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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. [ABSTRACT FROM AUTHOR]

Considering the requirement of avoiding obstacles in different planetary landing missions, this article presents a generalized method dealing with the obstacle avoidance constrained landing trajectory optimization problem with vectorized strategy, i.e., vector trajectory method (VTM). By introducing a trajectory direction constraint with vectorized description, the character of the obstacle avoidance trajectory can be more specifically depicted. Moreover, by satisfying proper trajectory direction constraint, the lander's particular performances, such as the observation to the target or probability of a safe flight, can be improved. To this end, the VTM and relevant theorem are first developed, revealing the relationship between the two aspects of obstacle avoidance constraint (i.e., distance constraint and trajectory direction constraint). Then, both aspects of constraints are uniformly transformed as the auxiliary angle magnitude constraint with the vectorized strategy, which significantly simplifies the solving procedure of obstacle avoidance constrained trajectory optimization problem. Finally, the proposed VTM is illustrated in detail through the examples with the planetary landing background of atmospheric entry and powered descent landing. [ABSTRACT FROM AUTHOR]

This article investigates the fuel-optimal guidance problem of the end-to-end human-Mars entry, powered-descent, and landing (EDL) mission. It applies a unified modeling scheme and develops a computationally efficient new optimization algorithm to solve the multiphase optimal guidance problem. The end-to-end EDL guidance problem is first modeled as a multiphase optimal control problem with different dynamics and constraints at each phase. Via polynomial approximation and discretization techniques, this multiphase optimal control problem is then reformulated as a polynomial programming problem. By introducing intermediate variables and quadratic equality constraints, a polynomial program is equivalently converted into a nonconvex quadratically constrained quadratic program (QCQP). Then, a novel customized alternating direction method of multipliers (ADMM) is proposed to efficiently solve the large-scale QCQP with convergence proof to a local optimum under certain conditions on the algorithmic parameters. The fuel savings under the end-to-end human-Mars EDL guidance are verified by comparing to the fuel consumption using the separate phase guidance approach. Furthermore, the computational efficiency of the customized ADMM algorithm is validated by comparing to the state-of-the-art nonlinear programming method. The robustness of the customized ADMM algorithm is verified via extensive simulation cases with random initial conditions. [ABSTRACT FROM AUTHOR]

Rapid and responsive Earth observation satellites enable the evaluation of disaster risk, improve relief effectiveness, and reduce suffering and fatalities in the event of sudden disaster events. One promising method for responsive space satellites is orbital maneuvering. This article describes a multitree search framework for multisatellite responsiveness scheduling considering orbital maneuvering, where multiple ground targets are cooperatively observed by multiple observation satellites over a short period of time. Based on the traditional tree search, the proposed method constructs multiple trees and distributes all the targets to multiple satellites, allowing the observation sequence of a single satellite to be optimized. To apply the tree search algorithm, a tree node collection (TNC) composed of the corresponding nodes in multiple trees is used to represent the state of each satellite. Before the expansion phase, one specific node in the TNC is determined for later expansion. A beam search is then used to optimize the observation sequence. Ground-track adjustment techniques using impulse maneuver are considered for visiting a given target. The proposed framework is more effective than other algorithms and achieves a better performance than the previous best method in a typical multisatellite responsiveness scheduling scenario. [ABSTRACT FROM AUTHOR]

A robust algorithm to solve the low-thrust fuel-optimal trajectory optimization problem for interplanetary spacecraft is developed in this article. The original nonlinear optimal control problem is convexified and transformed into a parameter optimization problem using an arbitrary-order Gauss–Lobatto discretization scheme with nonlinear control interpolation. A homotopic approach that considers the energy-to-fuel smoothing path is combined with an adaptive second-order trust-region mechanism to increase performance. The overall robustness is assessed in several fuel-optimal transfers with poor initial guesses. The results show a superior performance in terms of convergence and computational time compared to standard convex programming approaches in the literature. [ABSTRACT FROM AUTHOR]

Differential dynamic programming (DDP) is a well-recognized method for trajectory optimization due to its fast convergence characteristics. However, the original DDP requires a predefined final time and cannot handle nonlinear constraints in optimization. This prohibits the application of DDP for autonomous vehicles due to the heuristic nature of setting a final time beforehand and the existence of inherent physical limits. This article revisits DDP by dynamically optimizing the final time via the first-order optimality condition of the value function and using augmented Lagrangian method to tackle the issue of nonlinear constraints. The resultant algorithm is termed as flexible final time constrained differential dynamic programming (FFT-CDDP). Extensive numerical simulations for a three-dimensional guidance problem are used to demonstrate the working of FFT-CDDP. The results indicate that the proposed FFT-CDDP provides much higher computational efficiency and stronger robustness against the initial solution guess, compared with the off-the-shelf general purpose optimal control software (GPOPS) algorithm. [ABSTRACT FROM AUTHOR]

This article extends the optimal covariance steering (CS) problem for linear stochastic systems subject to chance constraints so as to account for an optimal allocation of the risk. Previous works have assumed a uniform risk allocation in order to cast the optimal control problem as a semidefinite program, which can be solved efficiently using standard SDP solvers. An iterative risk allocation (IRA) formalism is used to solve the optimal risk allocation problem for CS using a two-stage approach. The upper-stage of IRA optimizes the risk, which is a convex problem, while the lower-stage optimizes the controller with the new constraints. The process is applied iteratively until the optimal risk allocation that achieves the lowest total cost is obtained. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies. In this article, we consider both polyhedral and cone state chance constraints. Finally, we demonstrate the approach to a spacecraft rendezvous problem and compare the results with other competing approaches. [ABSTRACT FROM AUTHOR]

In an asteroid soft landing mission, the irregularly distributed gravitational field and unexpected external disturbances may lead to a significant deviation of the actual landing trajectory to the predesigned trajectory. Therefore, the capability of trajectory onboard generation is essential to meet the requirements of landing accuracy and safety. To this end, this article proposes a rapid trajectory generation algorithm for the fuel-optimal asteroid landing. First, two important properties of the fuel-optimal landing trajectory are revealed in detail with the presented theorems. Then, based on these properties, the problem of landing trajectory generation is transformed into an onboard parameter searching problem, which is of significant benefit for the real-time performance and convergence. The effectiveness of the proposed algorithm is verified through the 433 Eros soft landing mission based numerical simulations. It is shown that the proposed fuel optimal asteroid landing trajectory generation algorithm is valid with deviated initial conditions and irregularly distributed gravitational field. [ABSTRACT FROM AUTHOR]

On a grand scale, motion trajectories are usually defined by an origin, a sequence of waypoints, and a destination. A typical example is in air traffic management (ATM), where a flight from an origin passes several waypoints and arrives at a destination. The origin, the waypoints, and the destination contain useful information for trajectory modeling. On the other hand, due to trajectory design criteria and ATM restrictions and requirements, there are long-range dependencies in a flight trajectory. Such dependencies can be modeled by taking the origin, waypoints, and destination into account in trajectory modeling. In this article, we propose a class of conditionally Markov (CM) sequences to model such trajectories with long-range dependencies. First, we define a general CM sequence as a foundation. Then, we discuss its special cases for different scenarios. We derive dynamic models of these CM sequences in the Gaussian case. We show how parameters of the models can be learned from data or designed. We also justify the use of the proposed CM models for trajectory modeling. In addition, we obtain optimal filters and predictors for different models. Simulation demonstrations are given. [ABSTRACT FROM AUTHOR]

The design of multitarget rendezvous missions requires a method to quickly and accurately approximate the optimal transfer between any two rendezvous targets. In this article, an artificial neural-network-based method is proposed for the rapid approximation of optimal perturbed long-duration impulsive transfers. The relationship between the optimal transfer velocity increments and the initial right ascension of the ascending node difference between the departure body and the rendezvous target is analyzed, and the result suggests that the perturbed long-duration impulsive transfers should be divided into three types. An efficient database generation method is developed. Three regression multilayer perceptrons (MLPs) are trained individually and applied to approximate the corresponding types of transfers. The simulation results show that the well-trained MLPs are capable of quickly estimating the optimal velocity increments with a relative error of less than 3% for all three types of transfers. Additional tests of the debris chains with total velocity increments of several thousand m/s show that the estimation results are very close to the optimized results, with a final estimation error of less than 10 m/s. [ABSTRACT FROM AUTHOR]

In this article, a fast chance-constrained trajectory generation strategy incorporating convex optimization and convex approximation of chance constraints is designed so as to solve the unmanned vehicle path planning problem. A path-length-optimal unmanned vehicle trajectory optimization model is constructed with the consideration of the pitch angle constraint, the curvature radius constraint, the probabilistic control actuation constraint, and the probabilistic collision avoidance constraint. Subsequently, convexification technique is introduced to convert the nonlinear problem formulation into a convex form. To deal with the probabilistic constraints in the optimization model, convex approximation techniques are introduced such that the probabilistic constraints are replaced by deterministic ones while simultaneously preserving the convexity of the optimization model. Numerical results, obtained from a number of case studies, validate the effectiveness and reliability of the proposed approach. A number of comparative studies were also performed. The results confirm that the proposed design is able to produce more optimal flight paths and achieve enhanced computational performance than other chance-constrained optimization approaches investigated in this article. [ABSTRACT FROM AUTHOR]

In practical scenarios, flight trajectories shall be smooth to comply with the required curvature behavior. This article describes a trajectory generation method that is able to produce smooth control commands with an arbitrary order of smoothness. The system inputs are formulated analytically as trigonometric series in which the coefficients are to be determined by optimization. Effective implementations of the proposed method are presented. These include a numerical benchmark that shows how the order of the series shapes the results as well as the comparison with the optimal solution, and the unmanned aerial vehicle transition trajectory generation using a convex optimization framework integrated with the proposed design. [ABSTRACT FROM AUTHOR]

This article presents a new and fast indirect method for solving fuel-optimal descent trajectories in the gravitational field of an irregularly-shaped asteroid. The costates associated with a two-impulse descent trajectory are used as approximate costates for the costate initialization of a finite-thrust fuel-optimal trajectory planning problem. The approximate solutions of the initial velocity and mass costates are given in analytical forms. A simple shooting equation is derived to solve the approximate position costates. The two-impulsive descent trajectory is solved by an irregular gravitational Lambert solver. Based on the Lambert solver and approximate costates, an algorithm is proposed for trajectory optimization with varying time of flight. The effectiveness and efficiency of the proposed method are tested through the simulation of landing on the asteroid 433 Eros. Additionally, a computationally efficient approximate model is employed to replace the polyhedral model, which greatly improves the computational speed and enhance the ability to address uncertainties. [ABSTRACT FROM AUTHOR]

An exoatmospheric midcourse guidance law is proposed to intercept a ballistic missile during the free-flight phase. The proposed guidance law generates a thrust direction command for an antiballistic missile to hit the target at the predicted intercept point. For the predicted intercept point, the zero-effort-miss and zero-effort-velocity are determined based on the solutions of the two-body orbital boundary/initial value problems. The intercept point is predicted by using the trajectory shaping parameter that combines the zero effort trajectory and minimum time trajectory. A response surface model for the minimum interception time is constructed as a database, which is the polynomial function of the initial condition. The response surface model provides a predicted minimum time interception position for the midcourse guidance. Case studies are performed to demonstrate the performance of the proposed guidance law considering various uncertainties. [ABSTRACT FROM AUTHOR]

To improve the autonomy and reliability of asteroid landings, an intelligent approach to fast and reliable generation of optimal landing trajectories is proposed. Unfortunately, the indirect methods require good initial guesses for shootings. To address this issue, deep neural networks (DNNs) are developed to approximate the costates of the indirect methods and supply good initial solutions to achieve high success rate of shootings. This article focuses on the following three contributions. First, the original asteroid landing problems are connected with two-dimensional (2-D) asteroid-free transfer problems using model continuation and state transformation techniques. Second, DNNs are developed and optimized to approximate the costates of the 2-D transfers with high accuracy. Third, a systematical solution for asteroid landing trajectory optimization is developed, wherein the DNNs provide good initial solutions, and the accurate solutions for landings are obtained through a solution continuation process. Additionally, an alternative solution supplying strategy based on error statistics of DNN approximation is presented to take over the solution supplying when the predictions of DNNs fail to converge to the optima. Evaluations of the DNNs for solution supplying and simulations of landings on 433 Eros and 101955 Bennu are given to substantiate the effectiveness of the proposed techniques and demonstrate the performance of the developed algorithm. [ABSTRACT FROM AUTHOR]

This article proposes a bio-inspired algorithm called virtual motion camouflage (VMC) to reduce the dimension and computational cost of entry trajectory optimization problem for the reusable launch vehicle. In the VMC framework, the trajectory to be planned can be obtained by predefining the virtual prey motion according to the boundary conditions, then optimizing the reference point and path control parameters using sequential quadratic programming algorithm. Compared with Gauss pseudospectral method, due to the proposed approach reduce the number of discrete points and the equality constraints of the optimization model, it can improve the convergence speed and reduce computational cost effectively. Two minimum time entry examples, without and with no-fly-zone constraints, are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

For an unmanned aerial vehicle (UAV) carrying out a maritime radar surveillance mission, there is a tradeoff between maximizing information obtained from the search area and minimizing fuel consumption. This article presents an approach for the optimization of a UAV's trajectory for maritime radar wide area persistent surveillance to simultaneously minimize fuel consumption, maximize mean probability of detection, and minimize mean revisit time. Quintic polynomials are used to generate UAV trajectories due to their ability to provide complete and complex solutions while requiring few inputs. Furthermore, the UAV dynamics and surveillance mission requirements are used to ensure that a trajectory is realistic and mission compatible. A wide area search radar model is used within this article in conjunction with a discretized grid in order to determine the search area's mean probability of detection and mean revisit time. The trajectory generation method is then used in conjunction with a multiobjective particle swarm optimization algorithm to obtain a global optimum in terms of path, airspeed (and thus time), and altitude. The performance of the approach is then tested over two common maritime surveillance scenarios and compared to an industry recommended baseline. [ABSTRACT FROM AUTHOR]

Space debris has become a great threat to space activities. We study and optimize space missions to remove multiple space debris. These missions are efficient and economical in stabilizing the orbital environment. In this paper, we propose an intelligent global optimization algorithm named the evolving elitist club algorithm (EECA), and we study its application in multiple debris removal missions. The crucial design element of EECA is the elitist club, which is a population created using ant colony optimization (ACO) and then evolved using genetic algorithm operators. We describe two types of multiple debris removal missions: 1) single spacecraft removal mission; and 2) multiple spacecraft removal mission. We optimize them using EECA. The proposed algorithm is compared with the conventional tree search method and other ACO algorithms. We show that EECA is more efficient than other algorithms. Furthermore, a time distribution (TD) EECA is proposed to handle time-dependent problems, and the time-continuous update mechanism of time-varying pheromone in TD EECA presents a novel idea for combinatorial-continuous problems. [ABSTRACT FROM AUTHOR]

Electric solar wind sail (E-sail) is an innovative propulsion system, which can generate low and continuous thrust without any propellant by reflecting ions from the solar wind. Because the propulsive acceleration of E-sail is low and continuous, its trajectory is usually characterized by long flight time. In order to explore more flight plans, rapid trajectory design is useful for preliminary mission analysis and design. This paper presents a method for rapid generation of minimum-time, three-dimensional trajectories for an E-sail using the finite Fourier series shape-based method. Unlike the more conventional electric thruster, the thrust vector of an E-sail is constrained. In order to consider the characteristics of the E-sail thrust, inequality constraints of thrust acceleration are investigated based on a recent thrust model. The numerical simulation results show that the proposed method is useful to quickly design the flight trajectory of the E-sail by considering the actual characteristics of the thrust vector. [ABSTRACT FROM AUTHOR]

The electric sail is an innovative concept for spacecraft propulsion, which can generate continuous thrust without propellant by reflecting solar wind ions. In previous studies, the thrust of an electric sail is described by a classical model that neglects the effects of the electric sail attitude on the propulsive thrust modulus and direction. This paper reappraised the performance of the electric sail in the Vesta and Ceres exploration mission with an advanced thrust model that considers the effect of the spacecraft attitude on both the thrust modulus and direction. By using a hybrid optimization method, the trajectory optimization of the electric-sail-based spacecraft from earth to Vesta and Ceres is implemented in an optimization framework. Numerical results show that the minimal flight time with the advanced thrust model is longer than that with the classical model. The difference in performance between the classical and advanced models is attributable to overestimation of the maximum thrust cone angle and the thrust modulus by the classical model. [ABSTRACT FROM AUTHOR]

This study is motivated by the requirement of on-board trajectory optimization with guaranteed convergence and real-time performance for optimal spacecraft orbit transfers. To this end, a real-time optimal control approach is proposed using deep learning technologies to obtain minimum-time trajectories of solar sail spacecraft for orbit transfer missions. First, the minimum-time two-dimensional orbit transfer problem is solved by an indirect method, and the costate normalization technique is introduced to increase the probability of finding the optimal solutions. Second, by making novel use of deep learning technologies, three deep neural networks are designed and trained offline by the obtained optimal solutions to generate the guidance commands in real time during flight. Consequently, the long-standing difficulty of on-board trajectory generation is resolved. Then, an interactive network training strategy is presented to increase the success rate of finding optima by supplying good initial guesses for the indirect method. Moreover, a multiscale network cooperation strategy is designed to deal with the recognition deficiency of deep neural networks (DNNs) with small input values, which helps achieve highly precise control of terminal orbit insertion. Numerical simulations are given to substantiate the efficiency of these techniques, and illustrate the effectiveness and robustness of the proposed DNN-based trajectory control for future on-board applications. [ABSTRACT FROM AUTHOR]

This paper presents a guidance law for a booster to meet the requirements of scramjet transition. The straightforward open-loop and closed-loop guidance laws are combined together through a smooth switch. In the closed-loop guidance law, the worst case with a minimal lift-drag ratio is selected to obtain a nominal elevation angle. The excessive energy due to various uncertainties could be dissipated around this nominal trajectory adaptively. Numerical simulations are conducted to validate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Avionics and air traffic management (ATM) systems are evolving with the introduction of progressively higher levels of automation, toward attaining the ambitious operational, technical, and safety enhancements required to sustain the present growth of global air traffic. This paper presents novel 4-Dimensional Trajectory (4DT) functionalities that are being developed for integration in ATM and avionics systems to support trajectory based operations (TBO). The 4DT planning process, which is the main focus of the paper, is supported by a custom multiobjective variant of state-of-the-art optimal control algorithms, incorporating various operational, economic, and environmental factors. Capitalizing on the higher theoretical accuracy offered by optimal control algorithms compared to other methods, a key feature of the proposed approach is the introduction of a postprocessing stage to ensure that the mathematically optimal trajectories are translated into a set of standardized 4DT descriptors, which can be flown by state-of-the-art automatic flight control systems. Additionally, to support air-ground 4DT intent negotiation and validation in the TBO context, the 4DT postprocessing ensures that optimal trajectories are synthetically described by a limited number of parameters, minimizing the bandwidth requirements imposed on airborne data links. Simulation-based verification activities addressing operational efficiency improvements and computational performance in the terminal area ATM context support the viability of the proposed 4DT planning functionality for online tactical TBO. [ABSTRACT FROM AUTHOR]

Although the robustness of indirect methods is enhanced by the homotopic approach and switching detection technique when applied to fuel-optimal low-thrust trajectory optimization, the bottleneck in adjoint initialization still needs further investigation. This paper overcomes this bottleneck by the adjoint mapping between the Lagrange multipliers of direct methods to the adjoint variables. The nonconvex optimization problem deduced from direct methods is converted into a convex one by lossless convexification and successive convex programming. By combining these techniques, a framework is built to effectively solve the fuel-optimal low-thrust trajectory optimization problem. [ABSTRACT FROM AUTHOR]

This paper extends the multiple-hypothesis tracking (MHT) recursion to allow for multiple detections per target, per scan of data. We show that the generalized recursion admits the factorization of global-hypothesis probabilities, enabling track-oriented MHT. We propose a two-stage MHT implementation that allows tractable processing in this setting, and explore performance with respect to classical track-oriented MHT processing. [ABSTRACT FROM AUTHOR]

Fixed-wing unmanned aerial vehicles (UAVs) can be an essential tool for low-cost aerial surveillance and mapping applications in remote regions. There is, however, a key limitation, which is the fact that low-cost UAVs have limited fuel capacity and, hence, require periodic refueling to accomplish a mission. Moreover, the usual mechanism of commanding the UAV to return to a stationary base station for refueling can result in the fuel wastage and inefficient mission operation time. Alternatively, one strategy could be the use of an unmanned ground vehicle (UGV) as a mobile refueling unit, where the UAV will rendezvous with the UGV for refueling. In order to accurately perform this task in the presence of wind disturbances, we need to determine an optimal trajectory in three-dimensional taking UAV and UGV dynamics and kinematics into account. In this paper, we propose an optimal control formulation to generate a tunable UAV trajectory for rendezvous on a moving UGV that also addresses the possibility of the presence of wind disturbances. By a suitable choice of the value of an aggressiveness index that we introduce in our problem setting, we are able to control the UAV rendezvous behavior. Several numerical results are presented to illustrate the reliability and effectiveness of our approach. [ABSTRACT FROM AUTHOR]

A novel “blind and evade” guidance concept for an aerial target, which is exposed to a threat of two homing missiles, is presented. Each missile is assumed to measure solely its own line-of-sight (LOS) angle and share it with the other missile. Such information sharing enables the missiles to form a triangular measuring baseline relative to the target and to improve their estimation accuracy. However, if the separation angle between the two LOS vectors is small enough, the observability of such double-LOS measuring approach becomes weak. Motivated by this observation, the idea of the proposed concept is to bring the missiles on the same LOS with the target, i.e., blinding them, and then perform an appropriately timed target evasive maneuver. The target's guidance law is derived under the assumption of perfect information and formulated as an optimal control problem. Simulation results demonstrate the potential of the proposed defense concept. [ABSTRACT FROM AUTHOR]

The sensitivity of the initial guess in terms of optimizer based on an hp-adaptive pseudospectral method for solving a space maneuver vehicle's (SMV) trajectory optimization problem has long been recognized as a difficult problem. Because of the sensitivity with regard to the initial guess, it may cost the solver a large amount of time to do the Newton iteration and get the optimal solution or even the local optimal solution. In this paper, to provide the optimizer a better initial guess and solve the SMV trajectory optimization problem, an initial guess generator using a violation learning differential evolution algorithm is introduced. A new constraint-handling strategy without using penalty function is presented to modify the fitness values so that the performance of each candidate can be generalized. In addition, a learning strategy is designed to add diversity for the population in order to improve the convergency speed and avoid local optima. Several simulation results are conducted by using the combination algorithm; simulation results indicated that using limited computational efforts, the method proposed to generate initial guess can have better performance in terms of convergence ability and convergence speed compared with other approaches. By using the initial guess, the combinational method can also enhance the quality of the solution and reduce the number of Newton iteration and computational time. Therefore, the method is potentially feasible for solving the SMV trajectory optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, an impact angle control guidance law, which considers simultaneously the impact angle and seeker's look angle constraints, is proposed for a constant speed missile against a stationary target. An optimal control theory with state variable inequality constraint is used to design the guidance law, for which a control energy performance index with the weighting function of the range-to-go is minimized. Various forms of guidance and trajectory shaping are possible by selecting a proper gain of the weighting function. To handle the seeker's look angle limits when the missile trajectory is highly curved by controlling the impact angle, the proposed guidance law generates three types of acceleration commands as the guidance phases: the first acceleration command for an initial guidance phase makes an initial seeker's look angle reach the maximum look angle; the second one for a midguidance phase maintains the maximum look angle; the final one for a terminal guidance phase intercepts the target with the desired impact angle. The performance of the proposed guidance law was investigated with nonlinear simulations for various engagement conditions. [ABSTRACT FROM AUTHOR]

Reentry trajectory planning has become a key issue because of the rapid development of hypersonic vehicles. In this paper, an artificial bee colony (ABC)?based direct collocation method is proposed for reentry trajectory optimization. First, the reentry trajectory optimization problem is elaborated. The principles of the ABC algorithm are then introduced. Finally, the ABC-based direct collocation method is proposed. The control variables are discretized at a set of Legendre?Gauss collocation points and are optimized with the ABC approach. The parameters in ABC are assigned in terms of both the performance and the time cost of the algorithm. A penalty factor is adopted to modify the fitness value of some particular individuals in the colony so that every individual can be fully used. Series of comparative experimental results verify the feasibility and effectiveness of our proposed method. Further discussions and simulations are given for analyzing the impact of ABC parameters on the performance of the method. [ABSTRACT FROM AUTHOR]

This paper addresses a new trajectory tracking controller for quad-rotor aircrafts in the presence of time-varying aerodynamic effect and bounded external disturbance using the novel L1 adaptive control methodology augmented with nonlinear feed-forward compensations. The proposed augmented L1 adaptive controller achieves uniformly bounded transient and asymptotic tracking of the output signal for any designated bounded reference trajectory. Finally, simulations of tracking a circular reference trajectory are performed to illustrate the validity of the proposed controller. [ABSTRACT FROM AUTHOR]

Planar waypoint guidance synthesis methods for antiship missiles (ASMs) using optimal guidance laws are proposed. The energy optimal trajectory optimization problem with waypoint constraints is converted to an unconstrained optimization problem of finding the optimal boundary conditions at waypoints for the guidance laws. An optimal guidance law (OGL) for a 1st-order lag ASM with terminal constraints on the impact angle and lateral acceleration is newly proposed for this purpose. Theproposed method produces the energy optimal trajectory with high numerical efficiency. If the ASM is approximated by a lag-free system, optimal boundary conditions become waypoint passing angles which can be simply determined from a set of linear algebraic equations. Since there are no time-consuming numerical optimizations in this approach, the energy optimal trajectory passing through all the waypoints can be generated in real time. [ABSTRACT FROM AUTHOR]

A fully automatic tracking algorithm must be able to deal with an unknown number of targets, unknown target initiation and termination times, false measurements and possibly time-varying target trajectory behaviour. The approach presented in this paper follows the previously published integrated track splitting (ITS) framework which integrates a recursive calculation of the probability of target existence with multiscan trajectory estimation. This paper combines this framework with two multitarget tracking techniques. The first technique, joint multitarget tracking, enumerates and evaluates all feasible global measurement to track assignments resulting in a conditionally optimal but potentially computationally expensive technique. The second technique, linear multitarget (LM), achieves multitarget functionality by modulating clutter measurement density. LM is a suboptimal, but computationally very efficient technique. A simulation study is presented to show the effectiveness of this approach in the presence of nonuniform clutter when tracking targets in an environment where the targets perform violent manoeuvres. [ABSTRACT FROM AUTHOR]

An interacting multiple model (IMM) filter is presented for the real-time tracking of tactical ballistic missiles (TBMs). The novel aspects of the proposed IMM filter include the development of a constant axial force (CAF) Kalman filter, asymmetric IMM state interaction, and an entropy-based variation of the IMM mode probability update equation. Using data from a recent TBM defense (TBMD) test event, the proposed IMM filter is shown to yield consistent state estimates throughout the entire TBM trajectory, which includes a dual-stage boost during launch. [ABSTRACT FROM AUTHOR]

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets. [ABSTRACT FROM AUTHOR]

The linear trajectory of an airplane with constant velocity is obtained from Doppler shifts at stationary sensors, each yielding a corresponding time of closest approach, closest distance, and speed [3, 8]. Based on these inferences and on the sensors' locations, three sensors yield two candidate trajectories, and four sensors yield one-provided that the locations span R2 and R3, respectively: constituting observability for the problem at hand. [ABSTRACT FROM AUTHOR]

Scan-based emitter localization is a passive geolocation technique for stationary pulsed radars. In scan-based localization, knowledge of radar scan rate and radar beam intercept times are used to determine subtended angles of the radar location from receiver pairs. A collection of subtended angles is utilized to estimate the radar location. The paper presents a maximum likelihood (ML) scan-based localization algorithm and derives the Cramer-Rao lower bound (CRLB) for emitter location estimate. Based on maximization of the determinant of the Fisher information matrix, online gradient-based receiver trajectory optimization algorithms are developed. The effectiveness of the proposed algorithms is illustrated with simulation examples. [ABSTRACT FROM AUTHOR]

The Nash strategy in game theory has often been criticized as being ineffective in competitive multi-team target assignment problems, especially when compared with other simplistic strategies such as the random or greedy targeting strategies. This criticism arises from the fact that the Nash strategies may yield unpredictable results when paired with non-Nash strategies in non-zero sum games. In addition, the Nash equilibrium is generally more difficult to compute than strategies which do not attempt to anticipate the strategy of the other side. We seek to show that in multi-team target assignment problems the Nash strategy is superior to such simplistic strategies while also remaining computationally feasible. To demonstrate this point, we consider an attrition model consisting of two teams of nonhomogeneous fighting units simultaneously targeting each other and we compare the outcomes when various combinations of four targeting strategies are used on each side. The four strategies are: 1) the Random strategy where each unit selects its target randomly, 2) the Unit Greedy strategy where each unit chooses the target that optimizes its own performance only, 3) the Team Optimal strategy where the units coordinate their choice of targets so as to optimize the overall team performance while ignoring the possible strategy choices by the other team, and 4) the Team Nash strategy, calculated under the assumption that the other team is also using a Nash strategy. Because the computational requirements for calculating the Team Nash strategies may become unfeasibly large, we discuss an efficient method for approximating the Nash strategies using a neighborhood search algorithm called Unit Level team resource allocation (ULTRA). We compare the results for all 16 possible combinations of these four targeting strategies and show that for each team the Nash strategy outperforms all other strategies irrespective of the strategy employed by the other team. [ABSTRACT FROM AUTHOR]

A new methodology has been proposed to enhance inverse dynamics applications in the process of trajectory planning and optimization in terrain following flights (TFFs). The new approach uses a least square scheme to solve a general two-dimensional (2-D) TFF in a vertical plane. In the mathematical process, Chebyshev polynomials are used to model the geographical data of the terrain in a given route in a manner suitable for the aircraft at hand. The aircraft then follows the modeled terrain with sufficient clearance. In this approach the terrain following (TF) problem is effectively converted to an optimal tracking problem. Results show that this method provides a flexible approach to solve the TFF problem especially in conditions where the existing terrain to be flown over is not mathematically well behaved. [ABSTRACT FROM AUTHOR]

Many target tracking subsystems have the ability to schedule their own data rates; essentially they can ‘order’ new information whenever they need it, and the cost is in terms of the sensor resource. But among the unmanaged schemes, uniform sampling, in which a new measurement is requested periodically and regularly, Is the most commonly-used sampling scheme; deliberately nonuniform schemes are seldom given serious consideration. In this paper, however, we show that such schemes may have been discarded prematurely: a nonuniform sampling can have its benefits. Specifically, the nonuniform and uniform sampling schemes are compared for two kind of trackers: the probabilistic data association filter (PDAF), which updates its track based on a single scan of Information at a time; and N-D assignment (an optimization-based implementation of the multi-hypothesis tracker (MHT)), in which the sliding window involves many scans of observations. We find that given the ground rule of maintenance of the same overall scan rate (i.e., the same sensor effort) uniform sampling is always optimal for the single-scan tracker in the sense of track life. However, nonuniform sampling can outperform uniform sampling If a more sophisticated multi-scan tracker is used, particularly when 1) the target has a high process noise, and/or 2) the false alarm density is high, and/or 3) the probability of detection is high. [ABSTRACT FROM AUTHOR]

We describe the theory of a detect-track-confirm filter whose role is moving target detection and clutter suppression in surveillance data. The filter has broad generality due to the minimal assumptions made in developing the theory. Track confirmation is decided on the basis of a probability measure that is fully computable from clutter properties measured from surveillance data, without needing to assume target properties such as trajectory or detectability. Experimental results on real surveillance datasets are presented. [ABSTRACT FROM AUTHOR]

The question of inertial trajectory control of aircraft in the three-dimensional space is discussed. It is assumed that the nonilnear aircraft model has uncertain aerodynamic derivatives. The control system is decomposed into a variable structure outer loop and an adaptive inner loop. The outer-loop feedback control system accomplishes (x,y,z) position trajectory and sideslip angle control using the derivative of thrust and three angular velocity components (p,q,r) as virtual control inputs. Then an adaptive inner feedback loop is designed, which produces the desired angular rotations of aircraft using aileron, elevator, and rudder control surfaces to complete the maneuver. Simplification in the inner-loop design is obtained based on a two-time scale (singular perturbation) design approach by ignoring the derivative of the virtual angular velocity vector, which is a function of slow variables. These results are applied to a simplified F/A-18 model. Simulation results are presented which show that in the closed-loop system asymptotic trajectory control is accomplished in spite of uncertainties in the model at different flight conditions. [ABSTRACT FROM AUTHOR]

We present a novel empirical virtual sliding target (VST) guidance law for the midcourse phase of a long range surface-to-air missile that uses the simplicity of the conventional proportional navigation (PN)guidance law while exploiting the aerodynamic characteristics of a missile's flight through the atmosphere to enable the missile to achieve superior performance than that achieved by conventional PN guidance laws. The missile trajectory emulates the trajectory of an optimal control based guidance law formulated on a realistic aerodynamic model of the the missile-target engagement. The trajectory of the missile is controlled by controlling the speed of a virtual target that slides towards a predicted intercept point during the midcourse phase. Several sliding schemes, both linear and nonlinear, are proposed and the effect of the variation of the sliding parameters, which control the sliding speed of the virtual target, on the missile performance, are examined through extensive simulations that take into account the atmospheric characteristics as well as limitations on the missile in terms of the energy available and lateral acceleration limits. Launch envelopes for these sliding schemes for approaching and receding targets are also obtained. These results amply demonstrate the superiority of the proposed guidance law over the conventional PN law. [ABSTRACT FROM AUTHOR]

Proposes a narrowband technique based on the acoustical Doppler effect for estimating the trajectory of a turbo-prop aircraft in level flight with constant velocity as it transits over a ground-based passive acoustic sensor array. Acoustical Doppler effect; Parameter estimation with single sensor; Aircraft motion parameter estimation.

Describes the nonlinear filtering schemes for systems which allow non-Gaussian noise. Description of the most probable trajectory filtering approach; Hybrid approximation to nonlinear systems.

Presents information on a study which proposed an algorithm for determining the trajectory of a supersonic projectile intersecting a virtual target plane. Assumptions made about the trajectory; Time of arrival equations for an oblique hit; Expected random error; Conclusions.

Presents information on a study on the optimization of observer trajectories for fixed targets from a sequence of noisy bearing measurements. Problem definition; Numerical solution; Conclusions.

Presents information on a study on the analysis and compensation of trajectory deviations in airborne synthetic aperture radar systems. Frequency domain analysis; Simulation results; Conclusions.

Presents a study in which an estimation of target trajectory from passive sonar bearings and frequency measurements is modeled as a nonlinear multiresponse parameter estimation problem. Details on the study; What the results demonstrate.

Examines the performance analysis of source trajectory estimation using measurements provided by multiple platforms. Information on the basic problem in the target motion analysis (TMA); Details on the performance of any TMA algorithm; Detailed information on the study.