Farhan Faruqi - Academia.edu (original) (raw)

Papers by Farhan Faruqi

Differential Game Theory and Applications to Missile Guidance Nomenclature k: is the epoch (in a ... more Differential Game Theory and Applications to Missile Guidance Nomenclature k: is the epoch (in a discrete time game). P: is the set of players in a game. U: is the set of strategies available to all the players. U i : is the set of strategies available to player i. J ij (⋯): is the objective function for players i and j. X k : is the set of current state of a game at epoch k. U k : is the set of strategies available to a player at epoch k. u ij (k): is the strategy vector (input vector) available to player i against player j at epoch k. C k : is the set of constraints at epoch k. G k : is the set of elements of a discrete-time game. t: is the time in a continuous time (differential) game. X t : is the set of states of a game at time t. U t : is the set of strategies at time t. u ij (t): is the strategy vector (input vector) available to player i against player j at time t. C t : is the set of constraints at time t. G t : is the set of elements of a continuous time (differential) game. x ij (t): is the relative state vector of player i w.r.t. player j at time t. u i (t): is the strategy vector (input vector) of player i. F: is the state coefficient matrix. G: is the input coefficient matrix. Q: is the PI weightings matrix on the current relative states. S: is the PI weightings matrix on the final relative states. {R i , R j }: are PI weightings matrices on inputs.

Addressed here is the precision missile guidance problem where the successful intercept criterion... more Addressed here is the precision missile guidance problem where the successful intercept criterion has been defined in terms of both minimizing the miss distance and controlling the missile body attitude with respect to the target at the terminal point. We show that the H control theory when suitably modified provides an effective framework for the precision missile guidance problem. Existence of feedback controllers (guidance laws) is investigated for the case of finite horizon and non-zero initial conditions. Both state feedback and output feedback implementations are explored.

Proceedings of SPIE, Jun 26, 1997

Passive position location using bearings only information is a classical navigation problem, Vari... more Passive position location using bearings only information is a classical navigation problem, Various methods proposed to date use either triangulation or circulation rules in nonlinear filtering framework; like nonlinear least squares filtering method providing approximate maximum likelihood estimates and extended Kalman filtering method providing approximate minimum variance estimates. Both are approximate filters due to inherent linearization in these methods. A completely optimal nonlinear filter, referred to as Bayes' conditional density filter is presented in this paper. This method is not subjected to any linearization mechanisms as in other methods currently in use. However, the method is subjected to increased computational burden.

A precision guidance law is presented for three dimensional intercepts against a moving target. W... more A precision guidance law is presented for three dimensional intercepts against a moving target. We consider a measurement model representative of an optical sensor and optical flow calculations, the use of optical flow for guidance and navigation having been inspired by recent research into insect navigation. The guidance law is based on a circular navigation guidance, extended to three dimensions and adapted to this measurement model.

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), Jul 10, 2003

The problem of phase ambiguity resolution and ltering for interferometric GPS attitude determinat... more The problem of phase ambiguity resolution and ltering for interferometric GPS attitude determination is considered. Traditionally, the resolution of the phase ambiguity and the ltering stages were performed separately, with the lter formulated on the basis that the phase ambiguity i s correctly resolved. Should the pre-processing stage not resolve the ambiguity correctly, erroneous results may occur. In response, a unied solution is proposed in which the ambiguity resolution and ltering processes are combined under a Gaussian Sum Filtering (GSF) framework. The GSF naturally accounts for the measurement a m biguity b y generating multi-modal probability densities, which leads to a probabilistic interpretation of the attitude estimates. Simulations are performed to illustrate the eectiveness and functionality of the proposed solution.

This report presents a multivariable controller design for a generic missile travelling at hypers... more This report presents a multivariable controller design for a generic missile travelling at hypersonic speed. The controller is based on the theory of optimal control, and the solution is provided by a feedback controller known as a Linear Quadratic Regulator (LQR) for tracking the demands (lateral acceleration and roll rate) as closely as possible while keeping the actuator efforts (for deflecting aileron, elevator and rudder) small. In the computer simulation, the missile model is subject to various hypersonic flight conditions and gain scheduling is exercised as a function of dynamic pressure. The intial study assumes perfect knowledge of all the states for the controller design. Subsequently, a state observer (kalman filter) is introduced into the design to reflect a more practical synthesis where some of the states need to be estimated.

Isspa 96 Fourth International Symposium on Signal Processing and Its Applications Proceedings Vols 1 and 2, 1996

An integrated Global Positioning System/Inertial Navigation System (GPS/INS) navigation model is ... more An integrated Global Positioning System/Inertial Navigation System (GPS/INS) navigation model is developed specifically for aerospace applications involving high vehicle dynamics. To aid attitude determination a non-dedicated multiple GPS antenna configuration is employed. Simulated results show that the resulting Extended Kalman Filter (EKF) implementation provides robust estimates of the vehicle states. Additional investigation focusses upon filter performance sensitivity to antenna noise correlation and antenna displacements.

Acquisition, Tracking, and Pointing XI, 1997

In a realistic passive sonar environment, the received signal consists of multipath arrivals from... more In a realistic passive sonar environment, the received signal consists of multipath arrivals from closely separated moving targets. The signals are contaminated by spatially correlated noise. The differential MUSIC has been proposed to estimate the DOAs in such a scenario. This method estimates the 'noise subspace' in order to estimate the DOAs. However, the 'noise subspace' estimate has to be updated as and when new data become available. In order to save the computational costs, a new adaptive noise subspace estimation algorithm is proposed in this paper. The salient features of the proposed algorithm are: (1) Noise subspace estimation is done by QR decomposition of the difference matrix which is formed from the data covariance matrix. Thus, as compared to standard eigen-decomposition based methods which require O(N3) computations, the proposed method requires only O(N2) computations. (2) Noise subspace is updated by updating the QR decomposition. (3) The proposed algorithm works in a realistic sonar environment. In the second part of the paper, the estimated bearing values are used to track multiple targets. In order to achieve this, the nonlinear system/linear measurement extended Kalman filtering proposed is applied. Computer simulation results are also presented to support the theory.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

SPIE Proceedings, 1997

The problem of dynamic phase ambiguity resolution and filtering for interferometric GPS attitude ... more The problem of dynamic phase ambiguity resolution and filtering for interferometric GPS attitude determination is considered. Traditionally, the resolution of the phase ambiguity and the filtering stages were performed separately, with the filter formulated on the basis that the phase ambiguity is correctly resolved. Should the pre- processing stage not resolve the ambiguity correctly, erroneous results may occur. In response, a unified approach is proposed in which the ambiguity resolution and filtering processes are combined under a Gaussian sum filtering (GSF) framework. In addition, the consideration of the carrier Doppler shift information leads to a dynamic phase ambiguity resolution model which is naturally enveloped by the GSF paradigm. Simulated results in both static and dynamic attitude scenarios illustrate the statistical robustness of the GSF methodology.

Space Guidance, Control, and Tracking II, 1995

The Integrated Global Positioning System (GPS)/Inertial Navigation System (INS) is a cost effecti... more The Integrated Global Positioning System (GPS)/Inertial Navigation System (INS) is a cost effective way of providing an accurate and reliable navigation system for civil and military aviation. These systems also provide low cost solutions to mid-course navigation and guidance of medium and long range weapon systems. In this paper an error model is developed which can be used for GPS/INS filter mechanization. It is known that the model has a linear and a non-linear part. The latter consist of a quadratic function of system states and may be approximated by a noise term thereby allowing the use of the well known Kalman Filter (KF) design technique. KF algorithm suitable for this application is also developed, and computer simulation results for a typical aerospace application are given.

Control and Intelligent Systems, 2007

This paper introduces the concept of terminal attitude guidance as an alternative to precision gu... more This paper introduces the concept of terminal attitude guidance as an alternative to precision guidance and uses fuzzy control ideas in designing a control strategy for a pursuer in countering a manoeuvreing target. The fuzzy controller uses only angle measurements in the control strategy and produces satisfactory results in comparison to the LQR or H∞ type guidance controllers, although they were addressed in a precision guidance context. Both 2D and 3D cases have been considered.

The solution of the Fokker-Planck-Kolmogorov (FPK) forward diffusion equation in conjunction with... more The solution of the Fokker-Planck-Kolmogorov (FPK) forward diffusion equation in conjunction with Bayes’ conditional density lemma provides optimal (minimum variance) state estimates of any general stochastic dynamic system (SDS). It has been well documented in non-linear filtering literature that the analytical solution for the FPK equation is extremely difficult to obtain except in a few special cases. In this paper we propose the use of numerical solution of FPK to obtain the optimal state estimates of a non-linear dynamic system. The proposed method provides the conditional densities &om which the conditional means (the optimal state estimates) can be easily evaluated. The estimated conditional densities clearly violate the assump tions of Gaussianity implicitly required by Extended Kalman Filter (EKF) based approaches. The performance of the proposed method is compared with that of the EKF. Monte-Carlo simulation results are provided to show the superior performance of the dens...

IEEE Transactions on Aerospace and Electronic Systems, 1980

The problem of solving the matrix Riccati differential equation in the design of Kalman filters f... more The problem of solving the matrix Riccati differential equation in the design of Kalman filters for the target tracking problem is considered. An algebraic transformation method is used to reduce the order of the Riccati differential equation and to obtain explicit expressions for the filter gains (in terms of the interceptor/target separation range) which results in a substantial reduction of the computer burden involved in estimating the target states. The applicability of the transform technique is demonstrated for the receiver thermal noise and the target glint noise cases.

Abstract : This report presents a multivariable controller design for a generic missile travellin... more Abstract : This report presents a multivariable controller design for a generic missile travelling at hypersonic speed. The controller is based on the theory of optimal control, and the solution is provided by a feedback controller known as a Linear Quadratic Regulator (LQR) for tracking the demands (lateral acceleration and roll rate) as closely as possible while keeping the actuator efforts (for deflecting aileron, elevator and rudder) small. In the computer simulation, the missile model is subject to various hypersonic flight conditions and gain scheduling is exercised as a function of dynamic pressure. The initial study assumes perfect knowledge of all the states for the controller design. Subsequently, a state observer (kalman filter) is introduced into the design to reflect a more practical synthesis where some of the states need to be estimated.

Encyclopedia of Aerospace Engineering, 2010

... under 20.0 m in range for stand-alone C/A (coarse) code receiver and under 5.0 m for (precisi... more ... under 20.0 m in range for stand-alone C/A (coarse) code receiver and under 5.0 m for (precision) P-code. ... Using a constrained optimization technique trade off is achieved between stealth andpath length. ... The process is repeated until an optimum path solution is obtained. ...

In this report a 3-D mathematical modelfor multi-party engagement kinematics is derived suitable ... more In this report a 3-D mathematical modelfor multi-party engagement kinematics is derived suitable for developing, implementing and testing modern missile guidance systems. The model developed here is suitable for both conventional and more advanced optimal intelligent guidance schemes including those that arise out of the differential game theory. This model accommodates changes in vehicle body attitude and other non-linear effects such as limits on lateral acceleration and aerodynamic forces.