Digital accumulators in phase and frequency tracking loops

Results on the effects of digital accumulators in phase and frequency tracking loops are presented. Digital accumulators or summers are used extensively in digital signal processing to perform averaging or to reduce processing rates to acceptable levels. For tracking the Doppler of high-dynamic targets at low carrier-to-noise ratios, it is shown through simulation and experiment that digital accumulators can contribute an additional loss in operating threshold. This loss was not considered in any previous study and needs to be accounted for in performance prediction analysis. Simulation and measurement results are used to characterize the loss due to the digital summers for three different tracking loops: a digital phase-locked loop, a cross-product automatic frequency tracking loop, and an extended Kalman filter. The tracking algorithms are compared with respect to their frequency error performance and their ability to maintain lock during severe maneuvers at various carrier-to-noise ratios. It is shown that failure to account for the effect of accumulators can result in an inaccurate performance prediction, the extent of which depends highly on the algorithm used     

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.     

基于自适应FIR算法的交流伺服系统前馈控制

永磁同步电机(PMSM)交流伺服控制系统中由于电子器件的开关引起相电流非正弦变化,经坐标变换得到的交直轴电流含有谐波成分,引起电流环振荡及电磁转矩脉动。在分析相电流与交直轴电流高次谐波关系,以及交直轴电流高次谐波对电磁转矩影响的基础上,提出了一种基于自适应FIR滤波器的交流伺服系统前馈控制策略,并在该方法的基础上提出了变步长因子算法,根据误差值改变步长因子,在提高滤波器收敛速度的同时减小超调。该算法与传统的一阶低通滤波器相比,相位不滞后,灵敏度更高,且系统稳定。改进后的控制策略有效地降低交直轴电流谐波,抑制电流环振荡及电磁转矩脉动,提高PMSM交流伺服控制系统稳定性及动态响应。通过仿真与试验证明了该方法的可行性。     

Uniform Sampling Analysis of a Hybrid Phase-Locked Loop with a Sample-and-Hold Phase Detector

Phase-locked-loop (PLL) bit synchronizers often employ integrate-and-dump type phase detectors that provide phase error information only at discrete points in time. Usually these phase detectors are followed by sample-and-hold circuits to produce a stairstep error voltage as the input to a standard analog circuit loop filter. When the loop is configured in this manner, it is referred to as a hybrid PLL. Sampled-data analysis methods (Z transforms) are used to determine the stability and transient response of this loop.     

Phase-Frequency Detection in Sampled Phase-Locked Frequency Mlultipliers

Phase-locked high-frequency multipliers which do not have powergreedy frequency dividers in the feedback loop, but which do have a sample-and-hold circuit as a phase detector are hard to design, due to conflicting requirements which determine the choice for loop gain and loop bandwidth. A circuit is described that acts as a frequency control if the loop is not locked and as a phase control once the loop can be locked. The loop filter has to be optimized for the locked condition only, and the allowable preset error is more than 80 percent of the sample frequency. The circuit also indicates whether the oscillator frequency is an odd or an even multiple of the sample frequency. Pull-in is at least an order of magnitude faster than with phase control alone.     

Digital tracking filters with high order correlated measurement noise

The existing algorithms for the design of digital filters with colored measurement noise involve a restriction on the dimension of the measurement error model. Kalman filter equations and state space partition are used to formulate an optimal tracking filter without such restrictions. The input to the new filter are two consecutive measurements, and it is initialized by using the first available measurements and the error model correlation matrix. Several examples illustrate the filter formulation and initialization.     

Flexible loop filter design for spacecraft phase-locked receivers

A flexible loop filter design for spacecraft phase-locked receivers is proposed. The loop filter is implemented as digital hardware with coefficients that are set by registers. Either a perfect or an imperfect integrating loop filter can be effected. This flexibility is important since not one type of loop filter is preferred for all circumstances. An imperfect integrator is preferred when, as is often the case for spacecraft receivers, it is important to minimize the best-lock frequency drift of an idling loop. A perfect integrator is preferred when the tracking performance of the loop is the most important consideration     

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.     

Precise navigation using adaptive FIR filtering and time domainspectral estimation

This paper introduces a new low cost, short range, positioning system based on adaptive finite impulse response (FIR) filtering and time domain spectral estimation. The system can determine absolute positions with a high degree of accuracy and is well suited for real time navigation. The approach is based upon signal processing techniques and a priori knowledge of the system transfer function. The first step is to measure the phase response of the linear transfer function and then using a FIR filter the time response of the system can be determined. The FIR filter computes the time response by performing a deconvolution between the measured phase response, and the complex conjugate of the transfer function. By correlating the known input impulse response with the output of the FIR filter, an error term is generated. The time delay of the system is determined by adjusting the FIR filter coefficients to minimize the error term. Simulated analysis of the system indicates a worst case error of ±16 cm     

基于鉴相器的矢量跟踪环设计

基于鉴相器的矢量跟踪环是锁定导航卫星码和载波的一种跟踪算法,这种算法适合于在弱信号环境下进行跟踪。矢量环不仅充分利用信号跟踪和导航状态解算之间的内在耦合关系,而且每一通道中采用鉴相器和锁频环结合的方式,系统一步内完成信号跟踪和导航解算任务。反馈控制量NCO是由导航滤波器和环路内部滤波器共同产生。实验表明,矢量跟踪环具有快速重捕获特性,能够在弱信号的环境下运行,比起传统环路有更小的跟踪误差。     

Noise Dynamics of the Phase-Locked Loop with Signal Clipping

Employing techniques similar to the averaging methods of Krylov and Bogoliubov, an approximate noise analysis of the phase-locked loop with signal clipping is presented. The validity of the method is demonstrated by comparing the stationary probability density function for the phase error, generated by a system simulation, with the derived theoretical results. The latter portion of the paper discusses the relation of the phase-locked loop to Kalman-Bucy filter theory and presents a demodulator design that illustrates the self-adaptive properties attainable in phase-locked loops with signal clipping.     

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     

最佳平方逼近的异步时钟恢复插值滤波器设计

给出了一种异步时钟恢复的最佳平方逼近插值滤波器设计，该滤波器基于最小平方逼近理论，采用易于硬件实现的Farrow结构；克服了拉格朗日插值滤波器参数固定而窗函数截短插值滤波器结构复杂的问题。对我国航天测控设备的数字化和小型化具有较好的应用价值。     

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     

一种低噪声和高精度的频率合成技术

介绍了锁相环(PLL)技术和直接数字式频率合成(DDS)技术的基本工作原理,给出了一种提高DDS输出频率精度及减小其相位截断误差的方法。     

基于UKF准开环结构的高动态载波跟踪环路

 对高动态环境下的全球卫星导航系统（GNSS）载波信号跟踪方法进行了研究。在分析高动态载波信号模型的基础上,提出了一种基于无迹卡尔曼滤波（UKF）的准开环载波跟踪方法。此方法能够消除导航数据二进制相移键控(BPSK)调制的影响,并采用四维UKF相位估计模型提高跟踪精度,同时对估计值进行补偿以减少滤波器的滞后性。通过模拟接收机的高动态运动轨迹,从跟踪误差、跟踪结果和补偿效果3个方面,与基于卡尔曼滤波（KF）的锁频环(FLL)辅助锁相环(PLL)结构的传统跟踪方法进行比较,结果表明基于UKF的准开环跟踪方法能够有效地完成高动态环境下的载波跟踪。     

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.     

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     

一种基于盲同态解卷积的SAR成像自聚焦算法

针对大气扰动及飞行平台不稳引起机载合成孔径雷达(SAR)图像散焦的问题,提出了一种新的自聚焦算法来估算运动误差。该算法是基于运动误差函数及场景散射函数平滑特性的差异来进行估计的,利用复对数变换将图像的幅度与相位信息分离,进而分别对相位及幅度信息进行处理。运动误差通常为慢变函数,而场景的散射信息具有某种随机特性。因此,经过复对数变换后,运动误差及散射信息可以通过滤波器进行分离,将相位中的随机噪声去除,从而保留了慢变的运动误差函数。为了去除噪声信息,需要建立一个平滑滤波器,利用Daubechies小波的尺度函数构造Riesz基向量,从而建立了正交子空间,通过所建立信号子空间及噪声子空间组建平滑滤波器,最终可以获得准确的运动误差。在实验部分,分别利用仿真数据及实测数据对本文方法进行验证,最终结果分析表明该方法具有很高的估计精度及执行效率。     

利用“观测器”设计数字滤波网络

本文介绍利用“观测器”设计数字滤波网络的方法。本方法是先给出系统要求的闭环对象极点位置,然后求得满足系统特性的数字滤波网络;而惯用的对数频率法则是基于系统的开环对数频率特性,凭借设计者的经验选取某个网络,用工程作图法使系统特性去逼近希望的理想特性。显然,前者依赖于数字模拟计算,着重考虑网络的数字计算机实现;而后者则取决于设计者的经验,着重考虑网络的物理实现。 另外,本方法对问题的描述采用了状态表示法和矩阵矢量形式,便于数字网络设计的数值计算程序化,因而也就便于修改设计或跨型号的重新设计。