An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

A Generic Calculation Model for Aircraft Single-hit Vulnerability Assessment Based on Equivalent Target

Aircraft single-hit vulnerability/survivability is usually expressed as the probability of kill or the vulnerable area in case of being given a random threat （e.g. a fragment） hit on the aircraft. In this paper, introducing the ＂equivalent target method＂ in lethality field into the aircraft vulnerability assessment, a generic vulnerability calculation model is proposed. In order for a good representation of reality, the model considers the threat change of state-of-motion during the threat penetrating into the components successively. Application shows that the proposed generic model has solved the Pk/h （probability of kill given by a hit on the component） calculation problem in aircraft vulnerability assessment, and is easier to be computerized than other commonly used models.

Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher’s detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the non-detection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher’s detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.

Spatial Target Detection Based on the Measurement of Equivalent Blackbody Temperature

At low SNR cases, the distinction between spatial point-target and interferences as decoys is still a very difficult problem. Based on the characteristics that target and interferences as decoys and noise had different radiation intensity and radiation changing frequency, the concept of the equivalent blackbody temperature （EBT） was built and the calculation model of EBT was designed. The model could effectively reduce the interference of the space environment and fully show the radiation differences between point-target and interferences as decoys. It would be very effective in the detection of the target. In order to detect the target, the effective estimator of EBT was designed according to the observed data, and the system error and the variation range of the estimator of EBT were estimated. Finally the multi-frame estimator was designed to improve the estimation stability of EBT, and the use of this estimator would identify the point-target more effectively.

Multiple model PHD filter for tracking sharply maneuvering targets using recursive RANSAC based adaptive birth estimation

An algorithm to track multiple sharply maneuvering targets without prior knowledge about new target birth is proposed. These targets are capable of achieving sharp maneuvers within a short period of time, such as drones and agile missiles.The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems. However, the standard PHD filter operates on the single dynamic model and requires prior information about target birth distribution, which leads to many limitations in terms of practical applications. In this paper,we introduce a nonzero mean, white noise turn rate dynamic model and generalize jump Markov systems to multitarget case to accommodate sharply maneuvering dynamics. Moreover, to adaptively estimate newborn targets’information, a measurement-driven method based on the recursive random sampling consensus (RANSAC) algorithm is proposed. Simulation results demonstrate that the proposed method achieves significant improvement in tracking multiple sharply maneuvering targets with adaptive birth estimation.

Improved pruning algorithm for Gaussian mixture probability hypothesis density filter

With the increment of the number of Gaussian components, the computation cost increases in the Gaussian mixture probability hypothesis density(GM-PHD) filter. Based on the theory of Chen et al, we propose an improved pruning algorithm for the GM-PHD filter, which utilizes not only the Gaussian components’ means and covariance, but their weights as a new criterion to improve the estimate accuracy of the conventional pruning algorithm for tracking very closely proximity targets. Moreover, it solves the end-less while-loop problem without the need of a second merging step. Simulation results show that this improved algorithm is easier to implement and more robust than the formal ones.

Study on the detection of the multiple unresloved targets

When the returns come from two or more unresolved targets (the signals are not resolved in the frequency or time domains) in a monopulse radar system, the direction-of-arrival (DOA)estimate indicated by the monopulse ratio is not the true information of the tracked target.Then the tracking systems is influenced. An approach has been proposed to detect whether the returns come from a single target or two unresolved targets. The above approach is extended from two to three unresolved targets. The simulation indicates that the detection probability under the three unresolved targets is not sure to exceed the detection probability under the two unresolved targets.

Multiple extended target tracking algorithm based on Gaussian surface matrix

In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density（PHD） filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatially close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.

A cloud Bayesian network approach to situation assessment of scouting underwater targets with fixed-wing patrol aircraft

The battlefield situation changes rapidly because underwater targets'are concealment and the sea environment is uncertain.So,a great number of situation information greatly increase,which need to be dealt with in the course of scouting underwater targets.Situation assessment in sea battlefield with a lot of uncertain information is studied,and a new situation assessment method of scouting underwater targets with fixed-wing patrol aircraft is proposed based on the cloud Bayesian network,which overcomes the deficiency of the single cloud model in reasoning ability and the defect of Bayesian network in knowledge representation.Moreover,in the method,the cloud model knowledge deal with the input data of Bayesian network reasoning,and the advantages in knowledge representation of cloud theory and reasoning of Bayesian network are applied;also,the fuzziness and stochasticity of cloud theory in knowledge expression,the reasoning ability of Bayesian network,are combined.Then,the situation assessment model of scouting underwater targets with fixed-wing patrol aircraft is established.Hence,the directed acyclic graph of Bayesian network structure is constructed and the assessment index is determined.Next,the cloud model is used to deal with Bayesian network,and the discrete Bayesian network is obtained.Moreover,after CPT of each node and the transformation between certainty degree and probability are accomplished;the final situation level is obtained through a probability synthesis formula.Therefore,the target type and the operational intention of the other side are deduced to form the battlefield situation.Finally,simulations are carried out,and the rationality and validity of the proposed method are testified by simulation results.By this method,the battlefield situation can be gained.And this method has a wider application range,especially for large sample data processing,and it has better practicability.

Bistatic RCS Prediction with Graphical Electromagnetic Computing (GRECO) Method for Moving Targets

Graphical Electromagnetic Computing (GRECO) is recognized as one of the most valuable methods of the RCS (Radar Cross Section) computation for the high frequency region. The method of GRECO and Monostatic bistatic Equivalence Theorem was used to calculate the bistatic RCS for moving targets in the high frequency region. Some computing examples are given to verify the validity of the method. Excellent agreement with the measured data indicates that the method has practical engineering value.

Sensor radiation interception risk control in target tracking

This paper is mainly on the problem of radiation interception risk control in sensor network for target tracking.Firstly,the sensor radiation interception risk is defined as the product of the interception probability and the cost caused by the interception.Secondly,the radiation interception probability model and cost model are established,based on which the calculation method of interception risk can be obtained.Thirdly,a sensor scheduling model of radiation risk control is established,taking the minimum interception risk as the objective function.Then the Hungarian algorithm is proposed to obtain sensor scheduling scheme.Finally,simulation experiments are mad to prove the effectiveness of the methods proposed in this paper,which shows that compared with the sensor radiation interception probability control method,the interception risk control method can keep the sensor scheduling scheme in low risk as well as protect sensors of importance in the sensor network.

The principle of minimization of the equivalent load for design of launching vertical shiplift

Launching vertical shiplift is a type of shiplifts which have the advantages in characteristics of dynamics and statics, safety and simplicity in operation. But their applications are limited as the scales of mechanical equipments are too large. This paper puts forward the principle of minimization of the equivalent load for the general layout design of launching vertical shiplifts, based on the analysis of the load probability of the main hoists and their key mechanical equipments. The principle aims at determining the optimal weight of counterweight so that the equivalent loads of the main hoists of shiplifls are minimized, and larger ships are permitted to pass through. The theory and method presented in this paper have been applied in the design of the first step and third step shiplifts of the Goupitan Hydro Power Station. This has resulted in the breakthrough of the design and manufacture of launching vertical shiplifts so that the ships with tonnage of 500 t can pass through hydro dams for this type of shiplifts, comparing with the largest launching shiplift in Yantan Hydro Power Station with the 250 t shiplift.

Free clustering optimal particle probability hypothesis density(PHD) filter

As to the fact that it is difficult to obtain analytical form of optimal sampling density and tracking performance of standard particle probability hypothesis density(P-PHD) filter would decline when clustering algorithm is used to extract target states,a free clustering optimal P-PHD(FCO-P-PHD) filter is proposed.This method can lead to obtainment of analytical form of optimal sampling density of P-PHD filter and realization of optimal P-PHD filter without use of clustering algorithms in extraction target states.Besides,as sate extraction method in FCO-P-PHD filter is coupled with the process of obtaining analytical form for optimal sampling density,through decoupling process,a new single-sensor free clustering state extraction method is proposed.By combining this method with standard P-PHD filter,FC-P-PHD filter can be obtained,which significantly improves the tracking performance of P-PHD filter.In the end,the effectiveness of proposed algorithms and their advantages over other algorithms are validated through several simulation experiments.

Labeled box-particle CPHD filter for multiple extended targets tracking

In multiple extended targets tracking, replacing traditional multiple measurements with a rectangular region of the nonzero volume in the state space inspired by the box-particle idea is exactly suitable to deal with extended targets, without distinguishing the measurements originating from the true targets or clutter.Based on our recent work on extended box-particle probability hypothesis density(ET-BP-PHD) filter, we propose the extended labeled box-particle cardinalized probability hypothesis density(ET-LBP-CPHD) filter, which relaxes the Poisson assumptions of the extended target probability hypothesis density(PHD) filter in target numbers, and propagates not only the intensity function but also cardinality distribution. Moreover, it provides the identity of individual target by adding labels to box-particles. The proposed filter can improve the precision of estimating target number meanwhile achieve targets' tracks. The effectiveness and reliability of the proposed algorithm are verified by the simulation results.

Fast density peak-based clustering algorithm for multiple extended target tracking

The key challenge of the extended target probability hypothesis density (ET-PHD) filter is to reduce the computational complexity by using a subset to approximate the full set of partitions. In this paper, the influence for the tracking results of different partitions is analyzed, and the form of the most informative partition is obtained. Then, a fast density peak-based clustering (FDPC) partitioning algorithm is applied to the measurement set partitioning. Since only one partition of the measurement set is used, the ET-PHD filter based on FDPC partitioning has lower computational complexity than the other ET-PHD filters. As FDPC partitioning is able to remove the spatially close clutter-generated measurements, the ET-PHD filter based on FDPC partitioning has good tracking performance in the scenario with more clutter-generated measurements. The simulation results show that the proposed algorithm can get the most informative partition and obviously reduce computational burden without losing tracking performance. As the number of clutter-generated measurements increased, the ET-PHD filter based on FDPC partitioning has better tracking performance than other ET-PHD filters. The FDPC algorithm will play an important role in the engineering realization of the multiple extended target tracking filter.

Optimal models with maximizing probability of first achieving target value in the preceding stages

Decision makers often face the need of performance guarantee with some sufficiently high proba-bility. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probabilitycriterion for the first achieving target value. The objective is to find a policy that maximizes the probabilityof the total discounted reward exceeding a target value in the preceding stages. We show that our formula-tion cannot be described by former models with standard criteria. We provide the properties of the objectivefunctions, optimal value functions and optimal policies. An algorithm for computing the optimal policies forthe finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deter-ministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis,we approximate general models and prove the existence of ε-optimal policy for finite state space. We give anexample for the reliability of the satellite systems using the above theory. Finally, we extend these results tomore general cases.

Global track extraction for probability hypothesis density filter

The probability hypothesis density (PHD), a well-known scheme for multi-target tracking in clutters, can obtain peaks of possible tracks, and its cluster-indexed method is widely accepted in further track extraction. However, the track extraction may face high risk in the case that the targets are so approached that it is hardly to discern their measurements. The concept of the distance between track sets in two adjacent times is defined and a consistency measure metric between any two peaks in two adjacent times is further proposed based on 'global information', containing spatial information (topology feature) among tracks, along with the temporal information of each track. Then, a global track extraction method is proposed based on the consistency belief and four decision rules. Via the simulation comparison with the cluster-indexed method, the proposed method can avoid the track break and mistake association. © 2016 Beijing Institute of Aerospace Information.

A NEW DATA ASSOCIATION ALGORITHM USING PROBABILITY HYPOTHESIS DENSITY FILTER

Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,PHD filter has a closed form recursion (GMPHD). But PHD filter cannot estimate the trajectories of multi-target because it only provides identity-free estimate of target states. Existing data association methods still remain a big challenge mostly because they are com-putationally expensive. In this paper,we proposed a new data association algorithm using GMPHD filter,which significantly alleviated the heavy computing load and performed multi-target trajectory tracking effectively in the meantime.

Computational Studies on Detecting a Diffusing Target in a Square Region by a Stationary or Moving Searcher

In this paper, we compute the non-detection probability of a randomly moving target by a stationary or moving searcher in a square search region. We find that when the searcher is stationary, the decay rate of the non-detection probability achieves the maximum value when the searcher is fixed at the center of the square search region;when both the searcher and the target diffuse with significant diffusion coefficients, the decay rate of the non-detection probability only depends on the sum of the diffusion coefficients of the target and searcher. When the searcher moves along prescribed deterministic tracks, our study shows that the fastest decay of the non-detection probability is achieved when the searcher scans horizontally and vertically.

Searching for a Target Traveling between a Hiding Area and an Operating Area over Multiple Routes

We consider the problem of searching for a target that moves between a hiding area and an operating area over multiple fixed routes. The search is carried out with one or more cookie-cutter sensors, which can detect the target instantly once the target comes within the detection radius of the sensor. In the hiding area, the target is shielded from being detected. The residence times of the target, respectively, in the hiding area and in the operating area, are exponentially distributed. These dwell times are mathematically described by Markov transition rates. The decision of which route the target will take on each travel to and back from the operating area is governed by a probability distribution. We study the mathematical formulation of this search problem and analytically solve for the mean time to detection. Based on the mean time to capture, we evaluate the performance of placing the searcher(s) to monitor various travel route(s) or to scan the operating area. The optimal search design is the one that minimizes the mean time to detection. We find that in many situations the optimal search design is not the one suggested by the straightforward intuition. Our analytical results can provide operational guidances to homeland security, military, and law enforcement applications.