On Optimal Control of Linear Systems in the Presence of Multiplicative Noise

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programing. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an "enforced separation" solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.     

Ground Testing of Inertial Navigators to Improve Dynamic Performance

A ground testing method has been devised to evaluate the dynamic errors of an inertial navigation system. A trimmed stationary inertial system in the navigation mode can be subjected to programmed platform orm drift rates, and generate position outputs which are compared with those of a perfect navigator. The linearized error equations for this testing mode are derived and the resulting position error propagation is analyzed using Kalman filtering in order to identify the error sources. A simulated platform with a fixed set of error sources is analyzed to evaluate this testing concept. An example is presented to show that the gyro and accelerometer scale factor and misalignment error coefficients can be estimated.     

Pure proportional navigation against time-varying target manoeuvres

Capturability of the pure proportional navigation (PPN) guidance law against a target executing bounded piecewise continuous time-varying manoeuvres is investigated. A qualitative analysis is carried out to obtain a set of sufficient conditions for capture defined on the engagement parameters and initial conditions. These conditions are significantly less restrictive than the ones obtained previously by others using the Lyapunov method. It is shown that the actual capture region for time-varying target manoeuvres, obtained by using the conditions derived, is much larger than that obtained from the Lyapunov technique. We also show that though a bounded tine varying target manoeuvre does change the constant target manoeuvre capture region to some extent, it does not reduce it drastically. Further, we show that the worst case capture region is obtained when the target executes a constant manoeuvre equal to the bound on the manoeuvre level. Some bounds on the missile lateral acceleration are also obtained for certain regions in the engagement plane. These results are generalizations and extensions of existing results on the capturability of the PPN guidance law against targets executing constant or time-varying target manoeuvres     

Modeling of dynamic evolution of coronal loops

Parameters of expanding magnetic loops and arches and of mass flows generated by them in the corona have been computed in a 1D two-fluid approximation. Two possible trigger mechanisms of the coronal transients have been considered: (i) sudden increase of the background magnetic field strength, and (ii) heating and compression plasma inside these magnetic structures. We discuss the formation of shock waves and their dependence on dynamics and geometry of the magnetic structures.     

Asymptotically Stable Motions of a Gyro in a Spinning Vehicle

An analysis of the motion of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain constant angular velocity xz about the spin axis of the gyro is presented. The nonlinearity in the equation of motion of the gimbal is retained. Using the Lyapunov approach, regions are obtained in the k-xz plane where k is the torsional spring constant, for asymptotic stability and for global asymptotic stability, and an estimate of the region of stability in state space is presented. Analytical relations for the selection of the gyro parameters are derived.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Pulsations of the R Coronae Borealis stars

The radial pulsations of very luminous, low-mass models (L/M 10⁴, solar units), which are possible representatives of the R CrB stars, have been examined. These pulsations are extremely nonadiabatic. We find that there are in some cases at least one extra (strange) mode which makes interpretation difficult. The blue instability edges are also peculiar, in that there is an abrupt excursion of the blue edge to the blue for L/M sufficiently large. The range of periods of the model encompasses observed periods of the Cepheid-like pulsations of actual R CrB stars.     

Track-While-Scan Algorithm in a Clutter Environment

A track-while scan (TWS) algorithm is developed for targets in a clutter environment. The problem has been studied using only the position measurements [1, 5-8], but the simulation results have not been satisfactory. Modern processing techniques (FFT processor) ) in air traffic control and surveillance radar receivers provide both position and radial velocity. The radial velocity measurement may be conveniently used in the target-track correlation process, which will reduce the association ambiguity in the clutter environment. t. In the clear environment the algorithm using the position and radial velocity measurements has been treated in [3, 4]. A TWS algorithm, using both position and radial velocity measurements for targets in a clutter environment, is presented here. The algorithm obtained is nonlinear and adaptive. In order to evaluate the improvement due to radial velocity measurement a simulation has been performed on a digital computer. The algorithm was run with and without radial velocity measurements to compare its performances. An improvement was noted especially when the target path included an accelerated portion.