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.     

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     

Steady-State Noise Reduction Factors for the Exponential Filter

A technique is presented using state notation for deriving the steady-state noise reduction factors for an exponential filter. The technique is carried through to derive those factors for the third-order exponential filter.     

连续时间系统的定常状态估计器

 对于线性定常的连续时间系统,当系统和测量噪声为平稳白噪声过程时,研究了定常的状态估计器的设计方法。为了改进传统的Kalman-Bucy滤波器的瞬态性能,提出了两种新的性能函数的定义,从而给出了两种便于工程应用的修正的Kalman-Bucy滤波器。     

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.     

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.     

涡扇发动机变参数鲁棒H_∞滤波器设计

针对存在建模误差及测量噪声干扰条件下的涡扇发动机性能参数估计问题,标准卡尔曼滤波及其改进算法滤波估计误差收敛速度慢,滤波估计精度低,对不确定测量噪声及建模误差较为敏感,为此本文提出了一种变参数鲁棒H_∞滤波器设计方法。该方法采用仿射参数依赖Lyapunov函数设计满足H_∞性能指标要求的鲁棒滤波器,通过引入凸多胞技术,将参数依赖线性矩阵不等式(Linear Matrix Inequality,LMI)中变参数Lyapunov矩阵与系统系数矩阵之间耦合乘积导致的非凸优化问题,转化为常规LMI约束下的凸优化问题进行求解,降低了线性变参数(Linear Parameter Varying,LPV)鲁棒滤波器设计的保守性,得到了全局解。针对涡扇发动机的仿真结果表明:与扩展卡尔曼滤波器对比,采用该方法设计的滤波器具有较快的动态跟踪速度和较高的滤波精度,ΔFn的稳态估计误差不大于0.1%,ΔFn的相对估计误差不大于2.5%,同时对建模误差和测量噪声干扰具有较强的抑制能力。     

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.     

一种新的控制系统H∞/LTR设计方法

 提出了目标回路传递函数恢复的一种新的控制系统H∞/LTR设计方法,通过引入对控制量的加权,不仅可以保持LQR回路的特性,而且可以使控制器具有较低的增益和较小的带宽。此方法克服了LQG/LTR方法增益过高和LQR无穷带宽而引起的控制器对噪声特别敏感的缺点,从而达到抑制噪声的目的。与此同时,通过合理选择权函数,方法在回路中引入了积分环节,消除了静差,但却避免了增广,从而降低了系统的阶数。最后的实例验证了方法的可行性。     

Threshold Investigation of Phase-Locked Discriminators

This paper is primarily an investigaton of a second-order phased-locked loop in the threshold region, with the loop filter chosen as (1/1+?s) or (1+?1s/1+?s). First-order loop results are also given. Effects of loop parameters, detuning error, and modulation are studied. It is shown that the loop with filter (1+?1s/1+?s) can be built two ways with same bandwidth and damping. One loop gives much better threshold than the other. The analytical results are supported by computer simulation as well as experimental work obtained by hardware simulation of the loop.     

On Higher Order Discrete Phase-Locked Loops

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.     

Analytical Results for a Kalman Tracker Using Position and Rate Measurements

Analytical results are presented for determining the steady-state components of the gain and error covariance matrices of the two-state Kalman tracking filter with white noise maneuver capability.     

应用卡尔曼滤波的机载雷达跟踪系统

本文论述将滤波理论应用于机载雷达中对单个目标进行距离、速度、方位角和高低角跟踪的多环反馈系统。首先根据目标和天线的相对运动建立控制四坐标跟踪环所需的状态矢量微分方程,然后推导相应的非线性滤波算法。最后给出计算机的模拟结果。计算机模拟的结果清晰地说明采用最佳滤波的系统性能比通常的有很大改善,并且这种瞄准轴坐标系的最佳系统对目标的随机机动是不灵敏的。 本文所讨论的方法和得出的结论可以延用到地面雷达、舰载雷达以及其他有源和无源的跟踪系统。     

Planck-LFI 44 GHz back end module

This work describes the principle of operation, assembly and performance of one branch of the 44 GHz back end module (BEM) for the Planck low frequency instrument (LFI). This subsystem constitutes a fully representative branch of the qualification-model version (QM). It includes waveguide to microstrip transition, GaAs pseudomorphic high electron mobility transistor (PHEMT) low noise amplifiers (LNA), bandpass filter, square-law detector and dc amplifier. The fundamentals of the design of the RF part are described and all of the components have been tested individually before integration. Using single tone and wideband noise stimuli, the output voltage has been measured for several input powers, in order to obtain the sensitivity factor of the complete BEM. The effective bandwidth and the equivalent noise temperature have been calculated from the measurements, taking into account the frequency dependence on the noise source and the BEM. Finally, the low frequency output power spectrum has been obtained and a maximum 1/f knee frequency around 200 Hz has been measured with a 3 dB output signal video bandwidth above 50 KHz.     

Optimum Steady-State Position and Velocity Estimation Using Noisy Sampled Position Data

The Kalman filtering technique is used to obtain analytical expressions for the optimum position and velocity accuracy that can be achieved in a navigation system that measures position at uniform sampling intervals of T seconds through random noise with an rms value of ?x. A one-dimensional dynamic model, with piecewise-constant acceleration assumed, is used in the analysis, in which analytic expressions for position and velocity accuracy (mean square), before and after observations, are obtained. The errors are maximum immediately before position measurements are made. The maximum position error, however, can be bounded by the inherent sensor error by use of a sufficiently high sampling rate, which depends on the sensor accuracy and acceleration level. The steady-state Kalman filter for realizing the optimum estimates consists of a double integrator, the initial conditions of which are reset at each observation.     

惯导速度辅助下GPS接收机码环的噪声响应和动态跟踪性能分析

 本文推导了C/A码信号相干和非相干接收的GPS接收机码环的动力学方程,分析了码环的噪声响应和动态跟踪性能对码环带宽的矛盾要求,并提出了解决矛盾的方法:惯导速度辅助。分析结果表明:窄带宽码环经精度为1nmile/h的惯导系统速度辅助后,动态跟踪误差为无辅助时的1/1000,接收机将兼有抗强干扰和跟踪高动态的性能。     

直驱阀控制系统设计及验证

为提高直驱阀系统的动态特性和稳定性,设计了1种位置环加电流环的直驱阀双闭环控制系统,其中位置环采用比例积分控制加相位超前校正,电流环采用比例积分控制。在MATLAB平台上,开展了电流环仿真、位置环的参数辨识以及仿真;在由DSP和FPGA构成的验证平台上,开展了试验验证,电流环与位置环的控制效果与仿真模型均一致,获得了400 Hz以上的电流控制带宽和25 Hz以上的位置控制带宽。研究结果表明:此控制器设计及校正方法可有效提高直驱阀系统的动态特性和稳定性。     

Reconciling steady-state Kalman and alpha-beta filter design

The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, α and β. In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs     

宽带信号角跟踪和四通道单脉冲方案

分析了宽带信号角跟踪的特殊问题及其实现方案。基于互相关函数的角误差检测方法,推导出了在非相关噪声及相关噪声背景下差路信号的输出信噪比及其角度随机误差的数学表达式,进而给出了带宽增益和最佳带宽的概念,以及提高输出信噪比的方法。为了在低载噪比（C/N）时获得角捕获所需要的和路信号以及差路的归一化信号,提出了四通道单脉冲方案。最后归纳出了低C/N时宽带信号角捕获和角跟踪的几种方法并提出了建议。     

Analytical solution of discrete colored noise ECA tracking filter

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient ρ. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix Ψ(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation