Bernoulli Filter Research Articles

Cooperative object detection in road traffic

Multi-sensor object detection and tracking on a highway scene with radar measurements is presented. The estimation algorithm is the random finite set based Bernoulli filter, working in the Bayesian framework. The recursion for calculating the Bayes estimation is implemented as a particle filter. A method is presented for calculating the likelihoods, suitable for particle filtering performed with moving sensors, assuming additive Gaussian measurement noise. In our approach, for calculating the posterior estimate of the object state, the measurement likelihoods are computed in the state space, instead of the measurement space, by mapping each measurement to the global coordinate system. The map consists of a nonlinear and an affine part. While the affine transformation trivially preserves the Gaussian nature, the nonlinear is well-proven to be approximated as affine too. This approach allows the particles to be drawn directly from the state space, hence the evaluation of the measurement model is not needed, which saves computational power.

Auxiliary particle Bernoulli filter for target tracking

Target tracking is a popular topic in various surveillance systems. As a data association free method, the Bernoulli filter can directly estimate target state from plenty of uncertain measurements. However, it is not obvious for existing Bernoulli filters to select proposal distribution with small variance of weights. To address this problem, a novel auxiliary particle (AP) Bernoulli filter and its implementation are proposed in this paper. We employ the AP method in the Bernoulli filtering framework in order to choose robust particles from a discrete distribution defined by an additional set of weights, which reflect the ability to represent measurements with high probability. Limitation to the number of particles, the promising particles are used to propagate by extracting indices. On the other hand, the particles without significant contribution to approximation are discarded. In such case, the computational complexity of this filter is reduced. With the unscented transform (UT), the dynamics of maneuvering target are effectively estimated. The simulation results show advantages in comparison to the standard Bernoulli filter for general target tracking.

An improved Bernoulli particle filter for single target tracking

Single target tracking is widely applied in the current surveillance systems. The Bernoulli filter can complete the task of single target tracking using available measurements. However, the existing Bernoulli filters have estimation bias during the whole tracking process. Therefore, we present an improved Bernoulli filter and its particle implementation in this paper. Employed the weight optimization strategy, the under-estimated number of target is corrected by enlarging the maximal measurement-updated weight of sampling particle. In addition, the track identification strategy is applied to optimize number of the required particles and extract the actual target. Combined with the unscented transform for the complicated dynamic models, the nonlinear motion state of maneuvering target is effectively estimated. Besides, we extend the proposed filter in unknown clutter environment and estimate the mean clutter rate, which has significant application meaning owing to avoiding the assumption of the given detection profile. Finally, the numerical simulations demonstrate the tracking advantages with the promising results in comparison to the standard Bernoulli filter.

Performance Evaluation of a Bernoulli filter Based Multi-Vehicle Cooperative Object Detection

Abstract The paper presents the performance evaluation of a multi-sensor object detection algorithm applied in traffic situation. The chosen data fusion and estimation procedure is the Bernoulli particle filter, which is ideal for cooperative object detection, as it can handle the varying number of sensor measurement and object appearance-disappearance too. The simulated detectors are automotive radar sensors, capable of measuring object speed, distance and bearing. The filter performance is examined along four aspects: number of particles used, simulation timestep, sensor noise and object motion model noise. The applied noise models represent the quality of the equipped sensors and our lack of knowledge on object motion, therefore the robustness of the filter can be examined by varying these parameters. The amount of particles and the used timestep effect the demanded computational power and also the estimation error, hence the scaling of the algorithm can be measured. In order to obtain a statistically meaningful result, a batch of 50 runs for every parameter set were used.

Box-Particle Labeled Multi-Bernoulli Filter for Mltiple Extended Target Tracking

This paper focuses on real-time tracking of multiple extended targets in clutter based on labeled multi- Bernoulli filter. To address this problem, a novel approach is proposed within the recently presented box-particle framework. Unlike the traditional point-particle approach, the measurements of extended targets are modeled as in- terval measurements in this work, and the corresponding likelihood function is given based on interval analysis. Then, labeled multi-Bernoulli recursion for extended targets is implemented by box particles, referred to as BP-LMB filter. Furthermore, BP-MM-LMB filter is pro- posed to better accommodate the uncertainty of target dynamics by integrating the BP-LMB filter with interacting multiple models (IMM) algorithm. Simulations demon- strate that the proposed approach can significantly reduce the number of particles and well track multiple extended targets with less runtime.

Distributed Bernoulli Filters for Joint Detection and Tracking in Sensor Networks

We introduce in this paper a novel, fully distributed diffusion Bernoulli filter based on random information dissemination over a partially connected sensor network. The proposed algorithm allows the network nodes to cooperatively perform joint multiframe detection and tracking of an emitter that randomly appears in and disappears from a surveillance region. In addition, we also introduce an alternative flooding-based algorithm that reproduces exactly, in a fully distributed fashion, the optimal centralized Bernoulli filter based on all network node measurements. We derive two alternative low bandwidth implementations of the proposed filters, using respectively a marginalized sequential Monte Carlo (SMC) method and a hybrid Gaussian mixture model (GMM)/SMM scheme. The algorithms were evaluated in a simulated scenario where network nodes directly assimilate raw received signal strength measurements, subject only to possible measurement censoring.

Method and field experiment of target tracking via multi‐static Doppler shifts in high‐frequency passive radar

The passive radar (PR) systems working in the high-frequency (HF) band take advantage of numerous high-power stations and long wavelength, which are useful for anti-stealth, while suffering from the bad range resolutions compared with systems working in other bands. In this study, the method and field experiment of tracking a close-in moving target via only Doppler-shift data provided by an HF PR are described. The non-cooperative illuminators are far away from surveillance area, the direct wave and illumination wave reach the receiver and target, respectively, via reflection from the ionosphere, while the echo scattered from the target propagates directly to the receiver by line of sight. The Doppler measurement model in this particular multi-static scenario is proposed and the Gaussian mixture Bernoulli filter is introduced to process the Doppler data to estimate the target position and velocity. The experiment of tracking a close-in civilian aeroplane was carried out using an experimental PR system. The estimated target positions and velocities are provided and compared with the true values derived from the automatic dependent surveillance-broadcast data. The initial result indicates the feasibility of this method used in a practical PR system for moving target tracking.

A Gaussian mixture Bernoulli filter for extended target tracking with application to an ultra-wideband localization system

This paper presents a Gaussian mixture (GM) implementation of the Bernoulli filter for extended target tracking, which we call the extended target GM Bernoulli (ET-GM-Ber) filter. Closed form expressions for the ET-GM-Ber filter recursions are obtained. A clustering step is integrated into the measurement update stage in order to have a computationally tractable filter. Performance of the proposed filter is tested both on the simulated data and experimental data collected using an ultra-wideband (UWB) localization system. Simulations and experimental results demonstrate the accurate and effective performance of the proposed filter.

A Bernoulli Filter for Extended Target Tracking Using Random Matrices in a UWB Sensor Network

In this paper, we propose a new tractable Bernoulli filter based on the random matrix framework to track an extended target in an ultra-wideband (UWB) sensor network. The resulting filter jointly tracks the kinematic and shape parameters of the target and is called the extended target Gaussian inverse Wishart Bernoulli (ET-GIW-Ber) filter. Closed form expressions for the ET-GIW-Ber filter recursions are presented. A clustering step is inserted into the measurement update stage in order to have a computationally tractable filter. In addition, a new method that is consistent with the applied clustering method is embedded into the filter recursions in order to adaptively estimate the time-varying number of measurements of the extended target. The simulation results demonstrate the robust and effective performance of the proposed filter. Furthermore, real data collected from a UWB sensor network are used to assess the performance of the proposed filter. It is shown that the proposed filter yields a very promising performance in estimation of the kinematic and shape parameters of the target.

Asymmetric Threat Modeling Using HMMs: Bernoulli Filtering and Detectability Analysis

There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an HMM whose observations are cluttered. Within this context, this paper presents two important contributions. The first is a Bernoulli filter that can process cluttered observations and is capable of detecting whether there is an HMM present, and if so, estimate the state of the HMM. The second is an analysis of the problem that, for a given HMM model, is able to make statements regarding the minimum complexity that an HMM would need to involve in order that it be detectable with reasonable fidelity, as well as upper bounds on the level of clutter (expected number of false measurements) and probability of miss of a relevant observation. In a simulation study, the Bernoulli filter is shown to give good performance provided that the probability of observation is larger than the probability of an irrelevant clutter observation. Further, the results show that the longer the delays are between the HMM state transitions, the larger the probability margin must be. The feasibility prediction shows that it is possible to predict the boundary between poor performance and good performance for the Bernoulli filter, i.e., it is possible to predict when the Bernoulli filter will be useful, and when it will not be.

Joint detection scheme for cooperative spectrum sensing in cognitive radio network

In this paper, a new architecture of cognitive radio network (CRN) is presented for future dynamic spectrum sharing in time-variant flat fading (TVFF) channels. We consider a practical scenario where secondary users (SUs) are able to access the idle spectrum by secondary user routers (SU_Rs). Managed by a fusion center (FC), SU_Rs can work together to capture the idle spectrum, and then assign to the SUs. Besides, it is imperative to guarantee the wireless communication quality between primary base station (P_BS) and SU_Rs. Therefore, a new cooperative spectrum sensing (CSS) algorithm is suggested to recursively estimate the channel state information (CSI) while capturing the idle licensed band. The united mathematics model relies on a dynamic state-space model (DSM) and a Bernoulli filters (BF) algorithm. TVFF channels are modeled as finite-state Markov channel (FSMC). In order to reduce complexity of CSS, the particles are manipulated and reconstructed. Experimental simulations demonstrate that, by exploiting dynamic CSI, sensing performance of the new CSS algorithm will surpass the traditional schemes and this new architecture can be used in a realistic spectrum sharing system.

Bernoulli filter for range and Doppler ambiguous radar

A pulse Doppler radar worked in medium or high pulse repetition frequency (PRF) may suffer from range and Doppler ambiguities. The common method to solve ambiguities is to use multiple PRFs and do correlation between them. The ghosting problem may be caused by the false alarms in the correlation. When the signal-to-noise ratio is low, a low detection threshold is needed to guarantee the probability of detection, which may create a large amount of false alarms that are intractable for existing techniques. This study uses a Bayesian method to detect and track a single target in a range and Doppler ambiguous radar. The authors’ method is formulated based on the finite set representation of the target state and the recently developed Bernoulli filter. Besides, a sequential Monte Carlo implementation of the Bernoulli filter is proposed for the problem of range and Doppler ambiguous measurement. Simulation results show that the proposed filter can simultaneously detect and track the target using the ambiguous measurements in the presence of dense false alarms.

Joint underwater target detection and tracking with the Bernoulli filter using an acoustic vector sensor

In this paper, we study the problem of joint underwater target detection and tracking using an acoustic vector sensor (AVS). For this challenging problem, first a realistic frequency domain simulation is set up. The outputs of this simulation generate the two dimensional FRequency–AZimuth (FRAZ) image. On this image, the random finite set (RFS) framework is employed to characterize the target state and sensor measurements. We propose to use the Bernoulli filter, which is the optimal Bayes filter emerged from the RFS framework for randomly on/off switching single dynamic systems. Moreover, to increase the performance of detection and azimuth tracking in low signal-to-noise ratio (SNR) scenarios, a track-before-detect (TBD) measurement model for AVS is proposed to be used with the Bernoulli filter. Sequential Monte Carlo (SMC) implementation is preferred for the Bernoulli filter recursions. Extensive simulation results prove the performance gain obtained by the proposed approach both in estimation accuracy and detection range of the system.

Maneuvering target track-before-detect via multiple-model Bernoulli particle filter

Target tracking using non-threshold raw data with low signal-to-noise ratio is a very difficult task, and the model uncertainty introduced by target’s maneuver makes it even more challenging. In this work, a multiple-model based method was proposed to tackle such issues. The method was developed in the framework of Bernoulli filter by integrating the model probability parameter and implemented via sequential Monte Carlo (particle) technique. Target detection was accomplished through the estimation of target’s existence probability, and the estimate of target state was obtained by combining the outputs of modeldependent filtering. The simulation results show that the proposed method performs better than the TBD method implemented by the conventional multiple-model particle filter.

Deep Sensing for Next-Generation Dynamic Spectrum Sharing: More Than Detecting the Occupancy State of Primary Spectrum

In this paper, spectrum sensing is investigated and a new detection framework, namely, deep sensing (DS), is proposed for more challenging scenarios of future dynamic spectrum sharing. In contrast to existing methods, the DS scheme is designed to proactively recover and exploit some other informative states associated with realistic cognitive links (e.g., fading gains), except detecting the occupancy of primary-band. A unified mathematical model, relying on the dynamic state-space approach, is formulated, in which the Bernoulli random finite set (RFS) is further exploited to theoretically characterize complex DS procedures. A Bernoulli filter algorithm is suggested to recursively estimate unknown PU states accompanying related link information, which is implemented by particle filtering based on numerical approximations. The proposed DS algorithm is applied to detect primary users under time-varying fading channel, which may increase the observation uncertainty and, therefore, deteriorate the sensing performance. With this new framework, the time-varying fading gain, modeled as a stochastic discrete-state Markov chain (DSMC), is estimated along with unknown PU states. Simulations demonstrate that, by exploiting the underlying dynamic fading property, the sensing performance will surpass other traditional schemes. The DS scheme may be conveniently generalized to other applications, which will promote sensing performance and provides a new paradigm for next-generation spectrum sharing.

RSS-based joint detection and tracking in mixed LOS and NLOS environments

This paper considers the problem of joint detection and tracking in mixed line-of-sight (LOS) and non-line-of-sight (NLOS) environments by using received signal strength (RSS) measurements. A nonlinear target tracking model with multiple switching parameters has been proposed, in which multiple independent Markov chains are used to describe the switching of target maneuvers and the transition of LOS/NLOS measurements, respectively. Based on the proposed tracking model, a multi-sensor multiple model Bernoulli filter (MMBF) has been developed by employing the random finite set theory which can formulate the joint detection and tracking in a unified framework. To derive a closed-form expression to the MMBF, the Gaussian mixture implementations have been provided by applying the extended Kalman filter technique. A numerical example is provided involving tracking a maneuvering target by a sensor network with 30 nodes. Simulation results confirm the effectiveness of the proposed filter.

Bernoulli Filter for Extended Target in Clutter Using Poisson Models

This paper presents a joint detection and tracking filter for a single extended target in the presence of clutter measurements and missed detections. The filter is obtained by adapting the Poisson extended target model into the Bernoulli filter proposed by Mahler. The resulted filter is an optimal extended target joint detection and tracking filter. Predictor and corrector are derived follows the random set filtering framework. A particle filter implementation is presented, in which simplification methods are used to make it easy to be realized. Simulation results show that the proposed filter is effective at detection and tracking of extended target in dense clutter backgrounds.

Visual odometry based on a Bernoulli filter

In this paper, we propose a Bernoulli filter for estimating a vehicle’s trajectory under random finite set (RFS) framework. In contrast to other approaches, ego-motion vector is considered as the state of an extended target while the features are considered as multiple measurements that originated from the target. The Bernoulli filter estimates the state of the extended target instead of tracking individual features, which presents a recursive filtering framework in the presence of high association uncertainty. Experimental results illustrate that the proposed approach exhibits good robustness under real traffic scenarios.

OTHR multipath tracking using the bernoulli filter

A multipath target tracking and recognition algorithm is proposed for an over-the-horizon radar (OTHR) tracking system in the presence of detection uncertainty and clutter. This algorithm, multipath Bernoulli filter (MPBF), uses a generalization of the Bernoulli filter for joint detection and tracking of a single target. Due to multiple ionospheric propagation paths between the radar sites and the target, finite set statistics (FISST) is used to derive the likelihood function of MPBF. While the measurement models in OTHR are nonlinear, a closed-form solution in the form of Gaussian mixture is implemented by extended Kalman filter (EKF). Since multipath tracks occur in the multipath probabilistic data association (MPDA) algorithm and the original MPBF, a method is added in MPBF to identify which are the real or multipath tracks. Simulation results are presented to demonstrate that the proposed algorithm is capable of recognizing multipath tracks and has better performance over the MPDA.

Consensus Bernoulli Filter for Distributed Detection and Tracking using Multi-Static Doppler Shifts

In this letter, we study the problem of distributed detection and tracking of a target over a network of separately located Doppler-shift sensors. For this challenging problem, we propose consensus Gaussian mixture - Bernoulli (CGM-Ber) filter. The simulation results prove the robust and effective performance of the proposed approach in a challenging tracking scenario.