Bearings-only Tracking Research Articles

Particle Filter with Fine Resampling for Bearings-Only Tracking

To solve the nonlinear filtering problem in the Bearings-Only Tracking (BOT), an improved particle filter with fine resampling is proposed, called as PF-FR (Particle Filter with Fine Resampling). By introducing distance-comparing process and generating new particle based on optimized combination scheme, PF-FR filter performs better than generic PF-SIR filter both in terms of effectiveness and diversity of the particle system, hence, evidently enhancing tracking accuracy in bearings-only tracking problem. Simulations indicate that the proposed PF-FR algorithm is effective.

Efficient Parallel Implementation of State Estimation Algorithms on Multicore Platforms

For many applications in signal processing and control it is crucial that estimates of the state vector in a dynamic system can be obtained in real time. This poses the problem of producing algorithms that are fast enough to enable online execution. In this article, it is investigated how two of the most popular and powerful state estimation algorithms, the Kalman filter and the particle filter, can be efficiently implemented in parallel on a multicore architecture. The proposed parallel implementations are analyzed in terms of hardware requirements, such as memory bandwidth and available cache memory, to provide the desired speedup. The algorithms are exemplified by and evaluated in an adaptive filtering and a bearings-only tracking application. In the cases when original algorithms have been modified for parallelization, the accuracy of the estimates obtained is evaluated in comparison with that of the sequential algorithm. It is found that linear speedup, in the number of cores used, can indeed be achieved without loss of accuracy, for both state estimation algorithms.

Stereo bearings-only tracking of a wheelchair from a robot

Abstract This project deals with technical assistance for people of reduced mobility. The goal of this work is to have a mobile platform with an embedded prehensive arm (MANUS®) track a wheelchair. The use of this mobile unit in relation to the patient’s wheelchair is carried out on a master-slave basis. This study, therefore, has a plural-disciplinary nature: Science for the Engineer, Human, Social and Clinical Sciences. To ensure the tracking of the wheelchair by the mobile platform, we applied a stereo bearings-only tracking (BOT) paradigm to a single moving target. The observer, the mobile platform (robot), is equipped with two omnidirectional vision sensors, that each provides output with which we compute two bearing angles. Having two bearing angles makes it possible to track a manoeuvring target. In this paper we will show how we take advantage of the multi-sensor data fusion to improve the BOT process and hence obtain a more reliable wheelchair tracking.

Multi-prediction particle filter for efficient parallelized implementation

Abstract Particle filter (PF) is an emerging signal processing methodology, which can effectively deal with nonlinear and non-Gaussian signals by a sample-based approximation of the state probability density function. The particle generation of the PF is a data-independent procedure and can be implemented in parallel. However, the resampling procedure in the PF is a sequential task in natural and difficult to be parallelized. Based on the Amdahl's law, the sequential portion of a task limits the maximum speed-up of the parallelized implementation. Moreover, large particle number is usually required to obtain an accurate estimation, and the complexity of the resampling procedure is highly related to the number of particles. In this article, we propose a multi-prediction (MP) framework with two selection approaches. The proposed MP framework can reduce the required particle number for target estimation accuracy, and the sequential operation of the resampling can be reduced. Besides, the overhead of the MP framework can be easily compensated by parallel implementation. The proposed MP-PF alleviates the global sequential operation by increasing the local parallel computation. In addition, the MP-PF is very suitable for multi-core graphics processing unit (GPU) platform, which is a popular parallel processing architecture. We give prototypical implementations of the MP-PFs on multi-core GPU platform. For the classic bearing-only tracking experiments, the proposed MP-PF can be 25.1 and 15.3 times faster than the sequential importance resampling-PF with 10,000 and 20,000 particles, respectively. Hence, the proposed MP-PF can enhance the efficiency of the parallelization.

Object Tracking in 3-D Space with Passive Acoustic Sensors using Particle Filter

This paper considers the object tracking problem in three dimensional (3-D) space when the azimuth and elevation of the object are available from the passive acoustic sensor. The particle filtering technique can be directly applied to estimate the 3-D object location, but we propose to decompose the 3-D particle filter into the three planes particle filters, which are individually designed for the 2-D bearings-only tracking problems. 2-D bearing information is derived from the azimuth and elevation of the object to be used for the 2-D particle filter. Two estimates of three planes particle filters are selected based on the characterization of the acoustic sensor operation in a noisy environment. The Cramer-Rao Lower Bound of the proposed 2-D particle filter-based algorithm is derived and compared against the algorithm that is based on the direct 3-D particle filter.

SCKF-STF-CN: a universal nonlinear filter for maneuver target tracking

Square-root cubature Kalman filter (SCKF) is more effective for nonlinear state estimation than an unscented Kalman filter. In this paper, we study the design of nonlinear filters based on SCKF for the system with one step noise correlation and abrupt state change. First, we give the SCKF that deals with the one step correlation between process and measurement noises, SCKF-CN in short. Second, we introduce the idea of a strong tracking filter to construct the adaptive square-root factor of the prediction error covariance with a fading factor, which makes SCKF-CN obtain outstanding tracking performance to the system with target maneuver or abrupt state change. Accordingly, the tracking performance of SCKF is greatly improved. A universal nonlinear estimator is proposed, which can not only deal with the conventional nonlinear filter problem with high dimensionality and correlated noises, but also achieve an excellent strong tracking performance towards the abrupt change of target state. Three simulation examples with a bearings-only tracking system are illustrated to verify the efficiency of the proposed algorithms.

A Two-Stage Assignment-Based Algorithm for Asynchronous Multisensor Bearings-Only Tracking

We present a two-stage centralized algorithm for tracking multiple targets using spatially distributed bearings-only sensors that report the observations asynchronously. The sensors are assumed to be passive, i.e., they detect the energy emitted by the targets of interest to measure the bearing. The number of targets in the surveillance region is unknown a priori and the targets can enter or leave the surveillance region at any time. The measurement origin is also unknown since a detection can be due to the target being tracked, from a new target, or from clutter. In the first stage (the initialization stage) the proposed algorithm forms local bearings-only (mono) tracks for each sensor and combines these tracks to generate complete kinematic (stereo) tracks in the Cartesian coordinate frame. Once stereo tracks are formed, in the second stage, which is called the stereo tracking stage, bearing measurements are directly used to update the stereo tracks. This separation of the initialization and maintenance of the stereo tracks is lacking in many existing algorithms and results in improved performance. In this work we used the assignment-based technique to solve various data association problems that arise due to measurement origin uncertainty. Through extensive simulations we show that the proposed algorithm achieves better tracking accuracy while being computationally simpler than existing algorithms.

Bearings-only tracking with iterated extended risk sensitive filter

This paper concerns the application of an iterated extended risk sensitive filter (IERSF) to target tracking problems. The relative merits of IERSF vis-a-vis the extended risk sensitive filter (ERSF) for a bearings-only tracking problem using root mean square error (RMSE) and robustness with uncertainty in initial condition are explored. An ERSF weakness, specifically an accumulation error in the computation of innovation steps due to approximating nonlinear functions at a recently available prior estimate, is presented. By using the IERSF with proper tuning of risk factor and local iteration, the filtering divergence may be overcome, and a stable, robust, and unbiased estimation is satisfactorily obtained. With numerical simulation results, the tracking performance of IERSF is compared with the performance of ERSF and extended Kalman filter. The IERSF results in reduced estimation error without much of an increase in burden of the associated computational algorithm.

A novel robust two-stage extended Kalman filter for bearings-only maneuvering target tracking

A novel robust filter is proposed via embedding extended Kalman filter into an optimal two-stage Kalman filter, which is improved through a modified Sage-Husa noise statistics estimator. Meanwhile, strong tracking multiple fading factors are introduced in this paper to improve the tracking performance for high maneuvering targets. The new method provides an optimal estimation of the target state through a combination of the output of the first stage (a “bias-free” filter) and that of the second stage (a “bias-compensating” filter). Furthermore, the unknown statistical parameters of virtual noises are estimated online, and the predicted covariance can be adjusted in real time by fading factors when high maneuvers occur. Simulation results of tracking a maneuvering target by 3 passive sensors show that the proposed algorithm has advantages over the conventional method in terms of the numerical accuracy with only a little additional computational cost. Key words: Target tracking, two-stage Kalman filter, noise statistics estimator, multiple fading factors.

A New Algorithm for Bearings-Only Parametric Trajectory Tracking

For the single sensor target tracking with bearings-only measurements, a novel trajectory invariable-information target tracking algorithm was proposed, and bearings-only target can be tracked by the parameter trajectory. For the measure frequency of sensor is high, the mathematic model of bearings-only tracking is analyzed by dividing the trajectory into many linearization parts. The tracking parameter of bearings-only target trajectory is deduced, so the bearings-only target can be tracked by the parameter trajectory. The simulation results show that the new algorithm has a favorable tracking precision.

Multitarget bearings-only tracking using fuzzy clustering technique and Gaussian particle filter

In this paper, a novel multitarget bearings-only tracking algorithm that combines the fuzzy clustering data association technique together with a Gaussian particle filter (GPF) is presented. Firstly, to deal with the data association problem that arises due to the uncertainty of the measurements, the fuzzy clustering method with the maximum entropy principle is utilized, which eliminates those invalid measurements. Secondly, this paper employs GPF to update each target state independently, since it has a much-improved performance and versatility over other Gaussian filters, especially when nontrivial nonlinearities are present. Moreover, in the multisensor scenario, a statistic test method based on the cotangent values of bearings is proposed, for associating the target bearing data observed at each sensor. Simulation results demonstrate the effectiveness of the algorithm.

H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform

This paper is concerned with the H ∞ filtering for a class of nonlinear discrete-time systems. By embedding the unscented transform technique into the extended H ∞ filter structure, the unscented H ∞ filtering can be carried out using the statistical linear error propagation approach. Moreover, the unscented H ∞ information form filter has been developed for decentralized fusion by defining appropriate information state vectors and matrices. The novel filter achieves not only higher accuracy, but also robustness against model uncertainty. Simulation results for the frequency modulation demodulation and bearings-only tracking are presented to illustrate the effectiveness of the proposed method.

APPLYING THE FILTEING ALGORITHM WITH PARTICLE RESIDUAL CONSISTENCY MEASURE TO BEARINGS ONLY PASSIVE TRACKING

Aiming at the disadvantageous influence of evaluating particles weights on the filtering results in the bearings-only passive tracking of low signal-to-interference ratio,a novel particle filter algorithm based on particle residual consistency measure was proposed.Firstly,particle residual was used to realize the mapping transformation of sampling particle from state space to measurement space.Then,confidence level distance and confidence level matrix were constructed to complete the reasonable evaluation of particles weights.The new method effectively extracts and uses the latest measurement information and redundancy and complementary information among particles,which makes the evaluation results of particles weights more stable and reliable.Finally,experiments demonstrate the efficiency of the proposed algorithm.

Novel particle filtering algorithm with application to bearing-only tracking

The conventional bootstrap filter suffers a main drawback of not incorporating the latest observations.Therefore,this paper proposed a Kalman Particle Filter(KPF) algorithm,and applied this new algorithm to bearing-only target tracking.An improved scheme was presented to handle this problem and yield a Kalman particle filter.The underlying idea of the new algorithm is that each particle is updated using Kalman filter incorporating the coming observations.A bearing-only tracking model was experimented and compared with bootstrap filter and KPF.The experimental results verify its superiority.

Track initiation of bearings-only tracking based on ant navigation concept

A novel heuristic track initiation method is developed for the bearing-only multi-sensor–multi-target tracking system, in which each target is assumed to move with a straight line. The key idea of the proposed method is derived from the ant navigation concept in its foraging life, which differs from the traditional ant colony optimization algorithm, and it utilizes the concept of path integration and visual landmarks in ants’ navigation toolkit to find the exact positions of each target. Numerous numerical simulations are conducted and the effectiveness of the proposed track initiation method is verified according to the probability of correct track initiation.

Data Association Approach for Two Dimensional Tracking Based on Bearing-Only Measurements in Clutter Environment

This paper mainly studies angle-measurement based data association algorithm to overcome the existing problems in the applications of traditional association approaches for bearing-only target locating and tracking system. First, this paper proposes a fast track initiation approach for the system using a single passive sensor. In this approach, the rules of screening out threatening targets are set by analyzing the characteristics of target motion in two dimensional bearing-only coordinates. And the track initiation of threatening targets is implemented in the shortest time based on a modified heuristic algorithm using these rules. Then, other target tracks are initialized based on a logic-based algorithm in two dimensional bearing-only coordinates as a supplement. At last, by deeply studying different point-track association algorithms and comparing the association effect between JPDA and NNDA in bearingonly coordinate, suitable angle-measurement based association algorithm is presented. As the results, the confirming efficiency of the bearing-only measurements is improved and false tracking with the dense clutter is limited. The application of this algorithm has effectively resolved the track association problem of the bearing-only tracking using a single passive sensor. The application of the proposed approach in a simulation system proves its effectiveness and practicability.

Study of Algorithmic and Architectural Characteristics of Gaussian Particle Filters

In this paper, we analyze algorithmic and architectural characteristics of a class of particle filters known as Gaussian Particle Filters (GPFs). GPFs approximate the posterior density of the unknowns with a Gaussian distribution which limits the scope of their applications in comparison with the universally applied sample-importance resampling filters (SIRFs) but allows for their implementation without the classical resampling procedure. Since there is no need for resampling, we propose a modified GPF algorithm that is suitable for parallel hardware realization. Based on the new algorithm, we propose an efficient parallel and pipelined architecture for GPF that is superior to similar architectures for SIRF in the sense that it requires no memories for storing particles and it has very low amount of data exchange through the communication network. We analyze the GPF on the bearings-only tracking problem and the results are compared with results obtained by SIRF in terms of computational complexity, potential throughput, and hardware energy. We consider implementation on FPGAs and we perform detailed comparison of the GPF and SIRF algorithms implemented in different ways on this platform. GPFs that are implemented in parallel pipelined fashion on FPGAs can support higher sampling rates than SIRFs and as such they might be a more suitable candidate for real-time applications.

Track Processing Approach for Bearing-Only Target Tracking

This paper mainly studies angle-measurement based track processing approach to overcome the existing problems in the applications of traditional approaches for bearing-only target locating and tracking system. First, this paper gives suited data association algorithms including track initiation and point-track association. Moreover, a new tracking filtering association gate method is presented through analysis of the target motion characteristics in polar coordinates for improving bearing-only measurement confirming efficiency of real target and limiting false track overextension with the dense clutter. Then, by analyzing the feasibility of using multi-model technology, the IMM is adopt as filtering algorithm to solve existing problem in bearing-only tracking for complicated target motion in two dimensional angle plane. As the results, the two dimensional bearing-only tracking accuracy of real target is improved and false tracking is greatly limited. Moreover, computation cost of IMM is analyzed in view of the real-time demand of bearing- only tracking. Finally, this paper gives some concrete summary of multi-model choosing principle. The application of the proposed approach in a simulation system proves its effectiveness and practicability.

Optimal Orbital Rendezvous Maneuvering for Angles-Only Navigation

A NGLES-ONLY navigation has great potential for orbital rendezvous, satellite formation flight, and other relative motion applications, but is often discarded because of its inherent and misunderstood limitation in determining range. A common consensus in the published literature, regardless of the application, is that maneuvers are generally required to obtain target observability when using only anglemeasurements [1–6]. For the bearings-only tracking problem, Nardone and Aidala [7] and Hepner and Geering [8] also showed that certain types of maneuvers, particularly those maneuvers that cause position changes that lie along the instantaneous bearing lines associated with a constant velocity trajectory, do not necessarily guarantee observability. If certain maneuvers produce observability and others do not, then the next natural step that has received considerable attention is to determinewhichmaneuvers and trajectories are optimal in maximizing observability [9–16]. Despite these significant advances in deriving optimal maneuvers for the bearings-only tracking problem, these results are typically established on the premise of a constant moving target, an assumption valid for many naval applications that motivated the earlier research efforts but not applicable to orbital rendezvous. Although the influence of maneuvering for angles-only navigation has been considered for orbital rendezvous [17–19], there does not exist in the published literature derivations of performing optimal maneuvers to maximize observability. This Note develops the mathematical framework to analytically derive optimal maneuvers for angles-only navigation using a previously derived observability criteria [20–22]. The concept of having levels or degrees of observability is formally defined as a function of the measurement error and then used to form the theoretical foundation to derive optimal maneuvers that maximize the observability of the relative state. A simple yet common orbital rendezvous example is provided to illustrate the possibility of designing optimal orbital rendezvous maneuvers for angles-only navigation. Although the topic is introduced in the context of orbital rendezvous, the fundamental concepts can be applied to any linear dynamic system (and extended to nonlinear systems) for which the relative position and velocity are estimated using only angular measurements.

A Low-Power Memory-Efficient Resampling Architecture for Particle Filters

In this paper, we propose a compact threshold-based resampling algorithm and architecture for efficient hardware implementation of particle filters (PFs). By using a simple threshold-based scheme, this resampling algorithm can reduce the complexity of hardware implementation and power consumption. Simulation results indicate that this algorithm has approximately equal performance with the traditional systematic resampling (SR) algorithm when the root-mean-square error (RMSE) and lost track are considered. Experimental comparison of the proposed hardware architecture with those based on the SR and the residual systematic resampling (RSR) algorithms was conducted on a Xilinx Virtex-II Pro field programmable gate array (FPGA) platform in the bearings-only tracking context, and the results establish the superiority of the proposed architecture in terms of high memory efficiency, low power consumption, and low latency.