Target Doppler frequency estimation method based on FIR-IAA in clutter environment

Abstract

The present invention discloses a method for estimating a target Doppler frequency based on FIR-IAA in a clutter environment, and the steps include: uniformly gridding the Doppler frequency space to generate a pilot vector set; determining the range of the target Doppler frequency to be estimated; designing an FIR filter group; filtering the received signal and the pilot vector set; estimating the target Doppler frequency using an iterative adaptive algorithm; and calculating the resolution probability of the target Doppler frequency and the root mean square error of the estimated value. The present invention reduces the dimension of the required inverse matrix in IAA, solves the problems of large amount of calculation and high system complexity of the prior art algorithm, and uses an FIR filter with a null trap to effectively suppress clutter leakage while ensuring that the super-resolution of IAA is achieved, thereby enhancing the anti-clutter capability of the target Doppler frequency estimation and facilitating engineering implementation.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and further relates to a target Doppler frequency estimation method based on FIR filter-Iterative Adaptive Approach (FIR filter-Iterative Adaptive Approach) in a clutter environment in the field of radar parameter estimation technology. The present invention can be used to estimate the target Doppler frequency of a pulse Doppler radar receiving signal in a clutter environment. Background Art

[0002] Doppler frequency estimation technology uses the phase relationship between different signals received by the radar to solve the Doppler frequency of a moving target with a certain speed, obtain the speed information of the target, and provide a basis for the next step of target tracking and positioning. The Doppler frequency estimation method is mainly implemented by two algorithms based on the fast Fourier transform algorithm and the correlation operation algorithm. The algorithm based on the fast Fourier transform determines the frequency response characteristics of the matched filter according to the received signal. From the Schwarz inequality, it can be seen that the stronger the frequency point of the signal, the greater the filter amplification factor. Therefore, the inner product of the received signal and the pilot vector at each frequency point in the space is performed to obtain the amplitude-frequency characteristic curve. The Doppler frequency corresponding to the peak is the Doppler frequency of the target. The algorithm based on the correlation operation processes the covariance matrix of the received signal according to different cost functions, and obtains the power spectrum of the algorithm through a finite number of iterations until the difference between two adjacent weight vector matrices converges to zero. The Doppler frequency corresponding to the peak is the Doppler frequency of the target.

[0003] Cheng Yuanbing et al. proposed a three-dimensional parameter joint estimation method for estimating radar receiving angle and Doppler frequency in a dual-base MIMO radar based on the multidimensional Vandermonde structure characteristics of the parameter flow matrix in the paper "Joint estimation of receiving and transmitting angle and Doppler frequency of dual-base MIMO radar based on multidimensional Vandermonde structure" (Journal of Electronics and Information Technology, 2018, 40(9): 2258-2264). The steps of this method are as follows: first, construct a third-order tensor according to the multidimensional structural characteristics of the echo model; second, slice along the transmit dimension, receive dimension and pulse dimension to obtain three equivalent matrices; third, estimate the receiving and transmitting array flow matrix and Doppler flow matrix by combining the multidimensional Vandermonde structure characteristics and the Khatri-Rao product structure characteristics of the left singular matrix of the equivalent matrix; fourth, estimate the receiving and transmitting angle and Doppler frequency by the Root-MUSIC algorithm. The disadvantage of this method is that the Root-MUSIC algorithm requires characteristic decomposition of the covariance matrix of the received signal, which requires large amount of calculation, high algorithm complexity, and poor real-time performance in engineering implementation.

[0004] Guilin University of Electronic Technology has disclosed a method for estimating Doppler frequency in a PMF-FFT system in its patent application "A method for improving the accuracy of Doppler frequency estimation in a PMF-FFT system" (application number: 202110441079.1, application date: 2021.04.23, application publication number: CN 113253313A). The implementation steps of this method are: first, the output of the matched filter is doubled and zero-filled, and a 2N-point Fourier transform is performed; secondly, the frequency domain position coordinates of the peak value of the frequency domain signal amplitude are selected, and the interpolation direction is determined by the Quinn algorithm to obtain the movement amount of the spectral line interpolation shift; finally, the Doppler frequency estimate is calculated to reduce the frequency offset estimation error. However, this method still has the disadvantage that it only performs discrete Fourier transform in the PMF-FFT system and obtains the estimated value of the target Doppler frequency based on the discrete Fourier transform spectrum. In the case of low signal-to-noise ratio, when the signal frequency is close to the quantization frequency of the discrete Fourier transform, the Quinn algorithm estimation error is large and the resolution is low. Due to clutter leakage, the discrete Fourier transform method cannot be used to estimate the target Doppler frequency in a clutter environment. Summary of the invention

[0005] The purpose of the present invention is to propose a target Doppler frequency estimation method based on FIR-IAA in a clutter environment in view of the above-mentioned deficiencies in the prior art, so as to solve the problems in the prior art of poor target Doppler frequency estimation performance caused by large calculation amount and high algorithm complexity of the Root-MUSIC algorithm, large estimation error and low resolution of the Quinn algorithm, and the problem that the discrete Fourier transform method cannot perform target Doppler frequency estimation in a clutter environment due to clutter leakage.

[0006] To achieve the above purpose, the idea of ​​the present invention is: the present invention determines the received signal and uniformly grids the Doppler frequency space, obtains the pilot vector corresponding to the received signal and each frequency grid point, and performs a discrete Fourier transform on it. The range of the target Doppler frequency is determined according to the spectrum of the discrete Fourier transform, starting from the first Doppler frequency in the range, a Doppler frequency is taken at every interval L, and a total of B Doppler frequencies are obtained, each Doppler frequency is used as the center frequency of the FIR filter corresponding to the frequency, all FIR filters form an FIR filter group, and the weight vector of the FIR filter group is obtained. Since the number of filters in the FIR filter group is less than the total number of received signal pulses, the dimension of the inverse matrix in the traditional iterative adaptive algorithm is reduced, the algorithm calculation amount and system complexity are reduced, thereby solving the problem of large calculation amount and high algorithm complexity of the Root-MUSIC algorithm, and facilitating engineering implementation. The present invention filters the pilot vector at each frequency grid point in the received signal and space, realizes the transition from the pulse domain to the Doppler domain, so as to perform signal processing in the Doppler domain according to the steps of the iterative adaptive algorithm, thereby avoiding the problem of large estimation error and low resolution of the Quinn algorithm at low signal-to-noise ratio. Since the iterative adaptive algorithm has the characteristics of strong robustness and super-resolution, the resolution capability of the target Doppler frequency is improved. The present invention filters the received signal through an FIR filter and then applies the iterative adaptive algorithm. This process forms an FIR-IAA to estimate the target Doppler frequency. Since the FIR filter has a zero-pitching function, it can suppress the clutter leakage in the received signal, effectively reduce the side lobes of the IAA power spectrum, and enhance the anti-clutter capability of the target Doppler frequency estimation.

[0007] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0008] Step 1: Uniformly grid the Doppler frequency space to generate a pilot vector set:

[0009] According to the pulse repetition period T of the received signal r Determine the number and spacing of grid points, grid the Doppler frequency space uniformly, and generate the pilot vector set A(f), where T r The value of is determined by the pulse Doppler radar parameters;

[0010] Step 2: Determine the range of the target Doppler frequency to be estimated:

[0011] The received signal y is inner-producted with the pilot vector set A(f) to obtain the spectrum of discrete Fourier transform, and the range of target Doppler frequency is determined according to the spectrum;

[0012] Step 3, design the FIR filter bank:

[0013] Within the range of the target Doppler frequency, starting from the first Doppler frequency, a Doppler frequency is taken at every interval L, and a total of B Doppler frequencies are obtained. Each Doppler frequency is used as the center frequency of the FIR filter corresponding to the frequency, and all FIR filters form an FIR filter group;

[0014] Step 4: Filter the received signal and the pilot vector set:

[0015] According to the formula: y'=W H y,A'(f)=W H A(f), filter the received signal y and the pilot vector set A(f) respectively to realize the transformation from the pulse domain to the Doppler domain, where y' is the filtered received signal, W is the weight vector of the FIR filter group, (·) H is the conjugate transpose operation, A'(f) is the pilot vector set after filtering;

[0016] Step 5: Use iterative adaptive algorithm to estimate the target Doppler frequency:

[0017] The iterative adaptive algorithm is used to process the filtered data y' and A'(f) in the Doppler domain to obtain the IAA power spectrum, and the Doppler frequency corresponding to each IAA power spectrum peak is used as the estimated value of the respective target Doppler frequency.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] First, the present invention designs an FIR filter group in which the number of filters is less than the total number of received signal pulses, and filters the received signal and the pilot vector at each frequency grid point in space, thereby overcoming the shortcomings of the Root-MUSIC algorithm, such as large amount of calculation and high complexity, so that the present invention realizes the transition from the pulse domain to the Doppler domain. While ensuring that the method achieves IAA super-resolution, it reduces the dimension of the inverse matrix required in IAA, reduces the algorithm calculation amount and system complexity, and facilitates engineering implementation.

[0020] Second, the present invention uses an iterative adaptive algorithm in the Doppler domain to estimate the target Doppler frequency. Since the iterative adaptive algorithm has the characteristics of strong robustness and super resolution, it overcomes the defects of large estimation error and low resolution of the Quinn algorithm at low signal-to-noise ratio, thereby improving the resolution capability of the target Doppler frequency.

[0021] Thirdly, the present invention uses an FIR filter, which has a zero notch and can suppress clutter leakage in the received signal, so that the present invention effectively reduces the side lobes of the IAA power spectrum and enhances the anti-clutter capability of the target Doppler frequency estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of the present invention;

[0023] Figure 2 It is a simulation diagram of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0025] Reference Figure 1 The specific implementation steps of the present invention are further described in detail with reference to the accompanying drawings and embodiments.

[0026] Step 1: uniformly grid the Doppler frequency space to generate a pilot vector set.

[0027] Step 1.1, using the reciprocal relationship between the pulse repetition period and frequency of the received signal, according to the pulse repetition period T of the received signal r The number and interval of the grid points are determined to uniformly grid the Doppler frequency space. r is 1ms, according to the pulse repetition frequency f of the received signal r =1 / T r =1000Hz, divide the Doppler frequency space into 1001 grid points from 0Hz to 1000Hz, the interval between two adjacent grid points is 1Hz, and all grid points form a spatial frequency vector f = [f0,f1,...,f 1000 ].

[0028] Step 1.2, the pilot vector corresponding to each Doppler frequency grid point is: Among them, f k is the Doppler frequency of the kth grid point, a(f k ) is f k The corresponding pilot vector, e (·) is the exponential operation with the natural constant e as the base, j is the symbol of the imaginary unit, π is the circumference of the circle, d is the pulse position vector of the received signal, d=[0,1,...,M-1] T , M is the total number of pulses of the received signal.

[0029] Step 1.3, synthesize the pilot vectors corresponding to all Doppler frequency grid points in space into a complete pilot vector set: A(f) = [a(f0), a(f1), ..., a(f K )], where K is the total number of Doppler frequency grid points in space. In the embodiment of the present invention, the total number of pulses M of the received signal is 64, then the pulse position vector d of the received signal is [0, 1, ..., 63] TThe total number of Doppler frequency grid points is 1001, and the spatial frequency vector f composed of all grid points is [f0,f1,...,f 1000 ], then the complete pilot vector set

[0030] Step 2: determine the range of the target Doppler frequency to be estimated.

[0031] Step 2.1, using the pulse repetition frequency f of the received signal r The ratio of the received signal to the total number of pulses M is used to calculate the resolution of the discrete Fourier transform. r =1000Hz, the total number of pulses of the received signal M = 64, so the resolution of the discrete Fourier transform α = f r / M=15.625Hz.

[0032] Step 2.2, the received signal y is inner-producted with the pilot vector set A(f) to obtain the spectrum of discrete Fourier transform, and the range of target Doppler frequency is determined according to the spectrum. In the embodiment of the present invention, half of the resolution of discrete Fourier transform is used as a node, so two difficult-to-distinguish target Doppler frequencies are set as f and f respectively. m1 =500Hz, f m2 =507Hz, so the received signal According to y T ×A(f) formula, the inner product of the received signal y and the pilot vector set A(f) is taken to obtain the spectrum of discrete Fourier transform. The Doppler frequency corresponding to the peak of the spectrum is about 500 Hz, so the target Doppler frequency range is 472-535 Hz.

[0033] Step 3, design the FIR filter bank according to the target Doppler frequency range.

[0034] Step 3.1: Within the range of the target Doppler frequencies obtained in step 2, a Doppler frequency is taken every L interval starting from the first Doppler frequency, and the Doppler frequencies with intervals less than L are discarded, and a total of B Doppler frequencies are obtained, which are f m , f m+L , f m+2L , ..., f m+(B-1)L , taking each Doppler frequency as the center frequency of the FIR filter corresponding to that frequency, where L ≥ 2, f m is the first Doppler frequency in the target Doppler frequency range, i.e., the center frequency of the first FIR filter, f m+L is the L+1th Doppler frequency in the target Doppler frequency range, i.e., the center frequency of the second FIR filter. Similarly, f m+(B-1)LThe (B-1)×L+1th Doppler frequency in the target Doppler frequency range is the center frequency of the Bth FIR filter. In the embodiment of the present invention, the target Doppler frequency obtained in step 2 is in the range of 472-535 Hz, and a Doppler frequency is taken at every 7 Hz from 472 Hz, and a total of 10 Doppler frequencies are obtained, namely 472 Hz, 479 Hz, 486 Hz, 493 Hz, 500 Hz, 507 Hz, 514 Hz, 521 Hz, 528 Hz, and 535 Hz, and each Doppler frequency is used as the center frequency of the FIR filter corresponding to the frequency.

[0035] Step 3.2, all FIR filters form a FIR filter bank.

[0036] Step 4: Filter the received signal and the pilot vector set.

[0037] According to the following formula, the received signal y and the pilot vector set A(f) are filtered respectively:

[0038] y'=W H y

[0039] A'(f)=W H A(f)

[0040] Where y' is the filtered received signal, W is the weight vector of the FIR filter bank, (·) H is the conjugate transpose operation, and A'(f) is the filtered pilot vector set, which realizes the transformation from the pulse domain to the Doppler domain.

[0041] Step 5: Use an iterative adaptive algorithm to estimate the target Doppler frequency in the Doppler domain.

[0042] Since the iterative adaptive algorithm has the characteristics of strong robustness and super-resolution, it avoids the problem of large estimation error and low resolution of the Quinn algorithm at low signal-to-noise ratio. In order to improve the resolution ability of the target Doppler frequency, the present invention adopts an iterative adaptive algorithm to perform signal processing on the transformed data y' and A'(f) in the Doppler domain, thereby obtaining the IAA power spectrum. The Doppler frequency corresponding to the peak of the IAA power spectrum is the estimated value of the target Doppler frequency. While ensuring the super-resolution of IAA, this method reduces the dimension of the inverse matrix required in IAA, reduces the calculation amount of the algorithm and the system complexity, and is easy to implement in engineering.

[0043] Step 6: Calculate the resolution probability of the target Doppler frequency and the root mean square error of the estimated value.

[0044] Step 6.1, determine the conditions for successful target resolution.

[0045] According to the theoretical value of the target Doppler frequency, the search range of the IAA power spectrum peak is determined with one quarter of the discrete Fourier transform resolution as the node. The number of peaks detected within the range is equal to the number of signal sources as the condition for successful target resolution. If yes, the target is successfully resolved, otherwise, it is unsuccessful. In the embodiment of the present invention, the theoretical values ​​of the two target Doppler frequencies are f and f respectively. m1 =500Hz, f m2 =507Hz, the search range of the IAA power spectrum peak is defined as 497-512Hz at one quarter of the resolution on the left and right of the target Doppler frequency. Since the number of signal sources is 2, the condition for successful target resolution is that 2 peaks are detected within this range, otherwise it will be unsuccessful.

[0046] Step 6.2, set the number of Monte Carlo experiments and calculate the resolution probability of the target Doppler frequency.

[0047] Step 6.3, after completing the separation of the signal source, calculate the root mean square error between the estimated value and the theoretical value to complete the evaluation of FIR-IAA.

[0048] The effect of the present invention is further described below in conjunction with simulation experiments:

[0049] 1. Simulation experiment conditions:

[0050] The hardware platform of the simulation experiment of the present invention is: the processor is Intel(R) Core(TM) i5-7300HQ CPU, the main frequency is 2.50GHz, and the memory is 4.00GB.

[0051] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system and MATLAB R2016b.

[0052] 2. Simulation content and results analysis:

[0053] The simulation experiment of the present invention adopts the method of the present invention and the iterative adaptive algorithm of the prior art. In the environment of a single array element with 64 pulses in a single snapshot, the detection signal-to-noise ratio changes from 15dB to 30dB in steps of 3dB. 1000 Monte Carlo experiments are performed to obtain the estimated value of the target Doppler frequency. The resolution probability of the target Doppler frequency in the 1000 experiments and the root mean square error of the estimated value are statistically calculated, and a curve is drawn, as shown in FIG. Figure 2 shown.

[0054] Combine the following Figure 2 The simulation result diagram of the present invention is further described.

[0055] Figure 2(a) is a comparison diagram of the spectrum obtained by discrete Fourier transform and the IAA power spectrum obtained by the method of the present invention. Figure 2 The abscissa in (a) represents the Doppler frequency in Hz, and the ordinate represents the amplitude of the spectrum or IAA power spectrum in dB. Figure 2 The dashed curve in (a) represents the spectrum curve simulated by discrete Fourier transform method. Figure 2 The curve marked with a solid line in (a) represents the IAA power spectrum curve simulated by the method of the present invention.

[0056] Depend on Figure 2 In (a), it can be seen from the discrete Fourier transform spectrum that the discrete Fourier transform method cannot generate a peak at the target Doppler frequency in a clutter environment, so the target Doppler frequency estimation cannot be performed. However, it can be seen from the IAA power spectrum that the method of the present invention can generate a peak at the target Doppler frequency in a clutter environment. The Doppler frequency corresponding to each IAA power spectrum peak is the estimated value of the respective target Doppler frequency.

[0057] Figure 2 (b) and 2(c) are the estimated values ​​of the target Doppler frequency obtained by using the method of the present invention and the iterative adaptive algorithm respectively under the same simulation conditions. In the environment of a single array element with a single snapshot of 64 pulses, the target Doppler frequency resolution probability and the root mean square error comparison diagram of the estimated value are shown. Figure 2 (b) and 2(c) are comparison diagrams obtained when the detection signal-to-noise ratio changes from 15dB to 30dB in steps of 3dB. Figure 2 The horizontal axis in (b) represents the detection signal-to-noise ratio in dB, and the vertical axis represents the resolution probability of the target Doppler frequency. Figure 2 The horizontal axis in (c) represents the detection signal-to-noise ratio in dB, and the vertical axis represents the root mean square error of the target Doppler frequency estimate in Hz. Figure 2 The curves marked with “*” in (b) and (c) represent the simulation results using the iterative adaptive algorithm. Figure 2 The curves marked with "o" in (b) and 2(c) represent the result curves simulated using the method of the present invention.

[0058] Depend on Figure 2Comparison of the two curves in (b) shows that when the detection signal-to-noise ratio is 15dB, 18dB, 21dB, 24dB, 27dB and 30dB, the resolution probability of the target Doppler frequency obtained by the method of the present invention is 83.60%, 87.90%, 88.20%, 91.30%, 92.70% and 92.10% respectively, and the resolution probability of the target Doppler frequency obtained by the iterative adaptive algorithm is 87.30%, 91.00%, 92.40%, 93.90%, 95.20% and 93.40% respectively. It can be seen that under the same detection signal-to-noise ratio under the environment of a single array element single snapshot of 64 pulses, the resolution probability of the target Doppler frequency obtained by the method of the present invention and the iterative adaptive algorithm can reach more than 90% under high signal-to-noise ratio conditions, and the difference between the two is not large under low signal-to-noise ratio conditions.

[0059] Depend on Figure 2 Comparison of the two curves in (c) shows that when the detection signal-to-noise ratio is 15dB, 18dB, 21dB, 24dB, 27dB and 30dB, the root mean square errors of the target Doppler frequency estimation value obtained by the method of the present invention are 1.1432, 1.0968, 1.1165, 1.0775, 1.0724 and 1.1186Hz, respectively, and the root mean square errors of the target Doppler frequency estimation value obtained by the iterative adaptive algorithm are 1.0432, 1.0391, 0.9748, 0.9757, 0.9360 and 0.9324Hz, respectively. It can be seen that under the same detection signal-to-noise ratio of a single array element and a single snapshot of 64 pulses, the root mean square error of the target Doppler frequency estimation value obtained by the method of the present invention is slightly greater than the root mean square error of the target Doppler frequency estimation value obtained by the iterative adaptive algorithm, and both are within 1.2Hz.

[0060] The above simulation experiments show that: in the environment of a single array element with 64 pulses in a single snapshot, the resolution probability and the root mean square error of the estimated value of the target Doppler frequency obtained by the method of the present invention and the iterative adaptive algorithm are not much different, which proves that the method of the present invention has a super-resolution capability similar to that of the iterative adaptive algorithm and improves the accuracy of target Doppler frequency estimation.

Claims

1. A target Doppler frequency estimation method based on FIR-IAA in a clutter environment, characterized in that: Design a FIR filter bank, and after the received signal is filtered, use an iterative adaptive algorithm to estimate the Doppler frequency of the target; the specific steps of the frequency estimation method include the following: Step 1: Uniformly grid the Doppler frequency space to generate a pilot vector set: According to the pulse repetition period T of the received signal r Determine the number and spacing of grid points, grid the Doppler frequency space uniformly, and generate the pilot vector set A(f), where T r The value of is determined by the pulse Doppler radar parameters; Step 2: Determine the range of the target Doppler frequency to be estimated: The received signal y is inner-producted with the pilot vector set A(f) to obtain the spectrum of discrete Fourier transform, and the range of target Doppler frequency is determined according to the spectrum; Step 3, design the FIR filter bank: Within the range of the target Doppler frequency, starting from the first Doppler frequency, a Doppler frequency is taken at every interval L, and a total of B Doppler frequencies are obtained. Each Doppler frequency is used as the center frequency of the FIR filter corresponding to the frequency, and all FIR filters form an FIR filter group; Step 4: Filter the received signal and the pilot vector set: According to the formula: y'=W H y,A'(f)=W H A(f), filter the received signal y and the pilot vector set A(f) respectively to realize the transformation from the pulse domain to the Doppler domain, where y' is the filtered received signal, W is the weight vector of the FIR filter group, (·) H is the conjugate transpose operation, A'(f) is the pilot vector set after filtering; Step 5: Use iterative adaptive algorithm to estimate the target Doppler frequency: The iterative adaptive algorithm is used to process the filtered data y' and A'(f) in the Doppler domain to obtain the IAA power spectrum, and the Doppler frequency corresponding to each IAA power spectrum peak is used as the estimated value of the respective target Doppler frequency.

2. The estimation method according to claim 1, characterized in that: The steps for generating the pilot vector set A(f) described in step 1 are as follows: The first step is to calculate the pulse repetition frequency f of the received signal. r =1 / T r , dividing the Doppler frequency space from 0 Hz to f r Hz interval is 1Hz total f r +1 Doppler frequency grid point; The second step is to use the formula Get the pilot vector corresponding to each Doppler frequency grid point, where f k is the Doppler frequency of the kth grid point, a(f k ) is f k The corresponding pilot vector; The third step is to synthesize the pilot vectors corresponding to all Doppler frequency grid points in space into a pilot vector set: A(f) = [a(f0), a(f1), ..., a(f K )], where K is the total number of Doppler frequency grid points in space, K = f r +1.

3. The estimation method according to claim 1, characterized in that: The steps of the iterative adaptive algorithm described in step 5 are as follows: The first step is to Formula, calculate the diagonal elements in the initialization matrix P; The second step is to use R = A(f)PA H (f) Formula, solve the covariance matrix R, S represents the weight vector matrix, the diagonal elements of the weight vector matrix are given by the formula It is calculated that in each iteration, the diagonal elements in the initialization matrix P are Generate the P' matrix after the current iteration update, according to the formula R'=A(f)P'A H (f) Solve the updated R' matrix and repeat this step until the difference between two adjacent weight vector matrices converges to zero, and the IAA power spectrum is obtained.

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