On Signal Fluctuations in Tracking Systems

All tracking systems suffer, to some extent, from signal level fluctuations. The signal fluctuations are modeled by a Gaussian process and the noise performance of both linear and nonlinear first-order tracking systems is considered. In the nonlinear case, the Ito versus Stratonovich calculus difficulty arises, but it is resolved to make sense physically. Several analytical results are obtained which are useful in analyses of tracking systems.     

Constant-False-Alarm-Rate Processors for Locally Nonstationary Clutter

A technique for designing normalizing processors for locally non-stationary clutter is discussed. The design procedure assumes the logarithm of the clutter power varies as a polynomial with range. When the actual environment matches the design environment, the false-alarm rate is a constant that is independent of the polynomial coefficients. A measure of the relative target detection capability as a function of the number of normalization cells and the degree of the design-environment polynomial is given. The applicability of the processors to non-Rayleigh clutter is discussed.     

Cross Polarization in Radomes: A Program for Its Computation

A study is made of transmission by radomes, with particular reference to cross polarization, and of the consequent radiation patterns of the radome with its aerial for both linear and circular polarizations. The work is embodied in a computer program which considers a scanner of specifiable size, position, and power distribution at different orientations inside a multilayer radome of given dimensions, class of shape, and construction in terms of the number and properties of its layers. Initially, rays are traced from points on the scanner, and details of their paths and propagation are presented in tables of preliminary results; later, diffraction theory is used. Polar diagrams of cross polarization, of main beam, etc., are presented in final tables for the system. Nearly all the parameters are specifiable, and so the program has reasonably general applicability, and it can also assess the effects of bandwidth, tapering of layer thickness, complex permittivity, and other parameters of the system.     

An Analysis of Helicopter Rotor Modulation Interference

In satellite-to-helicopter communications, interference exists on the incoming signal when the receiving antenna is located below the rotor blades. A bound is established for the performance of a coherent fixed-tone ranging system operating at L band in this interference environment. The scalar diffracted field beneath the rotating blades, at L band and above, is found to satisfy the criterion of Fresnel diffraction, and is computed using the techniques of Fourier optics. The diffracted field is expressed in terms of a narrow-band signal. The amplitude and phase components are calculated from a Fourier Series expansion using the FFT algorithm. The significant harmonics of the phase component of the interference combine with the baseband of the narrow-band, phase-modulated ranging signal. This results in CW interference, and in rearrangement of the first-order, sideband, ranging-tone channel powers. The degradation in ranging accuracy is evaluated by computing the signal-to-interference (SIR) ratio for a set of ranging tones. The post-detection (SIR)PD at the output of the correlator is shown to be a function of the amplitude of the phase harmonics of the interference, the relative difference between the ranging tone and interference center frequencies (a function of rotor speed), the rangetone modulation indices, and the post-detection filter noise bandwidth.     

Degradation of Probability of Error Due to IF Filtering

The probability of error P(e) is computed in a binary communication system with a single-pole IF filter. The effect of time-bandwidth product foT and IF frequency to band width ratio f1/Ifo on P(e) is shown. The sampling time is optimized and the effect of nonoptimal sampling time on P(e) is calculated.     

Performance Degradation Due to Specular Multipath Intersymbol Interference

Plots of performance degradation are used to compare the effects of fading and intersymbol interference in a two- component specular multipath digital communications channel. Similar plots are then used to compare two practical receivers designed to combat the interference. Degradation plots are shown to allow easy identification of each receiver's range of usefulness, as well as identification of variance bounds demanded of channel parameter estimates which the receivers require.     

Origin of planetary atmospheres

The near absence of noble gases on earth, other than those of radioactive origin, indicates that the earth was formed by the accumulation of planetesimals; this process systematically excluded all constituents that did not enter into the solid phase. The atmosphere and the ocean with many of its dissolved salts have arisen from gases emitted from the earth's interior, a process that continues today. The oxygen in the earth's atmosphere plus a greater quantity that has been removed from the atmosphere to oxidize geologic materials, has arisen mainly from a small excess of photosynthesis over decay of organic material. The atmospheres of Mars and Venus have probably arisen in a manner similar to the atmosphere on earth, by emission from the planetary interiors. However, they have not received any oxygen from photosynthesis and so are nearly oxygen free. Mars has very little water in its atmosphere, and this can be explained by its lower than freezing average surface temperature. Venus also has very little water, and this requires an ad hoc explanation; one possibility is that Venus was formed from much drier planetesimals than was the earth. Mercury and the moon are virtually without atmospheres. Although some gases may be emitted from their interiors, they are presumably rapidly lost by escape. Whatever atmosphere they possess is probably due to the neutralized solar wind that impinges upon them. The outer planets retained volatiles, including hydrogen and helium, to a much greater extent than did the terrestrial planets.     

Formation and evolution of low-mass Algols

We discuss the origin, evolution and fate of low-mass Algols (LMA) that have components with initial masses less than 2.5 M₀. The semi-major axes of orbits of pre-LMA do not exceed 20–25 R₀. The rate of formation of Algol-type stars is 0.01/year. Magnetic stellar winds may be the factor that determines the evolution of LMA. Most LMA end their lives as double helium degenerate dwarfs with M₁/M₂ 0.88 (like L870-2). Some of them even merge through angular momentum loss caused by gravitational waves.     

Leveling of Analytic Platforms

Use of an analytic platform or strapdown system requires that the system em be initially leveled just as a conventional multigimbaled platform must be leveled. The process of leveling involves the determination of the orientation between the local vertical and an instrumented reference nce frame. With a conventional platform it is quite common to use a pair of servo loops to precess the inner gimbal until gravity signals are nulled on two orthogonally mounted accelerometers. The input axes of these two accelerometers thus define the horizontal plane and the platform is said to be leveled. A strapdown system, however, lacks the physical entity of the inner gimbal and consequently cannot be physically precessed into verticality. The method of leveling is nonetheless analogous if we consider the computational reference frame of the analytic platform to be the "alter ego" or counterpart of a physical inner gimbal. In general, strapdown leveling techniques can be divided into two categories: closed-loop leveling and open-loop leveling. These two techniques are quantitatively developed and discussed in this paper.     

Attitude Determination Via Nonlinear Filtering

The theory of nonlinear filtering has been applied to the problem of the attitude determination of a satellite. Two approximation methods have been studied with a view to practical implementation. Computer simulation results are included.