Target State Space Research Articles

Sequential Monte Carlo with Adaptive Lookahead Support for Improved Importance Sampling

The sequential Monte Carlo, also called the Bayesian particle filter, approximates a posterior probability density function of a latent target state from noisy sensor measurements using a set of Monte Carlo samples. These samples are predicted using an importance density function and then updated using the Bayes’s rule. The updated samples and their corresponding weights provide an estimate of the latent state. The said filtering process is iterated over time for tracking dynamic target states. It is critical to have enough particles in regions of the target state space that contribute to the posterior. The auxiliary and the improved auxiliary particle filters accomplish this by a process that mimics drawing from an importance density that leverages the incoming observation into the sampling step. However these filters are known to fail when the sensor measurements are highly informative and the diffusion over the state transition is large. This paper presents an improvement to the auxiliary particle filter by taking two support points that act as limits in a univariate state space within which particles are samples. The choice of the limits is adaptive. The proposed method is successfully tested using a nonlinear model using simulations.

NEURAL NETWORK SUPPORT FOR AUTOMATION OF OBJECT CONTROL WITH MULTIFACTORIAL INPUT UNDER CONDITIONS OF UNCERTAINTY

High dimension of the factors, their noisiness, subjectivity of the human factor breed high uncertainty in the implementation of effective monitoring and productive management in the areas of production and consumption, and hinder the optimal decisions making. In these conditions, it is appropriate to apply intelligent data analysis procedures based on artificial neural networks. Purpose of the study is to substantiate the technology for constructing of effective neural network models for automatic assessment of the object states and their control by finding the optimal values of input factors based on the analysis of the initial set of retrospective data. The desired product is set of neural network models for simultaneous assessment of the current object states and the calculation of the input factors values that ensure the achievement of the required objective function indicators. To automate the processes of recognizing the states of the study object and adapting the factors that bring the current state to the target one, a functional dependence of the states and factors is found based on forced learning of a synthesized models ensemble. The proposed technology and technical tools make it possible to automate the processes of classifying the states of the study objects, adapt the input factors to the target states, and evaluate the quality by model testing. The practical significance of the study results is in the creation of a universal toolkit for a whole class of objects in the tasks of automatic state classification and search for input factors space that is adequate to the target state space. Functionally, the ensemble of trained models can be implemented as a data analysis software unit in the format of two subsystems: for recognizing the states of the study object and adapting input factors to target states. Automation of the state classifying tasks and adapting the input set in the proposed technology that is performed on the basis of standard technical data analysis packages, makes it possible to increase the efficiency of decision-making and reduce financial costs in the implementation of industrial and commercial projects.

Label GM-PHD Filter Based on Threshold Separation Clustering.

Gaussian mixture probability hypothesis density (GM-PHD) filtering based on random finite set (RFS) is an effective method to deal with multi-target tracking (MTT). However, the traditional GM-PHD filter cannot form a continuous track in the tracking process, and it is easy to produce a large number of redundant invalid likelihood functions in a dense clutter environment, which reduces the computational efficiency and affects the update result of target probability hypothesis density, resulting in excessive tracking error. Therefore, based on the GM-PHD filter framework, the target state space is extended to a higher dimension. By adding a label set, each Gaussian component is assigned a label, and the label is merged in the pruning and merging step to increase the merging threshold to reduce the Gaussian component generated by dense clutter update, which reduces the computation in the next prediction and update. After pruning and merging, the Gaussian components are further clustered and optimized by threshold separation clustering, thus as to improve the tracking performance of the filter and finally realizing the accurate formation of multi-target tracks in a dense clutter environment. Simulation results show that the proposed algorithm can form a continuous and reliable track in dense clutter environment and has good tracking performance and computational efficiency.

Unscented Particle Filter Algorithm Based on Divide-and-Conquer Sampling for Target Tracking

Unscented particle filter (UPF) struggles to completely cover the target state space when handling the maneuvering target tracing problem, and the tracking performance can be affected by the low sample diversity and algorithm redundancy. In order to solve this problem, the method of divide-and-conquer sampling is applied to the UPF tracking algorithm. By decomposing the state space, the descending dimension processing of the target maneuver is realized. When dealing with the maneuvering target, particles are sampled separately in each subspace, which directly prevents particles from degeneracy. Experiments and a comparative analysis were carried out to comprehensively analyze the performance of the divide-and-conquer sampling unscented particle filter (DCS-UPF). The simulation result demonstrates that the proposed algorithm can improve the diversity of particles and obtain higher tracking accuracy in less time than the particle swarm algorithm and intelligent adaptive filtering algorithm. This algorithm can be used in complex maneuvering conditions.

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.

Cramer–Rao type bounds for sparsity-aware multi-sensor multi-target tracking

Conventionally, sparsity-aware multi-sensor multi-target tracking (MTT) algorithms comprise a two-step architecture that cascades group sparse reconstruction and MTT algorithms. The group sparse reconstruction algorithm exploits the apriori information that the measurements across multiple sensors share a common sparse support in a discretized target state space and provides a computationally efficient technique for centralized multi-sensor information fusion. In the succeeding step, the MTT filter performs the data association, compensates for the missed detections, removes the clutter components, and improves the accuracy of multi-target state estimates according to the pre-defined target dynamic model. In a recent work, a novel technique was proposed for sparsity-aware multi-sensor MTT that deploys a recursive feedback mechanism such that the group sparse reconstruction algorithm also benefits from the apriori knowledge about the target dynamics. As such, it is of significant interest to compare the tracking performance of these methods to the optimal multi-sensor MTT solution, with and without considering the missing samples. In this paper, we analytically evaluate the Cramer-Rao type performance bounds for these two schemes for sparsity-aware MTT algorithms and show that the recursive learning structure outperforms the conventional approach, when the measurement vectors are corrupted by missing samples and additive noise.

Dynamic programming track‐before‐detect algorithm for radar target detection based on polynomial time series prediction

An improved dynamic programming track-before-detect (DP-TBD) algorithm is proposed in this study. A new relaxed DP-TBD test statistic containing a term of state transition probability is derived. The state transition probability is designed according to the one-step prediction of the target state. An asymptotic and recursive solution is developed to obtain the state prediction by the polynomial time series model under the framework of weighted least squares. The impact of the weight parameter on the performance of the proposed algorithm is also investigated. The proposed algorithm can efficiently integrate the energy back-scattered along the admissible target trajectory in that the designed state transition probability enables the relaxed test statistic to distinguish real targets from the false ones more effectively. The prediction needs no priori information of target state space model and can be embedded in the recursion of the DP-TBD. Numerical simulations are provided to assess and compare the performance of the proposed algorithm. It turns out that the proposed algorithm has better detection and tracking performance than the basic one and is resilient to various target motion forms.

Aerial Vehicle Search-Path Optimization: A Novel Method for Emergency Operations

This paper presents a novel search-path optimization method for moving target search by an aerial vehicle, applicable to realistically sized search areas. For such missions, long endurance vehicles are needed, which are usually fixed-winged. The proposed method accounts for flight kinematics of fixed-wing and rotary-wing aerial vehicles. It additionally accounts for movements of the target, considerably increasing complexity of search-path optimization, compared to a static target. The objective is to maximize the probability to detect a conditionally deterministic moving target within a given time period. We propose a first K-step-lookahead planning method that takes flight kinematic constraints into account and in which the target and platform state space are heterogeneous. It consists of a binary integer linear program that yields a physically feasible search-path, while maximizing the probability of detection. It is based on the Max-K-Coverage problem, as it selects K waypoints while maximizing the probability that a target is within the field of view of a platform at one of these waypoints. This K-step-lookahead planning method is embedded in an iterative framework, where the probability of overlooking a target is fed back to the controller after observations are made. Simulations show the applicability and effectiveness of this method.

Box-Particle Implementation and Comparison of Cardinalized Probability Hypothesis Density Filter

This paper develops a box-particle implementa- tion of cardinalized probability hypothesis density filter to track multiple targets and estimate the unknown number of targets. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. In box-particle filter the huge number of traditional point observations is instead by a remarkably reduced number of interval measurements. It decreases the number of particles significantly and reduces the runtime considerably. The proposed algorithm based on box-particle is able to reach a similar accuracy to a Sequential Monte Carlo cardinalized probability hy- pothesis density (SMC-CPHD) filter with much less computational costs. Not only does it propagates the PHD, but also propagates the cardinality distribution of target number. Therefore, it generates more accurate and stable instantaneous estimates of target number as well as target state than the box-particle probability hypothesis density (BP-PHD) filter does especially in dense clutter environ- ment. Comparison and analysis based on the simulations in different probability of detection and different clutter rate have been done. The effectiveness and reliability of the proposed algorithm are verified by the simulation results.

A measurement-driven adaptive probability hypothesis density filter for multitarget tracking

This paper studies the dynamic estimation problem for multitarget tracking. A novel gating strategy that is based on the measurement likelihood of the target state space is proposed to improve the overall effectiveness of the probability hypothesis density (PHD) filter. Firstly, a measurement-driven mechanism based on this gating technique is designed to classify the measurements. In this mechanism, only the measurements for the existing targets are considered in the update step of the existing targets while the measurements of newborn targets are used for exploring newborn targets. Secondly, the gating strategy enables the development of a heuristic state estimation algorithm when sequential Monte Carlo (SMC) implementation of the PHD filter is investigated, where the measurements are used to drive the particle clustering within the space gate. The resulting PHD filter can achieve a more robust and accurate estimation of the existing targets by reducing the interference from clutter. Moreover, the target birth intensity can be adaptive to detect newborn targets, which is in accordance with the birth measurements. Simulation results demonstrate the computational efficiency and tracking performance of the proposed algorithm.

Multiple-model Rao-Blackwellized particle CPHD filter for multitarget tracking

To overcome high computational complexity and imprecise target estimates in existing multitarget tracking (MMT), a multiple-model Rao-Blackwellized particle cardinalized probability hypothesis density (CPHD) filter is presented in this paper. First, we derive the multiple-model CPHD filter to model maneuvering multitarget with uncertainties of each individual state and then make full use of the Rao-Blackwellization to divide the target state space into the nonlinear and linear parts to reduce space dimension. Furthermore, the nonlinear state is estimated by the particle filter with the sequential Monte Carlo method, and the linear part is predicted by the Kalman filter with the information embedded in the estimated nonlinear state. With respect to the tracking precision, we find that the proposed filter has small Wasserstein distance by eliminating unstable target number-estimates. Especially, the computational cost is significantly reduced due to the saved particles. Finally, the illustrative numerical studies are provided to demonstrate the tracking performance of the proposed filter is superior.

Intensity filters on discrete spaces

Multitarget tracking problems on discrete target state and sensor measurement spaces arise when measurements are grouped into histograms to reduce data volume and when target state space is quantized, or gridded. In such problems more than one target can occupy the same discrete target state, and any number of measurements can be observed in the histogram cells. The joint probability generating function (PGF) for the discrete problem is derived. The generating function of the Bayes posterior is derived by differentiating the joint generating function. Two summary statistics of the Bayes posterior process are given: the distribution of the total number of targets and the intensity function, or expected number of targets in each discrete state. Intensity filters are obtained by assuming these summary statistics are sufficient statistics. Several limiting forms are derived for small cell size.

A new multiple extended target tracking algorithm using PHD filter

A new multiple extended target tracking algorithm using the probability hypothesis density (PHD) filter is proposed in our study, to solve problems on tracking performance degradation of the extended target PHD (ET-PHD) filter under the nonlinear conditions and its intolerable computational requirement. It is noted that with the current Gaussian mixture implement of ET-PHD filter satisfying tracking performance could only be obtained under linear and Gaussian conditions. To extend the application of ET-PHD filter for nonlinear models, our study has derived a particle implement of ET-PHD (ET-P-PHD) filter. Our study finds that the main factors influencing the computational complexity of the ET-P-PHD filter are the partition number of measurement set and the calculation of non-negative coefficients of cells in partitions. With the pretreatment of measurements and application of a new K-means clustering based measurement set partition method, we have successfully decreased the partition number. In addition, a gating method for target state space, which is based on likelihood relationship between target state and measurement, is proposed to simplify the calculation of non-negative coefficients. Simulation results show that the algorithms proposed by our study could satisfyingly deal with multiple extended target tracking issues under nonlinear conditions, and lead to significantly lower computational complexity with tiny effect on tracking performance.

Evidence theory-based mixture particle filter for joint detection and tracking of multiple targets

In this study, a novel algorithm named evidence theory-based mixture particle filter is proposed for joint detection and tracking for a varying number of targets in a cluttered environment. The posterior distribution of multiple target state considered in single target state space is a multi-modal distribution with each mode corresponding to either a target or clutter. A general global posterior distribution is adopted, which consists of existing components propagated from the previous time step, and new components generated at the current time step to capture the newly appeared targets. An evidence theory-based framework is utilised to determine the structure of the global posterior distribution. A set of masses are used to describe the possible kinds of nature for each mixture component (e.g. it is from a target, clutter or undetermined at the current time step). The masses are then transformed to a set of Pignistic probabilities, based on which a decision process is utilised to determine the nature for each mixture component. The decision on the nature for each component (target or clutter) is made until sufficient information arrives, which avoids the misjudgement because of insufficient information efficiently.

Bernoulli Particle/Box-Particle Filters for Detection and Tracking in the Presence of Triple Measurement Uncertainty

This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler's framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient.

Cramer-Rao Bounds for Target Tracking Problems Involving Colored Measurement Noise

Recursive formulas are derived for computing the Cramer-Rao lower bound on the error covariance matrix associated with estimating the state vector of a moving target from a sequence of biased and temporally correlated measurements. The discussion is limited to deterministic motion with no process noise. Furthermore, the nonlinear mapping from the target state space to the observation space is assumed to be corrupted by additive noise. When the measurement noise process becomes temporally decorrelated, the recursive relation for computing the Cramer-Rao lower bound reduces to that originally obtained by Taylor [1]. Specific noise models are examined, and results are illustrated using an example. For the special case of the random walk process, it is shown that the recursive formula for the Cram?Rao lower bound reduces to the error covariance propagation equations of the prewhitening filter of Bryson and Henrikson [2].

Error-space estimate method for generalized synergic target tracking

To improve the tracking accuracy and stability of an optic-electronic target tracking system, the concept of generalized synergic target and an algorithm named error-space estimate method is presented. In this algorithm, the motion of target is described by guide data and guide errors, and then the maneuver of the target is separated into guide data and guide errors to reduce the maneuver level. Then state estimate is implemented in target state-space and error-space respectively, and the prediction data of target position are acquired by synthesizing the filtering data from target state-space according to kinematic model and the prediction data from errorspace according to guide error model. Differing from typical multi-model method, the kinematic and guide error models work concurrently rather than switch between models. Experiment results show that the performance of the algorithm is better than Kalman filter and strong tracking filter at the same maneuver level.

Full-field likelihood ratio detection for multistatic sensors in uncertain environments

As small networked sonobuoys become cheaper and more viable in the submarine warfare community, there is a growing demand for techniques to automatically process detection data from dense fields containing O(100) or more sonobuoys. The presentation describes a Bayesian framework for the incoherent integration of automatic detections from these dense sonobuoy fields. This framework recursively integrates likelihood ratio functions to form a cumulative posterior over a target state space. To be most effective, these methods exploit either empirical sensor performance models or physics-based signal excess sensor performance models. The presentation describes the use of each type of performance model and presents one method for handling uncertainties associated with signal excess predictions. The method presented starts with a prior on a set of possible environmental conditions. When a target is present in the detection data, the cumulative likelihood ratio will peak in the environment most consistent with the true environment.