A passive tracking filter for missile capture

A practical filter is suggested for ground-based missile tracking in a capture-guidance mode utilizing angle-only measurements from a passive missile sensor, and its performance is evaluated by a realistic system-simulation study. A missile-acceleration model that provides inputs to the filter is also suggested. The filter has a decoupled structure of independent azimuth and elevation channels, which requires fewer computations in solving the filter gain compared to a coupled structure. Simulation results show good tracking performance of the filter when used in association with the proposed missile-acceleration model     

Manoeuvring target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and manoeuvering target in clutter from angle-only measurements is presented and evaluated. The aim is to compare PFs to a well-established tracking algorithm, the IMM-PDA-EKF (interacting multiple model, probabilistic data association, extended Kalman filter), and to provide an insight into which aspects of PF design are of most importance under given conditions. Monte Carlo simulations show that the use of a resampling scheme which produces particles with distinct values offers significant improvements under almost all conditions. Interestingly, under all conditions considered here,using this resampling scheme with blind particle proposals is shown to be superior, in the sense of providing improved performance for a fixed computational expense, to measurement-directed particle proposals with the same resampling scheme. This occurs even under conditions favourable to the use of measurement-directed proposals. The IMM-PDA-EKF performs poorly compared with the PFs for large clutter densities but is more effective when the measurements are precise.     

Efficient Approximation of Kalman Filter for Target Tracking

A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.     

Suboptimal filter design with pseudomeasurements for targettracking

A suboptimal Kalman filter design method is presented for the problem of tracking a maneuvering target. The design method is essentially based on linear target dynamics and linear-like structured measurements called pseudomeasurements. The pseudomeasurements are obtained by manipulating the original nonlinear measurements algebraically. The resulting filter has computational advantages over other filters with similar performance. Also, a variant of the Berg model is proposed as a target acceleration model under the assumption of a coordinated turn maneuver. The proposed model is consistent with the underlying assumption. Monte Carlo computer simulation results are included to demonstrate the effectiveness of the proposed suboptimal filter associated with the target acceleration model     

Multiple model nonlinear filtering for low signal ground target applications

The design and implementation of a multiple model nonlinear filter (MMNLF) for ground target tracking using ground moving target indicator (GMTI) radar measurements is described. Like the well-known interacting multiple model Kalman filter (IMMKF), the MMNLF is based on the theory of hybrid stochastic systems. However, since it models the probability distribution for the target in a region, rather than just the distribution's first and second moments, a nonlinear filter is able to capture more fine-grained detail of the target motion and requires fewer models than typical IMMKF implementations. This is illustrated here with a two-model MMNLF in which one motion model incorporates terrain constraints while the second is a nearly constant velocity (CV) model. Another feature of the MMNLF is that it enables incorporation of prethresholded measurements. To implement the filter, the target state conditional probability density is discretized on a set of moving grids and recursively updated with sensor measurements via Bayes' formula. The conditional density is time updated between sensor measurements using alternating direction implicit (ADI) finite difference methods, generalized for this hybrid application. In simulation testing against low signal-to-interference-plus-noise ratio (SINR) targets, the MMNLF is able to maintain track in situations where single model filters based on either of the component models or filters that use thresholded data fail. Potential applications of this work include detection and tracking of foliage-obscured moving targets.     

Tracking a ballistic target: comparison of several nonlinear filters

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.     

A Tracking Filter in Spherical Coordinates Enhanced by De-noising of Converted Doppler Measurements

Tracking problem in spherical coordinates with range rate (Doppler) measurements, which would have errors correlated to the range measurement errors, is investigated in this paper. The converted Doppler measurements, constructed by the product of the Doppler measurements and range measurements, are used to replace the original Doppler measurements. A de-noising method based on an unbiased Kalman filter (KF) is proposed to reduce the converted Doppler measurement errors before updating the target states for the constant velocity (CV) model. The states from the de-noising filter are then combined with the Cartesian states from the converted measurement Kalman filter (CMKF) to produce final state estimates. The nonlinearity of the de-noising filter states are handled by expanding them around the Cartesian states from the CMKF in a Taylor series up to the second order term. In the mean time, the correlation between the two filters caused by the common range measurements is handled by a minimum mean squared error (MMSE) estimation-based method. These result in a new tracking filter, CMDN-EKF2. Monte Carlo simulations demonstrate that the proposed tracking filter can provide efficient and robust performance with a modest computational cost.     

基于广义Kalman估计的机载雷达高精度控制系统

 研究了在某型现役机载雷达系统中, 采用广义Kalman 滤波器方法来预估目标机的俯仰角和方位角,产生跟踪目标用的雷达天线驱动信号, 替代传统的速率陀螺测量元件来补偿本机机动所造成的扰动的方法,同时对探测信号本身所具有的延迟起到了补偿作用。对目标的运动采用直角坐标系中的Singer 模型描述, 而对测量信号则是应用极坐标系中的描述, 采用广义Kalman 滤波器来完成估计, 即在每一步的估计和控制中对计算测量方程进行线性化结果, 实现两种坐标系的转换。通过应用Matlab/ Simulink 软件对整个系统的建模、设计及仿真研究, 得到了满意的结果。     

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.     

Adaptive Tracking Filter for Maneuvering Targets

A general method of continually restructuring an optimum Bayes-Kalman tracking filter is proposed by conceptualizing a growing tree of filters to maintain optimality on a target exhibiting maneuver variables. This tree concept is then constrained from growth by quantizing the continuously sensed maneuver variables and restricting these to a small value from which an average maneuver is calculated. Kalman filters are calculated and carried in parallel for each quantized variable. This constrained tree of several parallel Kalman filters demands only modest om; puter time, yet provides very good performance. This concept is implemented for a Doppler tracking system and the performance is compared to an extended Kalman filter. Simulation results are presented which show dramatic tracking improvement when using the adaptive tracking filter.     

Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets

The majority of tactical weapons systems require that manned maneuverable vehicles, such as aircraft, ships, and submarines, be tracked accurately. An optimal Kalman filter has been derived for this purpose using a target model that is simple to implement and that represents closely the motions of maneuvering targets. Using this filter, parametric tracking accuracy data have been generated as a function of target maneuver characteristics, sensor observation noise, and data rate and that permits rapid a priori estimates of tracking performance to be made when maneuvering targets are to be tracked by sensors providing any combination of range, bearing, and elevation measurements.     

On a decoupled multitarget tracking algorithm

An analysis is conducted of the optimality of a decoupled tracking filtering algorithm for addressing the problem of tracking multiple targets with correlated measurements and maneuvers. It is proved that the decoupled filters are, in general, suboptimal and are not in fact Kalman filters. However, it is shown also that if the standard Kalman filter is asymptotically stable, the decoupled filters will converge asymptotically to the stable version of the standard Kalman filter. For the case of time-invariant measurement and process noise covariance, a simple sufficient condition guaranteeing the asymptotical stability of the decoupled filters are given     

Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

不完全量测下一类非线性光电跟踪系统滤波器设计

 随着不完全量测条件下探测概率的下降,传统光电跟踪系统的跟踪性能显著降低。为此,本文考虑将俯仰和偏航两个方向的角速度量测引入传统光电跟踪系统,并设计了不完全量测下基于置信度融合的目标跟踪滤波器。首先针对这类新型的光电跟踪系统建立了系统的量测模型,利用嵌套条件方法推导了转换量测误差前两阶矩的一致性估计;然后针对位置探测通道与角速度探测通道的4种数据探测情形设计了4个子滤波器,并根据探测通道的探测情况计算出各子滤波器的置信度,进而对各子滤波器的输出按置信度进行加权融合,得到了跟踪滤波器的全局输出;最后给出了非线性跟踪系统统计意义下的Cramer-Rao下界(CRLB)。Monte-Carlo仿真表明：在不完全量测下,相比传统光电跟踪系统,附加角速度量测的光电跟踪系统的跟踪性能有了显著提高,并且滤波器估计误差均方差(RMSE)已逼近非线性跟踪系统统计意义下的CRLB。     

A track filter for reentry objects with uncertain drag

A filter was developed for maintaining track on ballistic missiles whose drag profiles are unknown or deviate significantly from prior predictions. The filter employs an innovative form of a seven-state Kalman filter in which object drag is included as a state to be estimated. Using measurements of range, azimuth, and elevation, the filter can track endo- and exo-atmospheric targets on a wide variety of trajectories without requiring a priori tuning to account for variations in reentry angle, drag history, measurement signal-to-noise ratio, etc. The filter was designed to be implemented at the millimeter wave (MMW) radar (a high-range-resolution, narrow beamwidth, Ka-band radar) located at Kwajalein Missile Range (KMR) in the Marshall Islands. Extensive testing and comparisons using a high fidelity simulation showed the new filter to be robust to a wide variety of trajectories and substantially better than track filters presently used at KMR. The filter was coded to run efficiently in real time, installed at the MMW radar, and successfully used to track an intercontinental ballistic missile (ICBM) with varying drag characteristics through exo-atmospheric and reentry phases. The filter yielded a more accurate and responsive track than possible with the previously used filter on a similar trajectory     

A method for improving extended Kalman filter performance forangle-only passive ranging

A relatively simple method is presented which eliminates previously reported (Oct. 1985) erratic estimation performance associated with Cartesian formulations of the extended Kalman filter (EKF) for the 2D angle-only emitter location problem. The technique is based on an initialization procedure which combines a priori probability density function (pdf) information with single measurement a posteriori pdf information in a manner which is more efficient than the EKF. Simulation results are presented which demonstrate the utility of the technique as compared with a previously offered modified gain EKF     

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.     

Modeling and Estimation for Tracking Maneuvering Targets

A new approach to the three-dimensional airborne maneuvering target tracking problem is presented. The method, which combines the correlated acceleration target model of Singer [3] with the adaptive semi-Markov maneuver model of Gholson and Moose [8], leads to a practical real-time tracking algorithm that can be easily implemented on a modern fire-control computer. Preliminary testing with actual radar measurements indicates both improved tracking accuracy and increased filter stability in response to rapid target accelerations in elevation, bearing, and range.     

Nonlinear Estimation of Generalized Vector Shot Processes

A class of nonlinear filters for dynamical systems driven by generalized Poisson processes is developed. One of the filters, the maximum a posteriori (MAP) filter, is shown by a numerical example to be superior to other known predictors in getting the highest target hit probabilities, and it is relatively simple to implement. This filter has applications in both fire control and air traffic control of maneuvering piloted vehicles.     

A minimax approach to the design of Doppler filters

The detection of a target in correlated clutter, thermal noise, and extraneous interference is considered. The amplitude, phase and Doppler frequency of the signal are not known a priori. A general criterion is presented which measures the performance of a suboptimal test relative to an optimal test. The criterion is encompassed into a design procedure used to design Doppler filters. The procedure allows many design considerations to be taken into account, and results in a design which attempts to minimize the number of filters required. For low dimensionality the procedure results in single filter designs; for higher dimensionality multiple filters are designed. The performances of these systems are compared with the results obtained by Emerson (1978) and Andrews (1974). It is found that the procedure yields good filter designs under general conditions and may reduce the number of filters required compared with classical designs