Ballistic Object Research Articles

Zonotopic Distributed Fusion Over Binary Sensor Networks With Bit Rate Allocation: A Coding-Decoding Approach.

In this article, the zonotopic distributed fusion estimation problem is investigated for a class of general nonlinear systems over binary sensor networks subject to unknown-but-bounded (UBB) noises. The network communication from nodes to the fusion center is confined to the limited bit rate. To alleviate the impact from less measurement information of the binary sensor, a modified innovation is constructed to improve the estimation accuracy. Then, a novel coding-decoding approach is proposed to ensure that the decoder has the ability to decode information from each node. Based on the matrix weighting fusion method, a distributed fusion algorithm is put forward under the zonotopic set-membership filtering framework, and the F -radius of the local zonotopic sets are derived and minimized by selecting the filtering gain parameters. Moreover, the bit rate allocation scheme and the weighting coefficients are determined by resolving two optimization problems. In addition, a sufficient condition is established to guarantee the uniform boundedness of the F -radius of the fused zonopotic. Finally, the ballistic object tracking systems is utilized to illustrate the availability of the presented algorithm.

Jointly Distributed Filtering Based on Generalized Maximum Correntropy Criterion: Memory-Based Event-Triggered Cases

This article addresses jointly distributed entropy filtering issues based on the generalized maximum correntropy criterion (GMCC) for discrete-time stochastic parameter systems with fault and non-Gaussian noise effects. By taking current and historical triggered information, a memory-based event-triggered scheme with a time-varying threshold is put forward to govern the network communication. According to the constructed jointly distributed entropy filter with a two-step form, the upper bounds of the filtering error covariance matrices are derived and an ideal filter gain is obtained to maximize GMCC. Furthermore, an accessible gain is received via fixed-point iterative rules and the corresponding convergence is disclosed in theory. Finally, an application of the proposed distributed filter in ballistic object tracking is provided to show its effectiveness under non-Gaussian environments.

Feline urethral obstruction secondary to a ballistic foreign object

AbstractAn 8‐year‐old, male neutered, domestic shorthair cat was presented for stranguria, abnormal behaviour and azotaemia. A diagnosis of urethral obstruction was made based on a firm and painful urinary bladder that could not be expressed. Diagnostic workup, inclusive of bloodwork, urinalysis, urine culture and abdominal radiographs, revealed an intraluminal ballistic foreign object. A urinary tract infection was also diagnosed, suspected to be secondary to the ballistic foreign object. A cystotomy was performed and a metallic pellet was removed from the bladder lumen, with no overt signs of a penetrating injury appreciated on evaluation of the body wall and urinary bladder. Clinical signs resolved after surgical intervention, with normal urination appreciated at home after discharge. Urinary obstruction and infection secondary to an intraluminal foreign body is an unusual aetiology for a common feline presenting complaint, and diagnostic imaging should be strongly considered for any patient with a urinary obstruction.

Nonlinear robust estimation for tracking of ballistic target using risk sensitive cubature quadrature Kalman filter

In this paper, a risk sensitive estimator based on cubature quadrature Kalman filter is formulated and applied for tracking a ballistic object during its re-entry phase. The formulated algorithm is named here as risk sensitive cubature quadrature Kalman filter. The process model and measurement model for two dimensional ballistic target motion is described. The expression for measurement noise covariance is derived for Cartesian coordinate from polar coordinate. Also expression for initial error covariance is derived. The performance of the risk sensitive cubature quadrature Kalman filter is compared with the cubature quadrature Kalman Filter in terms of root mean square error. The simulation results reveal that for wrongly modeled process noise parameter, the risk sensitive filter performs better than their risk neutral counterpart. Moreover, risk sensitive cubature quadrature Kalman filter performs better than risk sensitive cubature Kalman filter. Since expression for measurement noise covariance as well as initial error covariance for two dimensional ballistic target motion is derived, other Gaussian filters may also be applied for tracking of ballistic objects.Article HighlightsThe process model for two dimensional ballistic target motion is described comprehensively.The expression for measurement noise covariance matrix for linear measurement model is derived for Cartesian coordinate from polar coordinate.The expression for initial error covariance matrix for the filter initialized from the first two measurements is derived.Risk sensitive filter based on cubature quadrature Kalman filter is applied for tracking of two dimensional ballistic target motion and improvement in performance over its risk neutral counterpart is found.Improvement in performance of risk sensitive filter based on cubature quadrature Kalman filter over risk sensitive filter based on cubature Kalman filter is found.

Ballistic Object Trajectory and Impact Point Estimation in the Reentry Phase From a Moving Passive Sensor

This article considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2-D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This article shows that the 3-D trajectory in the reentry phase can be obtained by estimating the target’s state at the end of the observation interval. The 7-d motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed, and 3-D position) is estimated by the maximum likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher information matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer–Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method.

3D Visualization of Objects in Heavy Scattering Media by Using Wavelet Peplography

In this paper, we propose three-dimensional(3D) visualization of objects in heavy scattering media by using peplography and wavelet transform. Conventional haze removal techniques can remove the light haze in the image by using various image processing algorithms or machine learning techniques. However, they may not provide a clear image under heavy scattering media. On the other hand, peplography can visualize the object by detecting ballistic object photons from heavy scattering media. Then, 3D image can be generated by integral imaging. However, it may not visualize 3D object information accurately because of the noise photons from scattering media. Therefore, the image quality for 3D object visualization may be degraded. To solve this problem, we use the discrete wavelet transform in peplography. It can detect the object photon signals from the scattering media and enhance 3D image contrast ratio by using a specific coefficient threshold technique. To prove our method, we carry out the optical experiments and compare with conventional haze removal method and peplography by using various image quality metrics such as correlation, structural similarity, and peak signal to noise ratio.

СХЕМНЫЕ РЕШЕНИЯ, СТРУКТУРА И СВОЙСТВА ГЕТЕРОГЕННЫХ МАТЕРИАЛОВ

Currently, heterogeneous materials based on titanium and aluminum alloys are widely used as promising armor materials. When a ballistic object is exposed to the armor material, brittle cracks that occur at the contact point spread in such a way that composite material is in state of decay both deep into and along the interlayer boundaries of the joint, while there is a violation of the composite structure and loss of the mechanical strength of the armor element. In this regard, the task of developing new reinforcement schemes for composite armor is urgent. One of the most promising technologies in the field of creating and developing new composite non-metallic armor materials is explosion bonding. The authors of the work proposed a new scheme for reinforcing a heterogeneous metal material by means of explosion bonding, which uses internal perforated reinforcing layers that serve as elements preventing the development of brittle fracture at the point of ballistic contact. To increase the efficiency of the destruction of a ballistic object in the composite structure, the authors proposed the formation of highly solid intermetallic compounds at the boundary between the metal of the base of a viscous metal matrix and the reinforcing element by subsequent heat treatment of the material. The conducted micro-X-ray spectral analysis of intermetallic compounds showed their correspondence to the chemical compound α-titanium (TiAl3). Comparison of the obtained level of physical and mechanical properties of the developed heterogeneous armored material with analogues suggests that the expected level of the composite protection class against small arms is in the range from Br4 to Br5 according to GOST R 50963-96 with an armor thickness of 40 to 60 mm, which makes it possible to reduce the weight of armored vehicles significantly and, as a result, increase its tactical and technical characteristics.

Black-Box Expectation–Maximization Algorithm for Estimating Latent States of High-Speed Vehicles

Tracking an object in a noisy environment is difficult, especially when unknown parameters affect the object’s behavior. In the case of a high-speed ballistic object, its trajectory is affected by changes in atmospheric conditions as well as various parameters of the object itself. To filter these latent factors of the dynamics model, this paper proposes a black-box expectation–maximization algorithm to estimate the latent parameters and enhance the accuracy of object tracking. The expectation step involves calculating the likelihood of observations through extended Kalman smoothing, which reflects the forward–backward probability combination. The maximization step involves optimizing the unknown parameter, which is the object mass, to maximize the likelihood through Bayesian optimization with Gaussian process regressions. Our simulation experiments show that our algorithm reduces the error of tracking a ballistic object’s position given noisy observations with unknown parameters.

METHOD OF EVALUATION OF VALUES OF COORDINATES OF POINT OF START SELF-REACTANCE OF INDEFINITE BALLISTIC OBJECT ON BASIS OF ПОЛИНОМИАЛЬНОЙ APPROXIMATION OF AREA OF TRAJECTORY ON RESULTS OUTWARDLY TRAJECTORY MEASURING

The method of evaluation of values of coordinates of point of start of ballistic object at that the mathematical model of motion contains indefinite parameters is offered in the article. Self-reactance vagueness of model of motion of ballistic object of определяеься by polynomial approximation inplane firing of coordinates of area of trajectory that is observed by the station outwardly trajectory measuring. In the measuring system of coordinates of value of coordinates of centre-of-mass of ballistic object settle accounts on results the outwardly trajectory measuring that contain random error terms. The coordinates of ballistic object are transferred from the measuring system of coordinates to the starting system of coordinates. An area of trajectory of ballistic object is in the starting system of coordinates, point-to-point beginning of supervision start, recommences by integration of the system of differential equalizations of motion of ballistic object in reverse speed-up time with next transformation of values of coordinates to the measuring system of coordinates. Analytical expressions and formulas are got for realization of calculations. The values of indexes of exactness of determination of coordinates of point of start of ballistic object depend, both from the sizes of errors of measuring of parameters of motion of the system outwardly trajectory measuring on the area of the looked after trajectory and from the amount of points on that proceeding in the previous area of trajectory came true. The increase of exactness of measuring of values of parameters of trajectory or amount of view points results in diminishing of value of standard deviation of coordinates of refurbishable point of start of ballistic object from her set values in a calculation model. The offered method can be used for development of the special mathematical providing the station outwardly trajectory measuring. Further researches can be sent to determination of rational values of errors by the station outwardly trajectory measuring and ground of sufficient amount of view for determination of values of coordinates of point of start points with a permissible error.

Ballistic Target Tracking with Use of Cinetheodolites

The paper addresses a problem of ballistic object tracking with the use of the cinetheodolite electro-optical tracking system. Electro-optical systems are applied for acquiring the trajectory data of missiles, satellites, and rockets used for delivery of satellites to their prevised orbits. Despite the importance of such systems and their applications, in the open literature there are no publications describing tracking algorithms processing data from cinetheodolites. The paper describes a model-based algorithm of estimation of position and parameters of target motion for such a system, developed by the authors. The model of the system, nonlinear both in its description of the target dynamics and the measurement equations, is presented in detail. The proposed algorithm of estimation is also described, and chosen simulation results are included in the paper. Furthermore, a comparison of the proposed estimation algorithm with other possible, but simpler algorithms is presented.

MODEL AND ALGORITHM FOR CALCULATION OF THE RADAR SIMULATOR OBJECT EFFECTIVE SQUARE OF SCATTERING

To reduce the cost of field tests of the ballistic objects (BO) simulators reflection properties, it is advisable to develop a model and algorithm for calculation of the radar objects effective surface scattering. As a simulator of ballistic objects a complex radar reflector, made of a lossfree dielectric is chosen. It looks like a spherical Luneburg lens with a coating of high-conductivity alloy as well as a truncated cone, disk, and cylindrical elements. The stages of aperture version of reflection from the inner surface of the Luneburg lens are proposed. A physical model of the reflection on the elements of design and the technique of modeling with a calculation algorithm of the effective surface scattering are developed. The algorithm of calculation of the ballistic objects resonance effective surface scattering is worked out. This algorithm is presented in a graphical form. The interface of the computing complex is presented. As a simulator of ballistic object we selected a complex radar reflector, made of a lossfree dielectric sphere with a coating of high-conductivity alloy as well as of a truncated cone, disk, and cylindrical elements. The comparative indicatrices of ballistic objects simulator are presented. The conclusion on the comparative analysis of the results of measurements in situ and modeling results is made. The examples of numerical calculations of the ESR of the head part of the BO simulator with increased ESR and increased all-aspect view are given. The options of the BO simulator head parts with increased ESR and increased all-aspect view with optimal placement of radar dielectric reflector and a corner unit with sectional placement of dielectric reflectors are analyzed.

Estimating angular velocities of a ballistic object using radial acceleration

We developed an algorithm for estimating the total velocity vector of a ballistic object based on its radial acceleration, without employing numerical optimisation methods. We supply a comparison between the efficiency of the algorithm functioning and an existing optimisation method.

Computational Investigation of High Velocity Ballistic Impact Test on Kevlar 149

The Kevlar is an organic high crystalline fiber belonging to the aromatic polyamide family extensively used for its strength. Kevlar fiber posses high cut resistance and flame resistance, hence they have a wide range of application in ballistic and defense [2]. This paper investigates how K-149 behaves mechanically under sudden high velocity impact, it also shows which types of Kevlar grade hold the maximum impact stiffness capacity. In addition it also predicts the stress induced on the specimen at the time of impact. The ballistic impact object considered as 9mm standard size bullet used in short gun. The assumed velocity for these cases is 650m/s. The specimens K-149 & k-49 taken to be rectangle with the standard size 50 mm x 50 mm. The computational analysis done on Kevlar 49 & 149 and the results have been compared with the help of the pictorial representation of post processing abaqus results and the best ballistic material can be chosen. This paper also provided the recommended research data to fill the technology gap in defense material science.

A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1

Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds.

Performance evaluation of several methods for tracking a ballistic object

A new evaluation method was proposed to solve the selection of nonlinear filters.The relevant Cramer-Rao lower bounds(CRLBs) were derived based on ballistic motion model with an unknown ballistic coefficient in two-dimensional space.The performance of extended Kalman filter,unscented Kalman filter,quadrature Kalman filter and cubature Kalman filter was analyzed in theory and compared through simulation based on the concluded theoretical CRLBs.Both the theoretical analysis and the simulation results have indicated that the performance of extended Kalman filter is fast but inaccurate,and the cubature Kalman filter is desirable due to a better trade-off between the tracking accuracy and the computational load.

基于概率假设密度滤波的中段弹道目标群红外多传感器组跟踪方法

The essentiality of cluster tracking for midcourse ballistic target group by low earth orbit(LEO) optical constellation is analyzed.And an improved method of cluster tracking is presented.The probability hypothesis density filter is used to track multi-target on the focal plane,filter out clutter,and estimate target number and state.Then for improving the stability of focal plane target tracking,an image registration method is adopted to adjust interframes target state estimation.Finally,the focal plane 2D centroid measurement of target group is computed based on the focal plane tracking results,and unscented Kalman filter(UKF) is adopted to track the 3D centroid of target group through multi-sensor fusion in sequence.Simulation results show that,the proposed method works well under different clutter rates,and gains a better precision than the traditional one.Meanwhile,it successfully realizes the tracking of each target on the space-based infrared focal plane.

基于概率假设密度滤波的中段弹道目标群红外多传感器组跟踪方法

基于概率假设密度滤波的中段弹道目标群红外多传感器组跟踪方法

Online Estimation of the Approximate Posterior Cramer-Rao Lower Bound for Discrete-Time Nonlinear Filtering

Although it is difficult to assess the achievable performance of nonlinear tracking applications, it nevertheless remains extremely important to do so. This paper illustrates how the mean and covariance of the estimated online state can be used to recursively calculate an approximate posterior Cramer-Rao lower bound (CRLB). Most CRLB implementations require the true state, but this is impractical except for appropriately designed experiments or simulations where the exact value of the state is given as prior knowledge. The performance of the approximate posterior CRLB (PCRLB) used in conjunction with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) for online state estimation are investigated. To test the validity of the proposed method, it was applied to the problem of tracking a ballistic object on reentry. Simulation results confirm the theory and reveal that the proposed approximate PCRLB is sufficiently accurate and that the PCRLB approximations obtained using different state filters are in general very close to each other.

Projectile Identification and Impact Point Prediction

This paper presents a multiple model procedure to estimate the state of a ballistic object in the atmosphere and identify it using radar measurements for the purpose of impact point prediction (IPP). A key aspect of the projectile identification is the identification of the mode of stabilization used, i.e., fin stabilization or spin stabilization. Measurements are taken during the first part of its trajectory up to apogee, and the final state estimate obtained by the multiple model estimator is then predicted to its impact point on Earth. For each model a different extended Kalman filter (EKF) is used for state estimation, and the model likelihoods are then used to identify the projectile. It is shown from simulations carried out on three fin-stabilized projectile trajectories (mortars of different caliber) and a spin-stabilized (howitzer) projectile trajectory that the projectile can be identified with a high probability and also that the impact point is predicted to a high degree of accuracy and with a consistent covariance. It is also shown that accurate modeling of the gyroscopic effect caused by the spinning of the howitzer projectiles is critical for IPP accuracy in the case of spin-stabilized projectiles. The key in the design of the multiple model filter (MMF) is the choice of the models, which based on the characteristics of the different projectile trajectories, have different state dimensions. A choice has to be made between too few state components, which leads to poor accuracy/consistency, and too many state components, in which case the accuracy and discrimination ability suffers because of too much uncertainty in the model.

An Improvement on Resampling Algorithm of Particle Filters

In this correspondence, an improvement on resampling algorithm (also called the systematic resampling algorithm) of particle filters is presented. First, the resampling algorithm is analyzed from a new viewpoint and its defects are demonstrated. Then some exquisite work is introduced in order to overcome these defects such as comparing the weights of particles by stages and constructing the new particles based on quasi-Monte Carlo method, from which an exquisite resampling (ER) algorithm is derived. Compared to the resampling algorithm, the proposed algorithm can maintain the diversity of particles thus avoid the sample impoverishment in particle filters, and can obtain the same estimation accuracy through less number of sample particles. These advantages are finally verified by simulations of non-stationary growth model and a re-entry ballistic object tracking.