Estimation and Tracking of a Ballistic Target Using Sequential Importance Sampling Method

In order to increase the tracking performance of ballistic targets, various estimation algorithms have been implemented in the literature. Extended Kalman Filter is one of the most widely used estimation algorithm which uses the nonlinear system and measurement models and linearization methods to estimate the state and state covariances. In the first part of this study, a ballistic coefficient state is augmented to the position and velocity states in an Extended Kalman Filter in order to estimate the target kinematics and identify the target ballistics. Since the observability of the ballistic coefficient state is weak, sufficient accuracy in the impact point estimation can not be obtained. In the proposed method, different sets of target ballistic coefficients with respect to varying target speed is known as a priori information. Using this a priori information, a multiple model Extended Kalman Filter which estimates only the kinematic states is utilized and aerodynamic forces acting on the ballistic target is accounted for in the state propagation. Each of the multiple model filters uses different a priori ballistic information set and likelhood of each filter is calculted in order to select one of the model and predict the impact point of the ballistic target.

Some aspects of detection and tracking of ballistic targets are analysed in this paper. In particular, the RCS model versus aspect angle is obtained for a notional target starting from its CAD model. Subsequently, the kinematic model of the ballistic target is derived; it includes the main forces acting on it, namely, the thrust, the drag and the gravity. On the basis of these two models it is possible to determine the detection probability of a notional L-band radar during the target flight and to build up an interactive multiple model (IMM) for target tracking. The performance evaluation of the design IMM tracking algorithm is obtained via Monte Carlo simulation. In particular, highly manoeuvring aircraft and ballistic targets in the boost phase are used to check the capability of the IMM.

This paper presents mathematical procedures to calculate the Cramer-Rao lower bound (CRLB) for a target track obtained by fusing two tracks given by two interactive multiple model (IMM) trackers filtering the plots received by two radars. The target under tracking is a ballistic target (BT) in reentry phase and it is assumed that the two sensors could have a detection probabilities Pd less than 1. Accurate BT tracking is required for: (i) impact point prediction, (ii) support to the kill assessment, and (iii) threat classification. Note that, to improve the performance, the method can be extended to the fusion of more than two sensor tracks. The paper is organized as follows: the problem is introduced in section 1; section 2 briefly recalls the models of BT dynamic and of the radar measures. Section 3 presents the tracking algorithm based on the IMM approach; section 4 contains the description of the CRLB evaluation problem and section 5 the results achieved in comparing the fusion of two BT tracks (each track is obtained from the IMM algorithm described in section 4) with the CRLB; Monte Carlo simulations is also used to quantify the fused track accuracies. Section 6 is pertinent to conclusions and follows on of the activity while references are reported in section 7.

The performance of ballistic target interception is critically dependent on the performance of the target state estimation. The estimation performance then strongly depends on the accuracy of the measurement model. The Gaussian uncertainty distribution has commonly been used for representing the statistical properties of sensor noise, due to its mathematical simplicity and effectiveness. However, seeker sensor measurements are often corrupted by glint noise which is highly non-Gaussian, and conventional Gaussian filtering algorithms are known to show unsatisfactory performance in the presence of glint noise. This research proposes the use of a particle filter for ballistic target tracking in a glint noise environment. The target tracking performance of the particle filter is compared with that of the extended Kalman filter.

A particle filter deals with state estimation problem or nonlinear models with non-Gaussian noise. In the framework of a particle filter, a resampling scheme is used to decrease the degeneracy phenomenon, however it also introduces the problem or sample impoverishment, which can be reduced by using the Markov Chain Monte Carlo (MCMC) method, such as the Metropolis-Hastings (M-H) algorithm. However, there are many possible choices within the family of M-H algorithms, and the performance of particle filters with MCMC moves is closely related to the choice of the M-H algorithm. This paper discusses the implementation of a particle filter with various M-H algorithms. A numerical example is presented, and the simulation results are given for discussion.

Particle filter methods are used in the estimation and tracking of the objects for non-linear and non-gaussian noise conditions. In this paper work the object estimation using partial resampling methods are discussed. On using partial resampling method resampling becomes faster. The performance of particle filter with partial resampling scheme is analyzed using the state estima-tion of a simple pendulum.

To deal with the problem of ballistic reentry target trajectory tracking, a novel particle filter algorithm is proposed to mitigate the particle degeneracy. It can eliminate the inefficient particles by judging the degree of particle degradation at each time and generates new particles based on the estimation state values and their covariance according to the degeneracy ratio of particles. Compared with Standard Particle Filter (SPF) algorithm and Unscented Particle Filter (UPF) algorithm, simulation results show that the proposed algorithm can achieve better tracking performance with lower computational burden for the trajectory reentry target tracking model. Especially in the case of ballistic target maneuver, the performance stability of the proposed algorithm is even more significant.

Wireless Sensor Network (WSN) is a new technology integrated with communications, embedded technology, and network functions; having capability of real-time collecting, communicating, and sensing, for which dynamic target locating and tracking is its critical task, as well as a basic element in its commercial and military application such as battlefield information accessing and traffic monitoring. Sensor target tracking is the technology of target location estimate based on measurements from corresponding sensors. An inaccurate estimated location may very easily lead to target tracking failure which reduces the reliability and stability of the target tracking [1]. Experts and scholars have done a lot of researches to solve problems exited in wireless sensor target tracking, and many new tracking algorithms have been proposed, among which tracking algorithms such as target contrail-fitting, linear prediction, Kalman filter, unscented Kalman filter(UKF) and particle filter[2] are most common applied. Sikdar, with his partners, has proposed target location tracking algorithm based on linear sensor which is proved better than conventional contrail fitting algorithm in its effects. Zhang Xiaoping , with his partners, has proposed WSN target tracking algorithm through modeling for quadratic polynomial motions which has improved target tracking accuracy[3]. However, there is a problem in common: all the algorithms above assume the tracking target contrail-fittings being in linear motion, while the actual contrail fitting is of uncertainty and variability, and the estimated accuracy can hardly be improved after being to a certain level. In this condition, the tracking error of the above algorithms can be greater [4]. Kalman filter algorithm can be applied for weakly nonlinear models, but for strongly nonlinear models, Unscented Kalman Filter algorithm can be better. Kalman filter work well in cases based on model-linear and Gaussian noise, thus its estimated accuracy is not that ideal [5, 6]. Particle filter algorithm is based on optimal regression Bayesian filtering algorithm in Monte Carlo simulation, which can accurately estimate the any distribution state with only a small amount of mobile anchor nodes. PF algorithm has distinguished advantages in processing non-linear, non-Gaussian cases [7]. However, in PF application process after several iterations, diversified degradation of the particles will occur, which is likely to lead a target tracking loss, thus further affect WSN target tracking accuracy [8]. In order to solve the diversified degradation of the particles in Particle Filter algorithm, this paper Research on the Target Tracking Algorithm for Wireless Sensor Network Based on Improved Particle Filter Liang Peng,Xinhan Huang, Li He

In radar tracking guidance, intelligent video surveillance, robot vision system, the parameters of position and velocity and steering state often need to get the target of interest, based on the motion characteristics of the target and further to control it. The filtering method is used to estimate the desired state parameters based on the functional relationship between the measured values and the state variables. This method is also called target tracking technique. At present, there are many target tracking technologies for different systems, but there is a big gap between the robustness and real-time requirements of the actual system. In order to solve the problem of large computation and bad real-time performance of Particle Filters, a real-time target tracking algorithm based on nonlinear mean shift and Particle Filters is proposed. The distribution of particles is closer to the actual posterior distribution by selecting the important probability density function. Furthermore, the nonlinear mean shift algorithm is integrated into the Particle Filters, so that the particles are further clustered into the real distribution. Finally, the algorithm is applied in the traffic video surveillance, and the effective tracking of the target motorcycle and vehicle is realized.

State and parameter estimation of nonlinear stochastic systems by evolution strategies based particle filter

In this paper, a novel multiple objects detection and tracking approach based on support vector machine and particle filter is proposed to track players in broadcast sports video. Compared with previous work, the contributions of this paper are focused on three aspects. First, an improved particle filter called SVR particle filter is proposed as the player tracker by integrating support vector regression (SVR) into sequential Monte Carlo framework. SVR particle filter enhances the performance of classical particle filter with small sample set and improves the efficiency of tracking system. Second, support vector classification combined with playfield segmentation is employed to automatically detect the players in sports video as the initialization of tracker. Third, a unified framework for automatic object detection and tracking is proposed based on support vector machine and particle filter. The experimental results are encouraging and demonstrate that our approach is effective

This paper presents an hybridization of particle filter and local search algorithms, called local search particle filter (LSPF), and its application to human-computer interaction. The proposed algorithm combines both sequential Monte Carlo (particle filter - PF) and local search methods to achieve an accurate real-time hand tracking. The system allows to control different mouse actions through a reduced set of hand movements and gestures. Hand are segmented using a skin-color model based on explicit RGB region definition. The proposed hybrid tracking method increases the performance of general particle filter. It also improves the quality of the hand tracking task (the standard deviation between hand spatial positions for LSPF is reduced a 75% with respect to the PF algorithm). More precisely, a local search enhances a hand-simulated mouse cursor to smoothly move and thus recognize gestures for performing their associate actions.

For state estimation problem, particle filter is generally used to construct the posterior probability density function by a set of particles, which is regarded as a solution to state estimation. Many techniques have been developed to improve performance of particle filter, at the cost of largely increased computational burden for each particle. In this paper, we propose a post-resampling based particle filter. The modified particle filter is capable of accurately representing the posterior probability density function through properly sampling particles. We applied the proposed particle filter to the classic bearings-only tracking problem. Simulation results showed that our modified particle filter had superior performance and reasonably computational cost, compared with the general approaches. It may provide a promising alternative to the existent particle filters.

Improved Particle Filter for Target Tracing Application based on ChinaGrid

Data assimilation is the process of estimating the state of dynamic systems (linear or nonlinear, Gaussian or non-Gaussian) as accurately as possible from noisy observational data. Although the Three Dimensional Variational (3D-VAR) methods, Four Dimensional Variational (4D-VAR) methods and Ensemble Kalman filter (EnKF) methods are widely used and effective for linear and Gaussian dynamics, new methods of data assimilation are required for the general situation, that is, nonlinear non-Gaussian dynamics. General Bayesian recursive estimation theory is reviewed in this thesis. The Bayesian estimation approach provides a rather general and powerful framework for handling nonlinear, non-Gaussian, as well as linear, Gaussian estimation problems. Despite a general solution to the nonlinear estimation problem, there is no closed-form solution in the general case. Therefore, approximate techniques have to be employed. In this thesis, the sequential Monte Carlo (SMC) methods, commonly referred to as the particle filter, is presented to tackle non-linear, non-Gaussian estimation problems. In this thesis, we use the SMC methods only for the nonlinear state estimation problem, however, it can also be used for the nonlinear parameter estimation problem. In order to demonstrate the new methods in the general nonlinear non-Gaussian case, we compare Sequential Monte Carlo (SMC) methods with the Ensemble Kalman Filter (EnKF) by performing data assimilation in nonlinear and non-Gaussian dynamic systems. The models used in this study are referred to as state-space models. The Lorenz 1963 and 1966 models serve as test beds for examining the properties of these assimilation methods when used in highly nonlinear dynamics. The application of Sequential Monte Carlo methods to different fixed parameters in dynamic models is considered. Four different scenarios in the Lorenz 1063 [sic] model and three different scenarios in the Lorenz 1996 model are designed in this study for both the SMC methods and EnKF method with different filter siz