Geolocation of a known altitude object from TDOA and FDOA measurements

Most satellite systems for locating an object on Earth use only time difference of arrival (TDOA) measurements. When there are relative motions between an emitter and receivers, frequency difference of arrival (FDOA) measurements can be used as well. Often, the altitude of an object is known (it is zero, for example) or can be measured with an altimeter. Two sets of geolocation solutions are proposed which exploit the altitude constraint to improve the localization accuracy. One is for TDOAs alone and the other for the combination of TDOA and FDOA measurements. The additional complexity by imposing the constraint is a one-dimensional Newton's search and the rooting of a polynomial. The covariance matrices of the new estimators are derived under a small measurement noise assumption and shown to attain the constrained Cramer-Rao lower bound (CRLB). When there is a bias error in the assumed altitude, using the altitude constraint will introduce a bias to the solution. Since applying the constraint decreases the variance, there is a tradeoff between variance and bias in the mean square error (MSE). The maximum allowable altitude error such that the constraint solution will remain superior to the unconstraint is given. Simulation results are included to corroborate the theoretical development.     

Analysis of Modeling and Bias Errors in Discrete-Time State Estimation

This paper concerns the effects of modeling and bias errors in discrete-time state estimation. The newly derived algorithms include the effect of correlation between plant and measurement noise in the system. The effects of nonzero mean noise terms and bias errors are considered. With plant or measurement matrix errors, divergence can occur. The local or linear sensitivity approach to error analysis, where the sensitivity is defined as a partial derivative with respect to a variable parameter taken about the modeled value, will not show this divergence due to neglect of higher order terms. Approximate algorithms are presented which circumvent the problem inherent in the local sensitivity approach. These make use of a "conditional bias" concept which views system error as a bias, conditioned on knowledge of the state estimates. It is shown that the actual error in optimum estimation is orthogonal to the residue error for suboptimum estimation where the residue error is defined as the difference between the actual estimation error and the optimum estimation error. Two examples, one concerning an integrated navigation system, demonstrate the theoretical results.     

二维耦合振荡器有源天线阵相位误差特性及其对天线方向图的影响

分析了二维耦合振荡器有源天线阵的相位误差特性及其对天线方向图的影响。分析结果表明,二维耦合振荡器有源天线阵的相位误差具有积累特性;阵元自由振荡频率的误差越小,阵元锁相带宽越大,波束指向误差越小;随着阵元自由振荡频率误差的增大,天线阵增益降低,副瓣电平抬高。     

Coarse quantization for data compression in coherent location systems

When emitter location systems measure time-difference-of-arrival (TDOA) and differential Doppler (DD) by coherently cross-correlating the signal pairs, data compression techniques are needed to facilitate data transfer of one of the signals to the receiving site of the other signal. Two block-adaptive quantization schemes are analyzed here to determine their impact on the signal-to-noise ratio (SNR) of the quantized signal as well as on the post-correlation SNR. Comparisons are made between two approaches: quantization of the real/imaginary (R/I) components or the magnitude/phase (M/P) components. For the M/P approach, a rule is derived for optimally allocating the bits between the magnitude and phase. The M/P approach provides better post-quantization/precorrelation SNR for most signals; however, when the SNR of the signal not being quantized is small, the post-correlation SNR can be largely unaffected by the quantization. In that case, there is little difference between R/I and M/P, even under the most favorable scenario for M/P.     

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.     

Some Results on Digital Chirp

Generating chirp waveforms by means of phase coding yields a simple, cost-effective mechanization. The coding process, however, introduces phase errors whose effect must be included in the design. An approximate analysis is presented, valid for moderate to high compression ratios, which allows error effects on compressed pulse amplitude and sidelobes to be calculated in a simple manner. The anaylsis provides criteria for selecting the coding bit width (sample rate), weighting network bandwidth, and phase-coder quantization interval and transition times. Weighting functions for maximizing the signal-to-noise ratio (SNR) or for producing desired close-in sidelobe performance are derived, as is an exact expression for the transmitted spectrum. Numerical results are presented for Gaussian and the maximum-SNR weighting. The results indicate that performance will be satisfactory for many applications.     

数字闭环光纤陀螺的调制串扰误差

 通过分析数字闭环光纤陀螺的阶梯波调制信号与输出死区、周期噪声干扰及小角速度漂移的关系,提出了调制串扰误差的概念。指出调制信号与探测器输出信号之间的电交叉耦合及调制信号产生的调制误差是产生调制串扰误差的干扰源。将调制串扰通道模型简化为比例环节和部分积分环节,并和光纤陀螺理想模型结合,建立了光纤陀螺调制串扰误差模型,利用该模型推导出了产生死区的条件及周期噪声干扰和小角速度漂移造成的输出偏差表达式,并对周期噪声的幅值、频率与陀螺输出量级、带宽之间的关系进行了定量分析。调制串扰误差的仿真和实验结果与理论分析结果基本一致,验证了调制串扰误差模型的正确性。     

Frequency-Agile Radar Signal Processing

Modern radars may incorporate pulse-to-pulse carrier frequency modulation to increase probability of detection, to reduce Vulnerability to jamming, and to reduce probability of interception. However, if coherent processing is used for clutter rejection, the frequency of N consecutive pulses must be held constant for N-pulse clutter cancellation or Doppler filtering. If M pulses are transmitted during the time the antenna illuminates a target, there are M/N coherently integrated echoes available for noncoherent integration in the computer or the operator's display to further improve the signal-to-noise ratio (SNR). In this paper, analytical and simulation methods are employed to determine the balance between coherent and noncoherent integration that yields the greatest SNR improvement. Attention is focused upon a model using peak selection of fast Fourier transform (FFT) Doppler channels and is compared to a reference model involving only a single Doppler channel. Curves of detectable SNR as a function of M and N are presented for both models.     

GPS选择可用性(SA)信号采集与建模

 分析了ＧＰＳ测量伪距的各组成部分,设计了一个ＧＰＳ数据实时采集系统,通过定位计算和时钟偏移滤波的方法分离ＳＡ误差信号,经检验指出ＳＡ误差信号基本是零均值的平稳随机过程,对一段时期定点观测到的ＳＡ误差信号进行ＡＲ（１３）的模型辨识,获得大量的模型数据,从时域和频域对模型参数进行分析得到一些有益的结论。     

Noise analysis of a digital tanlock loop

The noise performance analysis of a nonuniform digital phase-locked loop (DPLL), called the digital tanlock loop (DTL), is investigated by both analytic and computer-simulation methods. The results are presented in terms of phase error probability mass function and mean time to skip cycle versus input signal-to-noise ratio (SNR). These results are compared to the ones obtained with the conventional sinusoidal DPLL loop (DPLL). It is found that, for low-to-moderate input SNR, the DTL has only a slight improvement over the DPLL. The DTL, however, has larger linear characteristics than the conventional DPLL, which makes it attractive for applications that require an increased tracking range or as a first stage in carrier tracking systems based on optimum estimation procedures such as a Kalman smoother     

Theory of LDV Tracking Systems

The application of frequency-tracking systems to the analysis of laser doppler velocimeter (LDV) signals degraded by background noise has been studied both theoretically and experimentally. Expressions are derived for both the correlation function and the expected value of the phase derivative in the general case of noise off center from the Doppler frequency, and these results are specialized to specific cases of practical interest. Laboratory measurements of output signal-to-noise ratio (SNR) and dc error, for varying input SNR and noise center frequency offset, show good agreement with the theoretical predictions.     

基于定位误差修正的运动目标TDOA/FDOA无源定位方法

针对时差(TDOA)、频差(FDOA)无源定位的两步加权最小二乘(TSWLS)方法定位均方根误差(RMSE)和定位偏差适应测量噪声能力差的问题,在分析了影响两步法定位性能的因素基础上提出一种基于一阶泰勒级数展开的定位误差修正方法。该方法的第1步和两步法相同;其第2步避免了两步法第2步中引入估计偏差的平方运算,利用一阶泰勒级数展开得到第1步定位误差的线性最小均方估计,修正第1步定位结果得到目标位置和速度的最终估计,从理论上证明了该方法可以达到定位的克拉美罗下限(CRLB)。计算机仿真对比了新方法和TSWLS方法、基于泰勒级数(TS)展开的迭代极大似然(ML)方法以及约束总体最小二乘(CTLS)方法的定位性能,新算法复杂度和两步法相当,且均方误差和定位偏差低于两步法、泰勒级数法和CTLS方法。     

Phase Analysis in Multiple-Sensor Receivers with High Signal-to-Noise Ratio

The ideal phase detector characteristic is analyzed for estimating the phase difference between two stochastic input signals. This can essentially be described as a correlation process formed by multiplying the two input signals and extracting the phase. High signal-to-noise ratio conditions are assumed to linearize the system with respect to the noise. The effects of the nonlinearity on the signal are handled in terms of a series expansion and by using low-pass filtering on the receiver output. The mean square error of the system is calculated for some typical parameters.     

SNR-based multipath error correction for GPS differential phase

Carrier phase multipath is currently the limiting error source for high precision Global Positioning System (GPS) applications such as attitude determination and short baseline surveying. Multipath is the corruption of the direct GPS signal by one or more signals reflected from the local surroundings. Multipath reflections affect both the carrier phase measured by the receiver and signal-to-noise ratio (SNR). A technique is described which uses the SNR information to correct multipath errors in differential phase observations. The potential of the technique to reduce multipath to almost the level of receiver noise was demonstrated in simulations. The effectiveness on real data was demonstrated with controlled static experiments. Small errors remained, predominantly from high frequency multipath. The low frequency multipath was virtually eliminated. The remaining high frequency receiver noise can be easily removed by smoothing or Kalman filtering     

高频振荡器噪声分析

 本文将高频振荡器视为具有深度正反馈噪声放大器。对它分析,给出正弦波信号的谱、等效带宽及相位噪声谱;同时还提出诸如高频振荡器内部产生的随机游走噪声形成机理等新看法。     

A closed-form solution for moving source localization using LBI changing rate of phase difference only

Due to the deficiencies in the conventional multiple-receiver localization systems based on direction of arrival(DOA) such as system complexity of interferometer or array and amplitude/phase unbalance between multiple receiving channels and constraint on antenna configuration,a new radiated source localization method using the changing rate of phase difference(CRPD)measured by a long baseline interferometer(LBI) only is studied. To solve the strictly nonlinear problem, a two-stage closed-form solution is proposed. In the first stage, the DOA and its changing rate are estimated from the CRPD of each observer by the pseudolinear least square(PLS) method,and then in the second stage, the source position and velocity are found by another PLS minimization. The bias of the algorithm caused by the correlation between the measurement matrix and the noise in the second stage is analyzed. To reduce this bias, an instrumental variable(IV) method is derived. A weighted IV estimator is given in order to reduce the estimation variance. The proposed method does not need any initial guess and the computation is small. The Cramer–Rao lower bound(CRLB) and mean square error(MSE) are also analyzed. Simulation results show that the proposed method can be close to the CRLB with moderate Gaussian measurement noise.     

小波与BP神经网络联合反演GNSS IR高精度水库水位变化

GNSS-IR技术作为一种近地表遥感的新兴手段，在水库水位监测方面凭借其成本低、精度高等优势成为了研究热点。为了提高GNSS-IR技术反演水库水位变化的精度，提出了利用GPS、BDS双系统观测量基于小波分解与BP神经网络联合的方法反演水库水位变化。选取位于南水北调山东境内双王城水库GNSS变形观测站2017年10月1日—12月26日共87天的信噪比(SNR）数据为研究对象，分别利用小波分解和二阶多项式拟合两种方法消除其趋势项并生成SNR残差序列，然后进行Lomb-Scargle谱分析得到水库水位高度变化值，并与实测水位结果相比较。结果表明：各频段SNR利用小波分解和二阶多项式反演水位变化的平均均方根误差分别为0.1062m和 0.2245m，说明小波分解去趋势项的方法更优。最后，在小波分解去趋势项的基础上，利用阈值筛选出融合所用的频段(S1C、S2L、S5Q和S7I），分别采用均值算法、中值算法、随机森林算法和BP神经网络算法对GPS、BDS多频多模信号进行水库水位的融合反演。结果表明，对于水面较为平静的环境，以上算法均能实现厘米级的反演精度，其中BP神经网络算法用于水位反演的效果更优。     

贫燃预混旋流火焰热声特性研究

以贫燃预混旋流模型燃烧室为研究对象,以当量比为变化参数,从不稳定振荡频率、脉动压力幅值和分布、热释放响应特性等方面分析,研究了燃烧不稳定性从开始到极限环的非线性演化过程.利用低阶热声网络模型加以数值模拟验证.结果表明:脉动压力方均根、热释放响应会随着当量比的增大而呈现典型的非线性激发过程,火焰结构在发展过程中发生明显的变化.计算分析结果表明当量比低于0.7时计算结果与实验结果频率误差小于1%,而在当量比大于0.7时,计算结果与实验结果频率误差为13%.      

Preliminary Analysis of a Proposed High-Stability Frequency Standard Distribution System

A system for distributing a frequency reference, which involves the use of geostationary satellites and two-way microwave transmissions, seems capable of stabilities exceeding those of primary atomic standards. The principal sources of error are instabilities in oscillators in the system, imperfect geostationary orbits, additive noise, and radio propagation effects. Even extreme assumptions of propagation phase instability lead to very small errors. Thus the limitations on stability seem to be imposed by the hardware.     

随机共振锁频环路影响因素

针对随机共振锁频环路影响因素不够明朗的问题,在对随机共振锁频环路仿真验证的基础上,重点对信噪比、采样频率和系统参数对环路性能的影响进行了探究。首先,阐述了随机共振锁频环路基本原理,搭建了随机共振锁频环路模拟仿真平台。其次,通过设定不同的信噪比、采样频率和系统参数条件,观察随机共振锁频环路性能变化。最后,总结归纳出各条件对随机共振锁频环路的影响。仿真结果表明,信噪比越低,随机共振锁频环路对信号跟踪性能越差,且最低能够处理信噪比为Eb/N0=1dB的信号。采样频率在高于信号频率50倍时,提高采样频率虽可提高计算精度,但对环路跟踪性能改善作用不大。系统参数是决定随机共振效应能否发生及影响共振效果的关键因素,其表现为一个可供选择的数值区间。