Realistic True Proportional Navigation Research Articles

Anti-packet loss collaborative filtering trajectory prediction of maneuvering target realistic true proportional navigation law interception guidance law

In this paper, a realistic true proportional navigation (RTPN) law–guided interception method was designed based on anti-packet loss collaborative filtering track prediction, which solves the problems that traditional RTPN method not considers the interceptor saturation overload limit and the determination of the acquisition area of any maneuvering target. First, a distributed cooperative filtering algorithm is formulated to improve accuracy and robustness of data fusion caused by the measurement error of target trajectory and the packet loss of cooperative detection data in the process of interception. Then, a track prediction algorithm is proposed to improve the data transmission and the dynamic response delay of the interceptor itself. Finally, the simulation results are performed to illustrate the effectiveness of the developed approach.

Capturability of 3D RTPN guidance law against true-arbitrarily maneuvering target with maneuverability limitation

The capturability of the Three-Dimensional (3D) Realistic True Proportional Navigation (RTPN) guidance law is thoroughly analyzed. The true-arbitrarily maneuvering target is considered, which maneuvers along an arbitrary direction in 3D space with an arbitrary but upper-bounded acceleration. The whole nonlinear relative kinematics between the interceptor and target is taken into account. First, the upper-bound of commanded acceleration of 3D RTPN is deduced, using a novel Lyapunov-like approach. Second, the reasonable selection range of navigation gain of 3D RTPN is analyzed, when the maneuver limitation of interceptor is considered. After that, a more realistic definition of capture is adopted, i.e., the relative range is smaller than an acceptable miss-distance while the approaching speed is larger than a required impact speed. Unlike previous researches which present Two-Dimensional (2D) capture regions, the inequality analysis technique is utilized to obtain the 3D capture region, where the three coordinates are the closing speed, transversal relative speed, and relative range. The obtained capture region could be taken as a sufficient-but-unnecessary condition of capture. The new theoretical findings are all given in explicit expressions and are more general than previous results.

Performance analysis of realistic true proportional navigation against maneuvering targets using Lyapunov-like approach

The realistic true proportional navigation (RTPN) is a variant of the true proportional navigation (TPN) guidance law for mathematical tractability. Although the performance of RTPN against nonmaneuvering targets or maneuvering targets with specific acceleration forms has been widely analyzed before, its performance against arbitrarily maneuvering targets has still not been explored. In this paper, using the Lyapunov-like approach, the performance of RTPN against maneuvering targets, whose magnitude is arbitrary but upper-bounded and direction is vertical to the line-of-sight (LOS), is well studied. The upper bounds of the LOS rate and commanded acceleration of RTPN are obtained, and the capture region is also presented. The nonlinear relative dynamics between the missile and target is taken into full account. Finally, the proposed theoretical findings are demonstrated by numerical simulation examples.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the non-linear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Design of Missile Guidance Law via Variable Structure Control

The missile guidance law utilizing variable structure control is proposed. The acceleration command input is determined considering the target acceleration as an uncertainty. The proposed guidance law uses only the information for the target acceleration bound; therefore, the precise measuring of target acceleration during the maneuver is not required, and the robustness to the target maneuver is achieved. It is also shown that the proposed guidance law can be classie ed into the augmented true proportional navigation or the augmented realistic true proportional navigation guidance law. Numerical simulations show that the proposed guidance law yields better performance compared to existing guidance laws. ROPORTIONAL navigation guidance (PNG) was e rst developed during the 1950s, and during the 1970s and 1980s various PNG laws such as pure proportional navigation (PPN), true proportional navigation (TPN), the optimal guidance law (OGL), generalized TPN (GTPN), and realistic TPN (RTPN) have been developed. 1;2 Lots of studies have been performed to obtain analytical solutions as well as to analyze the capture regions of the guidance laws. With the development of accurate avionic sensors, augmented proportional navigation (APN) and the predictive guidance law (PGL) utilizing the information about target acceleration were also proposed. By analyzing the various guidance laws, the characteristics of the guidance laws, capture regions, and pursuing performance were compared. 1;2

Robust Guidance Law with L2 Gain Performance.

The guidance law design problem is formulated as a disturbance attenuation L2 gain control problem where target accelerations are regarded as unpredictable disturbances that are completely unknown, but bounded and guidance parameter errors are viewed as bounded control system parameter uncertainties. By using a Lyapunov-like approach to find the feedback control, a guidance law satisfying the L2 gain performance is derived from a linear time-varying mathematical model that describes the missile-target engagement. During the derivation of the guidance law, its robust stability is proved. Simulation results show that the presented guidance law provides strong robustness properties against heading error, guidance parameter errors, and target maneuvers; thus they obtain excellent miss-distance performance over the conventional realistic true proportional navigation guidance law.

Nonlinear Control for Missile Terminal Guidance

Variable Structure Control (VSC) technique is applied to the design of robust homing missile guidance laws. In the design procedure, the target’s maneuver is assumed to be unpredictable and is considered as disturbances. Guidance laws are then proposed to achieve the interception performance for both cases of longitude-axis control being available and unavailable. The proposed guidance laws are continuous which alleviate chattering drawback by classic VSC design. Results are obtained and compared with those by realistic true proportional navigation design to illustrate the benefits of the proposed design. [S0022-0434(00)00604-3]

A unified approach to proportional navigation

In this paper, the two major classes of proportional navigation (PN), namely, true proportional navigation (TPN) and pure proportional navigation (PPN) are analyzed and solved by a unified approach. The analytical tools used in the line-of-sight (LOS) referenced systems such as TPN, realistic true proportional navigation (RTPN), generalized true proportional navigation (GTPN) and ideal proportional navigation (IPN), are extended here to handle the interceptor velocity referenced systems such as PPN and its variants. It is found that the above two branches of guidance systems belong to a more general PN scheme which defines the acceleration of the interceptor as being proportional to the LOS rate with direction normal to an arbitrarily assigned vector L/spl I.oarr/. For example, L/spl I.oarr/ of TPN is LOS, and L/spl I.oarr/ of PPN is the interceptor's velocity. Every PN scheme associates with a specific form of L/spl I.oarr/. The optimal PN (OPN) problem which concerns the determination of the optimal direction L/spl I.oarr/ is also addressed. Under the proposed general PN scheme, its six special cases, i.e., TPN, RTPN, GTPN, IPN, PPN, and OPN are solved in a unified way from which many new relations among them can be revealed, and their performances can be compared on a common basis.

Comments on "True proportional navigation with maneuvering target"

In the paper by D. Ghose (Jan. 1994), the author rightly pointed about the unrealistic target maneuvers considered by C.D. Yang et al. (1989) and by P.J. Yuan (1992) and he carried out the analysis for the target maneuver which is inversely proportional to the relative velocity component normal to the line of sight (LOs). This target maneuver is somewhat near to a realistic one, but still it suffers from one drawback. With this maneuver, the target pulls a high acceleration when the interceptor is on a collision course and a negligible acceleration when the LOS rate is already high. The author discusses realistic true proportional navigation (RTPN) because conventional true proportional navigation (TPN) is not used in actual scenario. The result is a third-order nonlinear equation.

Analytical Solution of 3D Realistic True Proportional Navigation

The main goal of this paper is to derive the complete solutions of three-dimensional realistic true proportional navigation (3D RTPN) for nonmaneuvering targets. Three coupled nonlinear second-order state equations describing the relative motion are solved analytically without any linearization for performance and trajectory analysis. Properties of 3D RTPN such as capture region, range-to-go, time-to-go, and two aspect angles within spherical coordinates are all obtained in closed form.

Analytical solution of three-dimensional realistic true proportional navigation

True proportional navigation with varying closing speed is called realistic true proportional navigation, which is implemented in practice. Our main goal is to derive the complete solutions of three-dimensional realistic true proportional navigation for nonmaneuvering and maneuvering targets. Three coupled nonlinear second-order state equations describing the relative motion are solved analytically without any linearization for performance and trajectory analysis. Properties of three-dimensional realistic true proportional navigation such as capture region, range-to-go, time-to-go, and two aspect angles within spherical coordinates are all obtained in closed form. Furthermore, the two-player game between three-dimensional realistic true proportional navigation and threedimensional ideal proportional navigation is investigated analytically in the pursuit-evasion scenario, where a realistic true proportional navigation guided missile is designed to pursue an ideal proportional navigation guided target. It is found that an ideal proportional navigation guided target is much harder to intercept than a realistic true proportional navigation guided target. I. Introduction ROPORTIONAL navigation (PN) for short-range tactical misP siles is the optimal interceptive law in the sense of producing zero miss distance with the least integral square control effort. PN has been studied since the 1940s. During the four decades that followed, proportional navigation has been explored in many different ways, such as true proportional navigation, pure proportional navigation (PPN), generalized proportional navigation, realistic true proportional navigation (RTPN), and ideal proportional navigation It has long been recognized that there exists a significant difference in the way in which PN guidance law is analyzed and in the way in which it is implemented. Most analytical studies of PN assume that the closing velocity in the PN guidance law is constant, whereas in realistic situations, the instantaneous closing speed may be continuously estimated or measured using devices such as homing seekers with Doppler radar. To remove this difference, RTPN, which adapts to varying closing speed, has recently been proposed. Performance and trajectory analysis of two-dimensional RTPN was studied by

Analytical solution of 3D true proportional navigation

The commanded acceleration applying in the direction normal to the line of sight (LOS) between the interceptor and its target is called true proportional navigation (TPN). The main goal of this work is to derive the complete analytical solutions of three-dimensional (3D) TPN for nonmaneuvering and maneuvering targets. Three coupled nonlinear second-order state equations describing the relative motion are solved analytically without any linearization for performance and trajectory analysis. Properties of 3D TPN such as capture region, range-to-go, time-to-go, and two aspect angles within spherical coordinates are all obtained in closed form. Furthermore, the comparison between 3D TPN and 3D realistic true proportional navigation (RTPN) is investigated analytically in the two-player game where a TPN-guided missile is commanded to pursue a RTPN-guided target, and vice versa.

True proportional navigation with maneuvering target

We analytically obtain the capture regions for the true proportional navigation (TPN) missile guidance law against an intelligently maneuvering target. Two versions of TPN are considered. The first is the original TPN which assumes the commanded lateral acceleration to be directly proportional to the line-of-sight (LOS) rate only, the proportionality factor being an arbitrary constant or dependent only on the initial closing velocity. The other, known as RTPN (realistic TPN), assumes the commanded lateral acceleration to be directly proportional to the LOS rate and also the current closing velocity. The target is assumed to maneuver in such a way as to increase the LOS rate and thus directly oppose the proportional navigation (PN) philosophy of annulling the LOS rate. A necessary and sufficient condition for capture is derived for the original TPN, and using it, the exact capture region is obtained. A sufficient condition for capture is derived for RTPN and is used to obtain its capture region partially. Some necessary conditions for capture are also derived for RTPN and are used to obtain an upper bound on its complete capture region. Using these conditions some important results on the existence of capture regions and a comparative study of capturability of TPN laws are also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Capture region for a realistic TPN guidance law

This work obtains the capture region for a realistic true proportional navigation (RTPN) guidance law against a nonmaneuvering target where the assumption of constant closing velocity used in the guidance law is relaxed. This is a realistic departure from earlier treatments of TPN. A capture equation is obtained and a qualitative study carried out for both zero and non-zero miss distances. The results are shown to be significantly different from those of earlier studies, showing a degradation in the performance of the guidance law in the form of reduced capture region. An example problem is computationally solved to obtain the exact capture region for various values of miss distances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>