Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration     

应用卡尔曼滤波的机载雷达跟踪系统

本文论述将滤波理论应用于机载雷达中对单个目标进行距离、速度、方位角和高低角跟踪的多环反馈系统。首先根据目标和天线的相对运动建立控制四坐标跟踪环所需的状态矢量微分方程,然后推导相应的非线性滤波算法。最后给出计算机的模拟结果。计算机模拟的结果清晰地说明采用最佳滤波的系统性能比通常的有很大改善,并且这种瞄准轴坐标系的最佳系统对目标的随机机动是不灵敏的。 本文所讨论的方法和得出的结论可以延用到地面雷达、舰载雷达以及其他有源和无源的跟踪系统。     

一种非线性滤波器的误差分析及应用

针对一类具有未建模误差和扰动的非线性系统的状态估计问题,提出一种在线估计并补偿模型误差的非线性滤波算法,该算法利用非线性预测滤波(NPF)基于预测输出残差的方差最小的基本原则估计模型误差,冉利用扩展卡尔曼滤波(EKF)的思想对补偿后的模型进行状态估计;详细推导了状态估计误差及其方差阵的传播模型.以卫星姿态确定系统为例,...     

Quadratic extended Kalman filter approach for GPS/INS integration

GPS/INS integration system has been widely applied for navigation due to their complementary characteristics. And the tightly coupled integration approach has the advantage over the loosely coupled approach by using the raw GPS measurements, but hence introduces the nonlinearity into the measurement equation of the Kalman filter. So the typical method for navigation using measurements of range or pseudorange is by linearizing the measurements in an extended Kalman filter (EKF). However, the modeling errors of the EKF will cause the bias and divergence problems especially under the situation that the low quality inertial devices are included. To solve this problem, a quadratic EKF approach by adding the second-order derivative information to retain some nonlinearities is proposed in this paper. Simulation results indicate that the nonlinear terms included in the filtering process have the great influence on the performance of integration, especially in the case that the low quality INS is used in the integrated system. Furthermore, a two-stage cascaded estimation method is used, which circumvents the difficulty of solving nonlinear equations and greatly decreases the computational complexity of the proposed approach, so the quadratic EKF approach proposed in this paper is of great value in practice.     

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.     

Rao-blackwellised particle filtering in random set multitarget tracking

This article introduces a Rao-Blackwellised particle filtering (RBPF) approach in the finite set statistics (FISST) multitarget tracking framework. The RBPF approach is proposed in such a case, where each sensor is assumed to produce a sequence of detection reports each containing either one single-target measurement, or a "no detection" report. The tests cover two different measurement models: a linear-Gaussian measurement model, and a nonlinear model linearised in the extended Kalman filter (EKF) scheme. In the tests, Rao-Blackwellisation resulted in a significant reduction of the errors of the FISST estimators when compared with a previously proposed direct particle implementation. In addition, the RBPF approach was shown to be applicable in nonlinear bearings-only multitarget tracking.     

欠观测条件下的扩展增量 Kalman 滤波方法

建立欠观测条件下的非线性增量量测方程,并给出其线性化方法,在此基础上提出一种欠观测条件下的扩展增量Kalman滤波(EIKF)模型及其递推算法.工程实际中,由于环境因素的影响、测量设备的不稳定性等原因往往带来未知的系统误差,传统的扩展Kalman滤波(EKF)无法对这种未知的系统误差进行补偿和校正,结果产生较大的滤波误差,甚至导致发散.提出的扩展增量Kalman滤波方法能够成功地消除测量的系统误差,从而有效地提高非线性滤波的精度.该方法计算简单,便于工程应用.      

非线性滤波方法及其在飞行状态及参数估计中的应用

基于非线性系统高阶近似的思想,提出一种比推广卡尔曼滤波（ＥＫＦ）更接近非线性系统本质的近似滤波方法,并应用于飞行状态的参数估计（或称为飞行轨迹重构）问题。仿真和实际飞行数据计算结果表明：提出的非线性近似滤波方法比ＥＫＦ有更高的估计精度和更好的鲁棒性,对飞机机动形状、数据长度要求不高,滤波收敛速度快。利用飞行状态估计数学模型的具体特点,使计算量和存储量大幅度减少。该方法应用于非线性较强的飞行状态及参数估计问题。可得到比ＥＫＦ更好的结果。     

一种基于径向加速度的Singer-EKF机动目标跟踪算法

针对雷达均不能提供目标加速度信息,在目标机动时会出现跟踪精度差甚至跟踪发散的问题,提出一种基于径向加速度的Singer-EKF算法。该算法在信号处理阶段利用Radon-Ambiguity变换（RAT）估计出目标的径向加速度,并通过坐标转换将其引入量测向量中,然后采用基于Singer模型的扩展卡尔曼滤波（EKF）算法实现机动目标的跟踪。仿真验证了该方法的有效性,并与传统的不带径向加速度的扩展卡尔曼滤波（EKF）方法进行了比较,结果表明该方法在径向距离、位置、加速度和速度估计精度方面都有所提高。     

自校准扩展Kalman滤波方法

提出一种自校准扩展Kalman滤波(SEKF)方法,针对3种含有未知输入(如未知系统误差、突风、故障等)的不同的非线性系统模型,分别给出了滤波递推算法.在导航、信号处理、故障诊断等领域的许多非线性工程中,传统的扩展Kalman滤波(EKF)方法无法消除未知输入的影响,在滤波过程中往往产生较大误差甚至发散.提出的SEKF方法能够对这种未知输入进行补偿和修正,从而提高滤波精度.数值仿真算例表明:SEKF的滤波误差均值和标准差分别减少到传统EKF的1/12和1/4,有效地改善了滤波精度.并且该方法计算简单,便于工程应用.      

Tracking an incoming ballistic missile using an extended interval Kalman filter

The important tracking problem by radar of an incoming ballistic missile system, which contains uncertainty in modeling and noise in both dynamics and measurements, is studied. The classical extended Kalman filter (EKF) is no longer applicable to such an uncertain system, and so a new extended interval Kalman filter (EIKF) is developed for tracking the missile system. Computer simulation is presented to show the effectiveness of the EIKF algorithm for this uncertain and nonlinear ballistic missile tracking problem.     

无源定位跟踪滤波算法研究及仿真分析

首先介绍了几种无源定位跟踪滤波算法原理,包括扩展卡尔曼滤波（EKF）,无迹卡尔曼滤波器（EKF）,交互多模型滤波器（IMM）;然后通过建立几种不同模型来对每一种滤波算法进行仿真,依据仿真图形和误差结果对滤波算法进行分析,从而实现不同滤波模型根据目标运动状态进行监视和切换,这对无源定位跟踪算法精度的提高和实际应用有很大的...     

Use of the radial velocity measurement in target tracking

A new sequential filtering algorithm that incorporates the radial velocity measurement into a Kalman filter, in the presence of correlated range and radial velocity measurement errors, is presented. An analysis is given concerning its asymptotic behavior on the basis of analysis of its stochastic controllability and observability. The simulation results verify the analysis and show that the new algorithm is superior to the conventional extended Kalman filter (EKF) and close to an ideal filter.     

Nonlinear Estimation with Radar Observations

The nonlinearities of the radar measurement model equation are examined and their influence upon the accuracy of filtering and smoothing is determined. A simple algorithm by which the effects from these nonlinearities can be significantly reduced is derived. It consists of processing the radar observations in this order: azimuth, elevation, and range, using the azimuth residual to evaluate the elevation residual, and then using this combined result to evaluate the range residual. The accuracy of estimates obtained via the algorithm is compared with and shown to be superior to that of the extended Kalman filter (EKF). Furthermore, use of the algorithm does not increase the computational complexity of estimation beyond that of the EKF.     

Sequential nonlinear tracking using UKF and raw range-rate measurements

The three-dimensional (3D) converted measurements filtering (CMF) with both converted position and raw range-rate measurement is proposed to solve the Doppler radar target tracking, where the error between radar-target range and range rate are correlated. Firstly, not using pseudomeasurement constructed by product of range and range rate to reduce the high nonlinearity, the raw range-rate measurements are utilized by unscented Kalman filter (UKF), where the converted errors of the position and the range rate are decorrelated, then linear part (position measurements) and nonlinear part (range-rate measurement) are sequentially processed by Kalman filter (KF) and UKF. Secondly, based on the assumption of small measurement error, the mean and covariance of converted measurement errors are derived by second-order Taylor series expansion. Finally, the influence of the correlated coefficient rho between the range and range rate, and the range-rate noise deviation sigma_r are taken into account and extreme values of rho and sigma_r are used in Monte Carlo simulations. The results show that the proposed method is, in a sense, effective and practical     

均方意义下三维雷达无偏转换测量误差协方差阵的推导

在以前的研究中,无偏转测量误差协方差阵是基于当前测量值得到的.为了能利用所有历史数据以得到更精确的转换测量误差协方差阵估计,文中在均方意义下,推导了三维雷达的最优无偏转换测量误差协方差阵.     

Multiple model particle flter track-before-detect for range ambiguous radar

The middle pulse repetition frequency（MPRF）and high pulse repetition frequency（HPRF）modes are widely adopted in airborne pulse Doppler（PD）radar systems,which results in the problem that the range measurement of targets is ambiguous.The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio（SNR）is high enough.In this paper,a multiple model particle flter（MMPF）based track-beforedetect（TBD）method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment.By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number（PIN）as components of the target state vector,and modeling the incremental variable of the PIN as a three-state Markov chain,the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state fltering problem.At last,the hybrid fltering problem is implemented by a MMPF-based TBD method in the Bayesian framework.Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously,and succeeds in detecting and tracking weak targets with the range ambiguous radar.Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis（MH）method in low-SNR environment.     

一种基于三维到达角的无偏伪线性卡尔曼滤波

为了解决大场景下基于三维到达角的目标跟踪问题，提出了一种具有无偏性的伪线性卡尔曼滤波。首先，基于三维到达角信息对目标运动模型与量测模型进行建模；之后，对量测模型进行了伪线性化处理，得到了线性形式的目标量测模型。为了解决伪线性卡尔曼滤波存在的有偏性问题，提出了一种结合EKF（extend Kalman filter）的三维伪线性无偏卡尔曼滤波。仿真实验表明，该模型能够对非机动目标与机动目标有效跟踪，对于百公里级别的目标，当角测量误差从0.1°变化到0.5°，算法在仿真时间结束时均能将绝对位置误差降低至10 km以内，且算法的运行速度与EKF为同一个量级，同时兼顾了抗干扰能力、定位跟踪精度、运行效率的要求，能够为大场景下的目标跟踪提供有效方法。     

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     

基于EKF的天线罩误差斜率多模型估计方法

 提出一种新的滤波器结构,利用基于扩展卡尔曼滤波(EKF)的多模型(MM)算法,对天线罩误差斜率进行估计,降低天线罩误差对雷达自寻的导弹的影响,提高系统性能。在三维坐标下,创建包含导弹运动方程、目标运动方程、弹目相对运动方程的滤波模型。采用EKF算法,对包含天线罩误差的非线性观测方程进行线性化处理;依照多模滤波的思想,对天线罩误差进行离散建模,构建伪观测方程,更新模型概率,得到天线罩误差斜率的估计值;将斜率估计结果代入EKF,得到滤除天线罩误差影响的系统状态量估计结果并形成制导指令。仿真结果表明,所提方法可以有效地估计天线罩斜率,提高系统制导精度。