i.e. bias) and variance introduced by multipath onto the time-of-arrival estimate obtained using a noncoherent early-late gate discriminator. The results include the effect of front-end bandwidth and early-late gate spacing. We also investigate a blind method for cancelling the multipath, in order to improve the time-of-arrival estimate. Our approach uses early-late gate processing on an objective function derived from an adaptive finite impulse response (FIR) filter that attempts to match the crosscorrelation of the received signal with a multipath-free replica of the desired crosscorrelation. This method performs reasonably well, and decreases the multipath-induced pseudorange error by approximately a factor of 2, even in very stressing multipath environments.     

Clutter and jammer multipath cancellation in airborne adaptiveradar

Airborne surveillance radars must detect and localize targets in diverse interference environments consisting of ground clutter, conventional jamming, and terrain scattered jammer multipath. Multidimensional adaptive filtering techniques have been proposed to adaptively cancel this interference. However, a detailed analysis that includes the effects of multipath nonstationarity has been elusive. This work addresses the nonstationary nature of the jammer multipath and its impact on clutter cancellation and target localization. It is shown that the weight updating needed to track this interference will also modulate sidelobe signals. At the very least, this complicates the localization of targets. At the worst, it also greatly complicates the rejection of clutter. Several techniques for improving cancellation of jammer multipath and clutter are proposed, including 1) weight vector interpolation, extrapolation, and updating; 2) filter architecture, constraint, and beamspace selection; 3) prefilters; 4) 3-D STAP architectures; and 5) multidimensional sidelobe target editing     

ISAR imaging of targets at low elevation angles

The problem of inverse synthetic aperture radar (ISAR) image reconstruction of targets at low elevation angle is considered. In this geometric condition the main causes affecting the reconstructed ISAR image are the multipath effect due to the reflection of the Earth's surface and the angular motions of the target produced by external action like wind, fast maneuvering, and sea waves as in the case of ships. The aim of this work is to analyze the effects that the multipath and the target angular motions jointly produce on the ISAR image. The results show that multipath generates some artifacts in the image whereas the target oscillations undergo a spatial-dependent blurring of the point spread function of the ISAR system. These theoretical results are validated by presenting some numerical examples relevant to aircrafts and ships in rectilinear or circular motion. A wide discussion on possible solutions of this problem is made in the conclusion     

雷达低空目标俯仰角跟踪的C2算法研究

在单脉冲测角体制下,由于多径回波信号的干扰,极大地降低了雷达低空目标仰俯角跟踪精度,甚至丢失目标。通过对多路径反射环境模型分析,得出了岸、海基单脉冲雷达低空目标跟踪时仰俯角测量误差的产生原因,提出将传统的多目标分辨算法(C2算法)应用于低角多径环境下目标俯仰角的跟踪测量,并在不同多径反射环境下对不同高度、不同飞行速度和飞行方向的目标进行了仿真,得到良好的仿真结果,表明该算法可较大地提高俯仰角跟踪测量精度。通过对仿真结果的分析,验证了该算法在低空目标跟踪中的有效性和可行性。     

Model-based multifrequency array signal processing for low-angletracking

Tracking low-altitude targets over the sea is problematic because of interference between the direct and reflected signal. Standard monopulse trackers can experience large errors because of multipath maximum likelihood estimation (MLE) has been used to more accurately estimate the target height in the presence of multipath MLE is a model-fitting technique where the model parameters are chosen to maximize the likelihood function. It is shown that the type of observation model has a large effect on performance. Tracking performance is compared using three different observation models employing varying amounts of a priori information. Results are presented for different array sizes: eight and 32-element arrays and two-element subarrays typical of phase monopulse. Performance is compared with that of standard techniques such as Fourier beamforming and phase monopulse     

Multipath Angle Error Reduction Using Multiple-Target Methods

The usual methods of reducing multipath angle errors in monopulse tracking radar achieve only limited success because they do not attack the root of the problem. A more correct approach is to accept the multipath signal as a second target and utilize a two-target signal processor which angle tracks both wavefronts. The processor will decouple the return signals so that relatively interference-free data on both waves are obtained. In this paper a signal processor for separating signal from (N - 1) multipath components is developed. The processor is then specialized to the case of only one multipath signal and evaluated by a computer simulation. Data show that large improvements are possible as compared to the usual monopulse tracking system. In particular, the usual large bias errors at low elevation angles are eliminated. Tracking precision compares favorably with the theoretically best possible for two-target tracking systems.     

卫星伪距多路径时空建模研究

目前,多路径误差是制约GPS技术向更高精度发展的主要误差源.为了减小静态观测环境下的多路径误差,基于多路径误差周期重复性的特点,提出了一种自适应噪声分析结合经验模态分解的方法处理原始数据,采用多项式拟合构建了函数模型,并利用该函数模型对相邻天的观测数据进行处理.实验结果表明,利用所提方法对观测数据进行处理,可有效减小多...