Third-Order Loop Filter Design for Acceleration-Rate Tracking

A perfect third-order loop filter design that can be implemented as a digital filter is obtained which minimizes the noiseless steady-state acceleration rate (jerk) error for a fixed loop noise bandwidth. Simulations were performed to obtain transient responses of the third-order loop plus a sample fourth-order loop under a jerk input. The results enable one to obtain a loop design that minimizes the loop noise bandwidth required for a given steady-state jerk error and thus obtain better noise jitter performance.     

Analysis of a Dithering Loop for PN Code Tracking

The tracking performance of a dithering loop in the presence of white Gaussian noise is analyzed and compared to the performance of a delay-lock loop. Performance curves are presented.     

On the Acquisition Behavior of Binary Delay-Lock Loops

The acquisition problem for binary delay-lock loops is re-examined. Previous results obtained by Spilker and Gill on the maximum allowable search rate are shown to be in error. New results are given for the 2-? loop with video correlation and the 1-? loop with video and envelope correlation.     

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.     

A Comparison of Binary Delay-Lock Tracking-Loop Implementations

The delay-lock loop is a device for tracking the delay difference between two correlated waveforms. It is used as a synchronizing loop for binary communications and tracking. The delay tracking performance is derived for various radio-frequency implementations of the binary delay-lock loop. Amplitude and biphase modulation by pseudorandom sequences are considered. Three types of receivers are analyzed for each modulation: envelope correlation, phase-coherent correlation, and phase-lock demodulation followed by video correlation.     

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     

Dynamics of the Phase-Locked Loop without a Limiter

The general (nth order) phase-locked loop is analyzed, of which the amplitude is not constant. The input carrier signal is amplitude-modulated by wide-band stationary Gaussian noise, and the signal, superposed with the additive white stationary Gaussian noise, enters the nonlimited phase-locked loop. Under the above assumptions the loop can be shown to constitute an n-dimensional vector Markov process, so that the process satisfies the n-dimensional Fokker-Plank equation. The probability density function depends on the effective loop signal-to-noise ratio and the effective modulation power.     

Design and Performance of an Adaptive Kalman Receiver for Synchronous Data Transmission

A class of multilevel linear-modulation data-transmission systems, over unknown, slowly time-varying, and bandlimited channels is considered. It is shown how sequence estimation in the presence of Gaussian noise and intersymbol interference can be carried out by means of a discrete Kalman estimator. Moreover, the receiver can be provided with data-aided adaptive loops for performing channel identification, carrier recovery, and timing extraction. A computational method is presented to evaluate the average probability of error of the overall system in the presence of inter-symbol interference, additive noise, and phase-and sampling-synchronization errors. The method is based upon nonclassical one-and two-dimensional quadrature rules, which are outlined in the Appendix. As an example, numerical performance results related to a phase-shift-keying (PSK) system are given. The results are obtained by means of general-purpose and system-oriented computers.     

Modeling and analysis for the GPS pseudo-range observable

In this paper, a digital system for the Global Positioning System (GPS) pseudo-range observable is modeled and analyzed theoretically. The observable is measured in a GPS receiver by accurately tracking the pseudorandom noise (PRN) code phase of the input GPS signal using a digital energy detector and a digital delay lock loop (DDLL). The following issues are presented: (1) mathematical modeling of the digital PRN code acquisition and tracking system, (2) the closed-form expression derivation for the detection and false-alarm probabilities of the acquisition process and for the variance of code phase tracking error, and (3) the linear and nonlinear performance analysis of the DDLL for optimizing the receiver structures and parameters with tradeoff between the tracking errors due to receiver dynamics and due to input noise     

Phase-Locked-Loop Detection of Binary PSK Signals Utilizing Decision Feedback

A modified quadrature channel phase-locked-loop demodulator for binary phase-shift-keyed signals is presented. The modification, called decision feedback, is a practical implementation of decisiondirected channel measurement. Noise analyses are carried out for both additive and phase noise. An optimum loop filter is derived and the analyses include determination of probability of error for the system. The results of an analog simulation of the decision feedback technique are also included.     

Improved Carrier Tracking by Smoothing Estimators

Smoothing as a way to improve the carrier phase estimation is proposed and analyzed. The performance of first-and second-order Kalman optimum smoothers are investigated. This perfomance is evaluated in terms of steady-state covariance error computation, dynamic tracking, and noise response. It is shown that with practical amounts of memory, a second-order smoother can have a position error due to an acceleration or jerk step input less than any prescribed maximum. As an example of importance to the NASA deep space network (DSN), a second-order smoother can be used to track the Voyager spacecraft at Uranus and Neptune encounters with significantly better performance than a second-order phaselocked loop.     

Tracking the Frequency Translation of a Sum of Orthogonal Sinusoids

The maximum likelihood approach is used to derive a method for estimating and tracking the frequency translation of a signal consisting of a sum of orthogonal sinusoids corrupted by additive white noise. The likelihood function is reduced to an equivalent statistic expressed in terms of the squared magnitude of the finite Fourier transform of the received signal. A function that generates an error signal for a frequency translation tracking loop is derived, and a method of generating the error signal using the discrete Fourier transform (DFT) of the received signal weighted by a linear ramp is suggested. Two noise-free examples are presented.     

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     

Random Characteristics of the Type II Phase-Locked Loop

The results of a study of the characteristics of the second-order Type II phase-locked loop with a Gaussian noise input, and obtained by digital computer simulation, are presented. The digital simulation is described and the random state variables are defined such that their characteristics can be interpreted in terms of existing phase portraits of autonomous phase-locked loops. The statistics associated with the state variables, which are phase error and a measure of frequency error, and those associated with the number of cycles skipped and the mean time to unlock, are given.     

Interferences in Phase-Locked Loops

An analysis of the behavior of a second-order phase-locked loop is presented when an unwanted signal is added to the useful signal. Both signals are sinusoidal and unmodulated, and the analysis is made in the absence of additive noise. When the loop remains locked on the useful signal, a parasitic signal exists at the phase detector output. This signal produces a parasitic phase modulation of the VCO and a static phase error in the loop. The parasitic signal amplitude, the parasitic phase modulation index, and the static phase error are calculated. A necessary condition for the loop to remain in lock is derived. When the loop is initially unlocked, locking can occur either on the useful signal or on the unwanted signal, depending on the amplitude ratio and the frequency difference of the two signals. A formula allowing one to compute the pull-in time is obtained. When the loop locks on the useful signal, acquisition can be slower or faster than in the absence of an unwanted signal. The same phenomenon is observed when the loop locks on the unwanted signal.     

带通限幅器对锁相环噪声性能的影响

锁相环路中,在鉴相器前加上AGC（自动增益控制）,可以使环路性能在输入信噪比发生变化时保持稳定,带通限幅器也可以起到类似作用。尽管有一些文章对限幅器的性能作了研究,但是在PLL（锁相环）闭环条件下,鲜有文章分析其对环路噪声性能的影响。因此,文章以基本PLL环路的数学模型为基础,推导出PLL中分别加入相干AGC和带通限幅器后新的环路数学模型,以一阶PLL为例,计算和比较不同控制方式下环路相位误差均方值的变化,最后说明应当根据飞行任务的不同选择对环路更有利的控制方式。     

Noise Performance of a Gated Phase-Locked Loop

The objectives of this paper are two. The first is to show that a gated phase-locked loop (GPLL) is a tracking device whose operation approximates that of a maximum likelihood estimator of the phase of a pulsed sinusoid imbedded in noise. The second is to determine the behavior of theb loop in the presence of noise. It is found that the loop performance is equivalent to that of a continuous phase-locked loop driven by the same noise, plus a continuous sinusoid which has the same power as the pulsed sinusoid at the input of the GPLL.     

总体最小二乘算法在自适应信道均衡中的应用研究

分析了最小二乘解产生偏差的原因,推导出了最小二乘解偏差项的数学表达式。提出了一种基于瑞利商的变步长总体最小二乘求解方法。仿真试验表明,总体最小二乘算法的性能优于加权递归最小二乘算法,是一种适用于输入信号端含有噪声的自适应信道均衡算法。     

A Comparison of Second, Third, and Fourth Order Phase-Locked Loops

This paper presents data describing various performance characteristics of phase-locked loops, which were obtained for the purpose of determining an optimum selection of system order in view of typical operating conditions. With the functions optimized with respect to particular performance characteristics, calculations of the integrated square error and peak error with polynomial inputs are presented in terms of the noise bandwidth; and the generalized error coefficients are also provided in terms of the bandwidth with consideration for the use of both perfect and imperfect integrators. With specific input functions as provided by signals transmitted from earth satellites, an improved performance is demonstrated with the use of the higher order loops, and experimental results verify the calculations and also demonstrate the feasibility of the fourth order loop design.     

基于伪距信息的COMPASS-MEO导航卫星单星定轨分析

COMPASS-MEO导航卫星的伪距观测量包含星站距离、接收机钟差和卫星钟差以及各种噪声。本文首先分析了接收机钟差和卫星钟差在一定间隔内主要表现为线性变化的特性,可以考虑将接收机和卫星钟差作为测距的偏差和偏差变化率和轨道一起进行求解。其次,利用实测的MEO导航单星伪距数据,进行了数据预处理和定轨试验,分别对站间无时间同步信息和有时间同步信息两种情况进行定轨、残差分析和参数解算。使用重叠弧段、轨道预报和激光观测数据验证定轨结果的精度。结果表明,两种情况下的定轨结果无明显差别。该定轨方法可以运用于MEO导航单星精密轨道的计算。