T-IAA Based Target Doppler Frequency Estimation Method

Abstract

The present invention discloses a method for estimating the target Doppler frequency based on T-IAA. The specific steps thereof include: uniformly gridding the Doppler frequency space to generate a pilot vector set; determining the range of the target Doppler frequency to be estimated; setting a transformation matrix; performing transformation processing on the received signal and the pilot vector set; estimating the target Doppler frequency by using the iterative adaptive algorithm; and statistically calculating the resolution probability of the target Doppler frequency and the root mean square error of the estimated value. Based on the received signal of the pulsed Doppler radar, the present invention forms T-IAA by setting a transformation matrix and then estimating the target Doppler frequency in the Doppler domain by using the iterative adaptive algorithm. The method of the present invention ensures achieving the super-resolution of IAA while reducing the dimension of the inverse matrix required in IAA, reducing the computational amount of the algorithm and the system complexity, and facilitating engineering implementation.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar, and further relates to a method for estimating the target Doppler frequency based on the Transformed Iterative Adaptive Approach (T-IAA) in the technical field of radar parameter estimation. The present invention can be used to estimate the target Doppler frequency of the received signal of a pulsed Doppler radar. Background Art

[0002] Doppler frequency estimation technology uses the phase relationship between different signals received by a radar to calculate 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 methods for Doppler frequency estimation are mainly realized by two major algorithms: the algorithm based on the fast Fourier transform algorithm and the algorithm based on 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. According to the Schwarz inequality, the stronger the signal at a frequency point, the greater the amplification factor of the filter. Therefore, the inner product of the received signal and the pilot vector at each frequency point in space is calculated to obtain the amplitude-frequency characteristic curve, and the Doppler frequency corresponding to the peak value 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 through a finite number of iterations until the difference between adjacent weight vector matrices converges to zero, the power spectrum of the algorithm is obtained, and the Doppler frequency corresponding to the peak value is the Doppler frequency of the target.

[0003] Cheng Yuanbing et al. proposed a three-dimensional parameter joint estimation method for estimating the radar transceiver angle and Doppler frequency based on the multi-dimensional Vandermonde structure characteristics of the parameter manifold matrix in their published paper "Joint Estimation of Transceiver Angle and Doppler Frequency for Bistatic MIMO Radar Based on Multi-Dimensional Vandermonde Structure" (Journal of Electronics & Information Technology, 2018, 40(9): 2258-2264). The steps of this method are as follows: First, a third-order tensor is constructed according to the multi-dimensional structure characteristics of the echo model; Second, three equivalent matrices are obtained by slicing along the transmit dimension, receive dimension, and pulse dimension; Third, combining the multi-dimensional Vandermonde structure characteristics and the fact that the left singular matrix of the equivalent matrix has the Khatri-Rao product structure characteristics, the transceiver array manifold matrix and the Doppler manifold matrix are estimated; Fourth, the transceiver angle and Doppler frequency are estimated by the Root-MUSIC algorithm. The disadvantage of this method is that in the Root-MUSIC algorithm, it is necessary to perform eigenvalue decomposition on the covariance matrix of the received signal, which has a large amount of calculation, high algorithm complexity, and poor real-time performance in engineering implementation.

[0004] Guilin University of Electronic Technology disclosed a method for estimating Doppler frequency in a PMF-FFT system in its patent document "A Method for Improving the Estimation Accuracy of Doppler Frequency in PMF-FFT System" (Application No.: 202110441079.1, Application Date: April 23, 2021, Publication No.: CN 113253313A). The implementation steps of this method are as follows: First, zero-padding the output of the matched filter by one time and performing a 2N-point Fourier transform; Second, selecting the frequency-domain position coordinates of the peak of the frequency-domain signal amplitude, judging the interpolation direction through the Quinn algorithm, and obtaining the moving amount of spectral line interpolation and shifting; Finally, calculating the estimated value of Doppler frequency to reduce the frequency offset estimation error. However, the deficiency of this method is 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 estimation error of the Quinn algorithm is large and the resolution is low. Summary of the Invention

[0005] The object of the present invention is to address the deficiencies of the above-mentioned prior art and propose a method for estimating target Doppler frequency based on T-IAA to solve the problems of poor performance in estimating target Doppler frequency caused by large computational complexity and high algorithm complexity of the Root-MUSIC algorithm in the prior art, as well as the problems of large estimation error and low resolution of the Quinn algorithm.

[0006] To achieve the above object, the idea of the present invention is as follows: The present invention determines the received signal and evenly grids the Doppler frequency space to obtain the received signal and the pilot vector corresponding to each frequency grid point and performs discrete Fourier transform on them. According to the spectrum of the discrete Fourier transform, the range of the target Doppler frequency is determined, a transformation matrix is set, and channels less than the total number of received signal pulses are formed, so that the dimension of the inverse matrix in the traditional iterative adaptive algorithm is reduced, reducing the computational complexity of the algorithm and the system complexity, and solving the problems of large computational complexity and high algorithm complexity of the Root-MUSIC algorithm, which is convenient for engineering implementation. The present invention performs transformation processing on the received signal and the pilot vector at each frequency grid point in the space to realize the transformation from the pulse domain to the Doppler domain, so as to perform signal processing according to the steps of the iterative adaptive algorithm in the Doppler domain, thereby avoiding the problems 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 ability of the target Doppler frequency is improved. The received signal is processed by transformation and then the iterative adaptive algorithm is applied, and this process forms T-IAA for estimating the target Doppler frequency.

[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] Based on the pulse repetition period T of the received signal r Determine the number and interval of grid points, uniformly grid the Doppler frequency space, and generate a pilot vector set A(f), where the value of T r is determined by the parameters of the pulsed Doppler radar;

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

[0011] Take the inner product of the received signal y and the pilot vector set A(f) to obtain the spectrum of the discrete Fourier transform, and determine the range of the target Doppler frequency according to the spectrum;

[0012] Step 3: Set the transformation matrix T:

[0013] Within the range of the target Doppler frequency, form B channels less than the total number M of pulses of the received signal. The center frequency f of each channel T =[f m , f m+1 ,..., f m+B , f m is the minimum value of the target Doppler frequency range, f m+B is the maximum value of the target Doppler frequency range. Use the formula to set the transformation matrix T, where f r is the pulse repetition frequency of the received signal, f r =1 / T r , e (·) is the exponential operation with the natural constant e as the base, j is the imaginary unit symbol, π is the pi, d is the pulse position vector of the received signal, d = [0, 1,..., M - 1] T , and M is the total number of pulses of the received signal;

[0014] Step 4: Perform transformation processing on the received signal and the pilot vector set:

[0015] According to the formula: y' = T H y, A'(f) = T H A(f), perform transformation processing on the received signal y and the pilot vector set A(f) respectively from the pulse domain to the Doppler domain, where y' is the transformed received signal, (·) H is the conjugate transpose operation, and A'(f) is the transformed pilot vector set;

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

[0017] An iterative adaptive algorithm is adopted to perform signal processing on the transformed data y' and A'(f) in the Doppler domain to obtain the IAA power spectrum, and the Doppler frequency corresponding to each peak of the IAA power spectrum is used as the estimated value of its respective target Doppler frequency.

[0018] The present invention has the following advantages compared with the prior art:

[0019] First, by setting a transformation matrix, the present invention forms channels less than the total number of received signal pulses, and performs transformation processing on the received signal and the pilot vector at each frequency grid point in the space, overcoming the deficiencies of large computational complexity and high complexity of the Root-MUSIC algorithm, enabling the present invention to achieve the transformation from the pulse domain to the Doppler domain. While ensuring that this method achieves IAA super-resolution, it reduces the dimension of the inverse matrix required in IAA, reduces the computational amount of the algorithm and the system complexity, and is convenient for engineering implementation.

[0020] Second, the present invention uses an iterative adaptive algorithm to estimate the target Doppler frequency in the Doppler domain. 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 ability of the target Doppler frequency of the present invention. Description of the Drawings

[0021] Figure 1 is the flowchart of the present invention;

[0022] Figure 2 is the simulation diagram of the present invention. Detailed Embodiment

[0023] The following further describes the present invention in detail with reference to the drawings and embodiments.

[0024] Refer to Figure 1 and the embodiment to further describe the specific implementation steps of the present invention in detail.

[0025] Step 1: Uniformly grid the Doppler frequency space to generate a set of pilot vectors.

[0026] Step 1.1: Utilize the reciprocal relationship between the pulse repetition period and frequency of the received signal, and determine the number and interval of grid points according to the pulse repetition period T of the received signal r to uniformly grid the Doppler frequency space. In the embodiment of the present invention, the pulse repetition period T of the received signal r is 1 ms. According to the pulse repetition frequency f of the received signal r = 1 / T r= 1000 Hz, the Doppler frequency space is divided into 1001 grid points from 0 Hz to 1000 Hz, and the interval between adjacent two grid points is 1 Hz. All grid points form a spatial frequency vector f = [f0, f1,..., f 1000 .

[0027] Step 1.2, the pilot vector corresponding to each Doppler frequency grid point is: where, f k is the Doppler frequency of the k-th grid point, a(f k ) is the pilot vector corresponding to f k , e (·) is the exponential operation with the natural constant e as the base, j is the imaginary unit symbol, π is the pi, d is the pulse position vector of the received signal, d = [0, 1,..., M - 1] T , and M is the total number of pulses of the received signal.

[0028] Step 1.3, synthesize the pilot vectors corresponding to all Doppler frequency grid points in the 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 the 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 = [0, 1,..., 63] T , the total number of Doppler frequency grid points is 1001, and all grid points form a spatial frequency vector f = [f0, f1,..., f 1000 , then the complete pilot vector set

[0029] Step 2, determine the range of the target Doppler frequency to be estimated.

[0030] Step 2.1, use the ratio relationship between the pulse repetition frequency f r of the received signal and the total number of pulses M to calculate the resolution of the discrete Fourier transform. In the embodiment of the present invention, the pulse repetition frequency f r of the received signal = 1000 Hz, the total number of pulses M of the received signal = 64, so the resolution α of the discrete Fourier transform = f r / M = 15.625 Hz.

[0031] Step 2.2, take the inner product of the received signal y and the pilot vector set A(f) to obtain the spectrum of the discrete Fourier transform, and determine the range of the target Doppler frequency according to the spectrum. In the embodiment of the present invention, taking half of the resolution of the discrete Fourier transform as the node, so two indistinguishable target Doppler frequencies are set as f m1 = 500 Hz, f m2= 507Hz, so the received signal According to the formula of y T ×A(f), the inner product of the received signal y and the pilot vector set A(f) is calculated to obtain the spectrum of the discrete Fourier transform. The Doppler frequency corresponding to the peak of this spectrum is about 500Hz. Therefore, the range of the target Doppler frequency is 472 - 535Hz.

[0032] Step 3, set the transformation matrix T according to the range of the target Doppler frequency.

[0033] Step 3.1, within the range of the target Doppler frequency obtained in Step 2, form B channels that are less than the total number M of received signal pulses. The center frequency f of each channel T = [f m , f m+1 ,..., f m+B , where f m is the minimum value of the target Doppler frequency range, and f m+B is the maximum value of the target Doppler frequency range. In the embodiment of the present invention, the minimum value f m of the target Doppler frequency range is 472Hz, the maximum value f m+B of the target Doppler frequency range is 535Hz, and the interval between adjacent two channels is 7Hz. Therefore, the channel center frequency f T = [472, 479, 486, 493, 500, 507, 514, 521, 528, 535].

[0034] Step 3.2, to solve the problems of large computational amount and high algorithm complexity of the Root - MUSIC algorithm, set the transformation matrix and form channels that are less than the total number of received signal pulses. The set transformation matrix is as follows:

[0035]

[0036] Step 4, perform transformation processing on the received signal and the pilot vector set.

[0037] According to the following formula, perform transformation processing on the received signal y and the pilot vector set A(f) from the pulse domain to the Doppler domain respectively:

[0038] y' = T H y

[0039] A'(f) = T H A(f)

[0040] where y' is the transformed received signal, (·) H is the conjugate transpose operation, and A'(f) is the transformed pilot vector set.

[0041] Step 5: Estimate the target Doppler frequency in the Doppler domain using the iterative adaptive algorithm.

[0042] Since the iterative adaptive algorithm has the characteristics of strong robustness and super-resolution, it avoids the problems of large estimation error and low resolution of the Quinn algorithm at low signal-to-noise ratio. To improve the resolution ability of the target Doppler frequency, the present invention adopts the iterative adaptive algorithm to perform signal processing on the processed data y' and A'(f) in the Doppler domain, so as to obtain the IAA power spectrum. The Doppler frequency corresponding to the peak value of the IAA power spectrum is the estimated value of the target Doppler frequency. This method reduces the dimension of the inverse matrix required in the IAA while ensuring the super-resolution of the IAA, reduces the computational complexity of the algorithm and the system complexity, and is convenient for engineering implementation.

[0043] Step 6: Statistically analyze 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, taking one-fourth of the discrete Fourier transform resolution as the node, determine the search range of the peak value of the IAA power spectrum. Taking the number of detected peak values within this range equal to the number of signal sources as the condition for successful target resolution. If so, the target is successfully resolved; otherwise, it is not. In the embodiment of the present invention, the theoretical values of the two target Doppler frequencies are f m1 = 500Hz and f m2 = 507Hz. The search range of the peak value of the IAA power spectrum is delimited at one-fourth of the resolution on both sides of the target Doppler frequency as 497 - 512Hz. Since the number of signal sources is 2, the condition for successful target resolution should be detecting 2 peak values within this range, and other cases are not successful.

[0046] Step 6.2: Set the number of Monte Carlo experiments and statistically analyze the resolution probability of the target Doppler frequency.

[0047] Step 6.3: After separating the signal sources, calculate the root mean square error between the estimated value and the theoretical value to complete the evaluation of T-IAA.

[0048] The following further illustrates the effect of the present invention in combination with simulation experiments:

[0049] 1. Simulation experiment conditions:

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

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

[0052] 2. Simulation content and result analysis:

[0053] In the simulation experiment of the present invention, the method of the present invention and the iterative adaptive algorithm are used. In the environment of 64 pulses per single element per snapshot, the detection signal-to-noise ratio changes from 15 dB in steps of 3 dB to 30 dB, and the initial phase difference of the complex envelope changes from 0 in steps of to 2π in two cases. 1000 Monte Carlo experiments are respectively carried out to obtain the estimated values of the target Doppler frequency. The resolution probability of the target Doppler frequency and the root mean square error of the estimated values are statistically analyzed in 1000 experiments, and curves are drawn therefrom, as Figure 2 shown.

[0054] Next, in combination with Figure 2 the simulation result diagrams, the effects of the present invention will be further described.

[0055] Figure 2 are the comparison diagrams of the estimated values of the target Doppler frequency obtained respectively by using the method of the present invention and the iterative adaptive algorithm under the same simulation conditions. In the environment of 64 pulses per single element per snapshot, the resolution probability of the target Doppler frequency and the root mean square error of the estimated values are compared. Figure 2 (a) and 2(b) are the comparison diagrams obtained when the detection signal-to-noise ratio changes from 15 dB in steps of 3 dB to 30 dB. Figure 2 The abscissa in (a) represents the detection signal-to-noise ratio, with the unit of dB, and the ordinate represents the resolution probability of the target Doppler frequency. Figure 2 The abscissa in (b) represents the detection signal-to-noise ratio, with the unit of dB, and the ordinate represents the root mean square error of the estimated value of the target Doppler frequency. Figure 2 (c) and 2(d) are the comparison diagrams obtained when the initial phase difference of the complex envelope changes from 0 in steps of to 2π. Figure 2 The abscissa in (c) represents the initial phase difference of the complex envelope, with the unit of radian, and the ordinate represents the resolution probability of the target Doppler frequency. Figure 2 The abscissa in (b) represents the initial phase difference of the complex envelope, with the unit of radian, and the ordinate represents the root mean square error of the estimated value of the target Doppler frequency. Figure 2 The curve marked with "*" in Figure 2 represents the result curve of the simulation using the iterative adaptive algorithm,

[0056] and from Figure 2From the comparison of the two curves in (a), it can be seen that when the detection signal-to-noise ratios are 15 dB, 18 dB, 21 dB, 24 dB, 27 dB, and 30 dB respectively, the resolution probabilities of the target Doppler frequency obtained by using the method of the present invention are 82.90%, 89.30%, 89.80%, 92.60%, 91.80%, and 92.30% respectively, and the resolution probabilities of the target Doppler frequency obtained by using the iterative adaptive algorithm are 87.80%, 91.70%, 93.90%, 95.30%, 93.50%, and 94.20% respectively. It can be seen that in the environment of 64 pulses per single-element single snapshot at the same detection signal-to-noise ratio, the resolution probabilities of the target Doppler frequency obtained by using the method of the present invention and the iterative adaptive algorithm can both reach more than 90% in the case of high signal-to-noise ratio, and the difference between the two is not significant at low signal-to-noise ratio.

[0057] From Figure 2 From the comparison of the two curves in (b), it can be seen that when the detection signal-to-noise ratios are 15 dB, 18 dB, 21 dB, 24 dB, 27 dB, and 30 dB respectively, the root mean square errors of the estimated values of the target Doppler frequency obtained by using the method of the present invention are 1.1701, 1.1015, 1.0550, 1.0570, 1.0442, and 1.0709 Hz respectively, and the root mean square errors of the estimated values of the target Doppler frequency obtained by using the iterative adaptive algorithm are 1.0629, 0.9904, 0.9472, 0.9535, 0.9529, and 0.9508 Hz respectively. It can be seen that in the environment of 64 pulses per single-element single snapshot at the same detection signal-to-noise ratio, the root mean square error of the estimated value of the target Doppler frequency obtained by using the method of the present invention is slightly larger than that obtained by using the iterative adaptive algorithm, and both are within 1.2 Hz.

[0058] From Figure 2 From the comparison of the two curves in (c), it can be seen that when the initial phase difference of the complex envelope is 0, At 0, and 2π, the resolution probabilities of the target Doppler frequency obtained by the method of the present invention are 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 99.20%, 95.00%, 93.50%, 99.40%, 100% and 100% respectively, and the resolution probabilities of the target Doppler frequency obtained by the iterative adaptive algorithm are 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 100%, 98.80%, 96.40%, 96.00%, 99.50%, 99.90% and 100% respectively. It can be seen that in the environment of 64 pulses in a single snapshot of a single array element and with the same initial phase difference of the complex envelope, the resolution probabilities of the target Doppler frequency obtained by the method of the present invention and the iterative adaptive algorithm can reach 100% at most initial phase differences. When the initial phase difference is the difference between the two is not significant.

[0059] From Figure 2 the comparison of the two curves in (d), it can be seen that when the initial phase differences of the complex envelope are 0, and 2π respectively, the root mean square errors of the target Doppler frequency estimation values obtained by the method of the present invention are 0.2280, 0.1049, 0, 0.2665, 1.5035, 1.2769, 0.2236, 0, 0.0894, 0.2049, 0.4427, 0.5902, 0.6724, 0.6930, 0.6126, 0.4050 and 0.2168 Hz respectively, and the root mean square errors of the target Doppler frequency estimation values obtained by the iterative adaptive algorithm are 0.2145, 0.1000, 0.0447, 0.2775, 1.0490, 1.0230, 0.2510, 0.0548, 0.1342, 0.2145, 0.4019, 0.5025, 0.5273, 0.5279, 0.4849, 0.3635 and 0.2145 Hz respectively. It can be seen that in the environment of 64 pulses in a single snapshot of a single array element and with the same initial phase difference of the complex envelope, the difference between the root mean square errors of the target Doppler frequency estimation values obtained by the method of the present invention and the iterative adaptive algorithm is not significant and both are within 1.6 Hz, showing a change similar to a sine curve. This proves that in the environment of 64 pulses in a single snapshot of a single array element, the difference between the resolution probability of the target Doppler frequency and the root mean square error of the estimation value obtained by the method of the present invention and the iterative adaptive algorithm is not significant, proving that the method of the present invention has a super-resolution ability similar to the iterative adaptive algorithm and improves the accuracy of target Doppler frequency estimation.

Claims

1. A target Doppler frequency estimation method based on T-IAA, characterized in that Set a transformation matrix. After the received signal is processed by the set transformation matrix, an iterative adaptive algorithm is applied to estimate the Doppler frequency of the target. The specific steps of this frequency estimation method are as follows: 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 interval of grid points, evenly grid the Doppler frequency space, and generate a pilot vector set A(f), where T r is determined by the parameters of the pulsed Doppler radar; Step 2: Determine the range of the Doppler frequency of the target to be estimated: Take the inner product of the received signal y and the pilot vector set A(f) to obtain the spectrum of the discrete Fourier transform, and determine the range of the target Doppler frequency according to the spectrum; Step 3: Set the transformation matrix T: Within the range of the target Doppler frequency, form B channels that are much smaller than the total number M of received signal pulses. The center frequency f of each channel T =[f m , f m+1 ,..., f m+B , where f m is the minimum value of the target Doppler frequency range, f m+B is the maximum value of the target Doppler frequency range. Use the formula to set the transformation matrix T. Here, f r is the pulse repetition frequency of the received signal, f r =1 / T r , e (·) is the exponential operation with the natural constant e as the base, j is the imaginary unit symbol, π is the pi, d is the pulse position vector of the received signal, d = [0, 1,..., M - 1] T , and M is the total number of pulses of the received signal; Step 4: Perform transformation processing on the received signal and the pilot vector set: According to the formula: y' = T H y, A'(f) = T H A(f), perform transformation processing from the pulse domain to the Doppler domain on the received signal y and the pilot vector set A(f) respectively. Among them, y' is the transformed received signal, and (·) H is the conjugate transpose operation, and A'(f) is the transformed pilot vector set; Step 5: Use the iterative adaptive algorithm to estimate the target Doppler frequency: Adopt the iterative adaptive algorithm to perform signal processing on the transformed data y' and A'(f) in the Doppler domain to obtain the IAA power spectrum, and take the Doppler frequency corresponding to the peak value of each IAA power spectrum as the estimated value of the respective target Doppler frequency.

2. The target Doppler frequency estimation method based on T-IAA according to claim 1, wherein: The steps of generating the pilot vector set A(f) described in Step 1 are as follows: First step, according to the pulse repetition frequency f of the received signal r = 1 / T r , divide the Doppler frequency space into f + 1 Doppler frequency grid points with an interval of 1 Hz from 0 Hz to f r Hz; r ​ Step 2: Using the formula to obtain the pilot vector corresponding to each Doppler frequency grid point, where f k is the Doppler frequency of the k-th grid point, and a(f k ) is the pilot vector corresponding to f k ; Step 3: Synthesize the pilot vectors corresponding to all Doppler frequency grid points in the 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 the space, K = f r + 1.

3. The method for estimating the target Doppler frequency based on T-IAA according to claim 1, wherein: The steps of the iterative adaptive algorithm described in Step 5 are as follows: Step 1: According to the formula, calculate the diagonal elements in the initial matrix P; Step 2: Use \(R = A(f)PA\) H (f) formula to solve the covariance matrix \(R\). \(S\) represents the weight vector matrix, and the diagonal elements of this weight vector matrix are obtained from the formula Calculated. In each iteration process, let the diagonal elements in the initial matrix \(P\) Generate the current iteratively updated \(P'\) matrix. According to the formula \(R' = A(f)P'A\) H (f), solve the updated \(R'\) matrix, and continuously repeat this step until the difference between the weight vector matrices of two adjacent times converges to zero to obtain the IAA power spectrum.

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