Pointing Error Statistics in Optical Beam Tracking

In tracking optical beams from a source, a pointing error signal is derived from photodetecting the field in the receiver focal plane. This error signal is then used in some manner to control a gimballed system that continually points the receiver optics toward the source. When the source field undergoes turbulent transmission, the optical beam is attenuated and scattered, and the field is randomly defocused at the receiver. In this case the pointing error of the tracking system will evolve as a random vector process in time, statistically related to the random scattering, the photodetection process, and the dynamics of the gimballing system. Such vector processes have probability densities that satisfy well-known differential equations. These equations are derived in terms of accepted scattering models and tracking systems, assuming quadranttype error detectors are used in the focal plane. Approximate solutions are obtained and analyzed for typical operating conditions, and the manner in which the degree of scattering degrades the entire pointing operation is shown.     

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

Optimum Realizable Continuous Range Estimation

The ability to detect the presence or absence of a target is no longer the fundamental design criterion when the vehicle to be tracked is cooperative. In spacecraft tracking or navigation systems, for example, emphasis is placed on post-acquisition performance. Therefore, classical radar theory and design techniques are not specifically applicable. On the other hand, there are optimization techniques for extracting the tracking data from noise that are more to the point. In particular, optimum demodulation theory is directed specifically to the problem of continuously extracting data from a nonlinear modulation process. In this paper, the tracking properties of a multitone PM ranging signal are reviewed and are shown to be nearly optimum for cooperative vehicles. An optimum, but nonrealizable, maximum a posteriori (MAP) continuous estimator of range is derived for this signal. The linearized model of this receiver is the optimum nonrealizable Wiener filter for the data. Interpretation of this optimum nonrealizable estimator leads to a receiver design that is both practical and intuitively satisfying. With the aid of post-detection processing in the Wiener-Hopf sense, almost optimum performance is obtained from the resulting receiver, above threshold.     

机载相控阵雷达中抑制杂波的线性预测法

从一个多通道自回归过程拟合杂波信号的概念出发 ,提出了用线性预测法实现机载相控阵雷达的时空二维自适应信号处理。研究表明 ,杂波过程可以用一个低阶的多通道自回归过程很好地拟合 ,从而使用一个低阶的线性预测处理器以较低的代价实现准最优的处理。同时 ,这种低阶的线性预测处理器还具备冗余的自由度以对付除杂波外的其他有色噪声和干扰     

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning     

脉冲干扰对软件接收机的影响分析

卫星信号经过长距离传播,信号能量损耗严重,到达地面的功率很弱,容易受到各种干扰的影响。脉冲干扰为常见的干扰类型,所以针对不同功率、不同周期,以及不同占空比的脉冲干扰信号,通过接收前端采集受脉冲干扰的GPS L1信号,利用软件接收机及多相关器生成技术,详细分析了脉冲干扰对接收机信号捕获与跟踪性能的影响。分析结果表明,周期为1ms的脉冲干扰信号,能对接收机产生强烈的干扰效果,捕获图中的噪声明显增大;跟踪过程中,载噪比和相关值突发性减小,造成跟踪数据异常。而长周期的脉冲信号仅在脉冲到达时影响接收机的捕获和跟踪,但由于信号跟踪不能连续进行,导致伪距观测量的不连续与导航数据不能正常解码,从而干扰接收机。     

LINEAR PREDICTION APPROACH IN AIRBORNE ADAPTIVE ARRAYS

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Graphical Derivations of Radar, Sonar, and Communication Signals

The designer of a communication system often has knowledge concerning the changes in distance between transmitter and receiver as a function of time. This information can be exploited to reduce multipath interference via proper signal design. A radar or sonar may also have good a priori information about possible target trajectories. Such knowledge can again be used to reduce the receiver's response to clutter (MTI), to enhance signal-to-noise ratio, or to simplify receiver design. There are also situations in which prior knowledge about trajectories is lacking. The system should then utilize a single-filter pair which is insensitive to the effects induced by relative motion between transmitter, receiver, and reflectors. For waveforms with large time-bandwidth products, such as long pulse trains, it is possible to graphically derive signal formats for both situations (trajectory known and unknown). Although the exact form of the signal is sometimes not specified by the graphical procedure, the problem in such cases is reduced to one which has already been solved, i. e., the generation of an impulse equivalent code.     

Effects of a Finite-Width Decision Threshold on Binary CPSK and FSK Communication Systems

The function of the receiver in a binary digital communication system is to make a binary (?space?, ?mark? or ?"0?, ?1?) decision by comparing the signal values from the mark and space filters (or correlators) at known successive time intervals (?bit? or ?baud? time intervals). When the signal value out of the mark filter is greater than that out of the space filter, it is decided that mark or 1 is transmitted, and vice versa. It is of fundamental importance to know the exact instant of time at which the two filter outputs are to be compared. This is the problem of synchronization between the transmitter and the receiver. In this paper, we assume a system that is perfectly synchronized. In a practical system, the difference between the two filter outputs must differ from a threshold by some finite amount in order to cause the device to respond reliably. The examination of the effects of this dead zone (finite-width decision threshold) on digital transmission systems is of important practical interest. Its effects on binary differentially coherent phase-shift-keying, and m-level phase-shift-keying systems have been investigated previously. In this paper we consider its effects on binary coherent phase-shift-keying (CPSK), coherent orthogonal (CFSK), and noncoherent orthogonal (NCFSK) systems. The probability of bit error and the channel capacity of each system is obtained in terms of the dead zone threshold.     

Spectral Location of Rayleigh and "m" Fading Signals in White Gaussian Noise

The classical problem is considered of locating a fading sinusoidal signal known to be present in one of several frequency " cells," each of which contains additive white Gaussian noise. The signal fading is assumed to follow the popular Rayleigh distribution, but generalizations tions to non-Rayleigh fading are included in terms of the " in" distribution due to Nakagami. The channel observation time is allowed to be either predetermined or variable (corresponding, respectively, to " fixed sample size" and " sequential" reception), and the practically important situation of intermittent signal transmissions is also examined. Results are in the form of optimal and near-optimal receiver structures, and of measures of performance.     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.     

一种改进双块补零北斗导航接收机弱信号捕获方法

利用卫星导航系统对高轨航天器进行自主导航与高精度定轨,对接收机的捕获灵敏度要求极高,双块补零(DBZP)算法是无辅助下卫星导航弱信号捕获的理想方案,然而受限于数据处理量大,DBZP实际应用难度大。在深入分析双块补零机理的基础上,结合矩阵重构的思想,提出了一种改进双块补零北斗导航接收机弱信号捕获方法。该方法对参与块内相关运算的基带信号和本地测距码分别进行重构,解决了块内点数与快速傅里叶变换输入点数之间的矛盾,提高了北斗导航接收机弱信号捕获性能。仿真实验结果分析表明,改进双块补零算法对信噪比没有损失,可以保证对低至15dB·Hz的弱信号进行有效捕获,能够满足高轨航天器定轨、室内外无缝导航等对接收机高灵敏度的需求。本方法是在块内运算层面对DBZP进行优化,具备良好的通用性和可移植性,与优化相干积分策略的各种改进DBZP算法可以无缝对接,进一步提高北斗导航接收机信号处理的效能。同时,重构的思想也适用于其他采用码分多址信号的卫星导航系统的弱信号检测和捕获,对提升多星座卫星导航系统的基带信号处理性能具有参考意义。     

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.     

Detection by incoherent recombination with partial information

Matched filter (MF) detection in spread environments is often seriously degraded by the mismatch between the waveform replica and the composite signal formed by the spreading environment. Typically the spreading is caused by multiple delayed reflections due to scatter extent or multipath especially in shallow water sonar applications. It is possible to recover some detector performance by incoherent summation of weighted MF realizations in a process called incoherent recombining (IR). Several IR strategies for Gaussian data that assume varying amounts of prior scattering function (SF) information are examined, their receiver operating characteristics (ROCs) computed, and compared with those of the unrealizable “prescient” receiver (PR). They include optimally weighted and unweighted versions of the maximum likelihood estimator-correlator (EC), and variations of the “at-least-one” (ALO) detector that examines sequences of MF realizations declaring a detection if at least one threshold is crossed. As might be expected, performance improves with the accuracy of the prior information incorporated in the detector formulation     

北斗导航接收机高增益相干积分算法

近年来,针对弱信号的高灵敏度接收机已逐渐成为国内外的研究热点。加长相干积分时间可以提高信噪比,从而跟踪到更弱的信号。但是,北斗导航接收机跟踪环路并不可以无限加长相干积分时间,相干积分时间的长短和功效还受到卫星导航电文比特跳变的限制。为了消除导航电文比特跳变对相干积分的影响,提出了一种改进的基于最大似然估计的北斗信号位同步方法,完成位同步后再利用先猜后检的方法便可以实现长相干积分。利用软件接收机进行编程设计,仿真结果表明：该长相干积分算法能够稳定可靠地实现对弱信号的跟踪,20ms相干积分环路信噪比约提升12dB,40ms相干积分环路信噪比约提升15dB,80ms相干积分环路信噪比约提升17dB,提高了北斗导航接收机的灵敏度。     

Supplements to Active Filters in the VOR

This paper covers some important advances in understanding the problems associated with the VOR system, especially in connection with area navigation. Anomalies arising from airborne equipment, operating in the airborne environment, are described and analyzed. Factors contributing to overall system accuracy are treated with respect to VOR receiver response and to rate-limiting, filter means, with special attention to appropriate noise reduction systems providing zero or minimal time delay characteristics. The use of active filters in the VOR receiver is shown to be of major importance with regard to signal improvement and overall system accuracy. Active filters of the constant slew rate type have proved of significant value, both within the VOR receiver as well as in signal processing.     

The Polar plasma wave instrument

The Plasma Wave Instrument on the Polar spacecraft is designed to provide measurements of plasma waves in the Earth's polar regions over the frequency range from 0.1 Hz to 800 kHz. Three orthogonal electric dipole antennas are used to detect electric fields, two in the spin plane and one aligned along the spacecraft spin axis. A magnetic loop antenna and a triaxial magnetic search coil antenna are used to detect magnetic fields. Signals from these antennas are processed by five receiver systems: a wideband receiver, a high-frequency waveform receiver, a low-frequency waveform receiver, two multichannel analyzers; and a pair of sweep frequency receivers. Compared to previous plasma wave instruments, the Polar plasma wave instrument has several new capabilities. These include (1) an expanded frequency range to improve coverage of both low- and high-frequency wave phenomena, (2) the ability to simultaneously capture signals from six orthogonal electric and magnetic field sensors, and (3) a digital wideband receiver with up to 8-bit resolution and sample rates as high as 249k samples s^–1.     

Variance Analysis of the Angle Output Voltage for an Amplitude Monopulse Receiver

The amplitude-comparison monopulse receiver utilizes two overlapping antenna patterns to determine the angle of arrival of an incoming RF signal for use in a direction-finding application. The thermal noise introduced by the receiver distorts the signal, causing an error in determining the exact angle of arrival of the signal. The analysis derives an expression for the deviation of the angle output voltage, or the angular error, due to receiver noise as a function of 1) the angle of arrival and 2) the signal-to-noise ratios of the two channels of the receiver. A receiver using a square-law detector and one using a linear detector are analyzed.     

Interference Effects of Pseudo-Random Frequency-Hopping Signals

When a pseudo-random frequency-hopping signal is intercepted by a conventional receiver operating within the same frequency band, the interfering signal has the form of a pulse-amplitude modulated signal. Each pulse amplitude is dependent upon the hopping frequency and the selectivity characteristic of the victim receiver. The probability density function for the interfering pulse amplitude prior to demodulation is determined when the probability density function for the hopping frequency is uniform and the victim-receiver characteristic is 1) ideal flat bandpass, 2) single tuned, and 3) Gaussian shaped. It is shown that the average interfering pulse amplitude and interference power decrease as the frequency-hopping bandwidth increases with respect to the victim-receiver bandwidth. Fast Fourier transform computer techniques are used to obtain the probability density function of the interference amplitude in a Gaussian receiver when several (from 2 to 10) pseudo-random frequency-hopping systems are simultaneously using the same frequency band. The probability that the interference exceeds a prescribed threshold value is computed from the derived probability density functions. This probability may be used in signal-to-interference ratio calculations, to describe the capture effect, or to compute the expected number of clicks produced in an FM discriminator.     

GNSS receiver for GLONASS signal reception

This paper deals with the latest version of Experimental GNSS receiver built at the Czech Technical University and describes integration of GLONASS signal processing to the receiver. The new FPGA platform Virtex-D Pro by Xilinx is used and enables integration of whole digital signal processing of GNSS receiver into the single chip. The RE unit of the receiver is capable of processing all GLONASS frequency of the Li and L2 bands in two independent RE channels; each channel can process one band. The frequency selection of the appropriate satellite is accomplished in a digital correlator. The development flow of the GLONASS correlator is discussed herein. The complexity of the GLONASS correlator with complexity of GPS correlator is compared. The developed GLONASS correlator was tested in Simuelink tool during development. The next test was carried out using GLONASS simulator and real GLONASS satellite signal.