The article examines the features of the radar altimeter reflected signal modeling over the sea surface. The model operates at different wave heights, pitch and roll angels, speeds of the aircraft and widths of the antenna pattern. A brief description of the radio altimeter influencing factors is made. Modeling results are analyzed. The complex of hardware-in-the-loop (HIL) simulation with the implementation of the resulting mathematical model is considered.
The energy spectrum of sea waves is calculated (capillary model for ripples and TMA model for wind waves): ( ) =
( ) ∙ Φ( ∗, ℎ) ( ) =
∙ 2 (2 )4∙ 5 − ( 54 )4 ∙ γ − 2∙ 2 −1 (1) (2) where α is the scaling parameter; γ is the peak enhancement factor; is evaluated as 0,07 for f ≤ fp and 0,09 otherwise; F is fetch length; fp is the frequency at the spectral peak; Ф(f*,h) is the Kitaigorodoskii depth function.
According to this spectrum, the parameters for each elementary wave of sea surface are defined (height and wavelength, direction of propagation, wave phase, etc.). These data, together with the aircraft speed vector, current time and antenna direction are inserted into the analytical ( 0 ∙ [( + ( − ) ∙ ) ∙ + ( + ( − ) ∙ ) ∙ ] − Ω ∙ + ) (3) formula: where x, y is the actual location at time t; n is the number of wave trains; Vх,Vy is aircraft speed projection; Unx, Uny is waves speed projection; z + (Vх – Unx)t, y + (Vy – Uny) is offset in the Оxy plane; is the wave phase; is the direction of wave propagation; Ω is the pulsation; 0 is the wave number; Nf >> 1 is the number of waves; σ is the standard deviation of sea wave heights; С is the normalization constant. The resulting surface is converted into an unordered set of triangles by Delaunay triangulation (every three samples are grouped into facet) (Figure 1). Further, there is a calculation of each triangular facet parameters (facet area, center and normal vector).
As the result there is a finite region of formed facets that represents sea waves (Figure 2). In the mathematical model development of the radio altimeter beat-frequency waveform following assumptions were made: scan region is a square centered at the normal fall from the aircraft to the surface; antenna radiation pattern does not include side lobes (perfect antenna pattern); depending on the aircraft values of non-zero roll and pitch angles scan region extends to one or two sides.
The underlying surface is constructed as follows: taking into account the antenna pattern it is possible to construct a conical surface with a small number of faces. Further, this surface is determined by the intersection of the horizontal plane at a suitable distance. The rectangle is constructed from the resulting set by the extreme points. It includes all facets of sea surface.
The modeling algorithm of a signal reflected from the sea is as follows [
The radiation nature of FM radio altimeter leads to feedthrough signal effect at the input of the receiving antenna. This signal is generated by the parasitic electromagnetic coupling between transmitting and receiving antennas. The amplitude-modulated components of the signal have the greatest impact causing the voltage at the balanced mixer output. The main part of the noise voltage energy spectrum falls on the low-frequency portion in the area corresponding to the measured heights of flight.
The noise power at the balanced mixer output caused by the feedthrough signal does not depend on the height of the aircraft flight but the desired signal power decreases with the height increase. Thus there exists a certain height at which the powers become comparable which leads to deterioration of the radar altimeter accuracy.
The principle means of decreasing such a noise is improving the generator noise characteristics and increasing
isolation which is expressed by the rational placement of antennas on the aircraft [
Modeling results with different input parameters were obtained: wind speed variation, which leads to waves speed and height change in the sea surface; aircraft speed, pitch and roll angles, the height above the sea level; increasing (decreasing) antenna pattern.
The results are presented in Figures 5, 6, 7, 8, 9.
Each figure contains three graphs: 3-dimensional moving sea image, beat-frequency spectrum and beat-frequency signal.
Wind speed has a direct impact on the sea surface commotion. The faster wind speed, the faster wave formation and as a consequence the waves become higher. Heights variation determined by altimeter becomes larger than in perfectly flat surface. The spectrum amplitude is increased because of wave heights increasing. The maximum spectral range is more uncertain due to the spread of wave heights. Figure 5 shows plots at the wind speed of 1 m/s, Figure 6 shows the plots at the wind speed of 10 m/s.
In response to a weak deviation of the antenna pattern, the spectrum shifts to higher frequencies. This is due to the fact that in case of the aircraft deviation antenna pattern will scan long-distant facets and their frequencies will appear in the spectrum. If there is a strong deviation of antenna pattern (more than half of the antenna axis), the spectral maximum shifts in the region of high frequencies. Roll and pitch are 10 degrees in Figure 7.
The radio altimeter antenna pattern is one of the most important parameter. The wider it is, the higher should be the
stability of the altimeter at large angles of pitch and roll. The width of the presented model antenna pattern is 40 degrees,
which corresponds to the antenna pattern width of A-053 and A-052 altimeters [
Beat signal spectrum. Height over the sea = 30.375 m.
Spectrum width at 0.5 = 1000 Hz
Beat signal Ub(t)
One can observe a slight enlargement of the spectrum in the high frequency region when increasing the beam from 40 degrees to 60 degrees. It can be explained by the fact that with the beam width increase, the same and additional facets that are on the longer range with greater “amplitude” are also considered (Figure 8).
When decreasing antenna pattern, scanning area also decreases, and consequently the spectrum narrows (Figure 9).
Beat signal Ub(t)
Beat signal Ub(t)
We can determine the errors for each of the following spectrum assessment while calculating the heights above sea level.
The height measurement estimation errors above the sea in the absence disturbances at the sea surface and in the
presence of waves up to 4 meters high (wind speed is 10 m/s) are shown in figures 10 and 11. The measurements are
performed at attitudes up to 50 meters and typical conditions for radio altimeters operation [
Relative measurement error is defined by the following formula [
= Δ / (5)
The results are obtained by using the known measuring methods [
As we can see from the figures above, the center of spectrum gravity has the greatest error. The indication of height over the sea surface along the leading spectrum edge is the most accurate. 6
The Opportunities for HIL Simulation Using Altimeter Reflected Signal Complex IOS-RV The radio altimeter model that has been obtained in MatLab software product can be further transferred to reflected signal simulator IOS-RV for development, debugging and experimentation to establish radio navigation equipment that works on the sea surface.
IOS-RV allows simulating the time delay and attenuation of the microwave signal emitted by the radio altimeter in accordance with the specified parameters of flight altitude, pitch and roll angles, the type of the underlying surface, the speed of the aircraft and the antenna system.
IOS-RV is used for HIL simulation of the radio altimeter. It helps developers to more thoroughly examine the behavior of the radio altimeter in conditions close to real, and obtain all the necessary information about it.
Using HIL simulation the under study system operates in its normal mode but the real signal propagation and reflection channel are simulated by a special device in accordance with the given system conditions and its dynamical changes.
A mathematical model of the channel "radio altimeter - surface" provides the calculation of the current signal settings
on the receiving device input in accordance with the program by the certain algorithm. Physical model reproduces the
signals in the receive path input of the side-looking airborne radar. Signal parameters vary according to the mathematical
model. The antenna direction is set by the aircraft position. It is also predetermined by mathematical model. The signals
that were created this way are fed to the input of the side-looking airborne radar receiving device [
Thus, the information is converted from a mathematical model to the physical signal waveform. Therefore, the most important element of the simulator work quality is mathematical model operation algorithm. 7