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     

A Delay-Lock Loop for Tracking Pulsed-Envelope Signals

A sampled-data delay-lock loop (SDDLL) which tracks the arrival time of a biphase modulated, pulsed-envelope RF signal is described. A pseudo-noise (PN) code generator is used as the modulation source as in conventional delay-lock loop tracking devices. Time base shifting of the loop's local clock is performed by digital means. The technique permits the use of a stable-frequency clock to maintain accurate timing between timing correction instants. An expression is derived for the standard deviation of the timing error due to additive Gaussian noise at the SDDLL input. Experimental results are then given which include the effects of control-system quantization error on timing jitter. Assuming that the errors due to input noise and quantized timing corrections are independent and additive, the theoretical and experimental results agree to within approximately one decibel.     

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     

A Study on Particle Filters for Single-Tone Frequency Tracking

In this paper, we present an online approach for frequency tracking of a noisy sinusoid using sequential Monte Carlo (SMC) methods, also known as particle filters (PFs). In addition, apart from employing the classical Cartesian formulation model, we also develop two alternative dynamical models, namely, nearly constant frequency (NCF) and Singer, which are adapted from the maneuvering target tracking discipline, to describe the evolution of time-varying frequencies, and investigate their fitness to the frequency tracking application. When compared with conventional techniques whose performance is restricted to linear Gaussian models and/or to slowly varying frequencies, PFs are more flexible to handle situations where these conditions are violated. Extensive evaluations on the proposed new models and PF tracking algorithms are conducted with different sets of frequency inputs and levels of signal-to-noise ratio (SNR). According to the computer simulation results, it is found that PFs under all investigated models consistently outperform and are less sensitive to SNR levels than the extended Kalman filter (EKF). Furthermore, the results suggest that while none of the models perfectly fits all types of frequency inputs, NCF model is more suitable for moderately varying frequencies, whereas the Singer is more suitable for rapidly changing frequencies.     

Detection Performance of Soft-Limited Phase-Coded Signals

General analytic expressions are developed for the soft-limited digital pulse compressor (matched filter). This theoretical development is then used for the hardware realization of a two-channel (I,Q), 3-bit-limited digital pulse compressor with a compression ratio of 255: 1. The realized hardware uses state of the art integrated circuit devices. An experimental laboratory setup is described. This setup is used to study hard-limited versus 3-bit-limited matched-filter performance characteristics with the data in the following areas: 1) constant false alarm rate (CFAR) characteristics as a function of threshold settings and noise levels; 2) single target detection characteristics as a function of input signal-to-noise ratio (SNR); and 3) two target performance characteristics: a) the amplitude of a weaker target as a function of target ratio and target overlap; and b) the detection characteristics of a weaker target as a function of weaker target SNR, strong target SNR, and target overlap.     

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。     

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     

GPS接收机数字码跟踪环性能研究

建立了伪码捕获和跟踪过程的数学模型;推导出了伪码捕获的检测概率和虚警概率,提出了改进的双Dwell搜索方法;对一阶、二阶、三阶DDLL的动态跟踪性能及输入随机噪声影响进行了定量分析。研究结果表明,双Dwell搜索方法能显著缩短平均捕获时间,应根据不同的系统动态特点,选择不同的环路参数,以优化码跟踪环的特性。     

Proportional Tracking with Clipped-input Matched Filters

A proportional boresight-error measurement is described for tracking systems that is applicable to envelope-producing matched filters with hard-limited inputs. The error response is derived as a function of input SNR and the filter output SNR is estimated.     

Analysis of an all-digital data-transition tracking loop

An all-digital implementation of the data-transition tracking loop (DTTL) is proposed and analyzed. The input waveform is assumed to be nonreturn-to-zero (NRZ)-coded binary signals. The mathematical analysis of the loop is reduced to the study of a Markov chain which allows the derivation of expressions for the mean square phase error, steady-state probabilities, transient behavior (time to acquire and time to bit slippage), and bit error rate (BER). Theoretical results have been validated using a computer simulation of the loop. The all-digital implementation can take full advantage of advanced technology in memory and processing speeds     

遗传算法在低信噪比图象点目标检测中的应用

将遗传算法用于图象中低信噪比点目标的检测。在分析了点目标及背景特点的基础上,设计了编码方案及遗传操作算子,提出了合格个体保留法。仿真结果表明应用此算法,可实现信噪比为2dB的点目标的检测与跟踪。     

Graphical Analysis of a Digital Phase-Locked Loop

Under the assumption of negligible quantization error effect and no noise, a nonuniform sampling first-order digital phase-locked loop (DPLL) is analyzed by a graphical method which displays limit cycles and the cycle slipping phenomenon. The analysis suggests an upper bound to the model gain and, consequently, to the pull-in range. Moreover, this method enables one to obtain a closed-form expression of the acquisition time, accurate enough for the cases of practical interest.     

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.     

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。     

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。     

Signal-to-Noise Ratio of Arbitrary Power-Series Nonlinear Amplifier

A general analysis of the effect of an arbitrary power-series nonlinear amplifier followed by a coherent mixing device on signal-to-noise ratio (SNR) is performed. An expression is derived for the improvement factor which is defined as the logarithm of the ratio of the output SNR to the input SNR. This expression is applicable to the coherent amplitude detector and phase locked loop as well as noncoherent amplifier by appropriate selections of the detection angle. Moreover, the improvement factor can be obtained for noise with an arbitrary amplitude distribution. To demonstrate the applicability of this analysis, the improvement factors of the nonlinear amplifiers such as a power-law amplifier and a power-series amplifier with positive and negative discriminations are numerically calculated for the cases where the input noise amplitude distributions are Rician and triangular.     

北斗导航接收机频率稳定度传递算法

为了提高北斗导航接收机的灵敏度,提升其弱信号跟踪能力,通常需要利用长时间的相干积分来提高环路信噪比。但是,当相干积分时间加长到一定程度时,环路性能反而有所下降,信噪比提升也不能达到理论值。针对由剩余频率误差和晶振误差引起的相干积分能量损失问题,主要研究了频率偏差对环路跟踪性能的影响,并提出了利用频率稳定度传递策略辅助弱信号跟踪的方法,解决了北斗导航接收机弱信号跟踪性能提升的问题,最大程度地改善了相干积分的效果,实现了对弱信号的跟踪。利用软件接收机平台对提出的频率稳定度传递算法进行验证,仿真结果表明该算法可使环路信噪比提升4dB ~5dB,充分说明了其可行性及有效性。     

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.     

扩频应答机码跟踪环的一种实现方法

讨论了一种伪随机码跟踪环的特性，分析了码相关间隔、预检积分时间、环路带宽及信噪比等参数对码跟踪性能的影响。该方案不仅能够对PN码相位的变化作出调整，同时对PN码多普勒进行跟踪，较适合于测控应答机中PN码跟踪环的应用。     

Efficient target tracking using dynamic programming

A dynamic programming (DP) algorithm has been developed for the detection and tracking of subpixel-sized, low signal-to-noise ratio (SNR) targets observed by side-or forward-looking imaging sensors. A distinguishing feature of this approach is that target detection and tracking are combined into a single optimization procedure that takes into account statistical models of target motion, background noise, and clutter. Current work has led to a number of technical innovations that improve the performance and efficiency of the DP tracking algorithm, including the development of a new track scoring function, and an extension to the basic DP algorithm that reduces computation requirements by over an order of magnitude. A prototype infrared (IR) target tracking system incorporating these enhancements has been implemented for a step-starting IR camera application. Sensitivity improvements of several decibels over conventional sequential detection and tracking algorithms were realized