Sequential Monte Carlo Implementation Research Articles

A spawning particle filter for defocused moving target detection in GNSS-based passive radar

Global Navigation Satellite System (GNSS)-based passive radar (GBPR) has been widely used in remote sensing applications. However, for moving target detection (MTD), the quadratic phase error (QPE) introduced by the non-cooperative target motion is usually difficult to be compensated, as the low power level of the GBPR echo signal renders the estimation of the Doppler rate less effective. Consequently, the moving target in GBPR image is usually defocused, which aggravates the difficulty of target detection even further. In this paper, a spawning particle filter (SPF) is proposed for defocused MTD. Firstly, the measurement model and the likelihood ratio function (LRF) of the defocused point-like target image are deduced. Then, a spawning particle set is generated for subsequent target detection, with reference to traditional particles in particle filter (PF) as their parent. After that, based on the PF estimator, the SPF algorithm and its sequential Monte Carlo (SMC) implementation are proposed with a novel amplitude estimation method to decrease the target state dimension. Finally, the effectiveness of the proposed SPF is demonstrated by numerical simulations and preliminary experimental results, showing that the target range and Doppler can be estimated accurately.

Effective implementation and improvement of fast labeled multi-Bernoulli filter

Effective implementation of the fast labeled multi-Bernoulli (FLMB) filter is addressed for target tracking with interval measurements. Firstly, a sequential Monte Carlo (SMC) implementation of the FLMB filter, SMC-FLMB filter, is derived based on generalized likelihood function weighting. Then, a box particle (BP) implementation of the FLMB filter, BP-FLMB filter, is developed, with a computational complexity reduction of the SMC-FLMB filter. Finally, an improved version of the BP-FLMB filter, improved BP-FLMB (IBP-FLMB) filter, is proposed, improving its estimation accuracy and real-time performance under the conditions of low detection probability and high clutter. Simulation results show that the BP-FLMB filter has a great improvement of the real-time performance than the SMC-FLMB filter, with similar tracking performance. Compared with the BP-FLMB filter, the IBP-FLMB filter has better estimation performance and real-time performance under the conditions of low detection probability and high clutter.

Hölder Divergence-Based Reward Function for Poisson RFSs and Application to Multitarget Sensor Management

In this study, we propose a novel information theoretic reward function based on the statistical Hölder divergence. The Hölder divergence is the generalization of Cauchy-Schwarz divergence. We extend the Hölder divergence to the FISST densities, thus making it possible to use in the multi-object applications based on the RFS theory. We derive the analytic expressions for the extended Hölder divergence (EHD) for the case when the multi-target densities have the form of Poisson RFSs and apply it to the PHD filter in a sequential Monte Carlo implementation. We evaluated the performance of the proposed reward function in a multi-target sensor management problem where the next position of a moving observer is decided according to the value of the EHD-based reward function. The performance of the algorithm is compared against, in terms of OSPA metric, and it is shown that the proposed reward function is superior to other similar reward functions in multi-target sensor management literature. We also show that it is possible to adapt the management algorithm to different situations, such as static and dynamic environments.

Sequential Ensemble Monte Carlo Sampler for On-Line Bayesian Inference of Time-Varying Parameter in Engineering Applications

Abstract Several on-line identification approaches have been proposed to identify parameters and evolution models of engineering systems and structures when sequential datasets are available via Bayesian inference. In this work, a robust and “tune-free” sampler is proposed to extend one of the sequential Monte Carlo implementations for the identification of time-varying parameters which can be assumed constant within each set of data collected but might vary across different sequences of datasets. The proposed approach involves the implementation of the affine-invariant Ensemble sampler in place of the Metropolis–Hastings sampler to update the samples. An adaptive-tuning algorithm is also proposed to automatically tune the step-size of the affine-invariant ensemble sampler which, in turn, controls the acceptance rate of the samples across iterations. Furthermore, a numerical investigation behind the existence of inherent lower and upper bounds on the acceptance rate, making the algorithm robust by design, is also conducted. The proposed method allows for the off-line and on-line identification of the most probable models under uncertainty. The proposed sampling strategy is first verified against the existing sequential Monte Carlo sampler in a numerical example. Then, it is validated by identifying the time-varying parameters and the most probable model of a nonlinear dynamical system using experimental data.

Multiple extended target tracking based on gamma box particle and labeled random finite sets

A gamma box particle (GBP) implementation of the extended target generalized labeled multi-Bernoulli (ET-GLMB) filter is proposed in this paper, named the ET-GBP-GLMB filter. The filter can simultaneously estimate the unknown number, measurement rate states, kinematics states, extension states and tracks of extended targets in the presence of clutter, missed detection and data association uncertainty. In order to obtain the GLMB recursion of the ET-GBP-GLMB filter, an appropriate measurement likelihood function that comprehensively considers the measurement rate state, kinematics state and extension state of each extended target is introduced for a given measurement partition cell, and the specific implementation steps of the filter are derived with necessary interval operations and approximations. Further, an extended target GBP labeled multi-Bernoulli (ET-GBP-LMB) filter is proposed as an effective approximation of the ET-GBP-GLMB filter. The advantages and disadvantages of the two proposed filters are presented in simulation examples. The simulation results show that, compared with the gamma sequential Monte Carlo (GSMC) implementation of the ET-GLMB filter, the GBP implementation of the ET-GLMB filter can effectively reduce the number of particles and the amount of computation. Compared with the ET-GBP-GLMB filter, the ET-GBP-LMB filter can further reduce the computational burden. Compared with the extended target box particle probability hypothesis density (ET-BP-PHD) filter, the two proposed filters can obtain better estimation results.

Multiple targets tracking by using improved labeled multi-target multi-Bernoulli filter with FDA-MIMO radar

In the traditional multi-target multi-Bernoulli (MeMBer) filter, only the radar signal after constant false alarm rate (CFAR) is considered. In addition, it is also necessary to assume that the detection probability of the target and the covariance matrix of the measurement noise are known. In fact, the detection probability of the target and the covariance matrix of the noise are difficult to determine. Therefore, this paper proposes an improved labeled multi-target multi-Bernoulli (IL-MeMBer) filter that can avoid considering the detection probability of the target and the covariance matrix of the measurement noise. Firstly, the multi-target superposition measurement model of FDA-MIMO is given in the presence of false targets. Secondly, the target likelihood function under the superposition measurement model is derived by analyzing the characteristics of the traditional point measurement likelihood function and the Music spatial spectrum. Thirdly, considering the unknown and time-varying number of targets, the original echo signals without detection probability before (CFAR) processing, and no target tracks output by the traditional MeMBer filter, we put forward an analytical solution of the IL-MeMBer filter. Finally, a fusion strategy based on Euclidean distance is proposed to solve the problem that the same target can be estimated to have multiple tracks in the IL-MeMBer filter. In addition, the sequential Monte Carlo (SMC) implementation of the IL-MeMBer filter is provided. Numerical experiences verify the effectiveness and superiority of the proposed methods.

A Multisource Multi-Bernoulli Filter for Multistatic Radar

Compared with conventional monostatic or bistatic radar, multistatic radar has wider coverage and better performance localization and tracking accuracy. However, the multistatic radar architecture poses challenges to the implementation for multitarget tracking in coping with highly uncertainty of data association for the fusion of multisource information. In this paper, the theoretically rigorous formulas for the multisource multi-Bernoulli (MeMBer) filter are derived by using the Finite set statistics (FISST) calculus built on the standard MeMBer filter. The multisource MeMBer filter propagates a set of MeMBer parameters approximately characterizing the multisource corrected posterior multitarget random finite set (RFS). Since the equations for the proposed filter multisource corrector are computationally intractable, we go further to develop an analytic Sequential Monte Carlo (SMC) implementation of multisource MeMBer recursion. The theoretical analysis and simulations show that the proposed filter perform well and accommodate nonlinear multistatic radar tracking scenario under the approximate conditions.

Improved probability hypothesis density filter for multi‐target tracking of non‐cooperative bistatic radar

Non-cooperative bistatic radar refers to the passive bistatic radar using a non-cooperative radar as the illuminator of opportunity. Limited by the non-cooperation and bistatic configuration, multi-target tracking of the non-cooperative bistatic radar is confronted with challenges of low detection probability and high clutter. Based on the sequential Monte Carlo implementation of probability hypothesis density (PHD) filter, this study proposes an improved PHD (I-PHD) filter. Similar to the tracking gate in data association, whether each candidate target is detected at each time is determined and recorded, and the sequential probability ratio test distinguishes a real target and false target based on this record. To distinguish miss detection and target death, a new survival probability dependent on target position is defined, and the survival probability of a specific target drops rapidly when it is located near the boundary and moves outwards. To label targets and extract their states, a new method of track identification and state estimation is proposed. The simulation results illustrate that the proposed I-PHD filter can effectively track multiple targets of non-cooperative bistatic radar under low detection probability and high clutter and has superior performance than competing methods.

Multiple extended stealth target tracking from image observation based on non‐linear sub‐random matrices approach

The detection and tracking of extended stealth targets (ESTs) is a challenging task in radar technology, especially if from image observations because of the fluctuations of radar cross section. To overcome this challenge, multi-Bernoulli (MB) filter can be used to extract the extended target (ET) states in efficient and reliable manner. Recently, the MB-filter-based random matrices model (RMM) approach has been proposed for ellipsoidal ET tracking with additional state variables. However, RMM-MB filter is demonstrated with known detection profile, which is unsuitable for EST tracking. Thus, a joint detection and tracking of multiple ESTs based on track-before-detect (TBD) approach, which is an efficient way to track low-observable ESTs, is proposed. In EST-RMM-TBD scenarios, although the extension ellipsoid is efficient, it may not be accurate because of some missing useful information, such as size, shape, and orientation. To address this, a EST-sub-RMM-TBD composed of sub-ellipses is introduced, each representing an RMM. Based on such models, a sub-RMM-MB-TBD filter is used to estimate the kinematic states and extensions of sub-objects for each EST. Furthermore, a sequential Monte Carlo (SMC) implementation to estimate non-linear kinematic EST state is applied. The results indicate that the proposed SMC-sub-RMM-MB-TBD filter has more accurate cardinality estimation and smaller optimal sub-pattern assignment errors than the recent extended tracking filters.

Joint detection and tracking of extended stealth targets from image observations based on subrandom matrices

The challenge of joint detection and tracking of multiple extended targets (ETs) arises in many radar applications, especially for extended stealth targets (ESTs) with small signal-to-noise ratio (SNR). Recently, the multi-Bernoulli (MB) filter-based random matrix model (RMM) has been proposed for tracking ellipsoidal ETs. The MB-RMM filter depends on the measurements (position and range rate), which are extracted by thresholding the received signal. It is acceptable if SNR is high. The threshold must be less than the sufficient probability to avoid a high rate of false detections. This assumption is unsuitable for tracking extended-stealth targets (ESTs) with unknown detection probability. To this point, we address a track-before-detect-MB-RMM approach, which is an efficient way to solve the unknown detection profile issue. There is a considerable advantage of using unthresholded data in simultaneous detection and tracking. In this scenario, although the extension ellipsoid is efficient, it may not be accurate enough because of a lack of useful information, such as size, shape, and orientation. Therefore, we introduce a filter composed of subellipses where each one is represented by an RMM. Furthermore, a sequential Monte Carlo implementation is applied to estimate nonlinear kinematic ESTs’ state. The results confirm the effectiveness and robustness of the proposed filter.

Moving Target Detection in Multi-Static GNSS-Based Passive Radar Based on Multi-Bernoulli Filter

Over the past few years, the global navigation satellite system (GNSS)-based passive radar (GBPR) has attracted more and more attention and has developed very quickly. However, the low power level of GNSS signal limits its application. To enhance the ability of moving target detection, a multi-static GBPR (MsGBPR) system is considered in this paper, and a modified iterated-corrector multi-Bernoulli (ICMB) filter is also proposed. The likelihood ratio model of the MsGBPR with range-Doppler map is first presented. Then, a signal-to-noise ratio (SNR) online estimation method is proposed, which can estimate the fluctuating and unknown map SNR effectively. After that, a modified ICMB filter and its sequential Monte Carlo (SMC) implementation are proposed, which can update all measurements from multi-transmitters in the optimum order (ascending order). Moreover, based on the proposed method, a moving target detecting framework using MsGBPR data is also presented. Finally, performance of the proposed method is demonstrated by numerical simulations and preliminary experimental results, and it is shown that the position and velocity of the moving target can be estimated accurately.

Joint Tracking and Classification of Multiple Targets with Scattering Center Model and CBMeMBer Filter.

This paper deals with joint tracking and classification (JTC) of multiple targets based on scattering center model (SCM) and wideband radar observations. We first introduce an SCM-based JTC method, where the SCM is used to generate the predicted high range resolution profile (HRRP) with the information of the target aspect angle, and target classification is implemented through the data correlation of observed HRRP with predicted HRRPs. To solve the problem of multi-target JTC in the presence of clutter and detection uncertainty, we then integrate the SCM-based JTC method into the CBMeMBer filter framework, and derive a novel SCM-JTC-CBMeMBer filter with Bayesian theory. To further tackle the complex integrals’ calculation involved in targets state and class estimation, we finally provide the sequential Monte Carlo (SMC) implementation of the proposed SCM-JTC-CBMeMBer filter. The effectiveness of the presented multi-target JTC method is validated by simulation results under the application scenario of maritime ship surveillance.

Joint detection and tracking for stealth targets in noisy imagery based on variational Bayesian-sequential Monte Carlo-cardinality-balanced multitarget multi-Bernoulli filter

We explore the use of an improved particle filter to detect and track stealth targets (STs) in noisy imagery with unknown detection profile. Recently, a cardinality-balanced multitarget multi-Bernoulli (CBMeMBer) of variational Bayesian (VB) approximation has been proposed for tracking multitargets with unknown measurement variances. However, VB-CBMeMBer filter has been implemented with a known detection profile, which is unsuitable for ST tracking. The Bayesian track-before-detect (TBD) is an efficient way to detect low observable targets. A new VB-CBMeMBer-TBD filter is proposed to cope with jointly unknown detection profile and measurement variances for ST tracking. Furthermore, a sequential Monte Carlo implementation is applied to estimate augmented kinematic ST state. The results show that the proposed filter is more accurate than other filters in cardinality estimation and less optimal subpattern assignment errors.

DOA Tracking Based on Unscented Transform Multi-Bernoulli Filter in Impulse Noise Environment.

Aiming at the problem of multiple-source direction of arrival (DOA) tracking in impulse noise, this paper models the impulse noise by using the symmetric α stable (SαS) distribution, and proposes a DOA tracking algorithm based on the Unscented Transform Multi-target Multi-Bernoulli (UT-MeMBer) filter framework. In order to overcome the problem of particle decay in particle filtering, UT is adopted to select a group of sigma points with different weights to make them close to the posterior probability density of the state. Since the α stable distribution does not have finite covariance, the Fractional Lower Order Moment (FLOM) matrix of the received array data is employed to replace the covariance matrix to formulate a MUSIC spatial spectra in the MeMBer filter. Further exponential weighting is used to enhance the weight of particles at high likelihood area and obtain a better resampling. Compared with the PASTD algorithm and the MeMBer DOA filter algorithm, the simulation results show that the proposed algorithm can more effectively solve the issue that the DOA and number of target are time-varying. In addition, we present the Sequential Monte Carlo (SMC) implementation of the UT-MeMBer algorithm.

δ‐GLMB filter based on DI in a clutter

For the problem that the performance of existing multi-target tracking algorithm's serious degrades in a dense clutter environment, a novel Doppler information assistant δ-generalised labelled multi-Bernoulli (DI-δ-GLMB) filter is proposed. By introducing DI, a new measurement likelihood function is established, and the improved update equation based on the δ-GLMB filter framework is derived. In addition, a sequential Monte Carlo implementation method is given under the non-linear model. Simulation results show that compared with the DI probability hypothesis density filter and the standard δ-GLMB filter, the estimation of the proposed algorithm is more accurate and stable.

Refined PHD Filter for Multi-Target Tracking under Low Detection Probability.

Radar target detection probability will decrease as the target echo signal-to-noise ratio (SNR) decreases, which has an adverse influence on the result of multi-target tracking. The performances of standard multi-target tracking algorithms degrade significantly under low detection probability in practice, especially when continuous miss detection occurs. Based on sequential Monte Carlo implementation of Probability Hypothesis Density (PHD) filter, this paper proposes a heuristic method called the Refined PHD (R-PHD) filter to improve multi-target tracking performance under low detection probability. In detail, this paper defines a survival probability which is dependent on target state, and labels individual extracted targets and corresponding particles. When miss detection occurs due to low detection probability, posterior particle weights will be revised according to the prediction step. Finally, we transform the target confirmation problem into a hypothesis test problem, and utilize sequential probability ratio test to distinguish real targets and false alarms in real time. Computer simulations with respect to different detection probabilities, average numbers of false alarms and continuous miss detection durations are provided to corroborate the superiority of the proposed method, compared with standard PHD filter, Cardinalized PHD (CPHD) filter and Cardinality Balanced Multi-target Multi-Bernoulli (CBMeMBer) filter.

Multi-target tracking in distributed sensor networks using particle PHD filters

Abstract Multi-target tracking is an important problem in civilian and military applications. This paper investigates multi-target tracking in distributed sensor networks. Data association, which arises particularly in multi-object scenarios, can be tackled by various solutions. We consider sequential Monte Carlo implementations of the Probability Hypothesis Density (PHD) filter based on random finite sets. This approach circumvents the data association issue by jointly estimating all targets in the region of interest. To this end, we develop the Diffusion Particle PHD Filter (D-PPHDF) as well as a centralized version, called the Multi-Sensor Particle PHD Filter (MS-PPHDF). Their performance is evaluated in terms of the Optimal Subpattern Assignment (OSPA) metric, benchmarked against a distributed extension of the Posterior Cramer-Rao Lower Bound (PCRLB), and compared to the performance of an existing distributed PHD Particle Filter. Furthermore, the robustness of the proposed tracking algorithms against outliers and their performance with respect to different amounts of clutter is investigated.

Sensor Selection for Decentralized Large-Scale Multi-Target Tracking Network.

A new optimization algorithm of sensor selection is proposed in this paper for decentralized large-scale multi-target tracking (MTT) network within a labeled random finite set (RFS) framework. The method is performed based on a marginalized δ-generalized labeled multi-Bernoulli RFS. The rule of weighted Kullback-Leibler average (KLA) is used to fuse local multi-target densities. A new metric, named as the label assignment (LA) metric, is proposed to measure the distance for two labeled sets. The lower bound of LA metric based mean square error between the labeled multi-target state set and its estimate is taken as the optimized objective function of sensor selection. The proposed bound is obtained by the information inequality to RFS measurement. Then, we present the sequential Monte Carlo and Gaussian mixture implementations for the bound. Another advantage of the bound is that it provides a basis for setting the weights of KLA. The coordinate descent method is proposed to compromise the computational cost of sensor selection and the accuracy of MTT. Simulations verify the effectiveness of our method under different signal-to- noise ratio scenarios.

Novel Rao–Blackwellized jump Markov CBMeMBer filter for multi-target tracking

The jump Markov cardinality balanced multi-target multi-Bernoulli (JM–CBMeMBer) filter can estimate both state and number of targets from uncertain measurements. To deal with high computational complexity and imprecise estimations of the existing JM–CBMeMBer filters, we put forward a novel Rao–Blackwellized JM–CBMeMBer filter and its sequential Monte Carlo implementation in this paper. Different from the previous works, we first divide target state space into the nonlinear and linear components based on the Rao–Blackwellized theory, where the linear component is estimated by the Kalman filter (KF) and the results are applied to extract the nonlinear component in lower dimension state space. Moreover, the track management scheme is considered to simplify tracking parameters and distinguish target track. After analysis on computational complexity, the optimised Rao–Blackwellized filtering scheme is presented to reduce the number of the KF recursions. As a result, the computational complexity is reduced and the estimation accuracy is improved owing to small estimation covariance during the whole filtering process. Finally, the numerical simulation results are provided to show the reliability and efficiency of the proposed filter.

CBMeMBer filterwith adaptive target birth intensity

Appropriately modelling target-birth intensity is a significant but challenging issue in multi-target tracking systems. In existing cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filters, a priori knowledge about the locations where targets appear is required to model the target-birth intensity. Since the newborn targets can appear anywhere within the observation region, it is impractical to obtain such prior information. In this study, a novel CBMeMBer filter with adaptive target-birth intensity is presented, considering the newborn and surviving targets separately. The target-birth function of the target-birth intensity is modelled using current measurements rather than the known birth locations, and the target-birth magnitude is assigned by an allocation function rather than equally assigned. The new CBMeMBer filter can remove the restriction on the requirement of prior birth location information and can adapt well after continuous missing detection occurs. Simulations of the sequential Monte Carlo and Gaussian mixture implementations demonstrate the effectiveness of the proposed filter.