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 nonlinear 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.

Fracture process zone size and true fracture energy of concrete using acoustic emission

Acoustic emission (AE) energy, instead of amplitude, associated with each of the event is used to estimate the fracture process zone (FPZ) size. A steep increase in the cumulative AE energy of the events with respect to time is correlated with the formation of FPZ. Based on the AE energy released during these events and the locations of the events, FPZ size is obtained. The size-independent fracture energy is computed using the expressions given in the boundary effect model by least squares method since over-determined system of equations are obtained when data from several specimens are used. Instead of least squares method a different method is suggested in which the transition ligament length, measured from the plot of histograms of AE events plotted over the un-cracked ligament, is used directly to obtain size-independent fracture energy. The fracture energy thus calculated seems to be size-independent.

Approximate linear time ML decoding on tail-biting trellises in two rounds

A linear time approximate maximum likelihood decoding algorithm on tail-biting trellises is presented, that requires exactly two rounds on the trellis. This is an adaptation of an algorithm proposed earlier with the advantage that it reduces the time complexity from O(m log m) to O(m) where m is the number of nodes in the tail-biting trellis. A necessary condition for the output of the algorithm to differ from the output of the ideal ML decoder is deduced and simulation results on an AWGN channel using tail-biting trellises for two rate 1/2 convolutional codes with memory 4 and 6 respectively, are reported.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Capturability of realistic generalized true proportional navigation

The capturability of a realistic generalized true proportional navigation (RGTPN) guidance law, against a nonmaneuvering target, is analyzed. The RGTPN law is obtained by relaxing the somewhat unrealistic assumption of constant closing velocity, made in all earlier studies on generalized true proportional navigation (GTPN), and incorporating the actual time-varying value in the guidance law. Closed-form solutions for the complete capture region of RGTPN is obtained in terms of both zero and acceptable non-zero miss distances. It is shown that the capture region of RGTPN in the initial relative velocity space is significantly smaller than that of GTPN, for reasonable values of navigation constant (N) and angular direction (eta) of the missile commanded latax. However, for certain values of N and eta, capturability of RGTPN is found to be better. It is also shown that if in one of the versions of GTPN, which uses constant values of both the closing velocity and the line-of-sight (LOS) angular velocity in the guidance law, the corresponding realistic time-varying quantities are used, the capture region actually expands to cover the whole of the initial relative velocity space. A number of examples are given to compare the capture performance of RGTPN with other versions of the GTPN guidance laws.

Turning visual search time on its head

Our everyday visual experience frequently involves searching for objects in clutter. Why are some searches easy and others hard? It is generally believed that the time taken to find a target increases as it becomes similar to its surrounding distractors. Here, I show that while this is qualitatively true, the exact relationship is in fact not linear. In a simple search experiment, when subjects searched for a bar differing in orientation from its distractors, search time was inversely proportional to the angular difference in orientation. Thus, rather than taking search reaction time (RT) to be a measure of target-distractor similarity, we can literally turn search time on its head (i.e. take its reciprocal 1/RT) to obtain a measure of search dissimilarity that varies linearly over a large range of target-distractor differences. I show that this dissimilarity measure has the properties of a distance metric, and report two interesting insights come from this measure: First, for a large number of searches, search asymmetries are relatively rare and when they do occur, differ by a fixed distance. Second, search distances can be used to elucidate object representations that underlie search - for example, these representations are roughly invariant to three-dimensional view. Finally, search distance has a straightforward interpretation in the context of accumulator models of search, where it is proportional to the discriminative signal that is integrated to produce a response. This is consistent with recent studies that have linked this distance to neuronal discriminability in visual cortex. Thus, while search time remains the more direct measure of visual search, its reciprocal also has the potential for interesting and novel insights. (C) 2012 Elsevier Ltd. All rights reserved.

Joint data detection and dominant singular mode estimation in time varying reciprocal MIMO systems

This paper proposes an algorithm for joint data detection and tracking of the dominant singular mode of a time varying channel at the transmitter and receiver of a time division duplex multiple input multiple output beamforming system. The method proposed is a modified expectation maximization algorithm which utilizes an initial estimate to track the dominant modes of the channel at the transmitter and the receiver blindly; and simultaneously detects the un known data. Furthermore, the estimates are constrained to be within a confidence interval of the previous estimate in order to improve the tracking performance and mitigate the effect of error propagation. Monte-Carlo simulation results of the symbol error rate and the mean square inner product between the estimated and the true singular vector are plotted to show the performance benefits offered by the proposed method compared to existing techniques.

Capturability of Augmented Pure Proportional Navigation Guidance Against Time-Varying Target Maneuvers

This paper proposes a variation of the pure proportional navigation guidance law, called augmented pure proportional navigation, to account for target maneuvers, in a realistic nonlinear engagement geometry, and presents its capturability analysis. These results are in contrast to most work in the literature on augmented proportional navigation laws that consider a linearized geometry imposed upon the true proportional navigation guidance law. Because pure proportional navigation guidance law is closer to a realistic implementation of proportional navigation than true proportional navigation law, and any engagement process is predominantly nonlinear, the results obtained in this paper are more realistic than any available in the literature. Sufficient conditions on speed ratio, navigation gain, and augmentation parameter for capturability, and boundedness of lateral acceleration, against targets executing piecewise continuous maneuvers with time, are obtained. Further, based on a priori knowledge of the maximum maneuver capability of the target, a significant simplification of the guidance law is proposed in this paper. The proposed guidance law is also shown to require a shorter time of interception than standard pure proportional navigation and augmented proportional navigation. To remove chattering in the interceptor maneuver at the end phase of the engagement, a hybrid guidance law using augmented pure proportional navigation and pure proportional navigation is also proposed. Finally, the guaranteed capture zones of standard and augmented pure proportional navigation guidance laws against maneuvering targets are analyzed and compared in the normalized relative velocity space. It is shown that the guaranteed capture zone expands significantly when augmented pure proportional navigation is used instead of pure proportional navigation. Simulation results are given to support the theoretical findings.

MULTI-PITCH TRACKING USING GAUSSIAN MIXTURE MODEL WITH TIME VARYING PARAMETERS AND GRATING COMPRESSION TRANSFORM

Grating Compression Transform (GCT) is a two-dimensional analysis of speech signal which has been shown to be effective in multi-pitch tracking in speech mixtures. Multi-pitch tracking methods using GCT apply Kalman filter framework to obtain pitch tracks which requires training of the filter parameters using true pitch tracks. We propose an unsupervised method for obtaining multiple pitch tracks. In the proposed method, multiple pitch tracks are modeled using time-varying means of a Gaussian mixture model (GMM), referred to as TVGMM. The TVGMM parameters are estimated using multiple pitch values at each frame in a given utterance obtained from different patches of the spectrogram using GCT. We evaluate the performance of the proposed method on all voiced speech mixtures as well as random speech mixtures having well separated and close pitch tracks. TVGMM achieves multi-pitch tracking with 51% and 53% multi-pitch estimates having error <= 20% for random mixtures and all-voiced mixtures respectively. TVGMM also results in lower root mean squared error in pitch track estimation compared to that by Kalman filtering.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

Time-Resolved Resonance Raman Spectroscopic Studies on the Radical Anions of Menaquinone and Naphthoquinone

Quinones and their radical ion intermediates have been much studied by vibrational spectroscopy to understand their structure-function relationships in various biological processes. In this paper, we present a comprehensive analysis of vibrational spectra in the structure-sensitive region of both the naphthoquinone (NQ) and 2-methyl-1,4-naphthoquinone (MQ, menaquinone) radical anions using time-resolved resonance Raman and ab initio studies. Specific vibrational mode assignments have been made to all the vibrational frequencies recorded in the experiment. It is observed that the carbonyl and C-C stretching frequencies show considerable coupling in NQ and MQ radical anions. Further, the asymmetric substitution present in MQ with respect to NQ shows important signatures in the radical anion spectrum. It is concluded that assignments of vibrational frequencies of asymmetrically substituted quinones must take into consideration the influence of asymmetry on structure and reactivity.

Time-temperature histories of spherical food products during bulk forced-air precooling

A general mathematical model for forced air precooling of spherical food products in bulk is developed. The food products are arranged inline to form a rectangular parallelepiped. Chilled air is blown along the height of the package. The governing equations for the transient two-dimensional conduction with internal heat generation in the product, simultaneous heat and mass transfer at the product-air interface and one-dimensional transient energy and species conservation equations for the moist air are solved numerically using finite difference methods. Results are presented in the form of time-temperature histories. Experiments are conducted with model foods in a laboratory scale air precooling tunnel. The agreement between the theoretical and experimental results is found to be good. In general, a single product analysis fails to predict the precooling characteristics of bulk loads of food products. In the range of values investigated, the respiration heat is found to have a negligible effect.

Enhanced sensitivity in detection of Kerr rotation by double modulation and time averaging based on Allan variance

Experiments in spintronics necessarily involve the detection of spin polarization. The sensitivity of this detection becomes an important factor to consider when extending the low temperature studies on semiconductor spintronic devices to room temperature, where the spin signal is weaker. In pump-probe experiments, which optically inject and detect spins, the sensitivity is often improved by using a photoelastic modulator (PEM) for lock-in detection. However, spurious signals can arise if diode lasers are used as optical sources in such experiments, along with a PEM. In this work, we eliminated the spurious electromagnetic coupling of the PEM onto the probe diode laser, by the double modulation technique. We also developed a test for spurious modulated interference in the pump-probe signal, due to the PEM. Besides, an order of magnitude enhancement in the sensitivity of detection of spin polarization by Kerr rotation, to 3x10(-8) rad was obtained by using the concept of Allan variance to optimally average the time series data over a period of 416 s. With these improvements, we are able to experimentally demonstrate at room temperature, photoinduced steady-state spin polarization in bulk GaAs. Thus, the advances reported here facilitate the use of diode lasers with a PEM for sensitive pump-probe experiments. They also constitute a step toward detection of spin-injection in Si at room temperature.

Constraining the low-energy pion electromagnetic form factor with space-like and phase of time-like data

The Taylor coefficients c and d of the EM form factor of the pion are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4m(pi)(2) <= t <= t(in) and its value at one space-like point, using as input the (g - 2) of the muon. This is achieved using the technique of Lagrange multipliers, which gives a transparent expression for the corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in the literature and find agreement with the chiral perturbation-theory results for c. We obtain d similar to O(10) GeV-6 when c is set to the chiral perturbation-theory values.