Patent Publication Number: US-6992614-B1

Title: Radar altimeter

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   Not Applicable. 
   STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
   Not Applicable. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates generally to radar altimeters, and more particularly to frequency modulated continuous wave (FMCW) radar altimeters used for aviation navigation. 
   2. Description of Related Art 
   Frequency modulated continuous wave (FMCW) radar altimeters are used by pilots to determine the altitude of an aircraft in flight-critical situations, such as making an instrument landing in low visibility conditions. A FMCW radar altimeter generally comprises a transmitter that transmits a radio signal toward the ground surface, and a receiver that receives the radio signal after it has reflected from the ground surface. The receiver mixes the transmitted radio signal with the received reflected radio signal and thereby generates a difference signal. The receiver uses the frequency of this difference signal to determine the altitude of the aircraft (wherein the frequency is proportional to the altitude). This altitude measurement is then output to a radar altimeter display located within the cockpit of the aircraft. 
   One inherent problem with the design of a FMCW radar altimeter is that there will be a certain amount of coupling from the transmitter antenna to the receiver antenna. This antenna coupling is particularly problematic at higher altitudes where the magnitude of the antenna coupling signal is significant compared to the magnitude of the received reflected radio signal. As such, the receiver will occasionally lock on to the antenna coupling signal, and then erroneously use the frequency of the antenna coupling signal to determine the altitude of the aircraft. When this happens, the needle of the radar altimeter display drops to approximately 0 feet, resulting in undue pilot concern or even the loss of the pilot&#39;s confidence in the radar altimeter. 
   An attempt to solve this problem has been to utilize a switched filter in the receiver of a FMCW radar altimeter for the purpose of attenuating the antenna coupling signal at higher altitudes. The switched filter is designed to have one frequency response at lower altitudes (which passes both the difference signal and the antenna coupling signal) and another frequency response at higher altitudes (which passes the difference signal and attenuates the antenna coupling signal). Thus, in operation, the receiver will properly lock on to the difference signal both at lower altitudes (where the magnitude of the difference signal is relatively large compared to the magnitude of the antenna coupling signal) and at higher altitudes (where the antenna coupling signal has been attenuated). 
   There are several disadvantages, however, associated with the use of a switched filter within the receiver of a FMCW radar altimeter. For example, because the characteristics of a switched filter are fixed, various hardware components of the receiver must be changed in order to modify the filter parameters. As such, the switched filter may not be customized on an individual installation basis. Thus, there is a need for a FMCW radar altimeter that does not use a switched filter to attenuate the antenna coupling signal. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to a FMCW radar altimeter that generally comprises a transmitter and a receiver. The transmitter is operable to generate a radio signal at a specified modulation frequency, and transmit the radio signal toward the ground surface for reflection therefrom to thereby propagate a reflected radio signal. The receiver is operable to receive the reflected radio signal from the ground surface, and determine the altitude of the aircraft based on two different factors: (1) the modulation frequency of the radio signal; and (2) a difference frequency derived from the radio signal and the reflected radio signal. The receiver is also operable to control the transmitter so as to vary the modulation frequency of the radio signal based on the altitude of the aircraft. Preferably, the modulation frequency of the radio signal is greater at lower altitudes than at higher altitudes. 
   In an exemplary embodiment, the transmitter includes a variable rate modulator that generates a voltage waveform. The transmitter also includes a voltage controlled oscillator that generates a radio signal at a specified modulation frequency, which is controlled by the voltage waveform from the variable rate modulator. Also included is a transmitter antenna that transmits the radio signal toward the ground surface for reflection therefrom to thereby propagate a reflected radio signal. 
   The receiver includes a receiver antenna that receives the reflected radio signal from the ground surface, and also detects an unwanted antenna coupling signal from the transmitter antenna. A mixer is provided that mixes the radio signal, the reflected radio signal, and the unwanted antenna coupling signal and thereby generates a mixed signal. The mixer then demodulates the mixed signal into a baseband difference signal (having a difference frequency derived from the radio signal and the reflected radio signal) and a baseband antenna coupling signal. The receiver also includes a fixed filter designed to attenuate the baseband antenna coupling signal and pass the baseband difference signal. Significantly, the fixed filter has a single frequency response for all altitudes of the aircraft such that a switched filter is not required. 
   The receiver further includes an analog-to-digital converter that converts the baseband difference signal to a digital difference signal. A digital signal processor is also provided that determines the difference frequency from the digital difference signal, and then correlates the difference frequency to the altitude of the aircraft for the particular modulation frequency of the radio signal. The receiver also includes a microprocessor that controls the variable rate modulator of the transmitter so as to vary the modulation frequency of the radio signal based on the altitude of the aircraft. Preferably, the modulation frequency of the radio signal is varied when the altitude of the aircraft reaches one or more threshold altitudes, such that the modulation frequency is greater at altitudes below a particular threshold altitude than at altitudes above the particular threshold altitude. By varying the modulation frequency of the radio signal, the receiver is able to obtain more accurate altitude measurements when the aircraft is near the ground surface. 
   The present invention will be better understood from the following detailed description of the invention, read in connection with the drawings as hereinafter described. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram of a radar altimeter in accordance with an exemplary embodiment of the present invention, showing the various functional blocks of the transmitter and the receiver. 
       FIG. 2  is a graphical representation of the output of the mixer of the receiver shown in  FIG. 1 , wherein the radio signal has been modulated at the nominal modulation frequency. 
       FIG. 3  is a graphical representation of the output of the mixer of the receiver shown in  FIG. 1 , wherein the radio signal has been modulated at twice the nominal modulation frequency. 
       FIG. 4  is a graphical representation of the output of the mixer of the receiver shown in  FIG. 1 , wherein the radio signal has been modulated at four times the nominal modulation frequency. 
       FIG. 5  is a graphical representation of the frequency response of the fixed filter of the receiver shown in  FIG. 1 , showing attenuation of the baseband antenna coupling signal when the radio signal has been modulated at the nominal modulation frequency, twice the nominal modulation frequency, and four times the nominal modulation frequency. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   A frequency modulated continuous wave (FMCW) radar altimeter in accordance with an exemplary embodiment of the present invention is depicted in  FIG. 1  (with graphical representations of the functionality of the radar altimeter depicted in  FIGS. 2–5 ). While the invention will be described in detail hereinbelow with reference to this exemplary embodiment, it should be understood that the invention is not limited to the specific architecture of the radar altimeter shown in this embodiment. Rather, one skilled in the art will appreciate that a wide variety of radar altimeter architectures may be implemented in accordance with the present invention. 
   Referring to  FIG. 1 , a radar altimeter in accordance with an exemplary embodiment of the present invention includes a transmitter  10  (which generally comprises a variable rate modulator  12 , a voltage controlled oscillator  14 , a transmitter amplifier  16 , and a transmitter antenna  18 ) and a receiver  20  (which generally comprises a receiver antenna  22 , a receiver amplifier  24 , a mixer  26 , a mixed signal amplifier  28 , a fixed filter  30 , an analog-to-digital converter  32 , a digital signal processor  34 , and a microprocessor  36 ). Preferably, the radar altimeter is designed to comply with various aviation industry specifications known in the art, such as TSO C87, RTCA DO-178B and RTCA DO-160D. 
   As will be described in greater detail hereinbelow, transmitter  10  is operable to generate a radio signal at a specified modulation frequency, and transmit the radio signal toward the ground surface for reflection therefrom to thereby propagate a reflected radio signal. Receiver  20  is operable to receive the reflected radio signal from the ground surface, and determine the altitude of the aircraft based on two different factors: (1) the modulation frequency of the radio signal; and (2) a difference frequency derived from the radio signal and the reflected radio signal. Receiver  20  is also operable to control transmitter  10  so as to vary the modulation frequency of the radio signal based on the altitude of the aircraft, wherein the modulation frequency is greater at lower altitudes than at higher altitudes. As will be seen, by varying the modulation frequency of the radio signal based on the altitude of the aircraft, receiver  20  is able to utilize fixed filter  30  which has a single frequency response for all altitudes of the aircraft. In addition, receiver  20  is able to obtain more accurate altitude measurements when the aircraft is near the ground surface. 
   Looking more closely to transmitter  10  in  FIG. 1 , variable rate modulator  12  generally operates as a driver circuit for voltage controlled oscillator  14 . In particular, variable rate modulator  12  generates a voltage waveform that causes voltage controlled oscillator  14  to frequency modulate and thereby generate a FMCW radio signal. As such, the voltage waveform generated by variable rate modulator  12  controls the modulation frequency of the radio signal. As will be described in greater detail hereinbelow, microprocessor  36  of receiver  20  controls variable rate modulator  12  so as to change the voltage waveform generated by variable rate modulator  12  when the altitude of the aircraft reaches one or more predetermined threshold altitudes, thereby changing the modulation frequency of the radio signal. 
   Voltage controlled oscillator  14  is operable to receive the voltage waveform from variable rate modulator  12  and frequency modulate an RF waveform of constant amplitude to generate a FMCW radio signal. Typically, the center frequency of the FMCW radio signal is set to 4.3 GHz, although any center frequency may be used. The period of modulation may vary from 0.01 μs (corresponding to a modulation frequency of 100 Hz) to 0.0095 μs (corresponding to a modulation frequency of 105 Hz), although any period of modulation and corresponding modulation frequency may be used. Preferably, the radio signal is modulated such that the frequency increases and decreases linearly as it varies in time. As is known in the art, the slope of the radio signal is the frequency deviation rate and is typically expressed in hertz per foot (Hz/ft) of altitude. As will be described in greater detail hereinbelow, digital signal processor  34  of receiver  20  is able to use the modulation frequency and corresponding frequency deviation rate (in conjunction with a difference frequency described below) to provide an accurate measurement of the altitude of the aircraft above the ground surface. 
   Transmitter amplifier  16  is operable to receive the radio signal from voltage controlled oscillator  14  and increase the amplitude of the radio signal before it is transmitted through transmitter antenna  18 . Preferably, the output power of transmitter amplifier  16  is sufficient to ensure that the radio signal may be detected by receiver antenna  22  after reflection from the ground surface, which is particularly critical at higher altitudes of the aircraft. Thus, transmitter  10  may be “matched” to receiver  20  such that a transmitter having a lower output power may be used in connection with a receiver having better detection capabilities, and vice-versa. A typical output power for transmitter amplifier  16  is 160 mW. 
   Transmitter antenna  18  is operable to receive the radio signal from transmitter amplifier  16  and transmit the radio signal toward the ground surface. It should be understood that the radio signal then reflects off the ground surface to thereby propagate a reflected radio signal. Receiver antenna  22  is then operable to detect and receive the reflected radio signal propagated from the ground surface. 
   As is known in the art, transmitter antenna  18  and receiver antenna  22  are preferably mounted at least 20 inches apart near the point of aircraft rotation and as close as feasible to the receiver/transmitter box. It is also preferable to mount both antennas such that they are not located near other antennas or aircraft projections (including landing gear, flaps, etc.). Preferably, both antennas are mounted such that they point straight downward (e.g., within 6 degrees) when the aircraft is in level flight. 
   Because transmitter antenna  18  and receiver antenna  22  are both located on the same aircraft, it is known in the art that an unwanted antenna coupling signal will be generated from transmitter antenna  18  to receiver antenna  22 . As such, receiver antenna  22  will detect and receive both the reflected radio signal and the unwanted antenna coupling signal. As will be described below, the unwanted antenna coupling signal is attenuated by fixed filter  30  in accordance with the present invention. 
   Receiver amplifier  24  is operable to receive the reflected radio signal from receiver antenna  22  and increase the amplitude of the reflected radio signal so that it may be easily processed by subsequent circuitry within receiver  20 . Preferably, the output power of receiver amplifier  24  is great enough to meet the input requirements of mixer  26 , even at higher altitudes where the power of the reflected radio signal is weaker. Of course, receiver amplifier  24  will also increase the amplitude of the unwanted antenna coupling signal received from receiver antenna  22 . 
   Mixer  26  is operable to receive the reflected radio signal and the unwanted antenna coupling signal from receiver amplifier  24 , and is also connected to transmitter  10  so as to receive the radio signal from voltage controlled oscillator  14  prior to transmission. Preferably, mixer  26  receives the radio signal being transmitted at a specified time and the reflected radio being received at that same specified time. Mixer  26  is then operable to mix the radio signal with the reflected radio signal and the unwanted antenna coupling signal, and then demodulate these signals so as to generate a baseband difference signal and a baseband antenna coupling signal. The frequency of the baseband difference signal (hereinafter referred to as the “difference frequency”) is derived from the difference between the frequencies of the transmitted radio signal and the received reflected radio signal. One skilled in the art will understand that the difference frequency is proportional to the altitude of the aircraft, and ranges from f min  (corresponding to the altitude of the aircraft on the ground surface) to f max  (corresponding to the altitude of the aircraft at the maximum of the altimatic scale, commonly 2,500 feet above the ground surface). 
     FIGS. 2–4  are graphical representations of the output of mixer  26 , wherein the radio signal has been modulated at three different modulation frequencies, namely, a nominal modulation frequency (1×) of 100 Hz (see  FIG. 2 ), twice the nominal modulation frequency (2×) of 200 Hz (see  FIG. 3 ), and four times the nominal modulation frequency (4×) of 400 Hz (see  FIG. 4 ). Each of these graphical representations show the approximate frequencies and magnitudes of the baseband antenna coupling signal and the baseband difference signal for various altitudes of the aircraft. It should be understood that the magnitudes of the various signals are not to scale and are intended only to show the relative strength between the signals. Similarly, the frequencies of the various signals are approximated and are intended only to show the relative frequencies between the signals. It should further be understood that the modulation frequencies shown in the graphical representations of  FIGS. 2–4  are merely examples and that a plurality of other modulation frequencies could be used in accordance with the present invention (e.g., 1.5 times the nominal modulation frequency, 5 times the nominal modulation frequency, etc.). 
   In  FIG. 2 , the radio signal has been modulated at a nominal modulation frequency (1×) of 100 Hz, which corresponds to a frequency deviation rate of 40 Hz/ft. As can be seen, the frequency of the baseband antenna coupling signal is approximately 800 Hz. It should be understood that the exact frequency of the baseband antenna coupling signal may vary from installation to installation and is dependent on a number of variables, including antenna spacing and the length of the antenna cables. It can also be seen that the frequency of the baseband difference signal is approximately 20 kHz at an altitude of 500 feet and approximately 100 kHz at an altitude of 2,500 feet. Furthermore, it can be seen that the magnitude of the baseband antenna coupling signal is significantly less than the magnitude of the baseband difference signal at an altitude of 500 feet, and is also less than the magnitude of the baseband difference signal at an altitude of 2,500 feet. 
   In  FIG. 3 , the radio signal has been modulated at twice the nominal modulation frequency (2×) of 200 Hz, which corresponds to a frequency deviation rate of 80 Hz/ft. As can be seen, the frequency of the baseband antenna coupling signal is approximately 1.6 kHz. Again, it should be understood that the exact frequency of the baseband antenna coupling signal may vary from installation to installation and is dependent on a number of variables, including antenna spacing and the length of the antenna cables. It can also be seen that the frequency of the baseband difference signal is approximately 20 kHz at an altitude of 250 feet and approximately 100 kHz at an altitude of 1,250 feet. Furthermore, it can be seen that the magnitude of the baseband antenna coupling signal is significantly less than the magnitude of the baseband difference signal at an altitude of 250 feet, and is also less than the magnitude of the baseband difference signal at an altitude of 1,250 feet. 
   In  FIG. 4 , the radio signal has been modulated at four times the nominal modulation frequency (4×) of 400 Hz, which corresponds to a frequency deviation rate of 160 Hz/ft. As can be seen, the frequency of the baseband antenna coupling signal is approximately 3.2 kHz. Yet again, it should be understood that the exact frequency of the baseband antenna coupling signal may vary from installation to installation and is dependent on a number of variables, including antenna spacing and the length of the antenna cables. It can also be seen that the frequency of the baseband difference signal is approximately 20 kHz at an altitude of 125 feet and approximately 100 kHz at an altitude of 625 feet. Furthermore, it can be seen that the magnitude of the baseband antenna coupling signal is significantly less than the magnitude of the baseband difference signal at an altitude of 125 feet, and is also less than the magnitude of the baseband difference signal at an altitude of 625 feet. 
   Several observations can be made from the graphical representations of  FIGS. 2–4 . First, for any of the modulation frequencies, the frequency of the baseband difference signal is proportional to the altitude of the aircraft (i.e., the frequency increases as the altitude increases) and the magnitude of the baseband difference signal is inversely proportional to the altitude of the aircraft (i.e., the magnitude decreases as the altitude increases). Second, the frequency of the baseband difference signal is proportional to the modulation frequency of the radio signal (i.e., the frequency increases as the modulation frequency increases). 
   Third, the baseband difference signal will have approximately the same frequency for different combinations of altitude and modulation frequency. For example, the difference frequency is 20 kHz for: an aircraft flying at 500 feet with a modulation frequency of 100 Hz (see  FIG. 2 ); an aircraft flying at 250 feet with a modulation frequency of 200 Hz (see  FIG. 3 ); and an aircraft flying at 125 feet with a modulation frequency of 400 Hz (see  FIG. 4 ). Similarly, the difference frequency is 100 kHz for: an aircraft flying at 2,500 feet with a modulation frequency of 100 Hz (see  FIG. 2 ); an aircraft flying at 1,250 feet with a modulation frequency of 200 Hz (see  FIG. 3 ); and an aircraft flying at 625 feet with a modulation frequency of 400 Hz (see  FIG. 4 ). 
   As will be described in greater detail hereinbelow, the modulation frequency of the radio signal may be varied when the aircraft reaches one or more predetermined threshold altitudes. In general, the modulation frequency of the radio signal is greater at lower altitudes than at higher altitudes. Using a greater modulation frequency at lower altitudes causes the difference frequency of the baseband difference signal to be increased and shifted away from the frequency of the baseband antenna coupling signal. For example, looking to  FIG. 4 , it can be appreciated that an aircraft flying at 500 feet with a radio signal generated at four times the nominal modulation frequency (4×) of 400 Hz will produce a baseband difference signal having a difference frequency of approximately 80 kHz (as opposed to 20 kHz if the radio signal had been generated at the nominal modulation frequency (1×) of 100 Hz, as shown in  FIG. 2 ). It will be seen that varying the modulation frequency at one or more predetermined threshold altitudes enables the use of fixed filter  30  (described below) for all altitudes of the aircraft such that a switched filter is not required. 
   Referring again to  FIG. 1 , mixed signal amplifier  28  is operable to receive the baseband difference signal from mixer  26  and increase the amplitude of the baseband difference signal. Preferably, the output power of mixed signal amplifier  28  is sufficient to ensure that the baseband difference signal may be easily processed by downstream circuits within receiver  20 . Of course, mixed signal amplifier  28  will also increase the amplitude of the unwanted baseband antenna coupling signal received from mixer  26 . 
   Fixed filter  30  is operable to receive the baseband difference signal and the baseband antenna coupling signal from mixed signal amplifier  28 , and filter the unwanted baseband antenna coupling signal therefrom. A graphical representation of an exemplary frequency response of fixed filter  30  is shown in  FIG. 5 . In this example, fixed filter  30  comprises a band-pass filter that is tuned to pass signals within the 10 kHz to 100 kHz frequency range without attenuation. It can also be seen that the band-pass filter will pass the signals between 4-kHz and 10 kHz (with varying degrees of attenuation) and the signals between 100 kHz and 300 kHz (with varying degrees of attenuation). In addition, the band-pass filter will significantly attenuate all signals below 4 kHz and above 300 kHz. As such, in this example, the band-pass filter will pass any of the baseband difference signals shown in  FIGS. 2–4  (all of which fall within the 10 kHz to 100 kHz frequency range) and attenuate any of the baseband antenna coupling signals shown in  FIGS. 2–4  (all of which fall below 4 kHz). 
   Looking at  FIGS. 2–4  in conjunction with  FIG. 5 , it can be seen that increasing the modulation frequency of the radio signal at lower altitudes causes the baseband difference signals to increase in frequency and shift within the passband of fixed filter  30 . It should be understood that if the modulation frequency of the radio signal was not increased at lower altitudes, the baseband difference signals would fall below the passband of fixed filter  30  and would thus be attenuated (such that it would be necessary to use a switched filter having one frequency response at lower altitudes and another frequency response at higher altitudes). Thus, in accordance with the present invention, varying the modulation frequency of the radio signal at one or more predetermined threshold altitudes enables the use of fixed filter  30  having the same frequency response for all altitudes of the aircraft. 
   Referring again to  FIG. 1 , analog-to-digital converter  32  is operable to receive the baseband difference signal from fixed filter  30  and convert the baseband difference signal to a digital difference signal. Preferably, the sampling rate, resolution and spurious-free dynamic range of analog-to-digital converter  32  is selected to ensure that the converted signals comply with aviation industry specifications. Of course, it should be understood that any analog-to-digital converter that meets the conversion requirements for a particular application may be used. 
   Digital signal processor  34  is operable to receive the digital difference signal from analog-to-digital converter  32  and determine the difference frequency therefrom (which, as discussed above, is derived from the difference between the frequencies of the transmitted radio signal and the received reflected radio signal). Digital signal processor  34  is then operable to correlate the difference frequency to the altitude of the aircraft for the particular modulation frequency of the radio signal. In other words, digital signal processor  34  determines the altitude of the aircraft based on two different factors: (1) the modulation frequency of the radio signal; and (2) the difference frequency extracted from the digital difference signal. 
   For example, looking to  FIG. 2 , a radio signal modulated at the nominal modulation frequency (1×) of 100 Hz has a corresponding frequency deviation rate of 40 Hz/ft. At this modulation frequency, if the difference frequency extracted from the digital difference signal were 20 kHz, it follows that the altitude of the aircraft is 500 feet (i.e., 20 kHz divided by 40 Hz/ft). 
   As another example, looking to  FIG. 3 , a radio signal modulated at twice the nominal modulation frequency (2×) of 200 Hz has a corresponding frequency deviation rate of 80 Hz/ft. At this modulation frequency, if the difference frequency extracted from the digital difference signal were 20 kHz, it follows that the altitude of the aircraft is 250 feet (i.e., 20 kHz divided by 80 Hz/ft). 
   As yet another example, looking to  FIG. 4 , a radio signal modulated at four times the nominal modulation frequency (4×) of 400 Hz has a corresponding frequency deviation rate of 160 Hz/ft. At this modulation frequency, if the difference frequency extracted from the digital difference signal were 20 kHz, it follows that the altitude of the aircraft is 125 feet (i.e., 20 kHz divided by 160 Hz/ft). 
   In all three examples, it should be noted that the difference frequency extracted from the digital difference signal is 20 kHz. Thus, it is necessary to know both the difference frequency and the modulation frequency and corresponding frequency deviation rate of the radio signal in order to determine the altitude of the aircraft. 
   Referring yet again to  FIG. 1 , microprocessor  36  is operable to receive the altitude measurement from digital signal processor  34  and generate an output signal that is transmitted to the radar altimeter display located within the cockpit of the aircraft. Microprocessor  36  is also operable to control variable rate modulator  12  of transmitter  10  so as to vary the modulation frequency of the radio signal based on the altitude of the aircraft. Preferably, the modulation frequency of the radio signal is varied when the altitude of the aircraft reaches one or more predetermined threshold altitudes, such that the modulation frequency is greater at altitudes below a particular threshold altitude than at altitudes above the particular threshold altitude. Microprocessor  36  also transmits the modulation frequency to digital signal processor  34  for use in determining the altitude of the aircraft (described above). Of course, it should be understood that all of the various functions of microprocessor  36  could be incorporated into digital signal processor  34 . 
   An example will now be provided in which the modulation frequency of the radio signal is varied at two predetermined threshold altitudes in accordance with the present invention. Looking to  FIGS. 2–4 , the predetermined threshold altitudes may comprise 1,000 feet and 500 feet. In this example, when the aircraft is flying above 1,000 feet, the radio signal would be generated at the nominal modulation frequency (1×) of 100 Hz. When the aircraft drops below the first threshold altitude of 1,000 feet, the radio signal would be generated at twice the nominal modulation frequency (2×) of 200 Hz. Then, when the aircraft drops below the second threshold altitude of 500 feet, the radio signal would be generated at four times the nominal modulation frequency (4×) of 400 Hz. Of course, it should be understood that any number of predetermined threshold altitudes may be utilized in accordance with the present invention. 
   It can be appreciated that increasing the modulation frequency of the radio signal at lower altitudes enables the radar altimeter to obtain more accurate altitude measurements when the aircraft is near the ground surface. Specifically, when using a higher modulation frequency, a given change in altitude results in a larger change in difference frequency. For example, in  FIG. 4 , a change in altitude of 500 feet (e.g., 125 feet to 625 feet) would result in a change in difference frequency of 80 kHz (e.g., 20 kHz to 100 kHz). By contrast, in  FIG. 3 , a change in altitude of 500 feet (e.g., 250 feet to 750 feet) would result in a change in difference frequency of 40 kHz (e.g., 20 kHz to 60 kHz). Thus, at higher modulation frequencies, the increased resolution results in more accurate altitude measurements for lower altitudes of the aircraft. 
   While the present invention has been described and illustrated hereinabove with reference to an exemplary embodiment, it should be understood that various modifications could be made to this embodiment without departing from the scope of the invention. Therefore, the invention is not to be limited to the specific embodiment described and illustrated hereinabove, except insofar as such limitations are included in the following claims.