A significant reduction in the time required to obtain an estimate of the mean frequency of the spectrum of Doppler signals when seeking to measure the instantaneous velocity of dangerous near-Earth cosmic objects (NEO) is an important task being developed to counter the threat from asteroids. Spectral analysis methods have shown that the coordinate of the centroid of the Doppler signal spectrum can be found by using operations in the time domain without spectral processing. At the same time, an increase in the speed of resolving the algorithm for estimating the mean frequency of the spectrum is achieved by using fractional differentiation without spectral processing. Thus, an accurate estimate of location of the centroid for the spectrum of Doppler signals can be obtained in the time domain as the signal arrives. This paper considers the implementation of a fractional-differentiating filter of the order of 1 ⁄2 by a set of automation astatic transfer elements, which greatly simplifies practical implementation. Real technical devices have the ultimate time delay, albeit small in comparison with the duration of the signal. As a result, the real filter will process the signal with some error. In accordance with this, this paper introduces and uses the concept of a "pre-derivative" of 1 ⁄2 of magnitude. An optimal algorithm for realizing the structure of the filter is proposed based on the criterion of minimum mean square error. Relations are obtained for the quadrature coefficients that determine the structure of the filter.
A new method for the line-of-sight velocity estimation of a high-speed near-Earth object (asteroid, meteorite) is suggested. The method is based on use of fractional, one-half order derivative of a Doppler signal. The algorithm suggested is much simpler and more economical than the classical one, and it appears preferable for use in orbital weapon systems of threat response. Application of fractional differentiation to quick evaluation of mean frequency location of the reflected Doppler signal is justified. The method allows an assessment of the mean frequency in the time domain without spectral analysis. An algorithm structure for the real-time estimation is presented. The velocity resolution estimates are made for typical asteroids in the X-band. It is shown that the wait time can be shortened by orders of magnitude compared with similar value in the case of a standard spectral processing.
Radiolocation methods of probing minor celestial bodies (asteroids) by the nanosecond pulses can be used for monitoring of near-Earth space with the purpose of identification of hazardous cosmic objects able to impact the Earth.Development of the methods that allow to improve accuracy of determining the asteroids size (i.e. whether it measures tens or hundreds meters in diameter) is important for correctly estimating the degree of damage which they can cause (either regional or global catastrophes, respectively). In this paper we suggest a novel method of estimating the sizes of the passive cosmic objects using the radiolocation probing by ultra-high-resolution nanosecond signals to obtain radar signatures. The modulation envelope of the reflected signal, which is a radar portrait of the cosmic object, is subjected to time scale transformation to carrier Doppler frequency by means of radioimpulse strobing. The shift of a strobe within the probing period will be performed by radial motion of the object which will allow to forgo the special autoshift circuit used in the oscillographic technical equipment.The measured values of duration of radiolocation portrait can be used to estimate the mean radius of the object by using the average spatial length of the portrait. The method makes it possible to appraise the sizes of cosmic objects through their radiolocation portrait duration, with accuracy that is independent of the objects range.
This study is concerned with the problem of increasing the accuracy of a low-altitude altimeter employing the frequency modulation principle. A way to suppress the "discrete error" of the altimeter by employing additional «slow» frequency modulation of the carrier wave and averaging the resulting counts is considered. The benefit of such approach is simplicity of technical implementation manifesting in minimal changes in the microwave path and the recording device, which needs to run in averaging count mode. It is shown that, given a limited frequency band, the linear modulation form is not optimal. Results of error calculations presented are obtained via mathematical modelling of the altimeter’s operation for different shapes of the additional prequency modulation. It is shown that using complex shapes of the «slow» modulation with positive third derivative and optimizing for a given altitude range allows to reduce the average measurement error 2–3 times additionally relatively to the linear modulation form without expanding the occupied frequency band.
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