Posterior Cramer-Rao lower bounds for multitarget bearings-only tracking

Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.     

Posterior Cramer-Rao lower bounds for bearing-only tracking

In the state estimation of passive tracking systems, the traditional approximate expression for the Cramero-Rao lower bound （CRLB） does not take two factors into consideration, that is, measurement origin uncertainty aad state noise. Such treatment is only valid in ideal situation but it is not feasible in actual situation. In this article, considering the two factors, the posterior Cramer-Rao lower bound （PCRLB） recursion expression for the error of bearing-only tracking is derived. Then, further analysis is carried out on the PCRLB. According to the final result, there are four main parameters that play a role in the performance of the PCRLB, that is, measurement noise, detection probability, state noise and clutter density, amongst which the first two have greater impact on the performance of the PCRLB than the others.     

一种新的自适应机动目标跟踪算法

在＂当前＂统计（CS）模型基础上,提出了一种新的机动目标自适应滤波算法,当前统计模型-修正强跟踪滤波（CS-MSTF）算法。新算法在保留＂当前＂统计模型及强跟踪滤波器（STF）对一般机动目标跟踪精度高的优点的同时,作出以下改进：针对强跟踪滤波器在机动部分获得完美性能的同时,非机动部分的精度却不理想的缺陷,对预测误差协方差及渐消因子的计算作出修正,同时改进机动部分和非机动部分的精度;将目前常用的估计误差协方差的计算公式采用更加可靠的Joseph公式,增强了数值的稳定性和算法的鲁棒性。蒙特卡罗仿真表明,新算法的性能优于当前统计模型-强跟踪滤波（CS-STF）算法,能够进行有效估计。

Abstract：

Based on the ＂current＂ statistical model,a new adaptive maneuvering target tracking algorithm,CS-MSTF,was proposed. The new algorithm,keeping the merits of high tracking precision that the ＂current ＂ statistical model and strong tracking filter（STF） have in tracking maneuvering target has made the modifications as such：First,STF has the defect that it achieves the perfert performance in maneuvering segment at a cost of the precision in non-naneuvering segment,so the new algorithm modifies the prediction error covariance matrix and the fading factor to improve the tracking precision both of the maneuvering segment and non-maneuvering segment; The estimation error covariance matrix was calculated using the Joseph form,which is more stable and robust in numerical. The Monte-Carlo simulation shows that the CS-MSTF algorithm has a more excellent performance than CS-STF and can esitmate efficiently.     

OPTIMAL TARGET TRAJECTORY ESTIMATION AND FILTERING USING NETWORKED SENSORS

Target tracking using distributed sensor network is in general a challenging problem because it always needs to deal with real-time processing of noisy information. In this paper the problem of using nonlinear sensors such as distance and direction sensors for estimating a moving target is studied. The problem is formulated as a prudent design of nonlinear filters for a linear system subject to noisy nonlinear measurements and partially unknown input, which is generated by an exogenous system. In the worst case where the input is completely unknown, the exogenous dynamics is reduced to the random walk model. It can be shown that the nonlinear filter will have optimal convergence if the number of the sensors are large enough and the convergence rate will be highly improved if the sensors are deployed appropriately. This actually raises an interesting issue on active sensing： how to optimally move the sensors if they are considered as mobile multi-agent systems？ Finally, a simulation example is given to illustrate and validate the construction of our filter.     

New rapid transfer alignment method for SINS of airborne weapon systems

Transfer alignment is an effective alignment method for the strapdown inertial navigation system （SINS） of airborne weapon systems. The traditional transfer alignment methods for large misalignment angles alignment use nonlinear transfer align- ment models and incorporate nonlinear filtering. A rapid transfer alignment method with linear models and linear filtering for ar- bitrary misalignment angles is presented. Through the attitude quaternion decomposition, the purpose of transfer alignment is converted to estimate a constant quaternion. Employing special manipulations on measurement equation, velocity and attitude linear measurement equations are derived. Then the linear trans- fer alignment model for arbitrary misalignment angles is built. An adaptive Kalman filter is developed to handle modeling errors of the measurement noise statistics. Simulation results show feasibili- ty and effectiveness of the proposed method, which provides an alternative rapid transfer alignment method for airborne weapons.     

Method of target tracking with Doppler blind zone constraint

Doppler blind zone （DBZ） has a bad influence on the airborne early warning radar, although it has good detection performance for low altitude targets with pulse Doppler （PD） technology. In target tracking, the blind zone can cause target tracking breakage easily. In order to solve this problem, a parallel particle filter （PF） algorithm based on multi-hypothesis motion models （MHMMs） is proposed. The algorithm produces multiple possible target motion models according to the DBZ constraint. Particles are updated with the constraint in each motion model. Once the first measurement from the target which reappears from DBZ falls into the particle cloud formed by any model, the measurementtrack association succeeds and track breakage is avoided. The simulation results show that on the condition of different DBZ ranges, a high association ratio can be got for targets with different maneuverability levels, which accordingly improves the tracking quality.     

Bayesian target tracking based on particle filter

1 .INTRODUCTIONIn many fields including target tracking, robotics ,signal processing, ti me-series analysis , etc , theKal manfilter is one of the most widely used methodsfor esti mationinlinear Gaussiansystemand measure-ment models . However , the application of theKal man filter to nonlinear systems can be difficult .Most common approach is to use the extendedKal manfilter (EKF) .EKFsi mplylinearizes all non-linear models by using Taylor series expansions andcan, however , lead to p…     

Adaptive unscented Kalman filter for parameter and state estimation of nonlinear high-speed objects

An adaptive unscented Kalman filter (AUKF) and an augmented state method are employed to estimate the timevarying parameters and states of a kind of nonlinear high-speed objects. A strong tracking filter is employed to improve the tracking ability and robustness of unscented Kalman filter (UKF) when the process noise is inaccuracy, and wavelet transform is used to improve the estimate accuracy by the variance of measurement noise. An augmented square-root framework is utilized to improve the numerical stability and accuracy of UKF. Monte Carlo simulations and applications in the rapid trajectory estimation of hypersonic artillery shells confirm the effectiveness of the proposed method.     

Posterior Cramér-Rao Bounds for Nonlinear Dynamic System with Colored Noises

A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.     

UPF based autonomous navigation scheme for deep space probe

The autonomous ＂celestial navigation scheme＂ for deep space probe departing from the earth and the autonomous ＂optical navigation scheme＂ for encountering object celestial body are presented. Then, aiming at the conditions that large initial estimation errors and non-Gaussian distribution of state or measurement errors may exist in orbit determination process of the two phases, UPF （unscented particle filter） is introduced into the navigation schemes. By tackling nonlinear and non-Gaussian problems, UPF overcomes the accuracy influence brought by the traditional EKF （extended Kalman filter）, UKF （unscented Kalman filter）, and PF （particle filter） schemes in approximate treatment to nonlinear and non-Gaussian state model and measurement model. The numerical simulations demonstrate the feasibility and higher accuracy of the UPF navigation scheme.     

极坐标系中带多普勒量测的雷达目标跟踪

将仅仅考虑位置量测的二维去偏一致转换量测卡尔曼滤波算法进行推广,以解决包含多普勒量测且斜距误差和多普勒误差相关的雷达目标跟踪问题。首先用斜距和多普勒量测的乘积构造伪量测,以减小多普勒量测和目标运动状态之间的强非线性程度;然后用嵌套条件方法得到了转换量测误差前两阶矩的一致性估计;最后根据伪量测是目标运动状态二次函数的特性,用二阶EKF最优地实现了非线性跟踪滤波,其中为了进一步减小二阶EKF的近似误差,利用Cholesky分解实现了位置量测和伪量测的序贯处理。Monte-Carlo仿真结果表明采用新算法可以明显改善跟踪滤波器的性能。     

跟踪弹道目标的几种次最优滤波器

研究了通过雷达观测跟踪重返大气层阶段的弹道目标问题。考虑了一种状态方程和量测方程都具有高度非线性的数学模型并推导出估计误差的理论Cramer-Rao低界。我们设计了三种次最优滤波器并将其滤波性能和Cramer-Rao低界进行了比较。除了在非线性滤波中经常采用的EKF和UKF之外，提出了一种结合传统卡尔曼滤波和简化点Unscented变换的滤波器，仿真结果表明，新滤波器在精度和计算复杂性上均有良好表现。     

非线性系统中多传感器滤波跟踪型数据融合算法的研究

在非线性系统中，常用的跟踪滤波算法是基于扩展的卡尔曼滤波算法的融合算法，但是这种融合算法的跟踪精度并不是很高。本文根据对滤波器跟踪型数据融合的研究，提出了基于转换测量值卡尔曼滤波算法的非线性系统中的数据融合方法。研究表明，在利用激光干涉仪进行目标跟踪时，这种基于融合算法的集中式融合算法的跟踪性能优于分布式融合算法，但是，从仿真结果可以看出，两种融合算法的差别不大，结果基本相同，因此，在非线性系统中，基于转换测量值卡尔曼滤波算法的分布融合算法可以重构集中式融合算法。     

基于波形捷变的多传感器机动目标跟踪

针对现代战场中目标往往采用机动方式运动的情况,为了提高目标跟踪的准确性和精确性,结合多传感器数据融合的优点,提出了一种基于波形捷变的多传感器机动目标跟踪方法。该算法通过波形捷变来改变量测的精度。首先在现有文献的基础上,将波形捷变方式推广到二维空间,把雷达量测的克拉美罗下限（Cramer-Rao lower bound,CRLB）近似为量测误差协方差,由于该CRLB是关于发射波形参量的,从而把雷达跟踪的信号处理与数据处理结合在一起,通过波形参量的动态选择得到量测误差协方差的最小值。从而在整个雷达跟踪过程中提高信噪比（signal to noise ratio,SNR）,降低量测误差。其次,在数据处理上,采用多传感器数据融合及粒子滤波进一步提高机动目标跟踪的精度。最后,将该算法与传统的Kalman滤波、粒子滤波及只对一维空间的量测采用波形捷变的算法和交互多模型方法（interacting multiple model,IMM）进行仿真比较,仿真结果显示该算法对机动目标的跟踪精度显著提高。     

基于量测转换序贯滤波的GMPHD机动目标跟踪

针对多普勒雷达杂波环境下的多机动目标跟踪, 提出了一种基于去相关无偏量测转换序贯滤波的多模型高斯概率假设密度算法。针对量测的非线性, 将位置量测进行无偏量测转换, 将多普勒量测进行去偏量测转换, 并通过序贯滤波方式提高跟踪精度。针对多目标的机动性, 在高斯混合概率假设密度(Gaussian mixture probability hypothesis density, GMPHD)中引入多模型思想对模型相关的高斯分量进行预测、更新处理。仿真结果显示, 所提算法可以在杂波环境中实现有效的机动多目标跟踪, 与无迹卡尔曼多模型GMPHD相比不仅跟踪精度提升了38.15%, 而且大大改善了算法效率; 与无迹卡尔曼最适高斯近似GMPHD相比, 在效率上有小幅度的增加, 且跟踪精度提升了36.47%。     

多被动传感器UKF与EKF算法的应用与比较

针对多被动传感器条件下的目标跟踪问题,给出了推广卡尔曼滤波在多被动传感器条件下的具体算法;考虑到多被动传感器目标跟踪需要解决观测非线性的问题,故而将用于非线性系统的基于UT变换的UKF算法应用于所讨论的跟踪问题中,采用检测融合方案,将多个被动传感器的角度观测组合成量测向量,推导了多被动传感器的UKF滤波算法,实现了对目标在三维空间中的全被动跟踪.将两种算法进行了仿真比较,结果表明,采用多被动传感器的UKF算法可以获得比传统的推广卡尔曼滤波算法更为精确的跟踪效果.     

三维AoA目标跟踪的二次约束卡尔曼滤波算法

在基于到达角(angle of arrival, AoA)的三维目标跟踪中, 伪线性卡尔曼滤波具有稳定性高和计算复杂度低的优点, 但是严重的偏差问题使其跟踪精度迅速下降。针对该问题, 提出一种二次约束卡尔曼滤波(quadratic constraint Kalman filter, QCKF)算法。首先引入涉及所有观测噪声项的增广矩阵, 然后建立与线性卡尔曼滤波等价的目标函数并且附加含有二次项的约束条件, 以此降低偏差影响, 实现更准确的状态更新。QCKF算法采用广义特征值分解求解约束优化问题, 无法直接通过状态更新表达式推导其协方差矩阵, 因此利用约束条件以及矩阵扰动方法完成协方差矩阵更新。仿真分析表明, QCKF算法相较于其他非线性滤波算法具有更优的跟踪性能, 不仅在低噪声条件下可达到后验克拉美罗下界, 而且当噪声严重时能够显著降低跟踪误差, 并且计算开销不高。     

均方意义下的最优无偏转换测量Kalman滤波

转换测量Kahmal滤波(CMKF)在雷达跟踪领域得到了广泛的应用。然而，当目标位置的互距离测量误差比较大时，CMKF的性能将急剧下降。本文在均方意义下给出了一种新的无偏CMKF。这种滤波器的关键是在均方意义下推导无偏转换测量误差协方差阵的最佳估计。对于匀速运动目标，仿真结果表明本文方法可以得到好的滤波性能，而当方位测量误差比较大时，滤波性能的改善就更加明显。此外，对机动目标的情形亦进行了讨论。     

基于高程补偿的BLUE算法在塔康中的应用研究

基于塔康系统的斜距、方位和高程可对目标定位,但较大的量测误差影响定位精度。为提高估计精度,研究塔康中最佳线性无偏估计(best linear unbiased estimation, BLUE)滤波器的实现。建立地面站对目标的量测模型,并分析量测转换误差特性,推导出对应的BLUE滤波模型;针对目标从地面站上空过顶时出现无效量测的问题,通过对高程量测补偿的方法予以克服,解决传统算法在强非线性量测下误差较大的弊病。与经典方法的性能对比表明,改进算法有效地抑制了强非线性量测下的滤波发散,有很强的鲁棒性和实时性。     

引入测速信息的雷达导引头无偏转换跟踪方法

为了满足先进地空导弹对精确弹目交会信息的需求,基于自适应卡尔曼滤波算法,提出了一种引入测速信息的雷达导引头无偏转换跟踪方法。在当前统计模型的基础上,利用递推遗忘最小二乘法估计当前加速度,得到了状态方程。在雷达测量模型的基础上,分析了极坐标系下与笛卡尔坐标系下位置、速度信息的无偏转换关系,推导了无偏转换量测误差协方差矩阵真实值和利用量测信息估计真实值的表达式,得到了量测方程。通过滤波得到的状态和误差估计信息,改进了真实无偏转换量测协方差矩阵的估计算法。仿真结果验证了所提跟踪方法在滤波精度和跟踪速度上的良好性能。