Exact multisensor dynamic bias estimation with local tracks

An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70% compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented.     

基于不敏变换的动基座传感器偏差估计方法

提出了一种新的基于合作目标的动基座传感器误差绝对配准方法。该方法利用所获得的合作目标位置信息,将载体平台姿态角偏差转换为传感器测量偏差中的一部分,并建立偏差状态方程和测量方程。在此基础上,采用广义最小二乘方法以实现传感器测距误差的估计,不敏滤波的方法则用于实现平台载体的姿态偏差和角度测量偏差的实时估计。仿真结果表明,该方法实现简单,收敛速度快,可以实现单部动基座传感器的偏差估计。     

基于MLR的机动平台传感器误差配准算法

 基于固定平台传感器误差极大似然配准(MLR)算法,针对机动平台存在姿态角系统误差的问题,提出了对机动平台传感器系统误差和目标状态进行批处理离线估计的机动极大似然配准(MLRM)算法.该算法利用所有传感器对目标的量测值,通过把传感器量测向目标状态进行投影、对传感器系统误差和目标状态进行期望最大化迭代以及对目标的状态进行融合估计,最终实现量测、姿态角系统误差和目标状态的有效估计.仿真结果表明,该算法迭代收敛速度快,对系统误差估计精度高,对系统误差可观测性较低的配准环境的适应性强并且对传感器姿态角的相关性不敏感,具有很强的工程实用性.     

A Polynomial Prediction Filter Method for Estimating Multisensor Dynamically Varying Biases

The estimation of the sensor measurement biases in a multisensor system is vital for the sensor data fusion. A solution is provided for the estimation of dynamically varying multiple sensor biases without any knowledge of the dynamic bias model pa- rameters. It is shown that the sensor bias pseudomeasurement can be dynamically obtained via a parity vector. This is accom- plished by multiplying the sensor uncalibrated measurement equations by a projection matrix so that the measured variable is eliminated from the equations. Once the state equations of the dynamically varying sensor biases are modeled by a polynomial prediction filter, the dynamically varying multisensor biases can be obtained by Kalman filter. Simulation results validate that the proposed method can estimate the constant biases and dynamic biases of multisensors and outperforms the methods reported in literature.     

Dynamic Cramer-Rao bound for target tracking in clutter

Recently, there have been several new results for an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB, with both measurement origin uncertainty (i.e., in the presence of false alarms or random clutter) and measurement noise, is simply that without measurement origin uncertainty times a scalar information reduction factor (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e., objects with a stochastic motion); but this is only valid without measurement origin uncertainty. The present paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former. The effects of plant and observation dynamics on the CRLB are explored. Further, the CRLB is compared via simulation to two common target tracking algorithms, the probabilistic data association filter (PDAF) and the multiframe (N-D) assignment algorithm.     

KUPS: Knowledge-Based Ubiquitous and Persistent Sensor Networks for Threat Assessment

We propose a knowledge-based ubiquitous and persistent sensor network (KUPS) for threat assessment, in which "sensor" is a broad characterization. It refers to diverse data or information from ubiquitous and persistent sensor sources such as organic sensors and human intelligence sensors. Our KUPS for threat assessment consists of two major steps: situation awareness using fuzzy logic systems (FLSs) and threat parameter estimation using radar sensor networks (RSNs). Our FLSs combine the linguistic knowledge from different intelligent sensors, and our proposed maximum-likelihood (ML) estimation algorithm performs target radar cross section (RCS) parameter estimation. We also show that our ML estimator is unbiased and the variance of parameter estimation matches the Cramer-Rao lower bound (CRLB) if the radar pulses follow the Swerling II model. Simulations further validate our theoretical results.     

地空协同防空目标抗差跟踪算法

针对现有系统误差配准算法以已知系统误差变化模型为前提条件、相应的目标状态估计易受系统误差配准结果影响等不足之处,在机载雷达与地基雷达协同防空预警体系下,对系统误差存在情况下的目标跟踪问题进行了研究,并提出了有效的地空协同防空目标抗差跟踪算法。仿真结果表明所提算法可得到无偏、稳定、有效的目标状态估计,并且相对于系统误差目标状态联合估计算法,所提算法计算量小,对系统误差变化有很强的鲁棒性,可适应实际工程应用中可能出现的异常情况,为后续决策提供稳定有效的目标信息。     

Pursuer identification and time-to-go estimation using passive measurements from an evader

We present an algorithm for identifying the parameters of a proportional navigation guidance missile (pursuer) pursuing an airborne target (evader) using angle-only measurements from the latter. This is done for the purpose of classifying the missile so that appropriate counter-measures can be taken. Mathematical models are constructed for a pursuer with a changing velocity, i.e., a direction change and a speed change. Assuming the pursuer is launched from the ground with fixed thrust, its motion can be described by a four-dimensional parameter vector consisting of its proportional navigation constant and three parameters related to thrusting. Consequently, the problem can be solved as a parameter estimation problem, rather than state estimation and we provide an estimator based on maximum likelihood (ML) to solve it. The parameter estimates obtained can be mapped into the time-to-go until intercept estimation results are presented for different scenarios together with the Cramer-Rao lower bound (CRLB), which quantifies the best achievable estimation accuracy. The accuracy of the time-to-go estimate is also obtained. Simulation results demonstrate that the proposed estimator is efficient by meeting the CRLB.     

A multi-rate sensor fusion approach using information filters for estimating aero-engine performance degradation

Gas-path performance estimation plays an important role in aero-engine health management, and Kalman Filter(KF) is a well-known technique to estimate performance degradation. In previous studies, it is assumed that different kinds of sensors are with the same sampling rate, and they are used for state estimation by the KF simultaneously. However, it is hard to achieve state estimation using various kinds of sensor measurements at the same sampling rate due to a complex network and physical characteristic differences between sensors, especially in an advanced multisensor architecture. For this purpose, a multi-rate sensor fusion using the information filtering approach is proposed based on the square-root cubature rule, which is called Multi-rate Squareroot Cubature Information Filter(MSCIF) to track engine performance degradation. Soft measurement synchronization of the MSCIF is designed to provide a sensor fusion condition for multiple sampling rates of measurement, and a fault sensor is isolated by maximum likelihood validation before state estimation. The contribution of this paper is to supply a novel multi-rate informationfilter approach for sensor fault tolerant health estimation of an aero-engine in a multi-sensor system. Tests are conducted for aero-engine performance degradation estimation with multiple sampling rates of sensor measurement on both digital simulation and semi-physical experiment.Experimental results illustrate the superiority of the proposed algorithm in terms of degradation estimation accuracy and robustness to sensor failure in a multi-sensor system.     

Monopulse DOA estimation of two unresolved Rayleigh targets

This paper provides for new approaches to the processing of unresolved measurements as two direction-of-arrival (DOA) measurements for tracking closely spaced targets rather than the conventional single DOA measurement of the centroid. The measurements of the two-closely spaced targets are merged when the target echoes are not resolved in angle, range, or radial velocity (i.e., Doppler processing). The conditional Cramer Rao lower bound (CRLB) is developed for the DOA estimation of two unresolved Rayleigh targets using a standard monopulse radar. Then the modified CRLB is used to give insight into the boresight pointing for monopulse DOA estimation of two unresolved targets. Monopulse processing is considered for DOA estimation of two unresolved Rayleigh targets with known or estimated relative radar cross section (RCS). The performance of the DOA estimator is studied via Monte Carlo simulations and compared with the modified CRLB     

Architectures and algorithms for track association and fusion

Target tracking using multiple sensors can provide better performance than using a single sensor. One approach to multiple target tracking with multiple sensors is to first perform single sensor tracking and then fuse the tracks from the different sensors. Two processing architectures for track fusion are presented: sensor to sensor track fusion, and sensor to system track fusion. Technical issues related to the statistical correlation between track estimation errors are discussed. Approaches for associating the tracks and combining the track state estimates of associated tracks that account for this correlation are described and compared by both theoretical analysis and Monte Carlo simulations     

包含乘性噪声自适应修正的非合作目标相对导航算法

无人机（UAV）态势感知的任务是利用机载传感器对未知环境进行目标识别和引导,针对无人机与非合作目标间中远距离的相对导航问题,提出了一种基于角度和距离量测的相对状态估计算法。在现有滤波算法的基础上,为了提高精度和稳定性,本文利用了列文伯格-马夸尔特（LM）优化的思想对迭代卡尔曼滤波（IEKF）算法进行改进,提出了一种LM-IEKF算法,并推导该算法在迭代过程中的状态更新方程及协方差阵的递推公式。在此基础上,考虑到距离传感器由于信号相关特性而引入的乘性噪声,现有的加性噪声模型难以适应,因此,进一步提出了基于量测噪声自适应修正的Modified LM-IEKF方法,通过在线实时更新噪声阵提高滤波的精度,并设置渐消记忆指数平滑估计结果。算法验证结果表明,与现有的EKF、IEKF算法相比,在仅含加性噪声的情况下,LM-IEKF算法具有更好的性能;在包含乘性噪声的情况下,Modified LM-IEKF可以有效地估计量测噪声,与目前广泛使用的EKF算法相比,在综合相对位置和相对速度精度上分别提高了10%和23%。     

一种频域插值变化迭代频率估计方法

针对现有频率估计算法存在的复杂度高、频率估计能力弱、估计结果均方差大等缺点,在固定迭代AM（Aboutanios—Mulgrew）无偏频率估计算法基础上,提出一种频域插值变化迭代频率估计算法,推导了不同迭代参数实现无偏估计的充分条件,证明了有偏估计时本算法的收敛性和偏离度,通过设置不同迭代参数,可以实现无偏或有偏估计。仿真分析表明：当具有较高信噪比时,在整个频率估计范围内,该方法均方误差接近CRLB（Cramer-RaoLowerBound,克拉美一罗下限）;当FFT（FastFourierTransform,快速傅里叶变换）粗估计残余频率接近0．5时,该方法的均方误差优于CRLB,为CRLB的96％。     

Bayesian Approach to Extended Object and Cluster Tracking using Random Matrices

In algorithms for tracking and sensor data fusion the targets to be observed are usually considered as point source objects; i.e., compared with the sensor resolution their extension is neglected. Due to the increasing resolution capabilities of modern sensors, however, this assumption is often no longer valid as different scattering centers of an object can cause distinct detections when passing the signal processing chain. Examples of extended targets are found in short-range applications (littoral surveillance, autonomous weapons, or robotics). A collectively moving target group can also be considered as an extended target. This point of view is the more appropriate, the smaller the mutual distances between the individual targets are. Due to the resulting data association and resolution conflicts any attempt of tracking the individual objects within the group seems to be no longer reasonable. With simulated sensor data produced by a partly unresolvable aircraft formation the addressed phenomena are illustrated and an approximate Bayesian solution to the resulting tracking problem is proposed. Ellipsoidal object extensions are modeled by random matrices, which are treated as additional state variables to be estimated or tracked. We expect that the resulting tracking algorithms are also relevant for tracking large, collectively moving target swarms.     

2D雷达组网中目标高度估计误差的Cramér-Rao限

 在由2坐标雷达组成的雷达网中,推导了目标高度估计误差的CRLB(Cram&;#225;r-Rao限),并通过不同条件下的数值计算得到了一些结论。结果表明,目标高度估计误差的CRLB既与雷达的测角误差有关,也与目标和2个雷达站形成的夹角有关系,雷达配置在不同的高度上有利于目标高度估计的收敛性。这些结论对于2坐标雷达组网以及雷达网中的传感器管理具有指导意义。     

传感器位置误差条件下的约束总体最小二乘时差定位算法

 现代定位系统中,传感器往往被安放在运动平台上,其位置无法精确得知,存在估计误差,将严重影响对目标的定位精度。针对这一问题,提出基于约束总体最小二乘(CTLS)的到达时差(TDOA)定位算法。首先通过引入中间变量,将非线性TDOA定位方程转化为伪线性方程,再利用CTLS技术,全面考虑伪线性方程所有系数中的噪声。在此基础上推导了定位方程的目标函数,再根据牛顿迭代方法,进行数值迭代,快速得到精确解。采用一阶小噪声扰动分析方法,对该算法的理论性能进行了分析,证明了算法的无偏性和逼近克拉美-罗下限(CRLB)。仿真实验表明,该算法克服了现有总体最小二乘(TLS)算法不能达到CRLB、两步加权最小二乘(two-step WLS)算法在较高噪声时性能发散的缺陷,在较高噪声时定位精度仍然能达到CRLB。     

The modeling and estimation of asynchronous multirate multisensor dynamic systems

An asynchronous data fusion problem based on a kind of multirate multisensor dynamic system is studied. The system is observed by multirate sensors independently, with the state model known at the finest scale. Under the assumption that the sampling rates of sensors decrease successively by any positive integers, the discrete dynamic system models are established based on each single sensor and an asynchronous multirate multisensor state fusion estimation algorithm is presented. Theoretically, the estimate is proven to be unbiased and the optimal in the sense of linear minimum covariance, the fused estimate is better than the Kalman filtering results based on each single sensor, and the accuracy of the fused estimate will decrease if any of the sensors' information is neglected. The feasibility and effectiveness of the algorithm are shown through simulations.     

Airborne GMTI radar position bias estimation using static-rotatortargets of opportunity

In target tracking systems: using GMTI (ground moving target indicator) radars on airborne platforms, the locations of these platforms are available from GPS-based estimates. However, these estimated locations are subject to errors that are, typically, stationary autocorrelated random processes, i.e., slowly varying biases. In situations where there are no known-location targets to estimate these biases, the next best recourse is to use targets of opportunity at fixed but unknown locations. Such targets can be, e.g., static rotators (ground-based radars with rotating antenna), which yield detections in moving target indicator (MTI) radars. It is shown that these biases can be estimated in such a scenario, i.e., they meet the complete observability condition. Following this, the achievable accuracy for a generic scenario is evaluated. It is shown that accurate georegistration can be obtained even with a small number of measurements     

基于最大似然估计的TDOA/FDOA无源定位偏差补偿算法

在到达时差/到达频差(TDOA/FDOA)无源定位系统中,定位问题的非线性使得定位的结果存在偏差,特别是在噪声较大或者接收站布站不合理的情况下,定位的偏差尤其显著。针对这一问题,提出了一种基于最大似然估计的偏差补偿算法。该方法分为3步:首先,利用最大似然估计器对目标的位置和速度进行求解;其次,通过利用目标定位的估计值和含噪的测量值,对目标的位置和速度偏差值进行理论分析和推导;最后,将最大似然估计解减去理论偏差值,得到经过偏差补偿的新的目标定位解。理论分析和实验仿真证明,在一定噪声的情况下,所推导的目标位置和速度的理论偏差值与实际偏差值相符,并且经过偏差补偿后的定位算法,在保持目标定位的均方根误差(RMSE)与原最大似然算法一致的情况下,目标的位置和速度偏差值远远小于原最大似然算法的偏差值,目标定位精度得到了有效的提高。     

基于ECEF的广义最小二乘误差配准技术

 雷达组网数据处理首先要进行误差配准,来准确地估计和消除系统误差。传统的误差配准技术多基于球极投影,当雷达之间距离较远时,给配准结果引入一定的误差。基于地球中心坐标系(ECEF),提出了一种广义最小二乘的ECEF-GLS误差配准技术,较好地解决了远距离误差配准问题,误差分析表明,如果忽略模型线性化引入的误差,配准结果达到了CRLB下限。最后,使用仿真数据验证了算法的性能,并和Zhou提出的基于ECEF坐标系的最小二乘ECEF-LS误差配准算法进行了比较。