Skywave overthehorizon (OTH) radar systems have important longrange strategic warning values. They exploit skywave propagation reflection of high frequency signals from the ionosphere, which provides the ultralongrange surveillance capabilities to detect and track maneuvering targets. Current OTH radar systems are capable of localizing targets in range and azimuth but are unable to achieve reliable instantaneous altitude estimation. Most existing height measurement methods of skywave OTH radar systems have taken advantage of the micromultipath effect and been considered in the flat earth model. However, the flat earth model is not proper since large error is inevitable, when the detection range is over one thousand kilometers. In order to avoid the error caused by the flat earth model, in this paper, an earth curvature model is introduced into OTH radar altimetry methods. The simulation results show that application of the earth curvature model can effectively reduce the estimation error.
Skywave OTH radar works in the high frequency band (3–30 MHz), which uses the ionosphere to scatter the electromagnetic wave, observing the air and ground targets from top to bottom. Thus, skywave OTH radar has important longrange strategic warning value and a wide range of applications [
Skywave OTH radar systems are capable of localizing targets in range and azimuth but are unable to achieve reliable altitude estimation [
Currently, the methods that skywave OTH radar systems used to estimate the instantaneous altitude of the aircrafts can be divided into four kinds. (1) The superresolution method: this method uses modern spectral analysis method to distinguish echo delay of each propagation path and then estimates the target altitude. By this method, the height estimation is divided into three types: low altitude, intermediate altitude, and high altitude. But this technique can only be applied to analog data [
The methods mentioned above mostly consider the radar altimetry problem in the flat earth model. However, for skywave OTH radar systems, the detection range is thousands of kilometers, it will cause large errors to estimate target altitude with the flat earth model. Therefore, this paper will focus on how to introduce the earth curvature model into the altimetry method.
In this paper, a monostatic multipleinput multipleoutput (MIMO) radar system is considered, which consists of
So the
Denote
In order to be consistent with the motion model, the
In this paper, for generality, we consider a maneuvering aircraft which makes a 180° circular turn in
The parameters of the motion target.
Parameter  Notation  Value 

Initial ground range 

2000 km 
Ionosphere height 

350 km 
Aircraft initial height 

10 km 
Maximum horizontal velocity 

500 km/h 
Maximum descending velocity 

90 km/h 
Carrier frequency 

20 MHz 
Impulse repetition frequency 

50 Hz 
The target tracks in two dimensions are shown in Figures
The target’s track in the range direction.
The target’s track in the altitude direction.
An OTH radar system considering the micromultipath effect based on the flat earth model is illustrated in Figure
The micromultipath effect in the flat earth model.
Since our purpose in this paper is to estimate the instantaneous height of the target, for simplicity and without loss of generality, we only consider the 2D position and velocity (range direction
As the effect of the crossrange array apertures on the height estimation is small, only the effect of array apertures which lies in the range direction will be considered. Correspondingly both the transmit arrays and receive arrays are considered to be linear and located in the
As the micromultipath effect exists, the combination of the transmit path and receive path has four components: Path I (
In (
In general, the target’s track consists of the movement in the range and altitude direction. This section will discuss the Doppler frequency of the target flight in two directions and then deduce the instantaneous expression of the target height.
Suppose that both the range between the target and radar and the height of the target are the functions of time. As the height of the ionosphere
From (
To get the target height, it is necessary to know the target initial height. In practice, we can get
However,
For elimination of the impact by the error of
In this section, the micromultipath effect model, which is under the influence of the earth curvature, will be discussed. The micromultipath effect model in an OTH radar system of the earth curvature model is illustrated in Figure
The micromultipath effect in the earth curvature model.
Path I is shown in Figure
Path I in the earth curvature model.
According to the geometrical relationship,
The accurate value of
Path II is illustrated in Figure
Path II in the earth curvature model.
From Figure
Then
Consistent with the processing methods in the flat earth model, we suppose that
The four Doppler frequencies both consist of the components caused by
The ration of 11x to 12x.
To get the instantaneous height of the moving target, the initial height of the target
For Path I,
For Path II,
The aim of this section is to analyze and compare the difference of micromultipath effects between the flat earth model and the earth curvature model. The moving target model established in Section
The curves of Doppler frequencies of the four paths produced by the target’s movement in the flat earth model and the earth curvature model are shown in Figure
The Doppler frequency curves of the moving target in the flat earth model.
The Doppler frequency curves of the moving target in the earth curvature model.
At the moment
By comparison of Figures
The Doppler frequency difference between Path I and Path II in the flat earth model.
The Doppler frequency difference between Path I and Path II in the earth curvature model.
Figures
The Path I and Path II in two kinds of models.
Path I
Path II
The simulation results of Path I and Path II in two kinds of models.
Path I in the flat earth model
Path II in the flat earth model
Path I in the earth curvature model
Path II in the earth curvature model
The Doppler frequency difference
From (
Figure
The comparison of
Figure
The comparison of the movement tracks calculated in two kinds of earth models.
In order to use the effect of micromultipath, the transmission beam is requested to have a certain width to receive the echoes of four paths. Therefore, the transmission antenna beam width Ω must be larger than two times of the difference
The curve of the emission angles
The curve of the difference
The detection range of the skywave radar is limited in practice, for the emission angle
When the target’s altitude is close to the ground and the emission angle is
The illustration of the minimum detection range of the skywave radar.
The illustration of the maximum detection range of the skywave radar.
The emission angle
The emission angle
Taking the earth radius as
Skywave OTH radar systems can make use of the micromultipath effect to estimate the instantaneous altitude of maneuvering targets. The flat earth model is often used. However, ignoring the impact of the curvature of the earth, the analytical expressions of instantaneous target altitude are relatively simple, making it suitable for descriptive analysis. And the initial altitude has a great difference from actual altitude (600 meters) in the flat earth model. Moreover, the curvature of the earth should not be ignored for the thousands of kilometers’ detection in the skywave radar.
This paper focuses on the theoretical derivations about how to introduce the earth curvature model into the estimation of the target’s altitude. The expressions of the Doppler frequency in four paths are deduced. And the difference of two kinds of models is compared. Although the analytical expressions are quiet complicated, the estimation of the initial altitude is close to the actual one. Therefore, any altimetry methods that are based on real data can improve the estimation results by exploiting the altimetry correction factors derived from earth curvature model.
The authors declare that there is no conflict of interests regarding the publication of this paper.
At the point of finishing this paper, the authors would like to express their sincere thanks to the National Natural Science Foundation (no. 61201303) and the Fundamental Research Funds for the Central Universities (HIT.NSRIF.2013027).