Abstract:
A radar apparatus includes a receiving means that receives a reflected signal, a beat signal generation means that generates beat signals based on the reflected signal, a correlation matrix generation means that calculates correlation matrices based on the beat signals, a storing means that stores previous correlation matrices, an addition means that calculates addition correlation matrices by adding the correlation matrices to the previous correlation matrices, a detection means that detects a frequency component satisfying a predetermined condition by using the beat signals, an extraction means that extracts an extraction matrix corresponding to the detected frequency from the addition correlation matrices, and a direction calculation means that calculates a direction of the object with respect to the radar apparatus based on the extraction matrix.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application is based on and incorporates herein by reference Japanese Patent Application No. 2005-224636 filed on Aug. 2, 2005. 
   FIELD OF THE INVENTION 
   The present invention relates to a radar apparatus. 
   BACKGROUND OF THE INVENTION 
   There are various types of radar apparatus for detecting a distance and a direction of an object with respect to the radar apparatus. A frequency modulated continuous wave (FMCW) radar apparatus is a radar apparatus that continuously transmits a frequency-modulated radar signal to the object and detects the distance or a relative velocity of the object based on the transmitted radar signal reflected from the object. 
   In one method for detecting the direction of the object, a transmitting means for transmitting a radar signal mechanically turns and scans the transmitted radar signal reflected from the object. In another method that uses a digital beam forming (DBF) algorithm, the transmitting means is fixed and an antenna having multiple elements arranged in an array receives the transmitted radar signal. The received radar signal is digitally processed and the direction of the object is detected based on the digital signal. Specifically, in the DBF algorithm, an angular spectrum is generated based on the received radar signal on each of the elements and a peak of the angular spectrum is detected. The direction of the object is estimated based on the peak of the angular spectrum. 
   In a beamformer algorithm as the DBF algorithm, the angular spectrum is generated such that amplitudes of the received signal at a given time are connected as shown in  FIGS. 10A and 10B . A multiple signal classification (MUSIC) algorithm is known as a high-resolution direction of arrival (DOA) estimation algorithm. 
   In the DOA estimation algorithm, correlation matrices are calculated, eigenvalue expansions are performed on each of the correlation matrices, the angular spectrum is calculated from eigenvectors of the correlation matrices, and the direction of the object is calculated based on the angular spectrum. 
   A FMCW radar apparatus disclosed in U.S. Pat. No. 6,121,917 corresponding to JP-A-H11-133142 detects the direction of the object by using the beamformer algorithm. In the FMCW radar apparatus, a fast Fourier transform (FFT) is applied to the received wave signal to obtain a peak frequency of a distance power spectrum. Then, the beamformer algorithm is applied to only the peak frequency component of the received signal so that the amount of calculation required to detect the direction of the object is reduced. 
   However, when the beamformer algorithm is used in the radar apparatus, resolution of the radar apparatus depends on the number of elements arranged in the array. Therefore, the radar apparatus using the beamformer algorithm needs to be increased in size to obtain high resolution. 
   The high-resolution DOA estimation algorithm such as the MUSIC algorithm achieves the high resolution without an increase in the number of the elements. In the DOA estimation algorithm, the resolution may be increased by reducing noise with summation of the received signal with respect to time. The summation is performed such that a present angular spectrum calculated in a present process and a previous angular spectrum calculated in a previous process are summed up. 
   However, when the object moves, a frequency corresponding to the distance changes between in the previous process and in the present process. Therefore, the DOA estimation algorithm needs to be applied to all the frequency components of the received signal on each process to calculate the angular spectrum, and the calculated angular spectrum needs to be stored in a memory. The calculation of the angular spectrum requires an eigenvalue expansion that requires a lot of calculation. Therefore, when the angular spectrum is calculated on each frequency component, the amount of calculation is significantly increased. In the DOA estimation algorithm, the high resolution results in a significant increase in the amount of calculation. 
   SUMMARY OF THE INVENTION 
   In view of the above-described problem, it is an object of the present invention to provide a radar apparatus that achieves a high resolution without a significant increase in the amount of calculation. 
   A radar apparatus uses a DOA estimation algorithm performed at a predetermined time interval to detect an object. The radar apparatus includes a transmitting means that transmits a wave signal to the object, a receiving means that receives the transmitted wave signal reflected from the object, a beat signal generation means that generates a plurality of beat signals based on the received wave signal, a correlation matrix generation means that calculates a plurality of correlation matrices based on the beat signals with respect to each frequency component of the beat signals, an addition means that calculates a plurality of addition correlation matrices, a storing means that stores at least a portion of a plurality of previous correlation matrices calculated by the correlation matrix generation means at a previous time, a detection means that detects at least one frequency component of the beat signals, the frequency component satisfying a predetermined condition, an extraction means that extracts an extraction matrix from the addition correlation matrices, the extraction matrix corresponding to a frequency component closest to the frequency component detected by the detection means, and a direction calculation means that calculates a direction of the object with respect to the radar apparatus based on the extraction matrix. The receiving means includes a plurality of elements arranged in an array and each of the beat signals generated by the beat signal generation means corresponds to each of the elements. The addition means calculates the addition correlation matrices by adding the correlation matrices calculated by the correlation matrix generation means to the previous correlation matrices stored by the storing means. 
   In a conventional DOA estimation algorithm, correlation matrices are generated from beat signals. Then, angular spectrums are calculated from each eigenvector of each of the correlation matrices. The storing means stores the angular spectrums as previous information and the angular spectrums are used in a next process to reduce noise. 
   In the DOA estimation algorithm used in the radar apparatus, a position of the object (i.e., a frequency component indicating a presence of the object) is estimated from the beat signals and then an angular spectrum corresponding to the position is calculated. Correlation matrices calculated in a present process and previous correlation matrices calculated in a previous process are summed up to reduce noise. In the radar apparatus, therefore, the storing means stores the correlation matrices as the previous information, not the angular spectrums. 
   For example, in a MUSIC algorithm, the amount of calculation required to calculate the correlation matrices is about one-thirteenth the amount of calculation required to calculate MUSIC spectrums. Because the radar apparatus uses the correlation matrices instead of the angular spectrums to reduce the noise, a significant increase in the amount of calculation can be prevented. Thus, the radar apparatus achieves a high resolution without the significant increase in the amount of calculation. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objectives, features and advantages of the present invention will become more apparent from the following detailed description made with reference to the accompanying drawings. In the drawings: 
       FIG. 1  is a block diagram showing a radar apparatus according to a first embodiment of the present invention; 
       FIG. 2  is an arrangement of elements of a receiving antenna of the radar apparatus of  FIG. 1 ; 
       FIGS. 3A and 3B  are diagrams showing a principal of beat signals generated in the radar apparatus of  FIG. 1 ; 
       FIG. 4A  is a diagram showing a reflected wave signal received by the elements of the receiving antenna of the radar apparatus of  FIG. 1 ,  FIG. 4B  is FFT beat signals generated by applying a FFT to beat signals of  FIG. 3B , and  FIG. 4C  is a diagram showing a sum beat signal into which the FFT beat signals of  FIG. 4B  are summed; 
       FIG. 5  is a flow chart illustrating a process performed by a microcomputer of the radar apparatus of  FIG. 1 ; 
       FIG. 6  is a table showing the amount of calculation performed by the microcomputer of the radar apparatus of  FIG. 1 ; 
       FIG. 7  is a flow chart illustrating a process performed by a microcomputer of a radar apparatus according to a second embodiment of the present invention; 
       FIG. 8  is a flow chart illustrating a process performed by a microcomputer of a radar apparatus according to a third embodiment of the present invention; 
       FIG. 9  is a flow chart illustrating a process performed by a microcomputer of a radar apparatus according to a fourth embodiment of the present invention; and 
       FIG. 10A  is a diagram showing an angular spectrum generated when reflected wave signals arrive at elements from a front direction in a beam former method, and 
       FIG. 10B  is a diagram showing the angular spectrum generated when the reflected wave signals arrive at the elements from an oblique direction in the beam former method. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   First Embodiment 
   A radar apparatus  100  according to a first embodiment of the present invention will now be described with  FIGS. 1 to 5 . The radar apparatus  100  includes a transmitting antenna  11 , a receiving antenna  12  having N elements E 1 -EN arranged in an array, where N is a positive integer, a high-frequency switch  13 , a mixer  14 , an oscillator  15 , a digital-to-analog (D/A) converter  16 , an analog-to-digital (A/D) converter  17 , a microcomputer  18 , a switch controller  19 , and a timer  20 . 
   The microcomputer  18  outputs a digital transmit signal to the D/A converter  16 . The D/A converter  16  converts the digital transmit signal into an analog transmit signal and outputs the analog transmit signal to the oscillator  15 . The oscillator  15  outputs the analog transmit signal to the transmitting antenna  11  at a predetermined frequency. The transmitting antenna  11  converts the analog transmit signal into a radar signal and transmits the radar signal to an object. 
   The receiving antenna  12  receives the transmitted radar signal reflected from the object. The received radar signal is converted into an analog receive signal on each of the elements E 1 -EN. The high-frequency switch  13  in turn sends the analog receive signal to the mixer  14 . In the mixer  14 , the analog receive signal is mixed with the analog transmit signal to generate a beat signal on each of the elements E 1 -EN. The beat signal is input to the A/D converter  17  and converted into a digital receive signal. The digital signal is input to the microcomputer  18 . 
   The microcomputer  18  controls the high-frequency switch  13  through the switch controller  19  and controls a sampling rate of the A/D converter  17  though the timer  20 . The microcomputer  18  has a memory  21 . 
   The microcomputer  18  performs a distance calculation process for calculating the distance between the radar apparatus  100  and the object and a direction calculation process for calculating the direction between the radar apparatus  100  and the object. 
   Referring to  FIGS. 2 and 3 , the distance calculation process is described. 
   As shown in  FIG. 2 , the elements E 1 -EN of the receiving antenna  12  are spaced from each other by a predetermined spacing S. 
   There arises a time delay and a frequency shift between the transmitted radar signal, which is frequently modulated by the oscillator  15 , and the received radar signal. The time delay corresponds to the distance between the radar apparatus  100  and the object, and the frequency shift corresponds to a relative velocity between the radar apparatus  100  and the object. A phase shift of the received radar signal with respect to the transmitted radar signal increases with the distance between the radar apparatus  100  and the object. The distance and relative velocity between the radar apparatus  100  and the object can be detected based on the phase shift. Therefore, a beat signal is calculated as a frequency difference between the transmitted radar signal and the received radar signal. 
   As shown in  FIGS. 3A and 3B , the beat signal has a first beat frequency Bu in an increase area where the frequency of the transmitted radar signal increases, and has a second beat frequency Bd in a decrease area where the frequency of the transmitted radar signal decreases. Thus, the beat signal includes a first beat signal having the first beat frequency Bu and a second beat signal having the second beat frequency Bd. 
   When the receiving antenna  12  has the elements E 1 -EN, the beat signal is generated on each of the elements E 1 -EN. In the whole receiving antenna  12 , therefore, 2N beat signals are generated. Specifically, N first beat signals having the first beat frequency Bu and N second beat signals having the second beat frequency Bd are generated. 
   The distance and the relative velocity between the radar apparatus  100  and the object are given by the following equations:
 
 D={C·T /(4·Δ F )}·( BuH+BdH )  (1)
 
 V={C /(4· F 0)}·( BuH−BdH )  (2)
 
   In the above equations (1) (2), D represents the distance, V represents the relative velocity, C represents the speed of light, ΔF represents a frequency range of the transmitted radar signal, and F 0  represents the center of the ΔF. BuH is the first beat signal generated based on the received radar signal that is received by the element EH, where H is a positive integer less than or equal to N (i.e., 1≦H≦N). BdH is the second beat signal generated based on the received radar signal that is received by the element EH. 
   Referring to  FIGS. 4A-4C , the direction calculation process is described. The microcomputer  18  performs the direction calculation process at a predetermined time interval Ts. 
   First, a fast Fourier transform (FFT) is applied to each of the N beat signals Bu 1 -BuN to generate N FFT beat signals Bfu 1 -BfuN. Likewise, the fast Fourier transform (FFT) is applied to the N beat signals Bd 1 -BdN to generate N FFT beat signals Bfd 1 -BfdN. Although only the FFT beat signals Bfu 1 -BfuN are illustrated in  FIG. 4B , the FFT beat signals Bfd 1 -BfdN are processed in the same way as the FFT beat signals Bfu 1 -BfuN. 
   Next, a correlation matrix group RG of correlation matrices are generated by using each of the FFT beat signals. For example, in the case of  FIG. 4B , the correlation matrix group RG includes M correlation matrices R(F 1 )-R(FM), where M is a positive integer greater than 1. A correlation matrix R(FI) corresponds to a frequency FI, where I is a positive integer less than or equal to M (i.e., 1≦I≦M). When the receiving antenna  12  has the elements E 1 -EN, each of the correlation matrices R(F 1 )-R(FM) is an N×N matrix. 
   As described later, an addition correlation matrix group UG having addition correlation matrices U(F 1 )-U(FM) is generated such that the correlation matrix group RG generated in a present process is added to a previous correlation matrix group RoG that is the correlation matrix group RG generated in a previous process (i.e., Ts earlier) and stored in the memory  21 . The addition correlation matrix group UG has less noise than the correlation matrix group RG. The use of the previous correlation matrix group RoG as previous information reduces the noise. 
   A MUSIC algorithm used in the radar apparatus  100  is described below. The MUSIC algorithm allows the radar apparatus  100  to achieve the high resolution without an increase in the amount of calculation. 
   The FFT beat signals Bfu 1 -BfuN shown in  FIG. 4B  are summed up to generate a sum beat signal Bfu 0  shown in  FIG. 4C . As can be seen from  FIG. 4C , the sum beat signal Bfu 0  has less noise than each of the FFT beat signals Bfu 1 -BfuN. Likewise, the FFT beat signals Bfd 1 -BfdN are summed up to generate a sum beat signal Bfd 0  having less noise than each of the FFT beat signals Bfd 1 -BfdN. 
   When the received radar signal contains a reflected wave from the object, each of the sum beat signals Bfu 0 , Bfd 0  has peak strength. For example, in  FIG. 4C , the sum beat signal Bfu 0  has the peak strength at a frequency FP, where P is a positive integer less than or equal to M. The peak frequency FP is detected and an extraction matrix C(FP), which is an addition correlation matrix U(FP) corresponding to the peak frequency FP, is extracted from the addition correlation matrices U(F 1 )-U(FM) of the addition correlation matrix group UG. 
   Referring to  FIG. 5 , a process  500  including the distance calculating process and the direction calculating process is described. Although the beat signals Bu 1 -BuN are only discussed below, the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN. The microcomputer  18  performs the process  500  as an interrupt process at the predetermined time interval Ts. 
   The process  500  starts with step S 501 , where the microcomputer  18  obtains the beat signals Bu 1 -BdN. 
   Then, the process  500  proceeds to step S 502 , where the FFT is applied to each of the beat signals Bu 1 -BdN to generate the FFT beat signals Bfu 1 -BfuN. 
   Then, the process  500  proceeds to step S 503 , where the FFT beat signals Bfu 1 -BfuN are summed into the sum beat signal Bfu 0 . 
   Then, the process  500  proceeds to step S 504 , where the peak frequency FP of the sum beat signal Bfu 0  is detected. 
   Then, the process  500  proceeds to step S 505 , where the correlation matrix group RG having the correlation matrices R(F 1 )-R(FM) is calculated from the FFT beat signals Bu 1 -BdN generated in step S 502 . 
   Then, the process  500  proceeds to step S 506 , where each of the correlation matrices R(F 1 )-R(FM) of the correlation matrix group RG is multiplied by a weighting factor (1-K) and each of correlation matrices Ro(F 1 )-Ro(FM) of the previous correlation matrix group RoG is multiplied by a weighting factor K, where K is a fixed value between 0.0 and 1.0. As described above, the previous correlation matrix group RoG is the correlation matrix group RG that is generated in a previous loop (i.e., Ts earlier) of the process  500 . Then, the correlation matrix group RG multiplied by the weighting factor (1-K) and the previous correlation matrix group RoG multiplied by the weighting factor K are added together to produce the addition correlation matrix group UG having addition correlation matrices U(F 1 )-U(FM). Therefore, the addition correlation matrix U(FI), i.e., each of the addition correlation matrices U(F 1 )-(FM) of the addition correlation matrix group UG is given by:
 
 U ( FI )= R ( FI )·(1− K )+ Ro ( FI )· K   (3)
 
   Then, the process  500  proceeds to step S 507 , where the extraction matrix C(FP) is extracted from the addition correlation matrix group UG. The extraction matrix C(FP) is the addition correlation matrices U(FP) corresponding to the peak frequency FP detected in step S 504 , 
   Then, the process  500  proceeds to step S 508 , where an eigenvalue expansion of the extraction matrix C(FP) is performed. 
   Then, the process  500  proceeds to step S 509 , where a MUSIC spectrum is calculated based on an eigenvector of the extraction matrix C(FP). 
   Then, the process  500  proceeds to step S 510 , where the direction of the object in the increase area is calculated based on the MUSIC spectrum. Because the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN, the direction of the object in the decrease area is also calculated. 
   Then, the process  500  proceeds to step S 511 , where the correlation matrix group RG generated in step S 505  is stored in the memory  21  as the previous correlation matrix group RoG that is used in a next loop of the process  500 . 
   Then, the process  500  proceeds to step S 512 , where pair matching of the object is performed based on the strength of the sum beat signal Bfu 0 , the direction of the object in the increase area, the strength of the sum beat signal Bfd 0 , and the direction of the object in the decrease area. Thus, the distance and the relative velocity between the radar apparatus  100  and the object are detected. 
   After step S 512  is finished, the process  500  returns to step S 501 . 
   The correlation matrix group RG generated in a present loop of the process  500  is added to the previous correlation matrix group RoG that is generated in the previous loop of the process  500  and stored in the memory  21 . In such an approach, the addition correlation matrix group UG can have less noise than the correlation matrix group RG. 
   The peak frequency FP, which indicates the presence of the object, is detected and the extraction matrix C(FP) corresponding to the peak frequency FP is extracted from the additional correlation matrix group UG. The MUSIC spectrum is generated by using the extraction matrix C(FP). Specifically, the eigenvalue expansion is performed on only the extraction matrix C(FP) to generate the MUSIC spectrum. Therefore, the amount of calculation executed by the microcomputer  18  is very small, as compared to when the eigenvalue expansion is performed on each of the addition correlation matrices U(F 1 )-U(FM). 
   The previous information is stored in the memory  21  in the form of the correlation matrix for the following reason. 
     FIG. 6  is a table showing the amount of calculation for converting the FFT beat signals Buf 0 -BufN into each form per frequency (i.e., one of the frequencies F 1 -FM). In the table, R±R represents an addition/subtraction of real numbers and R×R represents a multiplication of real numbers. 
   As show in the table, 500 addition/subtractions and 500 multiplications are required to calculate one of the correlation matrices R(F 1 )-R(FM) from the FFT beat signals Bfu 1 -BfuN. Likewise, 3500 addition/subtractions and 3500 multiplications are required to calculate the eigenvectors of one of the correlation matrices R(F 1 )-R(FM) from the FFT beat signals Bfu 1 -BfuN. In other words, 3000 addition/subtractions and 3000 multiplications are required to calculate the eigenvectors from one of the correlation matrices R(F 1 )-R(FM). 
   In the case of  FIG. 4 , 500×M addition/subtractions and 500×M multiplications are performed to calculate the correlation matrices R(F 1 )-R(FM) from the FFT beat signals Bfu 1 -BfuN. For example, when the number M is 10, 50000 addition/subtractions and 50000 multiplications are performed to calculate the 10 correlation matrices R(F 1 )-R(F 10 ) from the FFT beat signals Bfu 1 -BfuN. 
   If the memory  21  stores the eigenvectors of each of the correlation matrices R(F 1 )-R(FM), 3000×M addition/subtractions and 3000×M multiplications are further performed to calculate the eigenvectors. However, the eigenvector of the correlation matrix R(FP) corresponding to the peak frequency FP is only used to generate the extraction matrix C(FP). Therefore, when the peak frequency in the previous loop is equal to that in the present loop, 3000×(M−1) addition/subtractions and 3000×(M−1) multiplications are wasted. Likewise, when the peak frequency in the previous loop is not equal to that in the present loop, 3000×(M−2) addition/subtractions and 3000×(M−2) multiplications are wasted. 
   In view of the amount of calculation, therefore, it is appropriate that the previous information should be stored in the memory  21  in the form of the correlation matrices R(F 1 )-R(FM). 
   Thus, the radar apparatus  100  achieves the high resolution without the increase in the amount of calculation. 
   Although the case where one object is detected is discussed in the first embodiment, the radar apparatus  100  can detect two or more objects. 
   For example, when the number of the objects is two and the distance between one object and the radar apparatus  100  is not equal to that between the other object and the radar apparatus  100 , the sum beat signal Bfu 0  has two peak strengths, i.e., two peak frequencies. In this case, two extraction matrices C(FP), one of which corresponds to one peak frequency and the other of which corresponds to the other peak frequency, are extracted from the additional correlation matrix group UG. The MUSIC spectrums are calculated based on each of the two extraction matrices C(FP) so that each direction of the two objects can be detected. 
   In contrast, when the distance between one object and the radar apparatus  100  is equal to that between the other object and the radar apparatus  100 , the sum beat signal Bfu 0  has only one peak strength. In this case, one extraction matrix C(FP) corresponding to the peak frequency is extracted from the additional correlation matrix group UG. The MUSIC spectrum is calculated based on the extraction matrix C(FP). Because the MUSIC spectrum contains signals indicating each direction of the two objects, i.e., the MUSIC spectrum has two peaks, each direction of the two objects can be detected. 
   Second Embodiment 
   Referring to  FIGS. 5 and 7 , a second embodiment of the present invention is described. In the second embodiment, the microcomputer  18  performs a process  700  shown in  FIG. 7  instead of the process  500  shown in  FIG. 5 . As shown in  FIG. 7 , the process  700  includes steps S 705 -S 711  instead of steps S 505 -S 511  of the process  500 . Although the beat signals Bu 1 -BuN are only discussed below, the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN. 
   After steps S 501 -S 504  are finished, the process  700  proceeds to step S 705 , where the correlation matrix group RG having the correlation matrices R(F 1 )-R(FM) is calculated from the FFT beat signals Bfu 1 -BfuN generated in step S 502 . 
   Then, the process  700  proceeds to step S 706 , where each of the correlation matrices R(F 1 )-R(FM) of the correlation matrix group RG is multiplied by the weighting factor (1-K) and each of previous addition correlation matrices Uo(F 1 )-Uo(FM) of a previous correlation matrix group UoG is multiplied by a weighting factor K. The previous correlation matrix group RoG is the addition correlation matrix group UG generated in a previous loop (i.e., Ts earlier) of the process  700 . Then, the correlation matrix group RG multiplied by the weighting factor (1-K) and the previous addition correlation matrix group UoG multiplied by the weighting factor K are added together to produce the addition correlation matrix group UG having the addition correlation matrices U(F 1 )-U(FM). Therefore, the addition correlation matrix U(FI), i.e., each of the addition correlation matrices U(F 1 )-(FM) of the addition correlation matrix group UG is given by:
 
 U ( FI )= R ( FI )·(1− K )+ Uo ( FI )· K   (4)
 
   Then, the process  700  proceeds to step S 707 , where the extraction matrix C(FP) is extracted from the addition correlation matrix group UG. The extraction matrix C(FP) is the addition correlation matrices U(FP) corresponding to the peak frequency FP detected in step S 504 . 
   Then, the process  700  proceeds to step S 708 , where the eigenvalue expansion of the extraction matrix C(FP) is performed. 
   Then, the process  700  proceeds to step S 709 , where the MUSIC spectrum is calculated based on the eigenvector of the extraction matrix C(FP). 
   Then, the process  700  proceeds to step S 710 , where the direction of the object in the increase area is calculated based on the MUSIC spectrum. Because the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN, the direction of the object in the decrease area is also calculated. 
   Then, the process  700  proceeds to step S 711 , where the addition correlation matrix group UG generated in step S 706  is stored in the memory  21  as the previous addition correlation matrix group UoG that is used in a next loop of the process  700 . 
   Then, the process  700  proceeds to step S 512 . 
   In the process  700 , thus, the previous additional correlation matrix UoG generated in the previous loop is used to generate the addition correlation matrix group UG. In such an approach, the addition correlation matrix UG can be generated based on two or more previous correlation matrix groups so that the addition correlation matrix group UG of the second embodiment can have less noise than that of the first embodiment. 
   Third Embodiment 
   Referring to  FIGS. 5 and 8 , a third embodiment of the present invention is described. In the third embodiment, the microcomputer  18  performs a process  800  shown in  FIG. 8  instead of the process  500  shown in  FIG. 5 . As shown in  FIG. 8 , the process  800  includes steps S 805 -S 811  instead of steps S 505 -S 511  of the process  500 . Although the beat signals Bu 1 -BuN are only discussed below, the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN. 
   After steps S 501 -S 504  are finished, the process  800  proceeds to step S 805 , where the correlation matrix group RG having the correlation matrices R(F 1 )-R(FM) is calculated from the FFT beat signals Bfu 1 -BfuN generated in step S 502 . 
   Then, the process  800  proceeds to step S 806 , where a correlation matrix R(FP) corresponding to the peak frequency FP detected in step S 504  is extracted from the correlation matrix group RG. Further, a previous correlation matrix Ro(FP) corresponding to the peak frequency FP is extracted from a previous correlation matrix group RoG having correlation matrices Ro(F 1 )-Ro(FM). The previous correlation matrix group RoG is the correlation matrix group RG that is generated in a previous loop (i.e., Ts earlier) of the process  800  and stored in the memory  21 . 
   Then, the process  800  proceeds to step S 807 , where the correlation matrix R(FP) is multiplied by the weighting factor (1-K) and the previous correlation matrix Ro(FP) is multiplied by the weighting factor K. Then, the correlation matrix R(FP) multiplied by the weighting factor (1-K) and the previous correlation matrix Ro(FP) multiplied by the weighting factor K are added together to produce the addition correlation matrix U(FP). Therefore, the addition correlation matrix U(FP) is given by:
 
 U ( FP )= R ( FP )·(1− K )+ Ro ( FP )· K   (5)
 
   Then, the process  800  proceeds to step S 808 , where the eigenvalue expansion of the addition correlation matrix U(FP) is performed. 
   Then, the process  800  proceeds to step S 809 , where the MUSIC spectrum is calculated based on the eigenvector of the addition correlation matrix U(FP). 
   Then, the process  800  proceeds to step S 810 , where the direction of the object in the increase area is calculated based on the MUSIC spectrum. Because the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN, the direction of the object in the decrease area is also calculated. 
   Then, the process  800  proceeds to step S 811 , where the correlation matrix group RG generated in step S 805  is stored in the memory  21  as the previous correlation matrix group RoG that is used in a next loop of the process  800 . 
   Then, the process  800  proceeds to step S 512 . 
   In the process  500  according to the first embodiment, the addition correlation matrix group UG having the addition correlation matrices U(F 1 )-U(FM) is generated such that the correlation matrix group RG is added to the previous correlation matrix group RoG. When the number of the objects is one, the sum beat signal Bfu 0  has only one peak frequency. Therefore, although each of the addition correlation matrices U(F 1 )-U(FM) is calculated, the addition correlation matrix U(FP) corresponding to the peak frequency FP is only used. In other words, the calculation of the addition correlation matrices U(F 1 )-U(FM) except for the addition correlation matrix U(FP) may result in waste. In contrast, in the process  800  according to the third embodiment, the addition correlation matrix U(FP) is generated such that the correlation matrix R(FP) is added to the previous correlation matrix Ro(FP). Thus, the wasted calculation can be avoided. 
   In the process  500 , the memory  21  needs to store the previous correlation matrix group RoG and the addition correlation matrix group UG at the same time. In contrast, in the process  800 , the memory  21  needs to store the previous correlation matrix group RoG and the addition correlation matrix U(FP) at the same time. Therefore, the memory  21  can have a small amount of storage capacity in the process  800 , as compared to in the process  500 . 
   Fourth Embodiment 
   A fourth embodiment of the present invention is described. In the third embodiment, the memory  21  stores each of the M correlation matrices R(F 1 )-R(FM) for the next loop. In contrast, in the fourth embodiment, the memory  21  stores M/2 correlation matrices R(F 1 ), R(F 3 ), R(F 5 ) . . . . Thus, the M correlation matrices R(F 1 )-R(FM) are thinned out to the M/2 correlation matrices R(F 1 ), R(F 3 ), R(F 5 ) . . . . In other words, the M correlation matrices R(F 1 )-R(FM) are alternately stored in the memory  21  such that the memory  21  stores the M/2 correlation matrices R(F 1 ), R(F 3 ), R(F 5 ) . . . . 
   For example, when the correlation matrices R(F 1 )-R(F 3 ) are generated in the Sth loop, where S is a positive integer, the memory  21  stores the correlation matrices R(F 1 ), R(F 3 ) as the previous correlation matrices Ro(F 1 ), Ro(F 3 ). In other words, the correlation matrix R(F 2 ) is not stored in the memory  21  in the Sth loop. In this case, if the peak frequency FP is F 2  in the (S+1)th loop, the previous correlation matrix Ro(F 2 ) is generated such that a weighted average of the previous correlation matrix Ro(F 1 ) is added to a weighted average of the previous correlation matrix Ro(F 3 ). 
   In the fourth embodiment, the microcomputer  18  performs a process  900  shown in  FIG. 9  instead of the process  500  shown in  FIG. 5 . As shown in  FIG. 9 , the process  900  includes steps S 905 -S 912  instead of steps S 505 -S 511  of the process  500 . Although the beat signals Bu 1 -BuN are only discussed below, the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN. 
   After steps S 501 -S 504  are finished, the process  900  proceeds to step S 905 , where the correlation matrix group RG having the correlation matrices R(F 1 )-R(FM) is calculated from the FFT beat signals Bfu 1 -BfuN generated in step S 502 . 
   Then, the process  900  proceeds to step S 906 , where it is determined whether the previous correlation matrix Ro(FP) corresponding to the peak frequency FP is stored in the memory  21 . 
   If the previous correlation matrix Ro(FP) is stored in the memory  21 , the process  900  proceeds to step S 908  directly. 
   If the previous correlation matrix Ro(FP) is not stored in the memory  21 , the process  900  proceeds to step S 908  through step S 907 , where the previous correlation matrix Ro(FP) is generated such that a weighted average of a previous correlation matrix Ro(FP−1) is added to a weighted average of a previous correlation matrix Ro(FP+1). 
   At step S 908 , the correlation matrix R(FP) corresponding to the peak frequency FP is extracted from the correlation matrix group RG. The correlation matrix R(FP) is multiplied by the weighting factor (1-K) and the previous correlation matrix Ro(FP) is multiplied by the weighting factor K. Then, the correlation matrix R(FP) multiplied by the weighting factor (1-K) and the previous correlation matrix Ro(FP) multiplied by the weighting factor K are added together to produce the addition correlation matrix U(FP). Therefore, the addition correlation matrix U(FP) is given by:
 
 U ( FP )= R ( FP )·(1− K )+ Ro ( FP )· K   (6)
 
   Then, the process  900  proceeds to step S 909 , where the eigenvalue expansion of the addition correlation matrix U(FP) is performed. 
   Then, the process  900  proceeds to step S 910 , where the MUSIC spectrum is calculated based on the eigenvector of the addition correlation matrix U(FP). 
   Then, the process  900  proceeds to step S 911 , where the direction of the object in the increase area is calculated based on the MUSIC spectrum. Because the beat signals Bd 1 -BdN are processed in the same way as the beat signals Bu 1 -BuN, the direction of the object in the decrease area is also calculated. 
   Then, the process  900  proceeds to step S 912 , where the correlation matrix group RG is thinned out and stored in the memory  21  as the previous correlation matrix group RoG that is used in a next loop of the process  900 . 
   Then, the process  900  proceeds to step S 512 . 
   As described above, in the process  900 , the correlation matrix group RG is thinned out and stored in the memory  21  as the previous correlation matrix group RoG. Thus, the memory  21  can have a small amount of storage capacity in the process  900 , as compared to in the process  800  according to the third embodiment. Even when the previous correlation matrix Ro(FP) is not stored in the memory  21 , the previous correlation matrix Ro(FP) is estimated from previous correlation matrices Ro(FP−1), Ro(FP+1). 
   (Modifications) 
   The embodiments described above may be modified in various ways. For example, the radar apparatus  100  may use the received radar signal received by some of the elements E 1 -EN of the receiving antenna  12 , not each of the elements E 1 -EN. In such an approach, the amount of calculation can be reduced. 
   The correlation matrix group RG or the addition correlation matrix group UG may be stored in the memory  21  after being compressed by a data compression algorithm. Thus, the memory  21  may store the previous information in a form of data containing elements of the correlation matrix group RG or the addition correlation matrix group UG. 
   The weighting factor K may be a variable. For example, when the received radar signal has considerable instantaneous noise, the weighing factor K may be increased. In such an approach, an influence of the noise can be reduced. 
   The algorithm used in the present invention can be applied to various types of the DOA estimation algorithms such as unitary-MUSIC algorithm, ESPRIT algorithm, unitary-ESPRIT algorithm, Capon algorithm, and Beam Former algorithm. In particular, when the unitary-MUSIC or the unitary-ESPRIT is used, only the real part of the matrix is stored in the memory  21 . Therefore, the amount of calculation can be significantly reduced and the memory  21  can have a very small amount of storage capacity. The algorithm used in the present invention also can be applied to a spatial smoothing algorithm. 
   The previous information (i.e., the previous correlation matrix group RoG, or the previous addition correlation matrix group UG) may be generated in two or more previous loop. For example, the previous information may be generated in two previous loop (i.e., generated 2Ts earlier). 
   The transmitting antenna  11  instead of the receiving antenna  12  may have the elements arranged in the array to generate the beat signals.