Bernoulli Filter Research Articles

Bernoulli filter with signal coherent integration for target detection and tracking in clutter environments

In practical applications, the target maneuvers might lead to high-order range migration (RM) and Doppler frequency migration (DFM) effects, which seriously degrade the performance of long-time coherent integration. In this case, the target detection and tracking performance will deteriorate due to insufficient signal energy and heavy clutter. To address this problem, a recursive algorithm based on the Bernoulli filter with long-time coherent integration is proposed in this paper for maneuvering target detection and tracking in low signal-to-noise ratio environments. The Keystone transform is used to correct the linear RM. Then, the matched filtering is performed based on the state to eliminate the high-order RM and DFM. According to the focused peaks in the range-time azimuth-Doppler domain, the target existence probability and dynamic states are estimated using an amplitude-aided Gaussian mixture Bernoulli filter. Simulations are performed to demonstrate the effectiveness of the proposed algorithm. Compared with traditional coherent integration methods based on parameter searching, the proposed algorithm acquires close integration performance with less computational complexity, and the target detection and tracking performance is improved with the aid of integrated signal amplitude.

Bernoulli Filter for Extended Target Tracking in the Framework of Possibility Theory

Extended objects give rise to a varying number of noisy measurements from its reflection (scattering or feature) points. Due to imperfect detection, only some of the feature points are detected in each scan of input data, while false alarms can also be present. The optimal sequential Bayesian state estimator in the framework of random set theory is the Bernoulli filter for an extended target (BF-X). In this paper we formulate and derive the analog of the BF-X in the framework of possibility theory, where uncertainty is represented using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">possibility</i> functions, rather than <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">probability</i> distributions. Possibility functions have the capacity to model partial (imprecise) probabilistic specifications and thus the main advantage of the proposed possibilistic BF-X, is enhanced robustness in the absence of precise measurements or dynamic models.

Performance Comparison of ToA and TDOA Based Tracking In Underwater Multipath Environments Using Bernoulli Filter

Abstract Underwater localization and tracking is a challenging problem and Time-of-Arrival and Time-Difference-of-Arrival approaches are commonly used. However, the performance difference between these approaches is not well understood or analysed adequately. There are some analytical studies for terrestrial applications with the assumption that the signal arrival times are not correlated. However, this assumption is not valid for underwater propagation. To present the distinct nature of the problem under the water, a high-fidelity simulation is required. In this study, Time-of-Arrival and Time-Difference-of-Arrival approaches are compared using a ray tracing based propagation model. Moreover, basic methods to mitigate the multipath propagation problem are also implemented for Bernoulli filters. Since the Bernoulli filter is a joint detection and tracking filter, the detection performance is also analysed. Comparisons are done for all combinations of filter and measurement approaches. The results can help to design underwater localization systems better suited to the needs.

Direct Target Joint Detection and Tracking Based on Passive Multi-Static Radar

Traditional target tracking is carried out based on the point measurements extracted from the radar resolution cells. This is not suitable for situations of low signal-to-noise ratio (SNR). In this paper, we aim to investigate the problem of the joint detection and tracking (JDT) of a target by directly using the received signals of passive multi-static radar without feeding the signals to matched filters. To this end, a novel likelihood function is proposed exploiting the statistical properties of coherent processing between the reference and surveillance signals. With such a likelihood function, the particle Bernoulli filter is employed to perform direct JDT (DJDT) of the target. A remarkable feature of the proposed method is that it is able to achieve satisfactory performance when the SNR of received signals is low. Furthermore, the proposed method cannot only achieve the existence and kinematic state of the target, but also the time-varying SNR of each receiver, which serves as an important input for sensor adjustment. The performance of the proposed method is verified via simulations.

From target tracking to targeting track: A data-driven yet analytical approach to joint target detection and tracking

This paper addresses the problem of real-time detection and tracking of a non-cooperative target in the challenging scenario with almost no a-priori information about target birth, death, dynamics and detection probability. Furthermore, there are false and missing data at an unknown yet low rate in the measurements. The only information given in advance is about the target-measurement model and the constraint that there is no more than one target in the scenario. To solve these challenges, we model the movement of the target by using a polynomial trajectory function of time (T-FoT), which aims to estimate the continuous-time trajectory of the target rather than a series of discrete-time point estimates as is done in most existing filters/trackers. Data-driven T-FoT initiation and termination strategies are proposed for identifying the (re-)appearance and disappearance of the target. During the existence of the target, real target measurements are distinguished from clutter if the target indeed exists and is detected, in order to update the T-FoT at each scan for which we design a least-squares estimator. Overall, our approach is Markov-free, data-driven yet analytical. Simulations using either linear or nonlinear systems are conducted to demonstrate the effectiveness of our approach in comparison with the Bayes optimal Bernoulli filters. The results show that our approach is comparable to the perfectly-modeled filters, even outperforms them in some cases while requiring much less a-priori information and computing much faster.

A general cardinalized probability hypothesis density filter

Based on random finite set, the probability hypothesis density (PHD) filter and the cardinalized PHD (CPHD) filter have been proposed for multitarget tracking as they are computational tractable. But the classical PHD and CPHD filter is not applicable when a target generates multiple detections. The general PHD filter was proposed to apply the PHD filter to arbitrary clutter and target measurement process. However, as a filter with better performance than the PHD filter, the CPHD filter for multiple-detection tracking is not proposed except the extended target CPHD filter and the multisensor CPHD filter. In our work, the general CPHD filter, which allows the clutter process and target measurement process to be arbitrary and performs better than the general PHD filter, is proposed. The proposed general CPHD filter is the general form of all kinds of CPHD filters, as well as all kinds of PHD filters and Bernoulli filters. In the simulation, the multiple-detection model of the over-the-horizon radar is used to demonstrate the tracking performance. The simulation results show that the proposed filter improves the accuracy of the state estimates and reduces the variance of the estimated number of targets.

Bayes‐optimal tracking of two statistically correlated targets in general clutter

The Bernoulli filter is a very general, computationally feasible Bayes-optimal approach for tracking a single disappearing and reappearing target, using a single sensor whose observations are corrupted by missed detections and a known, general point-clutter process. This paper shows how to generalise it to the dyadic labelled random finite set (DLRFS) filter—that is, a very general, computationally feasible Bayes-optimal approach for tracking two disappearing and reappearing and possibly correlated targets, using a single sensor whose observations are corrupted by missed detections and a known, general clutter process. It is further shown that, like the Bernoulli filter, the DLRFS filter is an exact special case of the labelled multitarget recursive Bayes filter (LMRBF)—and thus that, given the target and sensor models, there cannot be a theoretically better tracking filter. The paper also describes the relationship between the DLRFS filter and the (unlabelled) Gauss–Poisson filter of Singh, Vo, Baddeley, and Zuyev.

Bayesian Filtering for Dynamic Anomaly Detection and Tracking

This article presents a Bayesian approach for sequential detection of anomalies in the motion of a target and joint tracking. The anomaly is modeled as a binary (on/off) switching unknown control input that goes into action (begins to exist, or “switches on”) thereby modifying the object dynamics; and by ceasing its activity (becoming nonexistent, or “switching off”) returns the dynamics to nominal. The developed Bayesian framework brings together random finite set (RFS) theory to represent the switching nature of the anomaly, and optimal joint input and state estimation to sequentially update a hybrid state that incorporates a random vector for the kinematic state and a Bernoulli RFS for the unknown control input. In addition, a closed-form solution, the Gaussian-mixture hybrid Bernoulli filter (GM-HBF), has been developed to provide a customized solution for dynamic anomaly detection in the maritime domain characterized by linear Gaussian target dynamics. Based on the Ornstein–Uhlenbeck dynamic model for vessels, where the evolution of the object velocity is governed by a piecewise mean-reverting stochastic process, the anomaly can be represented by a change in the long-run mean velocity (i.e., the unknown control input) from the nominal condition that forces the vessel to deviate from its standard route. We demonstrate the effectiveness of the proposed GM-HBF in both simulated and real-world maritime surveillance applications and test its performance in the face of false measurements, detection uncertainty, and sensor data gaps.

Sensing spectrum sharing based massive MIMO radar for drone tracking and interception.

Radar sensors are becoming crucial for environmental perception in a world with the tremendous growth of unmanned aerial vehicles (UAVs) or drones. When public safety is a concern, the localization of drones are of great significance. However, a drone used for a wrong motive can cause a serious problem for the environment and public safety, given the fact that the dynamic movement of a drone’s emission signal and location tracking is different from existing positioning. This study proposes a safety zone characterized by the presence of N radars sensors with a goal to track and destabilized rogue drones attending to penetrate safety zones (stadium and school). Specifically, a new joint estimation based on a Gaussian filter has been introduced for spectrum sharing and detection awareness. The profit of this novel sensing method can be clearly seen when the two joint hidden states are taken into consideration. Therefore, the drone’s emission state is analyzed by estimating its movement jointly. Considering the drone’s unknown states and actual positioning, an algorithm is developed based on dynamic states space model. Where Bernoulli filter model is designed to estimate recursively the unknown stages of the drone and its changing location based on time. Meanwhile a power control acted from the radar to the targeted drones so that rogue drones are optimally tracked and destabilized over time. Furthermore, an expanding mechanism has been generated to accurately track the drone and enhance detection. A thoughtful result of the experimentation shows clearly that, even when the drone is moving, spectral detection can be performed accurately by chasing its positions. Its demonstrates at 90% of credibility that the original signal has a direct effect on the propagated signal. Therefore, the magnitude of the Doppler shift increases with frequency. And the clue of its positioning can be used for cognitive radio optimization.

Distributed joint target detection, tracking and classification via Bernoulli filter

This paper aims to solve the problem of distributed joint detection, tracking and classification (D-JDTC) of a target on a peer-to-peer sensor network. The target can be present or not, can belong to different classes, and depending on its class can behave according to different kinematic modes. Accordingly, it is modelled as a suitably extended Bernoulli random finite set (RFS) uniquely characterized by existence, classification, class-conditioned mode and class & mode-conditioned state probability distributions. Existing algorithms have been devised to perform target JDTC based on a single sensor and can only be easily extended to multiple sensors in a centralized configuration, wherein a fusion centre gathers measurements from all sensors. In this paper, by designing a suitable rule for fusing local posteriors that convey information on target existence, class, mode and state from different sensor nodes, a novel scalable and fault-tolerant D-JDTC Bernoulli filter is proposed, and its performance is evaluated by means of simulation experiments.

재진입 표적추적을 위한 복수 레이더 2단계 정보융합 기법

This paper proposes a two-stage track-to-track fusion algorithm for re-entry target tracking using multiple radars. The existing track-to-track fusion strategy relying only on the kinematic information shows unreliable target tracking performance when the target of interest is adjacent with other objects. To prevent tracking performance degradation due to false track fusion, the track paring hypothesis is evaluated using both the feature data and the kinematic data provided by radars. A recursive Bernoulli filter is desinged to discriminate the target identity by fusing binary decision data which correspond to the most probable track pairing hypothesis. Since our approach exploits the statistical property of the available decision data, it can enhance the target tracking and identification performance. Through the computer simulations for a typical re-entry target tracking scenario, the effectiveness of the suggested data fusion scheme is demonstrated.

伯努利滤波器在纯角度跟踪场景中的应用

伯努利滤波器在纯角度跟踪场景中的应用

伯努利滤波器在纯角度跟踪场景中的应用

伯努利滤波器在纯角度跟踪场景中的应用

Joint Bernoulli Filtering and MIMO Processing for Detection of Moving Targets in Shallow Ocean Environments

A joint multiple-input multiple-output (MIMO) processing framework is proposed to exploit spatial diversity and moving cues for the enhancement of target detection in a shallow ocean environment. Orthogonal signals are transmitted to illuminate different aspects of a target and beamforming operation is carried out over the received data for estimating target bearing. The target range is achieved by a replica correlation integrator where the beamformer outputs are matched with transmitted signals. After meanshift clustering algorithm is carried out over the bearing-range spectrums to generate the clutter centers, the potential trajectories of targets can be tracked by an improved Bernoulli filter with inputs of these centers. The at-sea experimental results have shown the effectiveness of the joint processing framework in MIMO detection of moving targets.

Bernoulli Filters for Multiple Correlated Sensors

The Bernoulli filter is a general, Bayes-optimal solution for tracking a single disappearing and reappearing target, using a single sensor whose observations are corrupted by missed detections and a general, known clutter process. Like virtually all target-tracking algorithms it presumes a hidden Markov model (HMM) structure on the sensor and target. Pieczynski's pairwise Markov model (PMM) relaxes this assumption, thereby addressing correlated sensor noise and non-Markovian target motion. In an earlier paper, we derived a “PMM Bernoulli filter” that obeys PMM rather than restrictive HMM sensor/target statistics. This paper generalizes both the HMM and PMM Bernoulli filters to the case of multiple, possibly correlated sensors, resulting in a general, Bayes-optimal single-target tracker for complexly correlated sensors.

Bernoulli filter for tracking maritime targets using point measurements with amplitude

Statistical performance of the Bernoulli Track-Before-Detect (TBD) algorithm for maritime radar is superior to that of the Bernoulli tracking filter which processes, in a conventional manner, the point measurements (PM) produced by a detector. However, the Bernoulli TBD is orders of magnitude computationally more intensive. In this paper we develop a hybrid algorithm that takes advantage of the amplitude information (exploited by the TBD algorithm), but operates in the framework of conventional point-measurement Bayesian tracking. The resulting filter is formulated using the Rao-Blackwell decomposition: a particle filter estimates the target amplitude, while the target position and velocity, given the amplitude, are estimated using a Gaussian mixture filter. Numerical results show that the statistical and computational efficiency of the new hybrid filter is between the two extremes, namely, the Bernoulli TBD and the Bernoulli PM tracker.

Passive target detection and tracking from electromagnetic field measurements

This paper presents a novel approach to the localization of moving targets in a complex environment based on the measurement of the perturbations induced by the target presence on an independently-generated time-varying electromagnetic field. Field perturbations are measured via a set of sensors deployed over the domain of interest and used to detect and track a possible target by resorting to a particle Bernoulli filter (PBF). To comply with real-time operation, the PBF works along with an artificial neural network (ANN) model of the environment trained offline via finite elements (FEs). The performance of the proposed algorithm is assessed via simulation experiments.

Target tracking in the framework of possibility theory: The possibilistic Bernoulli filter

The Bernoulli filter is a Bayes filter for joint detection and tracking of a target in the presence of false and miss detections. This paper presents a mathematical formulation of the Bernoulli filter in the framework of possibility theory, where uncertainty is represented using possibility functions, rather than probability distributions. Possibility functions model the uncertainty in a non-additive manner, and have the capacity to deal with partial (incomplete) problem specification. Thus, the main advantage of the possibilistic Bernoulli filter, derived in this paper, is that it can operate even in the absence of precise measurement and/or dynamic model parameters. This feature of the proposed filter is demonstrated in the context of target tracking using multi-static Doppler shifts as measurements.

Maneuvering Target Tracking Based on Multiple-model Multipath Bernoulli Filter

Aiming at the problem of maneuvering single target tracking in over the horizon radar system under the clutter environment, a novel multiple-model multipath Bernoulli filter (MM-MPBF) algorithm is proposed. First, the multipath target measurement model is established based on the finite set statistics, and then combining the multiple models method with the multipath Bernoulli filter to deal with the single maneuvering target tracking problem in over the horizon radar system. Finally, the simulation experiment is used to verify the performance of the MM-MPBF algorithm.

Robust single target tracking using determinantal point process observations

Abstract The efficiency and robustness of modern visual tracking systems are largely dependent on the object detection system at hand. Bernoulli and Multi-Bernoulli filters have been proposed for visual tracking without explicit detections (image observations). However, these previous approaches do not fully exploit discriminative features for tracking. In this paper, we propose a novel Bernoulli filter with determinantal point processes observations. The proposed observation model can select groups of detections with high detection scores and low correlation among the observed features; thus achieving a robust filter.