Fixed-interval retrodiction approach to Bayesian IMM-MHT formaneuvering multiple targets

In a Bayesian framework, we propose a hierarchy of suboptimal retrodiction algorithms that generalize Rauch-Tung-Striebel (RTS) fixed-interval smoothing to multiple hypothesis tracking (MHT) applications employing interacting multiple model (IMM) methods (IMM-MHT). As a limiting case we obtain new simple formulae for suboptimal fixed-interval smoothing applied to Markovian switching systems. Retrodiction techniques provide uniquely interpretable and accurate trajectories from ambiguous MHT output if a certain (small) time delay is tolerated. By a simulated example with two maneuvering targets that operate closely spaced under relatively hard conditions we demonstrate the potential gain by fixed-interval retrodiction and provide a quantitative idea of the achievable track accuracy and mean time delay involved     

A simple fixed-lag algorithm for tracking frequency rate-of-change

A family of simple fixed-lag frequency smoothing algorithms which provide good estimates of both frequency and frequency rate-of-change is reported. The smoothers were developed from a fixed-gain αβ tracker by replacing the recursive derivative estimator with a finite-impulse-response (FIR) differentiator. Simulation results are presented which show that the smoothing algorithms provide frequency estimates with a similar variance to those produced by the αβ filter but with greatly improved frequency-rate estimates. The smoothing algorithms and the αβ filter are also compared on the basis of the bias and delay introduced in the frequency-rate estimates. Although the results presented are for frequency estimation, the smoothing algorithms can be used in any single-input tracking application where some lag in the estimates is allowable     

Sensitivity Analysis of Finite-Lag Receivers

This paper presents the sensitivity analysis of a class of receivers called finite-lag receivers, introduced by the authors in [1] through [3]. Since these receivers are based on the use of fixed-lag smoothing techniques, algorithms for the calculation of large-scale and small-scale sensitivities of fixed-lag smoothing are derived using a state augmentation approach. Steady-state analysis of these algorithms shows that an explicit relation can be obtained between sensitivity coefficients of fixed-lag smoothing and filtering. The specific case of sensitivity to variations in the measurement (channel) noise is considered as an example. These results are applied to study the sensitivity performance of the finite-lag receivers for analog communication. It is shown, for example, that finite-lag receivers for AM signals, besides being superior in performance [1]-[3], [11], in terms of output SNR or error variance, are also much less sensitive to the additive noise power level, compared to zero-lag receivers.     

晃动环境下组合导航系统精度事后评估算法研究

海风、波浪、海流等因素会产生舰船的摇摆晃动,从而给舰船导航系统精度带来严重干扰.固定区间平滑滤波处理算法能够利用观测时间间隔内全部观测信息得到状态的最小方差估计,对导航精度进行事后评估.在研究晃动环境下的SINS/GP S组合导航应用平滑滤波算法的相关原理的基础上,首先利用Kalman滤波器进行组合导航,存储相关信息后按时间逆序利用固定区间平滑滤波算法进行事后分析.该方法可以针对不同的海况以及不同的海上作业需求,有效地为组合导航系统精度提供检验标准,考核各种海洋环境下的导航系统精度.     

基于固定区间最优平滑的传递对准精度评估

惯导系统传递对准是战术导弹发射前必须完成的任务,其对准精度直接影响导弹系统的制导精度。为评估传递对准精度性能,在介绍传递对准精度评估原理的基础上,研究了Kalman固定区间最优平滑算法;并从理论上分析了顺序滤波与逆序平滑的关系,得出平滑依赖于滤波的结论。通过实测数据半物理仿真试验证明了理论分析的正确性,表明固定区间最优平滑算法能有效地评估传递对准精度,并与间接法对比得出间接法与最优平滑算法具有一致性。     

R-T-S平滑算法与抗差Kalman在数据后处理中的应用

为了提高组合导航系统后处理精度和数据稳定性,将R-T-S最优固定区间平滑算法引入数据后处理中,在前向Kalman滤波的基础上,进行了后向R-T-S最优固定区间平滑处理,并针对GPS观测值中存在异常的问题,将抗差Kalman滤波算法引入数据后处理中,并对该算法进行实物仿真。结果表明,与传统Kalman滤波相比,R-T-S平滑算法不仅可以提高位置、姿态精度,而且在卫星信号失锁的情况下精度也得到显著改善,并且在不丢星的时刻,抗差Kalman滤波可以有效处理GPS信号中的异常观测值,遏制滤波发散,是一种有效的数据处理方法。     

Improved multi-target tracking in clutter by PDA smoothing

An algorithm is presented for the recursive tracking of multiple targets in cluttered environment by making use of the joint probabilistic data association fixed-lag smoothing (JPDAS) techniques. It is shown that a significant improvement in the accuracy of track estimation of both nonmaneuvering and maneuvering targets may be achieved by introducing a time lag of one or two sampling periods between the instants of estimation and latest measurement. Results of simulation experiments for a radar tracking problem that demonstrate the effects of fixed-lag smoothing are also presented     

Exact Bayesian and particle filtering of stochastic hybrid systems

The standard way of applying particle filtering to stochastic hybrid systems is to make use of hybrid particles, where each particle consists of two components, one assuming Euclidean values, and the other assuming discrete mode values. This paper develops a novel particle filter (PF) for a discrete-time stochastic hybrid system. The novelty lies in the use of the exact Bayesian equations for the conditional mode probabilities given the observations. Therefore particles are needed for the Euclidean valued state component only. The novel particle filter is referred to as the interacting multiple model (IMM) particle filter (IMMPF) because it incorporates a filter step which is of the same form as the interaction step of the IMM algorithm. Through Monte Carlo simulations, it is shown that the IMMPF has significant advantage over the standard PF, in particular for situations where conditional switching rate or conditional mode probabilities have small values     

Variable structure multiple model fixed-interval smoothing

This paper focuses on fixed-interval smoothing for stochastic hybrid systems. When the truth-mode mismatch is encountered, existing smoothing methods based on fixed structure of model-set have significant performance degradation and are inapplicable. We develop a fixed-interval smoothing method based on forward- and backward-filtering in the Variable Structure Multiple Model (VSMM) framework in this paper. We propose to use the Simplified Equivalent model Interacting Multiple Model (SEIMM) in the forward and the backward filters to handle the difficulty of different mode-sets used in both filters, and design a re-filtering procedure in the model-switching stage to enhance the estimation performance. To improve the computational efficiency, we make the basic model-set adaptive by the Likely-Model Set (LMS) algorithm. It turns out that the smoothing performance is further improved by the LMS due to less competition among models. Simulation results are provided to demonstrate the better performance and the computational efficiency of our proposed smoothing algorithms.     

An Approach to Fixed-Point Smoothing Problems

This paper examines the possibility of deriving fixed-point smoothing algorithms through exploitation of the known solutions of a higher dimensional filtering problem. It is shown that a simple state augmentation serves to imbed the given n-dimensional smoothing problem into a 2n-dimensional filtering problem. It is further shown that computation of the smoothed estimate and the corresponding error covariance does not require implementation of the 2n-dimensional filtering equations. Some new results involving systems with or without multiple time delays and having colored observation noise have been derived in order to illustrate the versatility of the proposed technique. It is also demonstrated that the present approach leads to an easier derivation of the continuous-time fixed-point smoothing algorithm reported in the literature.     

Tracking of multiple maneuvering targets using multiscan JPDA and IMM filtering

The paper considers the problem of tracking multiple maneuvering targets in the presence of clutter using switching multiple target motion models. A novel suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique. Unlike the standard single-scan JPDA approach, the authors exploit a multiscan joint probabilistic data association (mscan-JPDA) approach to solve the data association problem. The algorithm is illustrated via a simulation example involving tracking of four maneuvering targets and a multiscan data window of length two     

Novel Nonlinear Filtering & Prediction Method for Maneuvering Target Tracking

A new nonlinear filtering and prediction (NFP) algorithm with input es?imation is proposed for maneuvering target tracking. In the proposed method, the acceleration level is determined by a decision process, where a least squares (LS) estimator plays a major role in detecting target maneuvering within a sliding window. We first illustrate that the optimal solution to minimize the mean squared error (MSE) must consider a trade-off between the bias and error variance. For the application of target tracking, we then derive the MSE of target positions in a closed form by using orthogonal space decompositions. Then we discuss the NFP estimator, and evaluate how well the approach potentially works in the case of a set of given system parameters. Comparing with the traditional unbiased minimum variance filter (UMVF), Kalman filter, and interactive multiple model (IMM) algorithms, numerical results show that the newly proposed NFP method performs comparable or better in all scenarios with significantly less computational requirements.     

A recursive multiple model approach to noise identification

Correct knowledge of noise statistics is essential for an estimator or controller to have reliable performance. In practice, however, the noise statistics are unknown or not known perfectly and thus need to be identified. Previous work on noise identification is limited to stationary noise and noise with slowly varying statistics only. An approach is presented here that is valid for nonstationary noise with rapidly or slowly varying statistics as well as stationary noise. This approach is based on the estimation with multiple hybrid system models. As one of the most cost-effective estimation schemes for hybrid system, the interacting multiple model (IMM) algorithm is used in this approach. The IMM algorithm has two desirable properties: it is recursive and has fixed computational requirements per cycle. The proposed approach is evaluated via a number of representative examples by both Monte Carlo simulations and a nonsimulation technique of performance prediction developed by the authors recently. The application of the proposed approach to failure detection is also illustrated     

Interacting multiple model methods in target tracking: a survey

The Interacting Multiple Model (IMM) estimator is a suboptimal hybrid filter that has been shown to be one of the most cost-effective hybrid state estimation schemes. The main feature of this algorithm is its ability to estimate the state of a dynamic system with several behavior modes which can “switch” from one to another. In particular, the IMM estimator can be a self-adjusting variable-bandwidth filter, which makes it natural for tracking maneuvering targets. The importance of this approach is that it is the best compromise available currently-between complexity and performance: its computational requirements are nearly linear in the size of the problem (number of models) while its performance is almost the same as that of an algorithm with quadratic complexity. The objective of this work is to survey and put in perspective the existing IMM methods for target tracking problems. Special attention is given to the assumptions underlying each algorithm and its applicability to various situations     

Integrated active fault-tolerant control using IMM approach

An integrated fault detection, diagnosis, and reconfigurable control scheme based on interacting multiple model (IMM) approach is proposed. Fault detection and diagnosis (FDD) is carried out using an IMM estimator. An eigenstructure assignment (EA) technique is used for reconfigurable feedback control law design. To achieve steady-state tracking, reconfigurable feedforward controllers are also synthesized using input weighting approach. The developed scheme can deal with not only actuator and sensor faults, but also failures in, system components. To achieve fast and reliable fault detection, diagnosis, and controller reconfiguration, new fault diagnosis and controller reconfiguration mechanisms have been developed by a suitable combination of the information provided by the mode probabilities from the IMM algorithm and an index related to the closed-loop system performance. The proposed approach is evaluated using an aircraft example, and excellent results have been obtained     

引入神经网络的交互式多模型算法

在交互式多模型算法中引入神经网络算法以改进目标跟踪的精度。利用神经网络算法对基于机动目标“当前”统计模型的均值和方差自适应滤波算法进行修改,提高该算法的性能,然后采用交互作用多模型算法跟踪机动目标,提高了机动目标的跟踪精度。     

改进的基于隐马尔可夫模型的自适应IMM算法

针对机动目标跟踪中交互式多模型算法(IMM)的马尔可夫转移概率矩阵固定不变造成跟踪精度降低的问题,在已有的基于隐马尔科夫模型(HMM)的自适应IMM算法的基础上,对隐马尔可夫链的长度和Baum-Welch算法迭代次数的2个参数对该算法跟踪性能的影响,进行了深入研究分析,进一步明确了这2个参数选择的依据;并针对该算法在目标机动转换时峰值误差增大的问题,给出了2种修正方法,从而提出了改进的基于HMM的自适应IMM算法。最后,通过仿真分析了算法的参数和修正方法对跟踪性能的影响,并与传统IMM算法进行对比,证明了文章提出算法的有效性。     

Suboptimal Algorithms for Nonlinear Smoothing

This paper presents second-order algorithms for fixed- point and fixed-lag smoothing problems for nonlinear systems. The algorithms are obtained on the basis of the state augmentation approach, used earlier by the authors, for dealing with linear smoothing problems. Both discrete-and continuous-time forms of solutions are presented and the results are illustrated by considering a radar tracking problem. Some of the advantages of the proposed smoothing solutions compared to existing ones are also discussed.     

GNSS最优载波相位平滑伪距研究

平滑常数是影响载波相位平滑伪距精度的关键参数,实际数据处理时主要依据经验设定平滑常数。这种主观设定过程缺乏理论依据,无法达到最优平滑效果。针对此问题,以适用于实时GNSS载波相位平滑伪距的经典Hatch递推滤波算法为基础,在连续时间域上分析了载波相位平滑伪距误差的主要构成,给出了总误差估算公式,分析了平滑常数对平滑精度的影响传导机制。进一步,采用令平滑总误差最小为目标的极值法推导给出了最优载波相位平滑常数的计算公式,给出了最优载波相位平滑伪距的完整处理步骤。最优平滑常数算法在数学意义上最优,大幅压缩了伪距测量误差,又不会引入过大的电离层发散误差。通过两个实际算例,证明了算法有效性。     

基于交互多模估计策略的故障检诊方法

针对多模自适应（ＭＭＡＥ）故障检诊（ＦＤＤ）方法的局限性,提出了一种基于交互多模（ＩＭＭ）估计策略的动态系统中多重故障的检诊方法。交互多模估计是针对包含有结构以及参数的系统的一种效率较好的自适应估计技术,它提供了故障检测、诊断和状态估计的集中框架。通过对在传感器和作动器中含有多个故障飞机的仿真。结果表明,所提供的方法比其它方法能够更快、更可靠地检测和隔离出多重故障。