Generalized distributive law for ML decoding of space-time block codes

The problem of designing good space-time block codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well-known technique of decoding STBCs as conditional ML (CML) decoding. In this paper, we introduce a new framework to construct ML decoders for STBCs based on the generalized distributive law (GDL) and the factor-graph-based sum-product algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code, with respect to the constellation size, is strictly less than M-lambda, where lambda is the number of independent symbols in the STBC. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only half as complex as the CML decoder.

Extension of the universal erosive burning law to partly symmetric propellant grain geometries

This paper aims at extending the universal erosive burning law developed by two of the present authors from axi-symmetric internally burning grains to partly symmetric burning grains. This extension revolves around three dimensional flow calculations inside highly loaded grain geometry and benefiting from an observation that the flow gradients normal to the surface in such geometries have a smooth behavior along the perimeter of the grain. These are used to help identify the diameter that gives the same perimeter the characteristic dimension rather than a mean hydraulic diameter chosen earlier. The predictions of highly loaded grains from the newly chosen dimension in the erosive burning law show better comparison with measured pressure-time curves while those with mean hydraulic diameter definitely over-predict the pressures. (c) 2013 IAA. Published by Elsevier Ltd. All rights reserved.

Generalized distributive law for ML decoding of STBCs: further results

The problem of designing good Space-Time Block Codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well known technique of decoding STBCs as Conditional ML (CML) decoding. In [1], we introduced a framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm, and showed that for two specific families of STBCs, the Toepltiz codes and the Overlapped Alamouti Codes (OACs), the GDL based ML decoders have strictly less complexity than the CML decoders. In this paper, we introduce a `traceback' step to the GDL decoding algorithm of STBCs, which enables roughly 4 times reduction in the complexity of the GDL decoders proposed in [1]. Utilizing this complexity reduction from `traceback', we then show that for any STBC (not just the Toeplitz and Overlapped Alamouti Codes), the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras that is not multigroup or conditionally multigroup decodable, the GDL decoder provides approximately 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only about half as complex as the CML decoder.

Sliding mode control based guidance law with impact time constraints

In this paper, the sliding mode control based guidance laws to intercept stationary targets at a desired impact time are proposed. Then, it is extended to constant velocity targets using the notion of predicted interception. The desired impact time is achieved by selecting the interceptor's lateral acceleration to enforce a sliding mode on a switching surface designed using non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance law for different initial engagement geometries, impact times and salvo attack scenarios

Impact angle constraint guidance law using cubic splines for intercepting stationary targets

In this paper the cubic spline guidance law is presented for intercepting a stationary target at a desired impact angle. The guidance law is obtained from cubic spline curve based trajectory using an inverse method. The cubic spline t rajectory curve expresses the altitude as a cubic polynomial of the downrange. The guidance law is modified to achieve interception in the cases where impact angle is greater that or equal to 90◦. The guidance law is implemented in a feedback mode to maintain the desired impact angle and to reduce miss distance in the presence of lateral acceleration saturation and atmospheric distur- bances. The simulation results show that the guidance law fulfills all the requirements.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

Three Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control

In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory. The guidance law based on nonsingular terminal sliding mode guarantees finite time convergence of interceptor to the desired impact angle. In order to derive the guidance laws, multi-dimension switching surfaces are used. The stability of the system, with selected switching surfaces, is demonstrated using Lyapunov stability theory. Numerical simulation results are presented to validate the proposed guidance law.

Effect of catchment characteristics on the relationship between past discharge and the power law recession coefficient

This study concerns the relationship between the power law recession coefficient k (in - dQ/dt = kQ(alpha), Q being discharge at the basin outlet) and past average discharge Q(N) (where N is the temporal distance from the center of the selected time span in the past to the recession peak), which serves as a proxy for past storage state of the basin. The strength of the k-Q(N) relationship is characterized by the coefficient of determination R-N(2), which is expected to indicate the basin's ability to hold water for N days. The main objective of this study is to examine how R-N(2) value of a basin is related with its physical characteristics. For this purpose, we use streamflow data from 358 basins in the United States and selected 18 physical parameters for each basin. First, we transform the physical parameters into mutually independent principal components. Then we employ multiple linear regression method to construct a model of R-N(2) in terms of the principal components. Furthermore, we employ step-wise multiple linear regression method to identify the dominant catchment characteristics that influence R-N(2) and their directions of influence. Our results indicate that R-N(2) is appreciably related to catchment characteristics. Particularly, it is noteworthy that the coefficient of determination of the relationship between R-N(2) and the catchment characteristics is 0.643 for N = 45. We found that topographical characteristics of a basin are the most dominant factors in controlling the value of R-N(2). Our results may be suggesting that it is possible to tell about the water holding capacity of a basin by just knowing about a few of its physical characteristics. (C) 2015 Elsevier B.V. All rights reserved.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Scaling law characterizing the dynamics of the transition of HIV-1 to error catastrophe

Increasing the mutation rate, mu, of viruses above a threshold, mu(c), has been predicted to trigger a catastrophic loss of viral genetic information and is being explored as a novel intervention strategy. Here, we examine the dynamics of this transition using stochastic simulations mimicking within-host HIV-1 evolution. We find a scaling law governing the characteristic time of the transition: tau approximate to 0.6/(mu - mu(c)). The law is robust to variations in underlying evolutionary forces and presents guidelines for treatment of HIV-1 infection with mutagens. We estimate that many years of treatment would be required before HIV-1 can suffer an error catastrophe.

A Nonlinear Guidance Law for Impact Time Control

This paper discusses the problem of impact time control of an interceptor against a stationary target. A nonlinear guidance law is proposed with the interceptor heading angle variation as a function of the range to target. Closed-form expressions for the design parameters are derived for an exact analysis of the impact time. A feedback form of the guidance law is presented for addressing realistic implementation in the presence of autopilot lag. Using the closed-form expressions of the impact time, a cooperative guidance scheme is presented for simultaneous impact in a salvo attack. Extensive simulation studies are presented validating the analytic findings.

Nonlinear fatigue damage model based on the residual strength degradation law

In this paper, a logarithmic expression to describe the residual strength degradation process is developed in order to fatigue test results for normalized carbon steel. The definition and expression of fatigue damage due to symmetrical stress with a constant amplitude are also given. The expression of fatigue damage can also explain the nonlinear properties of fatigue damage. Furthermore, the fatigue damage of structures under random stress is analyzed, and an iterative formula to describe the fatigue damage process is deduced. Finally, an approximate method for evaluating the fatigue life of structures under repeated random stress blocking is presented through various calculation examples.

An adaptive sliding mode control law for the power maximization of the wind turbine system

POWERENG 2011