Survey of maneuvering target tracking. Part V. Multiple-model methods

This is the fifth part of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I and Part II deal with target motion models. Part III covers measurement models and associated techniques. Part IV is concerned with tracking techniques that are based on decisions regarding target maneuvers. This part surveys the multiple-model methods $the use of multiple models (and filters) simultaneously - which is the prevailing approach to maneuvering target tracking in recent years. The survey is presented in a structured way, centered around three generations of algorithms: autonomous, cooperating, and variable structure. It emphasizes the underpinning of each algorithm and covers various issues in algorithm design, application, and performance.     

Geometrical entropy approach for variable structure multiple-model estimation

The variable structure multiple-model(VSMM) estimation approach, one of the multiple-model(MM) estimation approaches, is popular in handling state estimation problems with mode uncertainties.In the VSMM algorithms, the model sequence set adaptation(MSA) plays a key role.The MSA methods are challenged in both theory and practice for the target modes and the real observation error distributions are usually uncertain in practice.In this paper, a geometrical entropy(GE) measure is proposed so that the MSA is achieved on the minimum geometrical entropy(MGE) principle.Consequently, the minimum geometrical entropy multiple-model(MGEMM) framework is proposed, and two suboptimal algorithms, the particle filter k-means minimum geometrical entropy multiple-model algorithm(PF-KMGEMM) as well as the particle filter adaptive minimum geometrical entropy multiple-model algorithm(PF-AMGEMM), are established for practical applications.The proposed algorithms are tested in three groups of maneuvering target tracking scenarios with mode and observation error distribution uncertainties.Numerical simulations have demonstrated that compared to several existing algorithms, the MGE-based algorithms can achieve more robust and accurate estimation results when the real observation error is inconsistent with a priori.     

Numerically robust implementation of multiple-model algorithms

Standard implementation of multiple-model (MM) estimation algorithms may suffer from numerical problems, especially numerical underflows, which occur when the true model is vastly different from one or more models used in the algorithm. This may be devastating to the performance of the MM algorithm. Numerical robust implementations of some of the most popular MM algorithms are presented. Simulation results are provided to verify the proposed implementation and to compare with the implementations with a lower bound     

Track-before-detect for Infrared Maneuvering Dim Multi-target via MM-PHD

In this paper, we present a novel and efficient track-before-detect (TBD) algorithm based on multiple-model probability hypothesis density (MM-PHD) for tracking infrared maneuvering dim multi-target. Firstly, the standard sequential Monte Carlo probability hypothesis density (SMC-PHD) TBD-based algorithm is introduced and sequentially improved by the adaptive process noise and the importance re-sampling on particle likelihood, which result in the improvement in the algorithm robustness and convergence speed. Secondly, backward recursion of SMC-PHD is derived in order to ameliorate the tracking performance especially at the time of the multi-target arising. Finally, SMC-PHD is extended with multiple-model to track maneuvering dim multi-target. Extensive experiments have proved the efficiency of the presented algorithm in tracking infrared maneuvering dim multi-target, which produces better performance in track detection and tracking than other TBD-based algorithms including SMC-PHD, multiple-model particle filter (MM-PF), histogram probability multi-hypothesis tracking (H-PMHT) and Viterbi-like.     

Multiple-model estimation with variable structure- part VI: expected-mode augmentation

A new class of variable-structure (VS) algorithms for multiple-model (MM) estimation is presented, referred to as expected-mode augmentation (EMA). In the EMA approach, the original set of models is augmented by a variable set of models intended to match the expected value of the unknown true mode. These models are generated adaptively in real time as (globally or locally) probabilistically weighted sums of mode estimates over the model set. This makes it possible to cover a large continuous mode space by a relatively small number of models at a given accuracy level. The paper presents new theoretical results for model-set design, a general formulation of the EMA approach, along with theoretical analysis and justification, and three algorithms for its practical implementation. The performance of the proposed EMA algorithms is evaluated via simulation of a generic maneuvering target tracking problem.     

基于冗余伪观测的自适应滤波算法

现有的二阶互差分(SOMD)算法能够给出与状态估计误差解耦的观测噪声协方差估计，但是需要满足冗余测量的条件，但这一条件往往难以满足。 针对这一问题，提出了一种利用状态预测值构造相邻2个时刻伪观测的方法，将原SOMD算法扩展到具有单测量的系统中。使用目标跟踪问题对该算法的有效性进行验证。仿真结果表明，当采样周期较小时，该算法能够忽略状态估计误差的影响并给出较准确的观测噪声方差，在精度和鲁棒性方面优于其他参考算法。     

Shifted Rayleigh filter: a new algorithm for bearings-only tracking

A new algorithm, the "shifted Rayleigh filter," is introduced for two- or three-dimensional bearings-only tracking problems. In common with other "moment matching" tracking algorithms such as the extended Kalman filter and its modern refinements, it approximates the prior conditional density of the target state by a normal density; the novel feature is that an exact calculation is then performed to update the conditional density in the light of the new measurement. The paper provides the theoretical justification of the algorithm. It also reports on simulations involving variants on two scenarios, which have been the basis of earlier comparative studies. The first is a "benign" scenario where the measurements are comparatively rich in range-related information; here the shifted Rayleigh filter is competitive with standard algorithms. The second is a more "extreme" scenario, involving multiple sensor platforms, high-dimensional models and noisy measurements; here the performance of the shifted Rayleigh filter matches the performance of a high-order bootstrap particle filter, while reducing the computational overhead by an order of magnitude.     

Feedback structure based entropy approach for multiple-model estimation

The variable-structure multiple-model（VSMM）approach,one of the multiple-model（MM）methods,is a popular and effective approach in handling problems with mode uncertainties.The model sequence set adaptation（MSA）is the key to design a better VSMM.However,MSA methods in the literature have big room to improve both theoretically and practically.To this end,we propose a feedback structure based entropy approach that could fnd the model sequence sets with the smallest size under certain conditions.The fltered data are fed back in real time and can be used by the minimum entropy（ME）based VSMM algorithms,i.e.,MEVSMM.Firstly,the full Markov chains are used to achieve optimal solutions.Secondly,the myopic method together with particle flter（PF）and the challenge match algorithm are also used to achieve sub-optimal solutions,a trade-off between practicability and optimality.The numerical results show that the proposed algorithm provides not only refned model sets but also a good robustness margin and very high accuracy.     

On joint track initiation and parameter estimation under measurement origin uncertainty

The problem of joint detection and estimation for track initiation under measurement origin uncertainty is studied. The two well-known approaches, namely the maximum likelihood estimator with probabilistic data association (ML-PDA) and the multiple hypotheses tracking (MHT) via multiframe assignment, are characterized as special cases of the generalized likelihood ratio test (GLRT) and their performance limits indicated. A new detection scheme based on the optimal gating is proposed and the associated parameter estimation scheme modified within the ML-PDA framework. A simplified example shows the effectiveness of the new algorithm in detection performance under heavy clutter. Extension of the results to state estimation with measurement origin uncertainty is also discussed with emphasis on joint detection and recursive state estimation.     

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%。     

基于标签多伯努利滤波的衍生目标跟踪算法

针对现有随机有限集(RFS)滤波器在低信噪比环境下对衍生目标跟踪性能严重下降的问题,提出了一种基于Delta扩展标签多伯努利(δ-GLMB)滤波器的改进算法。基于随机集理论和伯努利衍生模型,推导了新的预测方程,并采用了假设裁剪及分组手段和多伯努利近似技术以降低算法的计算量。针对假设增多引起的虚警问题,将多帧平滑思想和算法相结合,利用标签信息对新目标进行回溯处理。仿真结果表明,所提算法能对目标数目进行无偏估计,在低探测概率和强杂波环境下性能明显优于概率假设密度(PHD)算法,计算开销在衍生初始阶段增长快于PHD,目标较分散时低于PHD。     

Multiple-model estimation with variable structure. III. Model-groupswitching algorithm

A general multiple-model (MM) estimator with a variable structure (VSMM), railed model-group switching (MGS) algorithm, is presented. It assumes that the total set of models can be covered by a number of model groups, each representing a cluster of closely related system behavior patterns or structures, and a particular group is running at any given time determined by a hard decision. This algorithm is the first VSMM estimator that is generally applicable to a large class of problems with hybrid (continuous and discrete) uncertainties. It is also easily implementable. It is illustrated, via a simple fault detection and identification example, that the MGS algorithm provides a substantial reduction in computation while having identical performance with the fixed-structure Interacting Multiple-Model (FSIMM) estimator     

Identification of a discrete-time dynamical system

A novel generalized minimum variance (GMV) system identification algorithm is developed, and its performance is gauged against the established generalized least squares (GLS) estimation algorithm. The emphasis of the proposed GMV algorithm is on the rigorous treatment of measurement noise for dynamical system identification. A careful analysis of the measurement situation on hand yields a novel fixed-point calculation-based parameter estimation algorithm. The novel and established algorithms are compared in carefully performed and reproducible experiments which include measurement noise. Differences are apparent under small (measurement) sample operation, whereas under sufficient excitation, the algorithms produce statistically similar results     

K-Nearest Neighbor Particle Filters for Dynamic Hybrid Bayesian Networks

In state estimation of dynamic systems, Kalman filters and HMM filters have been applied to linear-Gaussian models and models with finite state spaces. However, they do not work well in most practical problems with nonlinear and non-Gaussian models. Even when the state space is finite, the dynamic Bayesian networks describing the HMM model could be too complicated to manage. Sequential Monte Carlo methods, also known as particle filters (PFs), have been introduced to deal with these real-world problems. They allow us to treat any type of probability distribution, nonlinearity and nonstationarity although they usually suffer major drawbacks of sample degeneracy and inefficiency in high-dimensional cases. We show how we can exploit the structure of partially dynamic hybrid Bayesian networks (PD-HBN) to reduce ``sample depletion' and increase the efficiency of particle filtering by combining the well-known K-nearest neighbor (KNN) majority voting strategy and the concept of evolution algorithm. Essentially, the novel method resamples the dynamic variables and randomly combines them with the existing samples of static variables to produce new particles. As new observations become available, the algorithm allows the particles to incorporate the latest information so that the fittest particles associated with a proposed objective rule will be kept for resampling. We also conduct a theoretical analysis on the proposed KNN-PF algorithm, and demonstrate the accuracy of the performance prediction with extensive simulations. Performance analysis and numerical results show that this new approach has a superior estimation/classification performance compared to other related algorithms.     

Multiple-model estimation with variable structure. IV. Design andevaluation of model-group switching algorithm

For pt. III see ibid., vol. 35, pp. 225-41 (1999). A variable-structure multiple-model (VSMM) estimator, called model-group switching (MGS) algorithm, has been presented in Part III, which is the first VSMM estimator that is generally applicable to a large class of problem with hybrid (continuous and discrete) uncertainties. In this algorithm, the model-set is made adaptive by switching among a number of predetermined groups of models. It has the potential to be substantially more cost-effective than fixed-structure MM (FSMM) estimators, including the Interacting Multiple-Model (IMM) estimator. A number of issues of major importance in the application of this algorithm are investigated here, including the model-group adaptation logic and model-group design. The results of this study are implemented via a detailed design for a problem of tracking a maneuvering target using a time-varying set of models, each characterized by a representative value of the expected acceleration of the target. Simulation results are given to demonstrate the performance (based on more reasonable and complete measures than commonly used rms errors alone) and computational complexity of the MGS algorithm, relative to the fixed-structure IMM (FSIMM) estimator using all models, under carefully designed and fair random and deterministic scenarios     

A formulation of multitarget tracking as an incomplete data problem

Traditional multihypothesis tracking methods rely upon an enumeration of all the assignments of measurements to tracks. Pruning and gating are used to retain only the most likely hypotheses in order to drastically limit the set of feasible associations. The main risk is to eliminate correct measurement sequences. The probabilistic multiple hypothesis tracking (PMHT) method has been developed by Streit and Luginbuhl in order to reduce the drawbacks of "strong" assignments. The PMHT method is presented in a general mixture densities perspective. The Expectation-Maximization (EM) algorithm is the basic ingredient for estimating mixture parameters. This approach is then extended and applied to multitarget tracking for nonlinear measurement models in the passive sonar perspective.     

Data fusion of decentralized local tracker outputs

An approach for fusing offboard track-level data at a central fusion node is presented. The case where the offboard tracker continues to update its local track estimate with measurement and system dynamics models that are not necessarily linear is considered. An algorithm is developed to perform this fusion at a central node without having access to the offboard measurements, their noise statistics, or the location of the local estimator. The algorithm is based on an extension of results that were originally established for linear offboard trackers. A second goal of this work is to develop an inequality constraint for selecting the proper sampling interval for the incoming state estimates to the fusion node. This interval is selected to allow use of conventional Kalman filter algorithms at the fusion node without suffering error performance degradation due to processing a correlated sequence of track state estimates     

Classification of radar targets using synthetic neural networks

Radar target classification performance of neural networks is evaluated. Time-domain and frequency-domain target features are considered. The sensitivity of the neural network algorithm to changes in network topology and training noise level is examined. The problem of classifying radar targets at unknown aspect angles is considered. The performance of the neural network algorithms is compared with that of decision-theoretic classifiers. Neural networks can be effectively used as radar target classification algorithms with an expected performance within 10 dB (worst case) of the optimum classifier     

改进的MMPHD机动目标跟踪方法

基于序列蒙特卡罗方法的经典多模概率假设密度滤波方法及其各种衍生方法,在预测过程中依据多个并行的状态转移模型,通过将大量粒子散布到下一时刻目标所有可能出现的状态空间实现目标状态的捕获,造成计算量大、目标跟踪精度差。为此,提出一种改进的多模粒子概率假设密度机动目标跟踪方法。该方法利用最新量测信息估计目标运动模型概率及模型参数,并将估计得到的目标模型应用到粒子概率假设密度滤波方法的预测过程中生成预测粒子,从而将大部分粒子聚合在目标最可能出现的状态空间邻域中,实现粒子的有效利用。数值仿真表明,所提方法不仅显著地减少了目标丢失个数,而且提高了目标跟踪精度。