Joint TDOA,FDOA and differential Doppler rate estimation: Method and its performance analysis

Considering the estimation accuracy reduction of Frequency Difference of Arrival(FDOA) caused by relative Doppler companding, a joint Time Difference of Arrival(TDOA),FDOA and differential Doppler rate estimation method is proposed and its Cramer-Rao low bound is derived in this paper.Firstly, second-order ambiguity function is utilized to reduce the dimensionality and estimate initial TDOA and differential Doppler rate.Secondly, the TDOA estimation is updated and FDOA is obtained using cross ambiguity function, in which relative Doppler companding is compensated by the existing differential Doppler rate.Thirdly, differential Doppler rate estimation is updated using cross estimator.Theoretical analysis on estimation variance and Cramer-Rao low bound shows that the final estimation of TDOA, FDOA and differential Doppler rate performs well at both low and high signal–noise ratio, although the initial estimation accuracy of TDOA and differential Doppler rate is relatively poor under low signal–noise ratio conditions.Simulation results finally verify the theoretical analysis and show that the proposed method can overcome relative Doppler companding problem and performs well for all TDOA, FDOA and differential Doppler rate estimation.     

GPS小波去噪的误差方差建模技术与试验

如何消除GPS观测数据的噪声以提高定位精度并估算消噪信号的误差方差对工程测量具有重要意义。在介绍小波多尺度分析的基础上,推导了在小波多尺度分析巾平滑信号误差的理论方差模型。并通过实际的GPS单点静态定位试验给予验证。试验结果表明,该方法在有效消除噪声的同时,计算得到的各尺度平滑信号的误差方差与理论方差模型基本一致。     

The Estimation of the "Center of Gravity" of a Photon Density Profile in Noise

A model for an optical position estimation system is developed employing the photon Poisson process theory. The position estimate is based upon the definition of a center of gravity (CG) of the power density profile of the optical source on the focal plane. An estimator structure is derived using maximum likelihood estimates of the image profile. The resulting estimate of the CG is shown to be unbiased and its variance is obtained. The variance is shown to depend upon the signal energy and noise level as well as upon the distance of the center from the initial counting point. Thus, a composite estimation system is presented which reduces the variance and yet yields a simple structure. Studies on star estimation have yielded position accuracies better than 0.1 seconds of arc for a 2.5 visual magnitude star in a background of equivalent intensity.     

Area Target Response of Triangularly Frequency-Modulated Continuous-Wave Radars

For a postulated model of the area target returns, the variance of the signal appearing at the detector output of a frequency-modulated continuous-wave radar is analytically and graphically displayed as a function of the range and Doppler spread. The influence of important system parameters like modulation frequency, measuring time, and frequency excursion are also included in the analysis. Closedform relationships are given for sawtooth or triangular frequency modulation and a Gaussian separable scattering function. A comparison is also made between the range noise of an ideal frequency detector and a zero-crossings counter.     

Spectrum Distortion Due to Frequency Instabilities in a Two-Way Coherent Doppler Radar

The power spectral density of the intermediate frequency signal in a coherent Doppler navigation radar is derived. The effects of antenna parameters, periodic frequency instabilities, signal two-way transit time, and transmitter frequency modulation noise are considered Several examples based on the measured frequency modulation noise of a solid-state source transmitter are presented. The results indicate the degree of loss in signal-to-noise ratio, and spectrum broadening due to an increase in signal transit time and/or frequency modulation noise.     

Doppler visibility of coherent ultrawideband random noise radar systems

Random noise radar has recently been used in a variety of imaging and surveillance applications. These systems can be made phase coherent using the technique of heterodyne correlation. Phase coherence has been exploited to measure Doppler and thereby the velocity of moving targets. The Doppler visibility, i.e., the ability to extract Doppler information over the inherent clutter spectra, is constrained by system parameters, especially the phase noise generated by microwave components. Our paper proposes a new phase noise model for the heterodyne mixer as applicable for ultrawideband (UWB) random noise radar and for the local oscillator in the time domain. The Doppler spectra are simulated by including phase noise contamination effects and compared with our previous experimental results. A genetic algorithm (GA) optimization routine is applied to synthesize the effects of a variety of parameter combinations to derive a suitable empirical formula for estimating the Doppler visibility in dB. According to the phase noise analysis and the simulation results, the Doppler visibility of UWB random noise radar depends primarily on the following parameters: 1) the local oscillator (LO) drive level of the receiver heterodyne mixer, 2) the saturation current in the receiver heterodyne mixer, 3) the bandwidth of the transmit noise source, and 4) the target velocity. Other parameters such as the carrier frequency of the receiver LO and the loaded quality factor of the LO have a small effect over the range of applicability of the model and are therefore neglected in the model formulation. The Doppler visibility curves generated from this formula match the simulation results very well over the applicable parameter range within 1 dB. Our model may therefore be used to quickly estimate the Doppler visibility of random UWB noise radars for trade-off analysis     

一种基于冗余测量的自适应卡尔曼滤波算法

针对目前自适应滤波算法的不足,在测量系统量测噪声方差未知的情况下,设计了一种基于冗余测量的自适应卡尔曼滤波(RMAKF)算法。通过对系统冗余测量值的一阶、二阶差分序列进行有效的统计分析,可以准确估计系统量测噪声统计特性,进而在滤波过程中自适应调节噪声方差阵R,提高滤波精度。以全球定位系统/惯性导航系统(GPS/INS)松组合导航系统为对象进行了仿真实验,结果表明该算法在测量系统噪声特性未知或发生改变时,可对其进行准确估计,在采用低精度惯性器件情况下,滤波结果较其他主要自适应卡尔曼滤波算法有较明显的改进。     

Phase-Locked Loop Behavior near Threshold

The phase-locked loop behavior is analyzed following the quasilinearization Booton's method. When the loop is locked on an unmodulated input signal with a static phase error, the phase detector nonlinearity produces an interaction between the static phase error and the voltage-controlled-oscillator (VCO) noise phase fluctuations. Formulas allowing one to compute the static phase error increase and the VCO phase variance increase are derived. When the input signal is phase modulated, there is an interaction between the static phase error, the VCO noise phase fluctuations, and the input signal phase modulation. Formulas are obtained that allow one to compute the loop loss of performances (static phase error increase and VCO phase variance increase) and the coherent phase demodulator output signal-to-noise ratio decrease. Finally, a slight modification to Booton's procedure is proposed, leading to results in better agreement with experimental data.     

Aperture error mitigation via local-state estimation for frequency-based emitter location

This paper considers the problem of locating a stationary coherent emitter via a single moving platform making frequency measurements in the presence of aperture state uncertainty. It is shown that the estimated emitter location is most sensitive to the receiving aperture velocity uncertainty. The required aperture velocity accuracy is determined through a noninfinitesimal perturbation analysis. A solution to location accuracy enhancement with a minimal hardware addition is attempted. It is shown that this can be achieved by mounting a high-resolution tri-axis microelectromechanical systems (MEMS) accelerometer at the aperture to measure its velocity, which can deviate significantly from that estimated by the on-board navigation system. The Doppler shifts of the GPS signal carrier frequency, whenever it can be acquired through the aperture, are also considered as a way to aid the aperture velocity measurement. A decentralized, federated processing method for the aperture velocity estimate referenced at the aperture, integrating all measurement data, is presented. An upper bound for the error of aperture velocity estimate is derived. The potential for significant accuracy enhancement for emitter location is demonstrated.     

增益幅度不同时信号二维方向角和多普勒频率的盲估计

 在各阵元增益幅度不一致的条件下,提出了一种起伏目标的二维方向角和多普勒频率盲估计的新方法。此方法在各阵元增益幅度不一致的条件下,仍可获得很好的估计性能,并能应用于各个信号的频率相同的场合。且具有对噪声不敏感,不需进行谱峰搜索,适用范围广等特点。仿真结果表明了此算法的有效性。     

一种提高脉冲雷达多普勒相位精度的方法

针对低信噪比条件下脉冲雷达模糊多普勒相位精度较低,可能导致相位测距时不能正确解相位模糊问题,基于EMD（Empirical Mode Decomposition,经验模式分解）区间阈值去噪方法,提出了一种新的提高多普勒相位精度的方法：利用EMD分解后各层信号的频率特性和能量特性,选取合适的阈值,并对各层信号进行区间阈值化处理,在提高信号信噪比的同时保持了信号的连续性.分别在回波信号噪声为高斯白噪声和AR（2）相关噪声的情况下,以及不同信噪比条件下,对该方法进行验证.仿真结果表明：在低信噪比条件下,当回波信号噪声为白噪声和相关噪声时,EMD区间阈值去噪方法能将回波信号信噪比提高5 dB,去噪性能优于小波阈值去噪方法,其对应多普勒相位精度能提高1倍以上.     

Statistical Analysis of Wide-Band Pseudorandom Matched Filter Sonars

A stochastic model of pseudorandom (PR) signals is adopted and a statistical analysis carried out of the velocity (i. e., Doppler) and acceleration tolerances of wide-band PR matched filter sonar systems. The reference functions for these correlation detection systems are considered to be time-compressed or time-expanded replicas of the transmitted signal. Results are derived for the case of a PR signal having a flat power spectral density over a finite bandwidth. It is shown that the velocity and acceleration tolerances are essentially independent of the signal bandwidth and that therefore the radar-derived expressions for the narrow-band tolerances can be extended to the wide-band sonar case. An interesting result is that the derived acceleration tolerance is approximately three times the widely used estimate that is based on the target remaining in the same Doppler channel over the integration time.     

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.     

子波域自适应滤波方法

推导和给出了噪声能量阈值的理论计算公式,并提出了一种实时估计信号噪声方差的有效方法,从而构成形式完整和实用的自适应相关计算子波阈滤波算法。仿真计算和分析表明：给出的方法具有良好的自适应性能和显著的滤波效果,在有效去除噪声的同时,很好保留了信号的主要细节。     

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.     

Eigenanalysis for interference cancellation with minimum redundancy array structure

In a previous work, the principles of the eigenanalysis method for interference cancellation was studied for uniform regular array (URA) structure, wherein the array elements are equally spaced. The main objective of this paper is to extend the results of that work to adaptive arrays with different geometry termed "minimum redundancy array" (MRA). An efficient method is presented to solve the minimum variance optimization problem and explicit analytical solutions are derived for the optimal weight vector and output noise variance of the eigencanceler. Performance analysis of the general N-element array was first derived and used to extract the performance of MRA. URA is also considered as a special case. The closed-form equation depicts the minimum variance noise residue for the single interference case, while an interactive procedure is suggested for the two interferences case. If there are more than two interferences, we propose to use direct numerical calculation.     

FM/AM Noise Test Set for a Pulsed Doppler Radar

A new test method to measure the amplitude noise and phase noise in both CW and pulsed CW signals of a Ku-band pulsed Doppler radar is described. These noises are measured in a simulated environment of radar operation; thus the test results may give direct information to determine radar subclutter visibility. In comparison with the conventional noise test method, this new method not only gives more meaningful results but also can obtain results much faster in testing. Actual test system design is described by block diagrams and theoretical analysis. A method to determine approximate frequency jitter in a transmitter signal is also described.     

基于Doppler估计的弹载接收机抗欺骗干扰研究

GNSS接收机在军用方面尤其是高精度制导武器中的应用日益增强.针对卫星信号易受敌方欺骗信号干扰的问题,设计一种基于Doppler频率估计的弹载接收机抗欺骗干扰的方法.首先分析了欺骗干扰和真实信号的Doppler变化特点;然后在捕获阶段利用残留信号检测存在欺骗干扰的卫星编号;最后根据弹载的高动态特性,在跟踪阶段采取扩展 Kalman 滤波器(EKF)进行载波Doppler频率估计,并根据Doppler变化的相似性提取出欺骗信号.通过仿真实验验证,该方法可以有效排除欺骗信号的干扰.     

Statistically Optimum Optical Data Processing with Automatic Focus Estimation

The problem of optimally processing data with unknown focus is investigated. Optimum data processors are found by the method of maximum likelihood under a variety of assumptions that apply to most of the situations arising in practice. The unknown focus may be either an unknown parameter or an unknown random variable; the signal may be of known form or a random function; it is further assumed that the signal is received in additive, white, Gaussian noise. The problems of jointly estimating other unknown parameters and, in the case of a random signal, jointly estimating the signal, are also treated. The asymptotic variance and correlation of the estimators is discussed. Electrooptical realizations of the maximum likelihood computers are given. An iterative method of solution of the likelihood equation is also discussed. The discussion and results are directly applicable to the processing of synthetic aperture radar data.