CN103344948B - Method for computing external illuminator radar cross-ambiguity function utilizing sparse Fourier transform - Google Patents
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Abstract
The invention relates to a method for computing an external illuminator radar cross-ambiguity function utilizing the sparse Fourier transform and belongs to the field of radar target acquisition processing. Firstly, point multiplication is carried out on direct wave signals and echo delay signals to construct a new vector, wherein the direct wave signals are received by an external illuminator radar antenna, and filtering and down extraction are carried out on the direct wave signals. Secondly, the sparse Fourier transform is carried out on the new vector, and therefore a Doppler tangent plane result of the cross-ambiguity function on the delay point is obtained. Lastly, parameters like target Doppler frequency shift can be estimated through the sparse Fourier transform results. Compared with a traditional method that cross-ambiguity function operation is carried out on the external illuminator radar through the Fourier transform, the method utilizes the sparse Fourier transform to solve the cross-ambiguity function and can greatly reduce operand of the cross-ambiguity function under the condition of long-time accumulation according to the characteristics that the number of targets appearing in the air in reality is limited and the targets have sparsity.
Description
Technical Field
The invention relates to a method for calculating a mutual fuzzy function of an external radiation source radar by utilizing sparse Fourier transform, belongs to the technical field of radar target detection, and particularly relates to a method for reducing the operation amount of the mutual fuzzy function of the external radiation source radar of a digital television under the condition of long-time coherent accumulation.
Background
The external radiation source radar is a bi/multistatic radar using non-cooperative radiation sources such as television signals, frequency modulation broadcast signals and the like as radiation sources. The target parameters are contained in the target echo, and the external radiation source radar system performs mutual fuzzy function processing by using direct waves received by the reference antenna and target echo signals received by the echo channel. The existence of the target corresponds to the peak value on the cross-fuzzy function plane, the existence of the target is judged through the cross-fuzzy function peak value, and parameters such as time delay, Doppler velocity and the like of the target are estimated through the position of the peak value on the two-dimensional plane. The cross-ambiguity function is defined as follows:
wherein echo (n) is an echo signal n time sampling point, refr (n) is a direct wave signal n time sampling point,*for the conjugate operator, m is the number of delay elements, q is the number of Doppler shift elements, and L is the length of the accumulated data. Suppose the signal sampling rate is Fs。
A Cross Ambiguity Function (CAF) performs two-dimensional correlation of time delay and frequency shift on a direct wave signal and a target echo signal, and can be implemented by Fast Fourier Transform (FFT).
Defining the delay of the echo signal received by the radar of the external radiation source and the conjugate complex multiplication of the direct wave signal to form new data: er (n) = echo (n + m) · refr*(n)，n∈[1,L]。
CAF can be represented by the following formula:
χ(m,w)=FFT[er] （2）
wherein, the FFT operation length is L.
In engineering, because the sampling frequency is far greater than the target Doppler frequency shift, the FFT operation directly performed on the data subjected to the time delay complex multiplication has huge calculation amount and is difficult to realize in real time, and most of the obtained data does not contain target information and is useless. In order to reduce traffic volume, the delayed complex multiplied signal is generally low-pass filtered and down-sampled to reduce data volume, and then FFT operation is performed.
Knowing that the length of the signal er is L, the signal er is filtered and decimated by M times to form a signal x, and the length of the signal x is N = L/M.
Calculating CAF using FFT can be expressed as:
χ(m,w)=FFT[x] （3）
wherein, x is data after low-pass filtering and M times down-sampling processing of a direct wave signal conjugate and echo signal delay product er.
In general, CAF employs long-term coherent accumulation with FFT to improve signal-to-noise ratio, detection probability, and frequency domain resolution. However, the FFT complex multiplication amount of the data with the length of N is O (N.log)2(N)/2) and the complex addition amount is O (N.log)2(N)), and increases proportionally with an increase in the number of processing data points N. For long-time accumulated CAF, the amount of computation is large.
Disclosure of Invention
The invention aims to provide a method for calculating a mutual ambiguity function of an external radiation source radar by using sparse Fourier transform.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for calculating a mutual fuzzy function of an external radiation source radar by utilizing sparse Fourier transform, which comprises the following steps:
the method comprises the following steps: multiplying m-point time delay echo (n + m) of nth sampling point of echo signal received by external radiation source radar antenna and nth sampling point refr (n) of direct wave by echo (n + m) refr*(n), the product of dot multiplication is er (n) (n is the [1, L ]]) Filtering er, extracting M times to form signal x (i), i ∈ [1, N [ ]]. Wherein, the length N of the signal x satisfies: n = L/M is an integer power of 2. The frequency domain of signal X is denoted X, and the frequency domain data length is also N, assuming that X contains k large-valued points (i.e., k possible targets).
Step two: and (3) calculating a result at a certain CAF delay point (m delay point) by using the SFFT.
χ(m,w)=SFFT[x] （5）
In practice, the number of targets is generally limited, each target corresponds to one peak in the CAF, the remaining part is a noise floor, and the peak of the whole CAF plane is Sparse, and at this time, the efficiency of calculating the spectrum by using Sparse Fast Fourier Transform (SFFT for short) is better than that of the existing FFT.
The overall thought of the step two is as follows: taking the product of the processed direct wave and the echo time delay as an SFFT input signal; firstly, rearranging the time domain of the signal; then, a filter is used for truncation; time domain aliasing accumulation is carried out, and FFT is carried out on the result; detecting a large-value point in the obtained FFT result; and finally, estimating the position and the amplitude of the frequency domain large value of the original signal by utilizing the obtained large value point through a coordinate conversion relation. The calculation of CAF using SFFT is not mentioned in the open literature. The SFFT algorithm comprises the following specific steps:
(1) and (3) spectrum arrangement:
defining the signal: s (i) = x (σ · i), i ∈ [1, N ]; where σ ∈ [1, N ] and is an odd number with the modulo inverse of N. If σ · i > N, s (i) = x ((σ · i) mod N), (σ · i) mod N denotes the remainder of σ · i to the modulus N.
Definition of σ-1Is the inverse of the sigma-modulo-N, and both satisfy the relation (sigma x sigma)-1) mod N =1. S (i) = X (σ) can be demonstrated-1·i)，i∈[1,N]. Where S is the frequency domain of signal S and X is the frequency domain of signal X. If σ-1·i>N, then s (i) = X ((σ)-1·i)mod N)。
(2) Signal filtering
Defining a flat window function g (i) (i ∈ [1, N ]), where g is a symmetric vector, and setting its effective length as w, w is a positive integer, and w < N.
Suppose the frequency domain of the flat window function G is G, which is also N long. G is required to satisfy the characteristics of small passband ripple and smooth stop band, i.e. for i e < - > N, N]，G(i)∈[1-，1+](ii) a To pair|G(i)|<(ii) a Wherein, for the oscillation ripple, ' pass band truncation factor ' and stop band truncation factor '.
Defining the signal: y (i) = g (i) · s (i), i ∈ [1, N ]. Therefore, w non-0 points exist in the signal y, and the rest N-w data are 0.
(3) Sampling FFT
Constructing a signal:i∈[1,B](ii) a Where B is both the spectral sub-sampling interval and the length of the signal z, B<w is an integer divisible by N,indicating rounding down (conversion to integers) the fractional data w/B.
The FFT is used to calculate the frequency domain value Z of signal Z, Z = FFT (Z), and Z is also B as long as Z. It can be demonstrated that the frequency domain of signal z satisfies z (i) = Y (i · N/B), i ∈ [1, B ], where B < w.
(4) Positioning cycle
Changing sigma, executing steps (1) to (3). Recording sigma in the step (1), and classifying Z obtained in the step (3) into a set Z _ SUM.
Defining the set J as the set containing d.k maximum amplitude coordinates in Z found in each step (3), wherein d >1 and is an integer. The coordinates in J can be viewed as a set of large-valued "like" positions taken in the field of view as Z.
J is mapped back to a large value "pre-image" with X as the observation domain. "primitive" set of positions I = { I ∈ [1, N [ ]]|hashσ(i) Is belonged to J }. Wherein,(I ∈ I) is defined as a 'hash function', and represents the mapping relation between the 'original image' and the 'image'. The new element number d.k.N/B of the 'original image' set is obtained by mapping each time.
Defining an offset function: oσ(i)=σ·i-hashσ(i)·N/B，i∈I。
And (5) executing the step (4) loc times.
(5) Evaluation loop
Changing sigma, executing steps (1) to (3). Recording sigma in the step (1), and classifying Z obtained in the step (3) into a set Z _ SUM.
And (5) executing the step (5) est times.
(6) Spectral magnitude estimation
Z _ SUM includes the first d.k large values in Z obtained by executing step (3) each time, and I and Z _ SUM correspond to a 'primary image' taking X as an observation domain. For I ∈ I, X (I) an estimated value ofhashσ(i)、oσ(i) Parameter σ used in (a) from step (a)4) And (5) each cycle.
And (6) performing the loop times, wherein the loop = est + loc is the total cycle number of the positioning and estimation.
Obtaining loops in the step (6)Value is taken asThe large value is used as the final pair XThe estimation result of (2).
The complex addition operation quantity in the second step is as follows: o [ (B.log)2B+size(I)+w)×loops+d·k×loc]。
Wherein size (I) represents the number of elements in set I.
The multiplication operation quantity in the second step is as follows: o [ (B.log)2B/2+size(I)+w)×loops+d·k·N/B×loc]。
Step three: and detecting parameters such as target Doppler and the like through the sparse Fourier transform result in the second step.
Has the advantages that: the mutual fuzzy function of the external radiation source radar is calculated by utilizing sparse Fourier transform, the target parameter can be effectively detected, and the operation amount of the mutual fuzzy function is not directly related to the data length, so that the mutual fuzzy function operation amount can be greatly reduced under the condition of long-time accumulation.
Drawings
FIG. 1 is a flow chart of the SFFT-based CAF algorithm;
FIG. 2 is a flow chart of the SFFT algorithm;
in the case that the data length N =2048 in fig. 3, the FFT is used, and the targets with close speeds cannot be effectively distinguished;
fig. 4 data length N =8192, SFFT is used in comparison with FFT calculation CAF results;
in fig. 5, when the number of large frequency spectrum values k =3, SFFT and FFT are used to calculate the CAF algorithm operation complexity contrast; (a) comparing SFFT with FFT complex addition times; (b) SFFT is compared to the FFT complex times.
Detailed Description
The invention will be described in detail below with reference to the accompanying drawings and specific embodiments, which are only intended to facilitate the understanding of the invention and are not intended to limit the invention.
The invention provides a method for calculating a mutual ambiguity function of an external radiation source radar by utilizing sparse Fourier transform. To verify the present invention, computer simulations were performed. The general flow of one embodiment of the present invention is given below in conjunction with fig. 1.
The method comprises the following steps: multiplying the echo time delay echo (n + m) received by an external radiation source radar antenna by the conjugate point of a direct wave refr (n) = echo (n + m) · refr*(n)（n∈[1,L]) Filtering the dot product result er, extracting M times, and constructing a new vector x (i) (i belongs to [1, N ]]）。
The radiation source adopts digital television broadcast signals, the bandwidth is Band =7.56MHz, and the carrier frequency is fc=674 MHz; baseband sampling rate of fs=9 MHz; low-pass filtered downsampling multiple M = 1200.
Suppose there are three targets at a certain time delay from the radar, with respective velocities v1=8m/s、v2=9m/s、v3=12 m/s, the Doppler frequency shifts corresponding to the three targets are respectively fd1=40.44Hz、fd2=35.95Hz、fd3=-53.92Hz。
Assuming conjugate point multiplicationThe length of the signal er is L =2048 × 1200, after low-pass filtering and M =1200 times of decimation, the number of FFT points is N =2048, and the corresponding frequency domain resolution is Δ f1=fsL ≈ 3.66 Hz. In this case, it is difficult to effectively distinguish the targets 1 and 2 having similar speeds, and the result is shown in fig. 3.
Step two: and calculating a CAF result at a certain delay point (m delay point) by using the SFFT.
The accumulation time is increased, and the length of the low-pass filtered, M =1200 downsampled data is N =8192, assuming that the newly composed signal length L =8192 × 1200. Corresponding frequency domain resolution of Δ f1=fs/L≈0.92Hz。
Fig. 2 shows the specific steps in step two of this embodiment. The SFFT is divided into 6 small steps as follows.
(1) And (3) spectrum arrangement:
signal: s (i) = x (σ · i), i ∈ [1, N ], where N = 8192.
The positioning cycle loc =3 parameters σ, in turn: 3011. 1687, 709; the estimation cycle est =8 parameters σ is in turn: 6323. 1243, 749, 919, 5691, 5369, 899, 7649.
(2) Signal filtering
Flat window function g (i): time domain effective length w = 1597.
The frequency domain G (i) parameters of the flat window function are: oscillation ripple =10-6(ii) a Passband truncation factor' =1.5 × 10-3(ii) a Stop band truncation factor =4.1 × 10-3。
(3) Sampling FFT
Constructing a signal:i∈[1,B]where B = 256.
Calculating the frequency-domain value of z: z = fft (Z).
(4) Positioning cycle
The parameter σ is selected in order according to the number of cycles of the positioning cycle, and (1) to (3) are executed. In the step (1), Z obtained in the step (3) is classified into a set Z _ SUM.
Set J is defined to contain d · k =6 sets of maximum amplitude coordinates in Z found in each step (3), where d = 2.
J is mapped back to a large value "pre-image" with X as the observation domain. "primitive" set of positions I = { I ∈ [1, N [ ]]|hashσ(i) Is belonged to J }. Wherein,each mapping results in a new number of elements d · k · N/B =192 of the set of "original images".
Offset function: oσ(i)=σ·i-hashσ(i)·N/B。
Loc =3 times is performed (4).
(5) Evaluation loop
The parameter σ is selected in order according to the number of cycles of the estimation cycle, and (1) to (3) are executed. Recording sigma in the step (1), and classifying Z obtained in the step (3) into a set Z _ SUM.
Est =8 times.
(6) Spectral magnitude estimation
Z _ SUM contains d · k =6 large values in the subsampled FFTs obtained in all steps (3), and I and Z _ SUM correspond to a "primary image" with X as the observation domain. For I ∈ I, X (I) an estimated value ofhashσ(i)、oσ(i) The parameter σ used in (3) comes from each cycle of steps (4), (5).
Perform (6) loops =11 times.
The step (6) obtains 11Value is taken asThe large value is used as the final pairThe estimation result of (2).
And the calculation of the frequency spectrum of the constructed signal in the first step can be completed through a plurality of times of positioning and estimation cycles.
During SFFT calculation: in the step (3), FFT is used for calculating the frequency domain of the signal with the data length of B, and the complex multiplication operation quantity is O [ w + B & log2B/2]The complex addition amount is O [ w + B & log2B]。
And (4) positioning, circulating, multiplying and adding the operation quantities respectively as follows: o [ (B.log)2B/2+d·k+w)×loc]、O[(B·log2B+d·k·N/B+w)×loc]。
And (5) estimating, circularly multiplying and adding the complex quantities respectively as follows: o [ (B.log)2B/2+w)×est]、O[(B·log2B+w)×est]。
And (6) estimating complex multiplication and complex addition operation quantities of the large frequency spectrum values: o [ size (I) Xlops ].
Through statistics, the SFFT complex multiplication number is 11458, the FFT complex multiplication number is 53248, the SFFT complex addition number is 23280, and the FFT complex addition number is 106496 in the present embodiment. The advantage of the operation amount of the SFFT is obvious under the condition of calculating the number of large data points.
Step three: and detecting parameters such as target Doppler and the like through the sparse Fourier transform result in the second step.
The results of this example are given in FIGS. 3 to 4. Through calculation, the Doppler frequency shifts of the three targets obtained by calculating the CAF by using the SFFT are-53.1 Hz, 36.6Hz and 41.2Hz in sequence, and are the same as the Doppler frequency shift information of the three targets obtained by calculating the CAF by using the FFT and consistent with the Doppler of a real target. Therefore, the target parameter information can be effectively obtained by the SFFT-based CAF.
SFFT-based CAF differs from FFT-based CAF in that: SFFT results in 0 at non-large CAF values, while FFT is not 0. The method is caused by the SFFT principle, and in order to enable the SFFT operation speed to be high, only frequency domain large value points are selected through positioning and estimation during calculation to assign values to results, and other positions are all 0. The CAF using SFFT results in only isolated peaks, SFFT can be seen as a description of the large-valued points of the frequency domain, while FFT is a description of the full frequency domain. Therefore, the SFFT operation efficiency is better than the FFT operation amount when there are a few large-valued points and a large number of frequency domain points.
The target is estimated by using the SFFT in the CAF, so that parameters such as Doppler frequency offset and the like of the target can be obtained more accurately. When the number of spectral maxima is fixed and k =3, the SFFT, the number of complex multiplications in the FFT operation, and the number of complex additions vary with the signal length as shown in fig. 5. It can be seen that as the signal length N increases, the amount of SFFT operations will be significantly less than the amount of FFT operations.
The above description is only exemplary of the present invention and should not be taken as limiting the scope of the present invention, and any modifications, equivalents, improvements and the like that are within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (2)
1. A method for calculating an external radiation source radar mutual ambiguity function by utilizing sparse Fourier transform is characterized by comprising the following specific steps:
(1) setting parameters:
constructing a signal: er (n) ═ echo (n + m) & refr*(n)，n∈[1,L](ii) a er (n) represents the multiplication of m-point delay of echo signal echo (n) and conjugate point of direct wave signal refr (n); wherein echo (n) samples echo signal at n time, refr (n) samples direct wave signal at n time,*m is the number of delay units;
defining the signal: x (i) is the ith sampling point of the data after filtering and down-sampling the signal er, and i belongs to [1, N ]; where N is the signal length and N is an integer power of 2; the frequency domain of the signal X is represented as X, assuming that X contains k large-value points, the large values corresponding to possible targets; k is an integer;
(2) and (3) spectrum arrangement:
defining the signal: s (i) x (σ · i), i ∈ [1, N ]; where σ ∈ [1, N ] and is an odd number with a modulo inverse for N, if σ · i > N, then s (i) ═ x ((σ · i) mod N), (σ · i) mod N denotes the remainder of σ · i modulo N;
definition of σ-1Is the inverse of the sigma-modulo-N, and both satisfy the relation (sigma x sigma)-1)mod N＝1；
(3) Signal filtering
Defining a flat window function g (i), wherein i belongs to [1, N ], making g a symmetric vector, and setting an effective length w, w < N and a positive integer:
assuming that the frequency domain of the flat window function G is G, and the length of G is N as same as that of G, G is required to satisfy the characteristics of small passband ripple and smooth stop band, i.e. for i e < - > N and' N]，|G(i)|∈[1-，1+](ii) a To pair| G (i) | <; wherein, for the oscillation ripple,' pass band truncation factor and stop band truncation factor;
defining the signal: y (i) g (i) s (i), i ∈ [1, N ], and thus, w non-0 points exist in the signal y, and the rest N-w data are 0;
(4) sampling FFT
Constructing a signal:i∈[1,B](ii) a Where B is both the spectral sub-sampling interval and the length of the signal z, B < w is an integer divisible by N,the decimal data w/B is rounded down and converted into integers;
calculating a frequency domain value Z of a signal Z by using FFT, wherein Z is FFT (Z), and the length of Z is the same as Z and is also B;
(5) positioning cycle
Changing sigma, and executing (2) to (4); recording sigma in the step (2), and classifying Z obtained in the step (4) into a set Z _ SUM;
defining a set J as a set containing d.k maximum amplitude coordinates in Z found in each step (4), wherein d >1 and is an integer; the coordinates in J are regarded as a large-value image position set obtained by taking Z as an observation domain;
mapping J back to a large value "primary image" with X as the observation domain; set of "primary image" positionsJ, wherein the content of the compound is,i belongs to I and is defined as a hash function, and represents the mapping relation between the original image and the image; mapping each time to obtain the new element number d.k.N/B of the 'original image' set;
defining an offset function: oσ(i)＝σ·i-hashσ(i)·N/B，i∈I；
Executing the step (5) loc times;
(6) evaluation loop
Changing sigma, and executing (2) to (4); recording sigma in the step (2), and classifying Z obtained in the step (4) into a set Z _ SUM;
executing the step (6) est times;
(7) spectral magnitude estimation
Z _ SUM comprises d.k large values in the subsampled FFT obtained in the step (4), and I and Z _ SUM correspond to a 'primary image' taking X as an observation domain; for I ∈ I, X (I) an estimated value ofhashσ(i)、oσ(i) The parameter σ used in (3) comes from each cycle of steps (5), (6);
executing the step (7) times of loops, wherein the loops is the total number of positioning and estimation cycles;
obtaining lops in the step (7)Value is taken asThe large value is used as the final pairThe estimation result of (2).
2. The method for calculating the radar cross-ambiguity function of the external radiation source by using the sparse Fourier transform as claimed in claim 1, wherein: and d is 2.
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