Design and Application of an Adaptive Tracking Filter Control System

The design of an adaptive tracking filter control system and its application to large flexible booster vehicles is described. The problem of elastic vehicle stability is considered along with its solution by conventional and adaptive techniques. The improvement in vehicle stability, which may be achieved with the adaptive tracking filter technique as compared to conventional techniques, is shown. The control system evolved uses two adaptive tracking filters to phase stabilize the first and second bending modes, in addition to conventional compensation techniques. The application of this adaptive technique to a vehicle in which the modal frequencies are in close proximity (<2.5 percent separation) is discussed. The mechanization of the adaptive control system involves the selection of design techniques and components that are electrically and physically compatible with the intended airborne application. The development of a suitable frequency tracking technique and tracking filter is described, in addition to the electronic and mechanical design of the adaptive control system prototype.     

Optimum Cross-Coupled Tracker for Pulse-Doppler Radar

Although there is a well-defined relation between range and range rate, in conventional pulse-Doppler tracking radars the range-gate and frequency control loops are usually closed independently. In this paper, the optimum cross- coupled stationary tracking filter is derived, in which the range error signal is used to boost the frequency loop, and vice versa. The filter is derived for a general case of target dynamics and uncorrelated white noise in both the range gate and frequency control channels. It is shown that its tracking performance is superior to that of the conventional uncoupled tracking loop for reliable frequency channel operation. In solving the usually difficult degenerated Riccati matrix equation, a simple solution is obtained by applying the method of completion of the square to matrixes.     

Waveform selective probabilistic data association

An adaptive, waveform selective probabilistic data association (WSPDA) algorithm for tracking a single target in clutter is presented. The assumption of an optimal receiver allows the inclusion of transmitted waveform specification parameters in the tracking subsystem equations, leading to a waveform selection scheme where the next transmitted waveform parameters are selected so as to minimize the average total mean-square tracking error at the next time step. Semiclosed form solutions are given to the local (one-step-ahead) adaptive waveform selection problem for the case of one-dimensional target motion. A simple simulation example is given to compare the performance of a tracking system using a WSFDA based tracking filter with that of a conventional system with a fixed waveform shape and probabilistic data association (PDA) tracking filter.     

无人机高速DS/FH混合扩频通信系统关键模块设计

针对UAV(Unmanned Aerial Vehicle,无人机)测控链路高抗干扰需求,给出了实现跳频速率20 000次/s的扩跳混合无人机测控数据链系统实现方案.系统采用跳频频率并行捕获模式.跳频源设计采用直接频率合成、DDS(Direct Digital Synthesis,直接数字频率合成)和PLL (Phase-Locked Loop,锁相环)相结合的混合频率合成技术.利用相位响应滤波器,通过正交调制技术完成MSK(Minimum Shift Keying,最小频移键控)、GMSK (GaussianMinimum Shift Keying,高斯最小频移键控)调制.通过推导得出2 bit差分解调输出与载波频率选择有关,且为四分之数据率的整数倍关系.然后通过实例分析给出了跳频频率间隔选取方法,即跳频间隔应当将临近跳频的主瓣分开,同时跳频载波频率应当设在其他跳频频谱的零点处.最后总结了高速扩跳频系统参数设计一般步骤.     

相控阵主动雷达导引头波形策略

针对高脉冲重复频率脉冲多普勒(HPRF-PD)体制的相控阵主动雷达导引头中存在的距离遮挡问题,设计了一种新的波形选择策略。首先,利用提出的脉冲重复频率(PRF)波形选择策略,离线计算得到距离对应PRF的波形查找表。然后,通过叉积自动频率控制环路滤波(CPAFCLF)算法预估下个相参处理间隔(CPI)导引头与目标间的径向相对速度,并联合提出的基于Sage-Husa带有速度预测的自适应"当前"统计模型(SH-ACSMVP)算法得到的距离跟踪值,获得下个CPI的距离预测值。在跟踪机动目标场景中,相比于"当前"统计(CS)模型跟踪算法及基于"当前"统计模型的自适应无迹卡尔曼滤波(CAUKF)算法,本文算法得到的距离预测误差更小,误差收敛速度更快。根据此距离预测值从波形查找表中选择波形发射,作为下个CPI的发射波形,实现后续跟踪阶段的抗距离遮挡,提高目标跟踪性能。仿真结果表明了本文所设计波形选择策略的正确性及有效性。     

Radar sensor using low probability of interception SS-FH signals

One of the best known weakness of radar sensors in defense and security applications is the necessity to radiate a signal, which can be detected by the target, so being possible (easy in fact) that the target is alerted about the presence of a radar before the radar is alerted about the presence of a target. In this context, Low Probability of Interception (LPI) Radars try to use signals that are difficult to intercept and/or identify. Spread spectrum signals are strong candidates for this application, and systems using special frequency or polyphase modulation schemes are being exploited. Frequency hopping, however, has not received much attention. The typical LPI radar at this moment of the technology is a CW-LFM radar. The simplicity of the technology is its best point. Polyphase codes, on the other hand have the inherent advantage of high instantaneous bandwidth regardless of observation time. But the complexity of the hardware is also higher. FH signals have traditionally been considered of lower performance but higher complexity, due to the difficulties to compensate the individual dopplers for the individual range cells in the receiver. One important point is that an FH radar must be clearly distinguished from an agile frequency radar. In the latter, a pulsed signal is transmitted using different frequencies from pulse to pulse. In an FH radar the frequency changes must be during the pulse. In fact, in an LPI FH radar, a CW frequency hopped signal is used. A radar system concept is proposed in which it shows how these problems can be overcome in a tracking application. Also, the signal format is analyzed under the scope of future decade digital interceptors, showing that, in fact, this kind of signal exhibits improvement in some performances and requires a hardware that is only slightly more complex than that needed for CW-LFM systems     

Frequency estimation techniques for high dynamic trajectories

A comparison is presented of four different estimation techniques applied to the problem of continuously estimating the rapidly varying parameters of a sinusoidal signal, observed in the presence of additive noise. Frequency estimates are emphasized, although phase and/or frequency rate are also estimated by some of the algorithms. These parameters are related to the velocity, position, and acceleration of the maneuvering receiver or transmitter. Estimated performance at low carrier-to-noise ratios and high dynamics is investigated for the purpose of determining the useful operating range of an approximate maximum likelihood estimator, an extended Kalman filter, a cross-product automatic frequency loop and a phase-locked loop. Numerical simulations are used to evaluate performance while tracking a common trajectory exhibiting high dynamics     

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     

DS/FH混合扩频测速技术研究

由于DS/FH混合扩频信号带宽较宽,传输信道难以保证信号在宽带条件下线性传输,信号会发生群时延畸变,导致载波相位不再连续,影响载波的稳定跟踪,从而使测速精度降低。本文提出了基于跳频图案同步辅助的鉴频方案,可以消除相位跳变对载波跟踪的影响,实现对扩跳信号载波的稳定跟踪,从而提高DS/FH混合扩频测速的精度。     

利用Singer模型的无陀螺姿态和角速度估计

 给出了一种利用Singer跟踪模型的扩展卡尔曼滤波器 (ExtendedKalmanFilter) ,用于无陀螺姿态和姿态角速度估计。在滤波器中 ,姿态和姿态误差分别由姿态四元数和误差四元数表示 ,而姿态角加速度由一阶Markov过程描述 ,从而避免采用姿态动力学模型。利用数值仿真计算验证了滤波器的性能。在所有的仿真过程 ,滤波器显示出快速收敛能力。稳态估计误差主要由测量更新频率和精度决定。     

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.     

二阶滑模跟踪微分器与带通滤波器频域分析

简要介绍了二阶滑模跟踪微分器的基本原理,应用描述函数法对其频率特性进行了分析。在此基础上设计了带通滤波器并对其频率特性进行了分析,给出了二阶滑模跟踪微分器及由其所构成带通滤波器的参数选择和调试方法。仿真结果表明,通过适当选取有关设计参数,带通滤波器能够从几种频率合成信号中提取出特定频率的信号。     

A simple fixed-lag algorithm for tracking frequency rate-of-change

A family of simple fixed-lag frequency smoothing algorithms which provide good estimates of both frequency and frequency rate-of-change is reported. The smoothers were developed from a fixed-gain αβ tracker by replacing the recursive derivative estimator with a finite-impulse-response (FIR) differentiator. Simulation results are presented which show that the smoothing algorithms provide frequency estimates with a similar variance to those produced by the αβ filter but with greatly improved frequency-rate estimates. The smoothing algorithms and the αβ filter are also compared on the basis of the bias and delay introduced in the frequency-rate estimates. Although the results presented are for frequency estimation, the smoothing algorithms can be used in any single-input tracking application where some lag in the estimates is allowable     

Altitude Estimation Using Asynchronous ? - ? Tracking Filters

In the analysis of the ?-? tracking filter it is usually assumed that the tracking filter and data source operate in synchronism at a constant data rate. However, in a multisensor environment in which the tracking algorithm operates at fixed intervals, the tracking filter cannot be synchronized with the sensors. An analytical solution is obtained for the case in which the tracking filter and data source operate asynchronously with a ?time-correction? process used to approximate the synchronous operation of the tracking filter. An example is given in which the effects of data quantization on the performance of an altitude tracking filter for air traffic control are examined. It is shown that the asynchronous operation of the tracking filter in the example without the time-correction process will result in significant errors in the predicted altitude.     

Cardinality compensation method based on information-weighted consensus filter using data clustering for multi-target tracking

In this paper, a cardinality compensation method based on Information-weighted Consensus Filter(ICF) using data clustering is proposed in order to accurately estimate the cardinality of the Cardinalized Probability Hypothesis Density(CPHD) filter. Although the joint propagation of the intensity and the cardinality distribution in the CPHD filter process allows for more reliable estimation of the cardinality(target number) than the PHD filter, tracking loss may occur when noise and clutter are high in the measurements in a practical situation. For that reason, the cardinality compensation process is included in the CPHD filter, which is based on information fusion step using estimated cardinality obtained from the CPHD filter and measured cardinality obtained through data clustering. Here, the ICF is used for information fusion. To verify the performance of the proposed method, simulations were carried out and it was confirmed that the tracking performance of the multi-target was improved because the cardinality was estimated more accurately as compared to the existing techniques.     

Best linear unbiased filtering with nonlinear measurements for target tracking

In tracking applications, target dynamics are usually modeled in the Cartesian coordinates, while target measurements are directly available in the original sensor coordinates. Measurement conversion is widely used such that the Kalman filter can be applied in the Cartesian coordinates. A number of improved measurement-conversion techniques have been proposed recently. However, they have fundamental limitations, resulting in performance degradation, as pointed out in a recent survey conducted by the authors. A filter is proposed here that is theoretically optimal in the sense of minimizing the mean-square error among all linear unbiased filters in the Cartesian coordinates. The proposed filter is free of the fundamental limitations of the measurement-conversion approach. Results of an approximate, recursive implementation are compared with those obtained by two state-of-the-art conversion techniques. Simulation results are provided.     

Estimation of Aircraft Target Motion Using Orientation Measurements

A new approach to estimating motion of a highly maneuverable aircraft target in an air-to-air tracking scenario is presented. An interactive filter system is developed that provides an improved estimate of target motion states by conditioning kinematic filter estimates on target aspect angle data. Pattern recognition techniques used with an electrooptical tracker are presumed to provide this target aspect information. A target orientation filter processes the aspect angle measurements by statistically weighting measured aspect angles with the current best estimate of target kinematics. The aerodynamic lift equation is used to relate approximate angle of attack to target velocity and acceleration. A novel statistical model for aircraft target normal acceleration is also developed to represent better the unknown target accelerations. Simulation results of realistic three-dimensional scenarios are presented to evaluate the performance of the interactive filter system.     

Kalman Filter Behavior in Bearings-Only Tracking Applications

The extended Kalman filter applied to bearings-only target tracking is theoretically analyzed. Closed-form expressions for the state vector and its associated covariance matrix are introduced, and subsequently used to demonstrate how bearing and range estimation errors can interact to cause filter instability (i.e., premature covariance collapse and divergence). Further investigation reveals that conventional initialization techniques often precipitate such anomalous behavior. These results have important practical implications and are not presently being exploited to full advantage. In particular, they suggest that substantial improvements in filter stability can be realized by employing alternative initialization and relinearization procedures. Some candidate methods are proposed and discussed.     

基于矢量跟踪的MEMS-SINS/GNSS深组合导航系统

针对在载体高动态运动时,由Doppler频移剧烈变化而导致的MEMS-SINS/GNSS组合导航系统精度降低的问题,修正了GNSS卫星信号模型,设计了一种深组合导航通道滤波器,并形成了完整的深组合导航方案。基于矢量跟踪结构的深组合导航方案,通过滤波器对载体的导航参数进行估计,将相互独立的各通道信息结合起来,并利用各卫星位置之间的关系,提高了高动态环境中的跟踪能力。仿真结果表明,基于矢量跟踪结构的深组合导航方案可以有效减少高动态对导航精度的影响,提高组合导航系统的输出精度。     

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。