Reduction of Radar Tracking Errors with Frequency Agility

Frequency agility with random frequency in each pulse gives an improvement in radar angle tracking with a monopulse radar. With a conical-scan tracking radar, the glint error is reduced but fading error can be increased, and the net result must be studied in each case. A theory, usable for calculating angle tracking errors with a frequency agile radar, is given, and two examples showing the error reduction are presented. According to the theory, one part of the glint or fading spectra is ``smeared out' to half the pulse repetition frequency. Another part, the size of which depends on the degree of correlation between pulses, keeps the form of the original spectrum.     

A Simple Approximate Formula for Glint Improvement with Frequency Agility

Referring to a previous paper on the subject, this correspondance gives a simple approximate formula for improvement in tracking accuracy that can be obtained by using frequency agility to reduce glint errors. The result turns out to be the smallest of two easily calculated ratios.     

On analytical evaluation of glint error reduction for frequency-hopping radars

Analytical techniques are presented for evaluating the glint error reduction of frequency-agile tracking radars employing discrete frequency-hopping (FH). The techniques can be used to compare the tracking accuracies obtained with different procedures for frequency selection. The cases of random, cyclic, and hybrid FH are worked out in detail. An illustration using a simple alpha-beta tracking filter indicates that the preferred type of frequency selection usually depends on the filter gains used in a specific application.<>     

Diversity methods in phase monopulse tracking-a new approach

A novel approach relating target glint (difference between the phase-front gradient of the scattered field and the true target direction vector) to the analytic properties of the overall field is used to suggest a method by which the error in conventional (single frequency) phase monopulse trackers can be reduced. The approximate relationship between glint and amplitude is briefly developed, and an improved glint reduction scheme appropriate for single frequency data is described. The effectiveness in reducing direction angle error is demonstrated with simulated data. It is shown how techniques devised for multiple frequency data sets can be applied to multiple aspect data sets.<>     

Kalman Filter Design for Target Tracking

The problem of solving the matrix Riccati differential equation in the design of Kalman filters for the target tracking problem is considered. An algebraic transformation method is used to reduce the order of the Riccati differential equation and to obtain explicit expressions for the filter gains (in terms of the interceptor /target separation range) which results in a substantial reduction of the computer burden involved in estimating the target states. The applicability of the transform technique is demonstrated for the receiver thermal noise and the target glint noise cases.     

Target racking with glint noise

In tracking targets, there can be an uncertainty associated with the measurements in addition to their inaccuracy, which is usually modeled by aDditive Gaussian noise. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. An algorithm is developed which can significantly improve the tracking performance when glint noise is present     

Radar Target Pointing Error Reduction Using Extended Kalman Filtering

A new method of reducing target glint errors in radar systems is presented. The target is modeled as n reflectors whose magnitudes and phases are known. The reflector positions are described by a dynamical model driven by white Gaussian noise. The resulting vibrations of the target reflectors produce glintlike pointing errors in the radar system. An extended Kalman filter is developed to estimate the positions of the target reflectors; this information is used to substantially reduce the pointing error due to glint. Data illustrating this glint reduction is given. The model is extended by the inclusion of clutter effects modeled in the same fashion as the glint phenomenon. The results presented indicate the limits of usefulness of this technique as a function of both receiver noise and relative clutter amplitude.     

Feedback median filter for robust preprocessing of glint noise

Glint noise may arise in a target tracking system. The non-Gaussian behavior of glint noise can severely degrade the tracking performance. Measurement preprocessing at the front-end of the tracker is an effective method to reduce glint noise. The preprocessor proposed by Hewer, Martin, and Zeh (1987), which used the computationally intensive M-estimator, may not be suitable for practical implementation. An alternative method employing the median filter is studied here. The median filter is well known for its simplicity and robustness. However, the efficiency of the median filter can be seriously degraded if input samples are not identically distributed. This is what we may encounter in the tracking problem. A feedback median filter is then proposed to overcome this impediment without substantially increasing complexity. Simulations show that the new preprocessor can greatly improve tracking performance in the glint noise environment.     

A nonlinear IMM algorithm for maneuvering target tracking

In target tracking, the measurement noise is usually assumed to be Gaussian. However, the Gaussian modeling of the noise may not be true. Noise can be non-Gaussian. The non-Gaussian noise arising in a radar system is known as glint noise. The distribution of glint noise is long tailed and will seriously affect the tracking performance. We develop a new algorithm that can effectively track a maneuvering target in the glint environment The algorithm incorporates the nonlinear Masreliez filter into the interactive multiple model (IMM) method. Simulations demonstrate the superiority of the new algorithm     

Bias compensation and tracking with monopulse radars in the presence of multi path

The problem of tracking targets in the presence of reflections from sea or ground is addressed. Both types of reflections (specular and diffuse) are considered. Specular reflection causes large peak errors followed by an approximately constant bias in the monopulse ratio, while diffuse reflection has random variations which on the average generate a bias in the monopulse ratio. Expressions for the average error (bias) in the monopulse ratio due to specular and diffuse reflections and the corresponding variance in the presence of noise in the radar channels are derived. A maximum maneuver-based filter and a multiple model estimator are used for tracking. Simulation results for five scenarios, typical of sea skimmers, with Swerling III fluctuating radar cross sections (RCSs) indicate the significance and efficiency of the technique developed in this paper-a 65% reduction of the rms error in the target height estimate.     

Maximum likelihood identification of glint noise

If the non-Gaussian distribution function of radar glint noise is known, the Masreliez filter can be applied to improve target tracking performance. We investigate the glint identification problem using the maximum likelihood (ML) method. Two models for the glint distribution are used, a mixture of two Gaussian distributions and a mixture of a Gaussian and a Laplacian distribution. An efficient initial estimate method based on the QQ-plot is also proposed. Simulations show that the ML estimates converge to truths     

高超声速滑翔目标自适应跟踪方法

针对机动模式复杂多变的高超声速滑翔目标跟踪问题,提出了一种机动频率自适应跟踪方法。采用介于常速度和常加速度模型之间的Singer模型来表征目标气动力加速度的变化,从而建立跟踪系统的状态方程。根据地基雷达量测量获得系统的量测方程,鉴于距离和角度信息的量级相差较大将其由球形量测量转换为位置量测量。为了适应高超声速滑翔目标灵活多样的机动模式,基于正交性原理和无迹卡尔曼滤波算法实现了Singer模型中机动频率参数的自适应。利用滤波信息计算得到能够反映状态模型误差大小的调整因子,用于放大Singer模型中的机动频率,进而调整状态方程的过程噪声以降低模型误差。通过对2种典型机动轨迹的跟踪仿真,并与交互式多模型等方法进行比较,结果表明所提方法的跟踪精度高、计算量小,能够较好地适应阶跃机动和连续幅值变化的机动。     

旋转变频频率捷变雷达本振跟踪误差的分析

 本文从旋转变频磁控管式频率捷变雷达的本振频率跟踪原理出发,分析了产生本振频率跟踪误差的主要因素。文中着重讨论了本振频率冷跟踪误差问题。同时也提出了热跟踪后本振频率跟踪误差项。分析前者,可以决定热跟踪电路应予修正的频率范围,而后者则是跟踪本振最终的误差。以上分析对如何采取措施提高系统的跟踪精度是有参考作用的。     

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.     

基于位置信息的高分辨雷达角闪烁抑制方法

角闪烁误差是导引头寻的制导的主要误差来源,基于高分辨力雷达的单脉冲测角算法可有效改善角闪烁现象。现有的研究大多基于幅度加权的思想,利用距离单元的幅度信息进行加权平滑处理。本文在现有高分辨测角算法的基础上,结合高分辨一维距离像的位置信息,提出了一种新的角度信息处理方法。该算法充分利用了距离像有效单元的目标信息,提高了角度测量精度。仿真实验表明该算法对角闪烁有较好的抑制作用。     

An interacting multiple model approach for target tracking withglint noise

The application of the interacting multiple model (IMM) estimation approach to the problem of target tracking when the measurements are perturbed by glint noise is considered. The IMM is a very effective approach when the system has discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties. It is shown that this method performs better than the “score function” method. It is also shown that the IMM method performs robustly when the exact prior information of the glint noise is not available     

Particle filters for tracking with out-of-sequence measurements

An extension is presented to the particle filtering toolbox that enables nonlinear/non-Gaussian filtering to be performed in the presence of out-of-sequence measurements (OOSMs) with arbitrary lag, without the need to adopt linearising approximations in the filter and without the degradation of performance that would occur if the OOSMs were simply discarded. An estimate of the performance of the OOSM particle filter (OOSM-PF) is obtained for bearings-only tracking scenarios with a single target and a small number of sensors. These performance estimates are then compared with the posterior Cramer-Rao lower bound (CRLB) for the state estimate rms error and similar performance estimates obtained from the oosm extended Kalman filter (OOSM-EKF) algorithms recently introduced in the literature. For a mildly nonlinear bearings-only tracking problem the OOSM-PF and OOSM-EKF are shown to achieve broadly similar performance.     

Theoretical analysis of the sequential lobing technique

A theoretical analysis of the sequential lobing technique for target angle tracking is presented. The signal power received by each antenna beam is assumed to pass through a logarithmic amplifier. A rigorous statistical approach is adopted in the analysis for both non-fluctuating and fluctuating targets. Closed form expressions are derived for the normalized mean error and rms error of the angle estimate for Swerling 0, I, II, and III targets. Results are compared with those obtained using a simplified approach for the non-fluctuating target     

Angular Glint and the Moving, Rotating, Complex Radar Target

Angular glint produces errors in radar-indicated target direction and in the Doppler frequency. Glint arises from phase perturbations of the radar signal echoed from a complex target, as compared to those from a point target. The phase gradient V? represents these glint effects very well. The direction of this vector is that of radar angle sensing. The Doppler shift is obtined from the dot product of the gradient and the target velocity. A procedure that isolates and measures glint phase variations alone, for the inaccessible target, is described.     

High-Resolution, Radar Coherent Linear FM Microwave Source

The microwave CLFM study was directed to generating 14 ?s S-band pulses of 1000 MHz bandwidth and an rms phase error of a few degrees. Over 972 MHz bandwidth, the sampled phase error relative to the reference was 7 degrees rms and 17 degrees peak, with a maximum Fourier component of 4 degrees. The FM pulse train is generated by a gated BWO driven by a stable linearizing waveform. Phase coherency during each pulse is obtained by a sampling technique, where the phase is corrected at intervals of 1/6 ?s, the RF phase having changed an integral number of cycles in each interval. Multiplication of the BWO signal by the sampling pulse train results in band-limited phase error pulses which are applied in a feedback loop. Pulse-to-pulse coherency is obtained by phase lock of the BWO starting frequency to the crystal reference. Feedback leveling holds the output constant to 0.3 dB. The basic MITRE technique was originally demonstrated at 10 MHz in 1964. Range results measured with the X-band model radar using the CLFM generator are given and confirm the phase errors of the CLFM.