Interacting multiple model filter for tactical ballistic missile tracking

An interacting multiple model (IMM) filter is presented for the real-time tracking of tactical ballistic missiles (TBMs). The novel aspects of the proposed IMM filter include the development of a constant axial force (CAF) Kalman filter, asymmetric IMM state interaction, and an entropy-based variation of the IMM mode probability update equation. Using data from a recent TBM defense (TBMD) test event, the proposed IMM filter is shown to yield consistent state estimates throughout the entire TBM trajectory, which includes a dual-stage boost during launch.     

Maneuvering Target Tracking in Dense Clutter Based on Particle Filtering

An improved particle filtering(IPF) is presented to perform maneuvering target tracking in dense clutter.The proposed filter uses several efficient variance reduction methods to combat particle degeneracy,low mode prior probabilities and measure-ment-origin uncertainty.Within the framework of a hybrid state estimation,each particle samples a discrete mode from its poste-rior distribution and the continuous state variables are approximated by a multivariate Gaussian mixture that is updated by an unscented Ka...     

Manoeuvring target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and manoeuvering target in clutter from angle-only measurements is presented and evaluated. The aim is to compare PFs to a well-established tracking algorithm, the IMM-PDA-EKF (interacting multiple model, probabilistic data association, extended Kalman filter), and to provide an insight into which aspects of PF design are of most importance under given conditions. Monte Carlo simulations show that the use of a resampling scheme which produces particles with distinct values offers significant improvements under almost all conditions. Interestingly, under all conditions considered here,using this resampling scheme with blind particle proposals is shown to be superior, in the sense of providing improved performance for a fixed computational expense, to measurement-directed particle proposals with the same resampling scheme. This occurs even under conditions favourable to the use of measurement-directed proposals. The IMM-PDA-EKF performs poorly compared with the PFs for large clutter densities but is more effective when the measurements are precise.     

ADAPTIVE MULTIPLE MODEL FILTER USING IMM AND STF

Consider a discrete- time stochastic hybridsystem　 x( k 1 ) =f( k, ( k) ,x( k) ,m( k 1 ) ) ζ( k,m( k 1 ) ) q( k) ( 1 )　 z( k 1 ) =h( k 1 ,x( k 1 ) ,m( k 1 ) ) v( k 1 ,m( k 1 ) ) ( 2 )where state x∈ Rn;measurement z∈ Rm;input∈ Rp;modeling noise q( k)∈ Rqis a zero- mean,Gaussian white noise with covariance Q( k) ;measurement noise v( k 1 )∈ Rm is also a zero-mean,Gaussian white noise with covariance R( k 1 ) ;q( k) and v( k) are statistically indepen-dent. Th…     

基于鱼群优化粒子滤波的捷联惯导系统初始对准方法

针对传统捷联惯导系统静基座初始对准模型的维数较高,导致滤波算法的解算实时性较差的问题,设计出一种基于鱼群优化粒子滤波的两位置初始对准方法。首先,建立了捷联惯导系统的两位置初始对准模型。由于该模型中不存在惯性器件的随机常值影响,因此,在确保初始对准精度的前提下,有效降低了初始对准模型维数;然后,利用鱼群优化算法改善了粒子滤波算法中粒子样本的分布,提高了粒子滤波算法的收敛速度和预测精度。仿真结果验证,采用该初始对准方法,可以有效提高初始对准的精度,且满足系统对实时性的要求。     

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.     

Multiple model nonlinear filtering for low signal ground target applications

The design and implementation of a multiple model nonlinear filter (MMNLF) for ground target tracking using ground moving target indicator (GMTI) radar measurements is described. Like the well-known interacting multiple model Kalman filter (IMMKF), the MMNLF is based on the theory of hybrid stochastic systems. However, since it models the probability distribution for the target in a region, rather than just the distribution's first and second moments, a nonlinear filter is able to capture more fine-grained detail of the target motion and requires fewer models than typical IMMKF implementations. This is illustrated here with a two-model MMNLF in which one motion model incorporates terrain constraints while the second is a nearly constant velocity (CV) model. Another feature of the MMNLF is that it enables incorporation of prethresholded measurements. To implement the filter, the target state conditional probability density is discretized on a set of moving grids and recursively updated with sensor measurements via Bayes' formula. The conditional density is time updated between sensor measurements using alternating direction implicit (ADI) finite difference methods, generalized for this hybrid application. In simulation testing against low signal-to-interference-plus-noise ratio (SINR) targets, the MMNLF is able to maintain track in situations where single model filters based on either of the component models or filters that use thresholded data fail. Potential applications of this work include detection and tracking of foliage-obscured moving targets.     

航空发动机气路故障诊断的SANNWA-PF算法

针对航空发动机非线性、非高斯的特点,提出一种用于航空发动机气路故障诊断的自适应神经网络权值调整粒子滤波（SANNWA PF）算法。该算法根据粒子分布情况确定分裂和调整的粒子数目,进而根据粒子权重采用正态分布的方式进行分裂,采用反向传插(BP)神经网络进行权值调整,缓解了粒子的退化和贫化,具有更强的自适应性能和跟踪能力。通过一维非线性跟踪模型和航空发动机气路故障诊断仿真研究表明:SANNWA PF算法具有良好的非高斯性能,相对粒子滤波一维非线性追踪模型估计精度提高约21%,航空发动机气路故障诊断在高斯噪声和非高斯噪声下分别提高约30%和26%,诊断速度分别提高约7倍和10倍。      

Interacting multiple model fixed-lag smoothing algorithm forMarkovian switching systems

We investigate a suboptimal approach to the fixed-lag smoothing problem for Markovian switching systems. A fixed-lag smoothing algorithm is developed by applying the basic Interacting Multiple Model (IMM) approach to a state-augmented system. The computational load is roughly d (the fixed lag) times beyond that of filtering for the original system. In addition, an algorithm that approximates the “fixed-lag” mode probabilities given measurements up to current time is proposed. The algorithm is illustrated via a target tracking simulation example where a significant improvement over the filtering algorithm is achieved at the cost of a time delay (i.e., data up to time k are used to produce the smoothed state estimate at time k-d where the fixed large d>0). the IMM fixed-lag smoothing performance for the given example is comparable to that of an existing IMM fixed-interval smoother. Compared with fixed-interval smoothers, the fixed-lag smoothers can be implemented in real-time with a small delay     

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     

Efficient particle filtering for road-constrained target tracking

The variable-structure multiple-model particle filtering approach for state estimation of road-constrained targets is addressed. The multiple models are designed to account for target maneuvers including "move-stop-move" and motion ambiguity at an intersection; the time-varying active model sets are adaptively selected based on target state and local terrain condition. The hybrid state space is partitioned into the mode subspace and the target subspace. The mode state is estimated based on random sampling; the target state as well as the relevant likelihood function associated with a mode sample sequence is approximated as Gaussian distribution, of which the conditional mean and covariance are deterministically computed using a nonlinear Kalman filter which accounts for road constraints in its update. The importance function for the sampling of the mode state approximates the optimal importance function under the same Gaussian assumption of the target state.     

混响室复合模调谐法研究

本文针对在混响室内进行大型设备电磁兼容测试的方法,将直接照射法和标准模调谐法相互结合,提出了复合模调谐法,该方法在天线直接照射测试区域的同时步进搅拌器,使得测试面上不同位置处所经历的最大场强值满足一定的均匀性.并利用三种不同的方法对空腔混响室的一个测试面进行了场均匀性校准,通过对实验方法的描述以及对测试数据的整理和分析...     

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.     

非线性非高斯秩滤波方法

基于秩滤波原理,提出一种非线性非高斯秩滤波方法,给出其递推过程.目前常用的非线性滤波方法有无迹Kalman滤波和粒子滤波,无迹Kalman滤波只适用于高斯分布的情况,粒子滤波方法却存在粒子退化及重采样引起的粒子贫化问题.而非线性非高斯秩滤波方法不仅适用于常见的多元t分布、多元极值分布等非高斯分布的非线性滤波,并且计算简单、工作量小,便于工程应用.从仿真算例可以看到,该方法的滤波精度与无迹Kalman滤波和粒子滤波方法相比提高了500%以上.      

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

Track labeling and PHD filter for multitarget tracking

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approaches (as, e.g., MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter has been proposed and particle filtering techniques have been developed to implement the PHD filter. In the particle PHD filter, the track labeling problem is not considered, i.e., the PHD is obtained only for a frame at a time, and it is very difficult to perform the multipeak extraction, particularly in high clutter environments. A track labeling method combined with the PHD approach, as well as considering the finite resolution, is proposed here for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD in the resolution cell to get the estimated number and locations of the targets at each time step, and then perform the track labeling ("peak-to-track" association), whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard particle PHD filter. For example, in group target tracking, if we are interested in the motion of a specific target, we can track this target, which is not possible for the standard particle PHD filter, since the standard particle PHD filter does not keep track labels. Using our approach, multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging, and termination     

Reliable flight performance assessment of multirotor based on interacting multiple model particle filter and health degree

Multirotor has been applied to many military and civilian mission scenarios. From the perspective of reliability, it is difficult to ensure that multirotors do not generate hardware and software failures or performance anomalies during the flight process. These failures and anomalies may result in mission interruptions, crashes, and even threats to the lives and property of human beings. Thus, the study of flight reliability problems of multirotors is conductive to the development of the drone industry and has theoretical significance and engineering value. This paper proposes a reliable flight performance assessment method of multirotors based on an Interacting Multiple Model Particle Filter (IMMPF) algorithm and health degree as the performance indicator. First, the multirotor is modeled by the Stochastic Hybrid System (SHS) model, and the problem of reliable flight performance assessment is formulated. In order to solve the problem, the IMMPF algorithm is presented to estimate the real-time probability distribution of hybrid state of the established SHS-based multirotor model, since it can decrease estimation errors compared with the standard interacting multiple model algorithm based on extended Kalman filter. Then, the reliable flight performance is assessed with health degree based on the estimation result. Finally, a case study of a multirotor suffering from sensor anomalies is presented to validate the effectiveness of the proposed method.     

基于CPHD的双层粒子滤波目标跟踪算法

常规基于势概率假设密度滤波(Cardinalized Probability Hypothesis Density,CPHD)的粒子滤波(Particle Fil? ter,PF)跟踪算法应用于多目标跟踪时,容易遇到因粒子数量增加而带来的运算效率下降、目标数目估计不准的问题。文章基于常规粒子滤波 CPHD跟踪算法,通过部署双层粒子,提出基于势概率假设密度滤波的双层粒子滤波 (Two-Layer Particle Filter-CPHD,TLPF-CPHD)算法,以便提高目标数目及状态估计精度。仿真实验结果证明,相比于常规 PF-CPHD算法,新算法具有更好的目标数目和状态估计准确性。     

Tracking a 3D maneuvering target with passive sensors

A novel application of the interacting multiple models (IMM) algorithm in which passive infrared sensors are fused for tracking a target maneuvering in three dimensions is discussed. More accurate models of target motion are proposed to improve performance. When the general models are used to describe the maneuvering periods, it is shown that the IMM behaviour is not satisfactory, in that the innovations associated with the different models do not discriminate between the corresponding target maneuvering regimes. The turning of the Markov chain transition matrix, i.e., a priori information, is then crucial to obtaining the correct ordering of the a posteriori regime probabilities. On the contrary, a more satisfactory behavior of the IMM algorithm is obtained by carefully selecting the target motion models in the different regimes     

Multiple-model adaptive estimation using a residual correlationKalman filter bank

We propose a modified multiple model adaptive estimation (MMAE) algorithm that uses the time correlation of the Kalman filter residuals, in place of their scaled magnitude, to assign conditional probabilities for each of the modeled hypotheses. This modified algorithm, denoted the residual correlation Kalman filter bank (RCKFB), uses the magnitude of an estimate of the correlation of the residual with a slightly modified version of the usual MMAE hypothesis testing algorithm to assign the conditional probabilities to the various hypotheses that are modeled in the Kalman filter bank within the MMAE. This concept is used to detect flight control actuator failures, where the existence of a single frequency sinusoid (which is highly time correlated) in the residual of an elemental filter within an MMAE is indicative of that filter having the wrong actuator failure status hypothesis. This technique results in a delay in detecting the flight control actuator failure because several samples of the residual must be collected before the residual correlation can be estimated. However, it allows a significant reduction of the amplitude of the required system inputs for exciting the various system modes to enhance identifiability, to the point where they may possibly be subliminal, so as not to be objectionable to the pilot and passengers