Ballistic Object Research Articles

Synchronisation of vision-based sensor networks with variable frame rates

This paper introduces a synchronisation methodology for distributed vision-based sensor networks with clock skew or variable frame rates. The methodology requires a ballistic or otherwise predictive object to be tracked by the sensor network and used to calibrate the clock skew and/or relative variable frame rates between the cameras. The relative time stamp of each image captured can be extracted using the dynamic model of the predictive object. The time stamps and a best fit correlation are used to synchronise all the cameras (and their video streams) that are tracking the same predictive object. In sport the predictive object is likely to be a ballistic object such as a ball or a player in flight, while in security applications, the predictive object may be trains, cars or other objects travelling at predictable speeds in known locations.

RESEARCH ON INFRARED IMAGING SIMULATION OF MIDCOURSE BALLISTIC OBJECT TARGET COMPLEX

The simplified radiance model of midcourse ballistic target and the infrared focal plane model based on point spread function and target tail were presented.By integrating the calculations for target space position and the position in 2-D focal plane projected from 3-D space,the imaging of midcourse ballistic object target complex in space-based infrared sensor was simulated.By analysing the simulation results,it was found out that the midcourse ballistic object target complex would give rise to new challenges for detection and tracking techniques of space-based infrared sensor.The methods to solve these challenges were given here.

The characteristics and consequences of the break-up of the Fengyun-1C spacecraft

The intentional break-up of the Fengyun-1C spacecraft on 11 January 2007 via a hypervelocity collision with a ballistic object created the most severe artificial debris cloud in Earth orbit since the beginning of space exploration. More than 2000 debris of the order of 10cm or greater in size have been identified by the US Space Surveillance Network. The majority of these debris reside in long-lived orbits. The NASA Orbital Debris Program Office has conducted a thorough examination of the nature of the Fengyun-1C debris cloud, using Space Surveillance Network (SSN) data for larger debris and special Haystack radar observations for smaller debris. These data have been compared with the NASA standard satellite break-up model for collisions, and the results are presented in this paper. The orbital longevity of the debris have also been evaluated for both small and large debris. The consequent long-term spatial density effects on the low Earth orbit regime and the potential effect of the debris cloud on the growth of the near-Earth satellite population have been addressed.

Noncontact ballistic motion measurement using a fiber-optic confocal sensor

A fiber-optic confocal sensor for noncontact ballistic measurements is described. Determination of motion at velocities of 1.7 km/s with an uncertainty as small as ±0.3% is demonstrated for both a projectile and a free-surface target. The fibers detect the passage of the object at their conjugate image points created by low F/# optics. This results in an output signal comprising a train of sharp pulses each precisely identifying when the ballistic object traverses an image point. Since the ballistic object does not contact the sensor at the time of imaging, the measurements do not perturb the motion, enabling multi-fragment measurement, as well as repetitive measurements of the same object point.

Estimating the ballistic coefficient of a re-entry vehicle

Theoretical bounds for estimating the ballistic coefficient of a ballistic object during the re-entry phase have been addressed. One essential characteristic of the vehicle trajectory is its deceleration when it reaches dense atmospheric layers. The intensity of the phenomenon is proportional to a scalar, called the ballistic coefficient. This leads to an highly nonlinear time-varying dynamic. To understand the dimensioning parameters for estimating the ballistic coefficient, accurate approximations of the Fisher information matrix are developed. The main result is a closed-form expression of a lower bound for the variance of the ballistic coefficient estimate.

A Comparison of Two CramÉr–Rao Bounds for Nonlinear Filtering with<tex>$rm P_d ≪ 1$</tex>

The paper presents a comparative study of two recently reported Crame/spl acute/r-Rao lower bounds (CRLBs) for nonlinear filtering, both applicable when the probability of detection is less than unity. The first bound is the information reduction factor CRLB; the second is the enumeration method CRLB. The enumeration method is accurate but computationally expensive. We prove in the paper that the information reduction factor bound is overoptimistic, being always less than the enumeration CRLB. The theory is illustrated by two target tracking applications: ballistic object tracking and bearings-only tracking. The simulations studies confirm the theory and reveal that the information reduction factor CRLB rapidly approaches the enumeration CRLB as the scan number increases.

Radar fusion to detect targets. Part III

In two previous papers [2,3] (Signal Processing 82 (8) (August 2002) 1096; 80 (9) (September 2000) 1833) the authors have described the concept of cueing a microwave radar (MR) by exploiting the detection of a low-frequency radar (LFR); the target of interest was an aircraft in [2] and a ballistic object in [3]. This study considers again the detection and tracking of a ballistic target by extending the cueing chain to include early measurements provided by a sensor (for instance an infrared camera) installed on board of low-orbit satellites. The mathematical approach, conceived in [3], aimed at obtaining detection and tracking performance of target, is then extended to the present study to analyse a more realistic scenario that involves the exploitation of early measurements provided by space-borne sensors. The advantage of the satellite cueing is put in evidence.

Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry

Tracking of a ballistic re-entry object from radar observations is a highly complex problem in nonlinear filtering. The paper adopts a one-dimensional vertical motion model with unknown ballistic coefficient, derives and analyses the posterior Cramér–Rao lower bounds (CRLBs) for this problem, and compares the error performance of three nonlinear filters against the theoretical CRLBs. The considered nonlinear filters include the extended Kalman filter, the unscented Kalman filter and the bootstrap (particle) filter. Taking into account the computational and statistical performance, the unscented Kalman filter is found to be the preferred choice for this application.

Cramer-Rao bound for nonlinear filtering with Pd>1 and its application to target tracking

The paper investigates the Cramer-Rao bound for discrete-time nonlinear filtering in the case where the probability of detection of a sensor is less than unity. The theoretical formula involves the evaluation of exponentially growing number of possible miss/detection sequences. An approximation of the theoretical bound for practical applications, such as target tracking, where the number of sensor scans is large, is proposed. An application of the developed techniques to the well-known filtering problem of tracking a re-entry ballistic object is also presented.

Tracking a ballistic target: comparison of several nonlinear filters

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.

Radar fusion to detect targets. Part II

In a previous paper [3] the Authors have described the concept of cueing a microwave radar by exploiting the detection of a low frequency radar; the target of interest was an aircraft. In this publication the study is extended to the case in which the target is a ballistic object. This study differs from the previous one for the electromagnetic and the kinematics characteristics of the target. The mathematical approach conceived in the previous paper has been extended to the present study case. The ranging advantage of using the cueing system is demonstrated also in the case of ballistic target.

Evaluation of the rate constants of dissociative and ternary recombination reactions of argon ions on the basis of the results of ballistic experiments

AbstractExperimental data on the change in the electron density in the wake of a ballistic object traveling at velocities V ∞=3.4–4.9 km/s in argon at pressures p ∞=30–100 Torr are processed and analyzed. A reaction scheme is proposed which takes into account the recombination of charged particles, processes of ionic conversion, and the excited states of the atom. The solution of the equations of a nonequilibrium boundary layer for flow in the wake is used to formulate the inverse problem of determining the rate constants for dissociative recombination Ar 2 + +e→Ar+Ar and ternary recombination Ar++e+Ar→Ar+Ar. The “nearest-neighbor” approximation is used to obtain theoretically an expression for the ternary recombination coefficient as a function of temperature and pressure. Numerous solutions of inverse problems and a comparison with experiments demonstrates the validity of the expression obtained for the ternary recombination coefficient. It is shown that this expression is valid for moderate pressures and complements the Pitaevskii result for low pressures and the Langevin result for high pressures.