Nonlinear parameter estimation method for inter-pulse non-repetitive waveform radar distance blind area

Abstract

The invention discloses a non-linear parameter estimation method for an inter-pulse non-repetitive waveform radar distance blind area, and the method comprises the steps: firstly building a pulse string echo signal model which can describe the combined influence of inter-pulse agility and a distance blind area effect for a monostatic pulse radar employing an inter-pulse non-repetitive waveform based on the idea of a compressed sensing theory; the method comprises the steps that firstly, a distance-Doppler joint dictionary with pulse train incomplete features is constructed based on the model, then a two-dimensional joint sparse signal model suitable for the distance blind area effect is established, finally, a sparse reconstruction algorithm is adopted to solve the model, a distance-Doppler scattering coefficient matrix is obtained, and high-precision estimation of target parameters is achieved. The method provided by the invention effectively solves the problems of energy diffusion and limited resolution when the complex modulation waveform is processed by the existing method, and realizes the high-precision and high-resolution estimation of the target parameter under the combined action of the distance blind area effect and the inter-pulse parameter agility.

Description

Technical Field

[0001] This invention belongs to the field of radar target parameter estimation technology, specifically relating to a nonlinear parameter estimation method for the range blind zone of inter-pulse non-repetitive waveform radar. Background Technology

[0002] Non-repetitive inter-pulse waveforms enhance signal uncertainty by pseudo-randomly switching multiple parameters such as repetition frequency, initial phase, and carrier frequency between pulses. This results in superior anti-interference and anti-interception capabilities, as well as unambiguous ranging and velocity measurement. Therefore, this type of waveform is widely used in various monostatic pulse radar systems, exhibiting particularly outstanding performance in applications such as airborne detection, early warning, and surveillance.

[0003] For monostatic pulse radar systems employing non-repetitive inter-pulse waveforms, existing processing methods typically include matched filtering, range gate alignment, phase compensation, and non-uniform discrete Fourier transform (DFT) steps, ultimately generating a range-Doppler (range-Doppler) power spectrum. However, range gate alignment and DFT can cause energy diffusion in the range and Doppler dimensions, respectively, affecting parameter estimation accuracy. Furthermore, with low signal bandwidth and a limited number of pulses, this method often struggles to effectively distinguish nearby targets. It is noteworthy that monostatic pulse radars typically use a shared transmit / receive antenna and operate in a time-division multiplexing manner, meaning echoes cannot be received during transmission, creating a range blind zone. This blind zone effect prevents the effective reception of some target echoes, resulting in incomplete pulse train characteristics, leading to target energy loss and weakening the accumulation effect. In severe cases, it can even cause the target signal to be submerged in the background, significantly impacting range-Doppler estimation performance.

[0004] In recent years, compressed sensing theory has become an important method for parameter estimation in radar signal processing due to its superior performance in sparse signal reconstruction, and it has been widely used in the field of range-Doppler estimation. The paper "Analysis of Frequency Agile Radar via Compressed Sensing, IEEE Transactions on Signal Processing, 2018, 66(23): 6228-6235" systematically analyzes the sparse reconstruction characteristics of the dictionary matrix of frequency agile radar from a theoretical perspective, derives the Spark condition and cross-coherence limit, and gives the upper bound of the probability of the maximum recoverable target number, verifying the effectiveness of the compressed sensing method under inter-pulse carrier frequency agile modulation. However, this method is mainly aimed at single-parameter carrier frequency agile systems and does not involve the signal structure complexity caused by multi-parameter joint modulation. The paper "Research on Sparse Reconstruction Technology of Two-Dimensional Jitter Radar Signals with Frequency Hopping and Frequency Repetition Rate (FRP), Journal of Electronics and Information Technology, 2021, 43(6): 1728-1736" constructs a range-Doppler sparse signal model for the joint jitter system of frequency hopping and FRP and adopts a multi-observation vector focus-based underdetermined system solver method to achieve joint sparse reconstruction of target range-Doppler. Under the joint agile modulation of inter-pulse carrier frequency and FRP, it effectively improves the parameter estimation accuracy and resolution performance. However, although this method considers the change of pulse repetition interval under FRP agile modulation, it still assumes that the target echo is limited to a single pulse repetition interval and fails to model and characterize the fast and slow time coupling phenomenon caused by the target echo crossing multiple pulse repetition intervals. More importantly, this method is based on the assumption of pulse train integrity and does not fully consider the joint modulation characteristics caused by the range blind zone effect and the inter-pulse parameter agility. Patent CN114397628A proposes a sparse signal modeling and reconstruction method applicable to a joint agile system of load rate, repetition frequency, and spatial domain. Through Kronecker dictionary design and subspace tracking algorithm, it achieves target parameter estimation for multi-parameter joint modulation under inter-pulse non-repetitive waveform conditions. However, this method also fails to consider the time coupling problem caused by the target echo spanning multiple pulse repetition intervals under inter-pulse repetition agile modulation, as well as the complex modulation characteristics under the combined effects of range blind zone and inter-pulse parameter agility. Therefore, it still has certain limitations in terms of modeling flexibility and adaptability to complex scenarios.

[0005] In summary, although existing compressed sensing methods have made some progress in multi-parameter joint modulation such as inter-pulse carrier frequency and repetition frequency, they do not adequately consider the joint modulation characteristics of multi-parameter agility and range blind zone effect in monostatic pulse radar under inter-pulse non-repetitive waveform system. There is still a lack of a unified modeling and efficient reconstruction systematic method. There is an urgent need to develop high-resolution and high-precision target parameter estimation technology that takes into account both complex modulation characteristics and range blind zone effect. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a nonlinear parameter estimation method for the range blind zone of inter-pulse non-repetitive waveform radar. This method solves the problem of complex signal structure and difficult model construction caused by the combined modulation of multi-parameter joint agility under the inter-pulse non-repetitive waveform system and the range blind zone effect in monostatic pulse radar during the construction of existing compressed sensing sparse signal models.

[0007] The technical solution adopted in this invention is: a nonlinear parameter estimation method for the range blind zone of inter-pulse non-repetitive waveform radar, the specific steps of which are as follows:

[0008] Step 1: Set the radar system parameters and perform initialization settings;

[0009] The radar system parameters are initialized, including the carrier frequency f. c Intra-pulse signal duration T, intra-pulse signal bandwidth B, sampling frequency F s Sampling interval T s Number of pulses N, and the transmission time t of the m-th pulse. m With initial phase φ m and pulse repetition interval T pm .

[0010] Where m = 0, 1, ..., N-1.

[0011] Step 2: Based on Step 1, read the raw echo data from the radar receiver and construct a pulse train echo signal model that considers the range blind zone;

[0012] Step 21: Read the raw echo data from the radar receiver;

[0013] Step 22: Model the pulse train echo signal considering the distance blind zone;

[0014] Step 3: Based on Step 2, construct a distance-Doppler joint dictionary with pulse train incomplete features;

[0015] By combining the modulation characteristics of inter-pulse agile waveforms with the incomplete features of pulse trains, the range-related phase term, Doppler-related phase term, and indicator function are modeled as a whole to construct a range-Doppler joint steering vector with pulse train incomplete features, forming the corresponding dictionary matrix.

[0016] Step 4: Based on Step 3, construct a two-dimensional sparse modeling framework for the matching distance-Doppler joint dictionary, that is, establish a distance-Doppler joint sparse signal model based on the distance blind zone effect;

[0017] Step 5: Solve the range-Doppler joint sparse signal model described in Step 4 using a sparse reconstruction algorithm, and output the target range-Doppler scattering coefficient matrix to achieve nonlinear parameter estimation for the range blind zone of inter-pulse non-repetitive waveform radar.

[0018] Furthermore, step 2 is specifically as follows:

[0019] Step 21: Read the raw echo data from the radar receiver;

[0020] Imagine a monostatic pulse radar transmitting a pulse train signal with pseudo-random jumping characteristics in a single CPI. The corresponding baseband signal s(t) is expressed as follows:

[0021]

[0022] Where t represents the time variable; rect(·) represents the rectangular window function; and x(t) represents the baseband signal within the pulse. Together, they constitute the intrapulse waveform s of the m-th pulse. m (t). For non-repetitive inter-pulse waveforms, the pulse repetition interval of the fixed-parameter waveform is T. p The offset of the pulse repetition interval of the m-th pulse is δ. m Then T pm =T p +δ m , and δ m It follows a uniform distribution.

[0023] Assume there are Q targets within the radar's detection range, and consider the Doppler effect and noise caused by these targets. Define the noise process. The real part a(t) and the imaginary part b(t) are both zero-mean real Gaussian white noise processes, and their variances are both σ. 2 And they are independent of each other, denoted as The complex noise process ζ(t) follows a zero-mean complex Gaussian distribution with variance . Recorded as The expression for the echo signal z(t) received by the radar is as follows:

[0024]

[0025] in, Let i represent the real number field, and iid denote independent and identically distributed; σ k , τ dk f dk Let represent the scattering coefficient, time delay, and Doppler frequency of the k-th target, respectively.

[0026] Step 22: Model the pulse train echo signal considering the distance blind zone;

[0027] Discretize the range-Doppler two-dimensional space into a sufficiently fine grid and assume the target is located at a grid point. Then discretize equation (2) and extend it to a vector superposition of all resolution units in the two-dimensional space. Let the range dimension and Doppler dimension each include N... f and N s Considering the discrete units and the range blind zone effect caused by the monostatic pulse system, the expression for the pulse train echo signal z(l) of the discretized l-th sampling sequence is as follows:

[0028]

[0029] Where, σ i,j The Doppler frequency is f di The time delay is τ dj The scattering coefficients corresponding to the resolving units constitute a two-dimensional scattering coefficient matrix. Let l denote the complex field; ζ(l) denotes the sampling of the noise process ζ(t); l = l0, l1, ..., l M-1 This represents the sampling sequence, where M represents the number of sampling points, and l M-1 T represents the Mth sampling point in the sampling sequence. s Let s(l) represent the sampling interval, s(l) represent the baseband signal corresponding to the l-th sampling sequence, and I[·] represent the indicator function, the specific expression of which is as follows:

[0030]

[0031] Within the observation interval, the time delays of the nearest and farthest targets are set to τ. min With τ max The expressions for the sampling sequences at the leftmost and rightmost points of the observation interval are as follows:

[0032]

[0033] in, This indicates rounding down to the nearest integer.

[0034] Furthermore, step 3 is specifically as follows:

[0035] First, define the intermediate variable expression as follows:

[0036]

[0037] Where y(l;i,j) represents the Doppler frequency f di The time delay is τ dj The l-th sample value corresponding to the resolution unit. Then, a range-Doppler joint steering vector with pulse train incompleteness characteristics can be constructed, expressed as follows:

[0038]

[0039] Where, α i,j This corresponds to the Doppler frequency f. di and delay τ dj The guide vector, [·] T This represents the matrix transpose operation.

[0040] Finally, a joint distance-Doppler dictionary A with pulse train incompleteness features can be constructed, expressed as follows:

[0041]

[0042] Furthermore, step 4 is specifically as follows:

[0043] Based on the dictionary matrix A constructed in step 3 and the corresponding sparse signal model, equation (3) is further characterized as follows:

[0044]

[0045] Then, equation (9) is used to construct a measurement vector. The specific expression is as follows:

[0046]

[0047] Set variables Θ and ζ, as shown in the following expression:

[0048]

[0049] Where Θ represents the scattering coefficient vector to be recovered, obtained by column expansion of the two-dimensional scattering coefficient matrix σ; ζ represents the observation noise vector. The expression for the measurement vector Z is as follows:

[0050] Z = AΘ + ζ (12).

[0051] Furthermore, in step 5, the sparse reconstruction algorithm adopts the orthogonal matching pursuit algorithm. When the distance blind zone effect is not considered, the indicator function constraint I[s(l)=0] is removed in the pulse train echo signal modeling derivation considering the distance blind zone in step 22.

[0052] The beneficial effects of this invention are as follows: This invention discloses a nonlinear parameter estimation method for the range blind zone of inter-pulse non-repetitive waveform radar. Based on the idea of ​​compressed sensing theory, firstly, for monostatic pulse radar using inter-pulse non-repetitive waveforms, a pulse train echo signal model is established that can characterize the combined effects of inter-pulse agility and range blind zone. Then, based on this model, a range-Doppler joint dictionary with pulse train incomplete characteristics is constructed to accurately reflect the structural characteristics of the echo signal. Next, a two-dimensional joint sparse signal model suitable for the range blind zone effect is established to characterize the relationship between the target scattering coefficient and the observation data. Finally, a sparse reconstruction algorithm is used to solve the model to obtain the range-Doppler scattering coefficient matrix, thereby achieving high-precision estimation of target parameters. The method of this invention overcomes the problems of complex signal structure and difficult model construction caused by the joint modulation of multi-parameter agility under the pulse non-repetitive waveform system and the range blind zone effect in monostatic pulse radar during the construction of sparse signal models. It effectively solves the problems of energy diffusion and resolution limitation in existing methods when dealing with such complex modulation waveforms. In particular, in monostatic pulse radar, the signal loss caused by the range blind zone effect further weakens the resolution performance. It realizes high-precision and high-resolution estimation of target parameters under the combined effect of range blind zone effect and pulse parameter agility. Attached Figure Description

[0053] Figure 1 This is a flowchart of a nonlinear parameter estimation method for the range blind zone of inter-pulse non-repetitive waveform radar according to the present invention.

[0054] Figure 2 This is a schematic diagram of radar signal transmission and reception in an embodiment of the present invention.

[0055] Figure 3 This is a schematic diagram of the single-objective simulation results in an embodiment of the present invention.

[0056] Figure 4 This is a schematic diagram of the performance curves for a single-target scenario in an embodiment of the present invention.

[0057] Figure 5 This is a schematic diagram of the simulation results of the nearest target in an embodiment of the present invention.

[0058] Figure 6 This is a schematic diagram of the performance curves of the adjacent target scene in an embodiment of the present invention. Detailed Implementation

[0059] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0060] This embodiment primarily employs simulation experiments for verification, and all steps and conclusions have been verified correctly using Matlab 2022b. To facilitate the description of this invention, the following terms are first explained:

[0061] Term 1: Distance blind spot;

[0062] In monostatic pulse radar, because the transmit and receive antennas work in a time-division multiplexing manner, the echo cannot be received during the transmission period, resulting in targets within a certain range being undetectable. This range is called the range blind zone.

[0063] Term 2: Pulse train incompleteness characteristics;

[0064] This refers to the pseudo-random jump characteristic of pulse repetition intervals under the non-repetitive waveform system. When this characteristic works in conjunction with the distance blind zone effect, the pulse train located in the blind zone will be blocked, forming a pseudo-random incomplete characteristic.

[0065] Term 3: Interpulse non-repetitive waveform;

[0066] This refers to a pulse sequence composed of multiple coherent pulses, where intra-pulse or inter-pulse parameters exhibit pseudo-random variations between pulses. This type of waveform exhibits strong randomness and complex modulation characteristics, which helps improve the anti-jamming capability and low-interception performance of radar systems.

[0067] Term 4: Nonlinear parameter estimation;

[0068] This refers to the process of extracting target parameters from observation data using nonlinear optimization methods. Unlike existing linear processing procedures (such as pulse compression, beamforming, and moving target detection), this method typically models the parameter estimation problem as a constrained nonlinear optimization problem, where the objective function or constraints contain nonlinear functions, and obtains the target parameters to be estimated through iterative algorithms.

[0069] like Figure 1 The flowchart of a nonlinear parameter estimation method for the range blind zone of inter-pulse non-repetitive waveform radar according to the present invention is shown below. The specific steps are as follows:

[0070] Step 1: Set the radar system parameters and perform initialization settings;

[0071] The radar system parameters are initialized, including the carrier frequency f. c Intra-pulse signal duration T, intra-pulse signal bandwidth B, sampling frequency F s Sampling interval T s Number of pulses N, and the transmission time t of the m-th pulse. m With initial phase φ m and pulse repetition interval T pm .

[0072] Where m = 0, 1, ..., N-1.

[0073] The specific initialization simulation parameters of the radar system in this embodiment are shown in Table 1.

[0074] Table 1

[0075] parameter numerical values unit <![CDATA[Carrier frequency (f c )]]> 10 GHz <![CDATA[Pulse repetition interval (T pm )]]> ms Intrapulse signal duration (T) 10 Intrapulse signal bandwidth (B) 10 MHz <![CDATA[Sampling frequency (F s )]]> 10 MHz Number of pulses (N) 16 indivual

[0076] Step 2: Based on Step 1, read the raw echo data from the radar receiver and construct a pulse train echo signal model that considers the range blind zone;

[0077] The radar signal transmission and reception diagram in this embodiment is shown below. Figure 2 As shown.

[0078] Step 21: Read the raw echo data from the radar receiver;

[0079] Imagine a monostatic pulse radar transmitting a pulse train signal with pseudo-random jumping characteristics in a single CPI. The corresponding baseband signal s(t) is expressed as follows:

[0080]

[0081] Where t represents the time variable; rect(·) represents the rectangular window function; and x(t) represents the baseband signal within the pulse. Together, they constitute the intrapulse waveform s of the m-th pulse. m (t). For non-repetitive inter-pulse waveforms, the pulse repetition interval of the fixed-parameter waveform is T. p The offset of the pulse repetition interval of the m-th pulse is δ. m Then T pm =T p +δ m , and δ m It follows a uniform distribution.

[0082] Assume there are Q targets within the radar's detection range, and consider the Doppler effect and noise caused by these targets. Define the noise process. The real part a(t) and the imaginary part b(t) are both zero-mean real Gaussian white noise processes, and their variances are both σ. 2 And they are independent of each other, denoted as The complex noise process ζ(t) follows a zero-mean complex Gaussian distribution with variance . Recorded as The expression for the echo signal z(t) received by the radar is as follows:

[0083]

[0084] in, Let i represent the real number field, and iid denote independent and identically distributed; σ k , τ dk f dkLet represent the scattering coefficient, time delay, and Doppler frequency of the k-th target, respectively.

[0085] Equation (2) provides a more generalized expression framework, which not only explicitly introduces the modulation term caused by inter-pulse agility, but also has good versatility and scalability. The versatility is reflected in its ability to express the intra-pulse waveform s m Modeling of (t): This expression allows s m (t) It can employ any modulation method such as linear frequency modulation, frequency coding, or phase coding; its scalability is reflected in its ability to modify s m (t) Introducing a pulse-time-varying modulation factor to describe the dynamic changes of the waveform within a pulse between different pulses. Since the non-repetitive waveform between pulses causes the pulse repetition interval to jump pseudo-randomly, when this characteristic works together with the range blind zone effect, the pulse train located in the blind zone is blocked and exhibits pseudo-random incomplete characteristics. Therefore, it is necessary to extend equation (2) to construct a more refined signal model that can describe the range blind zone effect.

[0086] Step 22: Model the pulse train echo signal considering the distance blind zone;

[0087] Equation (2) only considers Q targets from each range-Doppler resolution cell and does not account for the range blind zone effect. To achieve a more comprehensive modeling analysis, the range-Doppler two-dimensional space is discretized into a sufficiently fine grid, and the targets are set to be located at these grid points. Thus, Equation (2) can be discretized and extended to a vector superposition of all resolution cells in the two-dimensional space. Let the range dimension and the Doppler dimension each include N f and N s Considering the discrete units and the range blind zone effect caused by the monostatic pulse system, the expression for the pulse train echo signal of the discretized l-th sampling sequence is as follows:

[0088]

[0089] Where, σ i,j The Doppler frequency is f di The time delay is τ dj The scattering coefficients corresponding to the resolving units can form a two-dimensional scattering coefficient matrix. Let l denote the complex domain; ζ(l) denotes the sampling of the noise process ζ(t); l = l0, l1, ..., l M-1 This represents the sampling sequence, where M represents the number of sampling points, and l M-1 T represents the Mth sampling point in the sampling sequence. s Let represent the sampling interval, s(l) represent the baseband signal corresponding to the l-th sampling sequence, and I[·] represent the indicator function, which can be used to make logical judgments on the range blind zone. It can also be replaced with other function forms, and the specific expression is as follows:

[0090]

[0091] Within the observation interval, the time delays of the nearest and farthest targets are set to τ. min With τ max The expressions for the sampling sequences at the leftmost and rightmost points of the observation interval are as follows:

[0092]

[0093] in, This indicates rounding down to the nearest integer.

[0094] Step 3: Based on Step 2, construct a distance-Doppler joint dictionary with pulse train incomplete features;

[0095] From equation (3), we can see that t m While describing the time variable in the Doppler term, it also appears in the range-related term, causing the range dimension and the Doppler dimension to no longer have an independent structural relationship. Furthermore, I[s(l)=0] effectively characterizes the incomplete features of the pulse train. Combining the modulation characteristics of the inter-pulse agile waveform with the incomplete features of the pulse train, the range-related phase term, the Doppler-related phase term, and the indicator function can be modeled as a whole, thereby constructing a range-Doppler joint steering vector with incomplete pulse train features, and further forming the corresponding dictionary matrix.

[0096] To facilitate subsequent expression, let's first define the intermediate variable expression as follows:

[0097]

[0098] Where y(l;i,j) represents the Doppler frequency f di The time delay is τ dj The l-th sample value corresponding to the resolution unit. Then, a range-Doppler joint steering vector with pulse train incompleteness characteristics can be constructed, expressed as follows:

[0099]

[0100] Where, α i,j This corresponds to the Doppler frequency f. di and delay τ dj The guide vector, [·] T This represents the matrix transpose operation.

[0101] Finally, a joint distance-Doppler dictionary A with pulse train incompleteness features can be constructed, expressed as follows:

[0102]

[0103] Step 4: Based on Step 3, construct a two-dimensional sparse modeling framework for the matching distance-Doppler joint dictionary, that is, establish a distance-Doppler joint sparse signal model based on the distance blind zone effect;

[0104] Based on the dictionary matrix A constructed in step 3 and the corresponding sparse signal model, equation (3) is further characterized as follows:

[0105]

[0106] Then, equation (9) is used to construct a measurement vector. The specific expression is as follows:

[0107]

[0108] To facilitate further simplification of equation (10), variables Θ and ζ are set, and the expression is as follows:

[0109]

[0110] Where Θ represents the scattering coefficient vector to be recovered, obtained by column expansion of the two-dimensional scattering coefficient matrix σ; ζ represents the observation noise vector. The expression for the measurement vector Z is as follows:

[0111] Z=AΘ+ζ (12)

[0112] Equation (12) is the range-Doppler joint sparse signal model that takes into account the range blind zone effect. This model fully considers the influence of the range blind zone effect and can be used as the basis for subsequent sparse reconstruction.

[0113] Step 5: Solve the range-Doppler joint sparse signal model described in Step 4 using the sparse reconstruction algorithm, and output the range-Doppler scattering coefficient matrix to realize the nonlinear parameter estimation for the range blind zone of inter-pulse non-repetitive waveform radar.

[0114] For solving the model shown in Equation (12), existing methods (such as the least squares method) often lead to noise amplification and are therefore not advisable. Several algorithms have been proposed to solve this problem, and their specific details will not be elaborated here. Considering the high dimensionality of Θ, sparse reconstruction is usually accompanied by large computational overhead.

[0115] To improve reconstruction efficiency in practical applications, this embodiment employs the orthogonal matching pursuit algorithm, a representative greedy solution strategy. Furthermore, when the range blind zone effect is disregarded (i.e., the indicator function constraint I[s(l)=0] is removed in the above derivation), the method of this invention is also applicable to the case without a range blind zone. Finally, the target range-Doppler scattering coefficient matrix can be output, achieving high-precision estimation of the target parameters.

[0116] This embodiment further includes simulation verification. First, a simulation experiment was conducted on a monostatic pulse radar system using inter-pulse non-repetitive waveforms. The system parameter settings are shown in Table 1. The experiment aims to verify the estimation effect of the method of this invention and to compare it with existing methods. To evaluate the performance of the method of this invention, this embodiment uses the root mean square error (RMSE) as the main evaluation index. Depending on the error calculation method, this embodiment introduces two RMSE definitions, as follows:

[0117] a) RMSE based on parameter estimation:

[0118]

[0119] Among them, M c Indicates the number of Monte Carlo experiments. Let y represent the distance or velocity estimated from the peak position in the scattering coefficient matrix or power spectrum in the nth Monte Carlo experiment, and let y represent the true distance or velocity of the target.

[0120] b) RMSE based on scattering coefficient matrix or power spectrum:

[0121]

[0122] in, This represents the estimated scattering coefficient matrix or power spectrum obtained in the nth experiment; u represents the corresponding true scattering coefficient matrix or power spectrum under the simulation settings. F Let M represent the Frobenius norm of the matrix. In the simulation, M is set to... c =1000.

[0123] Figure 3 and Figure 4 The simulation results and performance curves for a single-objective scenario are shown (RMSE for the single-objective scenario). a ). Figure 3 (a) and (b) are the range-Doppler power spectra of the matched filter-non-uniform discrete Fourier transform method in the cases of no range blind zone and with range blind zone, respectively. Figure 3 In (a), when there is no blind spot, a distinct main peak appears at the target location; while Figure 3 In (b), the target signal is almost completely submerged by the background due to the range blind zone. Figure 3 (c) and (d) show the reconstruction results of the method of the present invention under the conditions of no range blind zone and with range blind zone. Both can accurately recover the target in the range-Doppler domain. Among them, the reconstruction effect under the blind zone is basically consistent with that under the condition of no blind zone, showing high estimation accuracy. Figure 4(a) and (b) show the RMSE of the scattering coefficient vectors or power spectra in the range and velocity dimensions under different signal-to-noise ratios. a Trends. It is easy to see that, regardless of the presence of a range blind zone, the method of this invention outperforms the matched filtering-non-uniform discrete Fourier transform method across the entire signal-to-noise ratio range. Even with a range blind zone, the RMSE of the method of this invention remains high. a Although energy loss increased slightly, the overall performance was still significantly better than existing methods. Figure 4 (c) and (d) further demonstrate the RMSE at different target distances. a The trend of change. As the degree of occlusion in the distance blind zone intensifies, the estimation error of the matched filter-non-uniform discrete Fourier transform method increases significantly; in contrast, the method of this invention remains stable even in the case of blind zone, and its error is basically consistent with that in the case of no blind zone, close to zero.

[0124] Figure 5 and Figure 6 The simulation results and performance curves (RMSE of the nearby target scene) are shown. b ). Figure 5 (a) and (b) are the power spectra of the matched filter-non-uniform discrete Fourier transform method in the cases of no distance blind zone and with distance blind zone, respectively. Figure 5 Although a main peak appears in (a), the two targets are difficult to distinguish, the energy diffusion is obvious, and a false peak appears in the non-target region; Figure 5 In (b), the target signal is almost completely submerged in the background due to the range blind zone. Figure 5 (c) and (d) show the reconstruction results of the method of the present invention under the conditions of no range blind zone and with range blind zone. Both can clearly distinguish two neighboring targets in the range-Doppler domain, and the reconstruction effect under the blind zone is basically the same as that under the condition of no blind zone, showing high estimation accuracy and resolution capability. Figure 6 (a) and (b) respectively show the RMSE of the range-Doppler scattering coefficient matrix or power spectrum under different signal-to-noise ratios and target ranges. b The overall trend of change is consistent with that of the single-target scenario, so it will not be elaborated here.

[0125] In summary, simulation results clearly demonstrate that the method of this invention achieves high-precision and high-resolution parameter reconstruction performance even in the presence of range blind zone effects, significantly outperforming existing methods. This invention proposes a joint range-Doppler estimation framework that simultaneously considers inter-pulse agility and range blind zone effects, effectively alleviating the energy diffusion and resolution limitations inherent in existing matched filtering-non-uniform discrete Fourier transform methods. Furthermore, to address the pulse train incompleteness caused by the range blind zone, a customized joint range-Doppler dictionary and a corresponding two-dimensional sparse signal model are designed, ensuring the accuracy and resolution performance of target parameter estimation. The method of this invention can be widely applied to various monostatic pulse radar systems.

[0126] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A nonlinear parameter estimation method for inter-pulse non-repeating waveform radar distance blind area, the specific steps are as follows: Step 1, set the radar system parameters and make initialization settings; initializing settings for radar system parameters, the radar parameters including: Carrier frequency f c , intra-pulse signal time width T, intra-pulse signal bandwidth B, sampling frequency F s , sampling interval T s , number of pulses N, emission time t of the mth pulse m and initial phase φ m , and pulse repetition interval T pm ; Wherein, m=0, 1,..., N-1; Step 2, based on step 1, read the original echo data from the radar receiver, and construct a pulse train echo signal model considering the distance blind area; Step 21, read the original echo data from the radar receiver; Step 22, pulse train echo signal modeling considering the distance blind area; Step 3, based on step 2, construct a distance-Doppler joint dictionary with pulse train missing characteristics; Combined with the modulation characteristics of inter-pulse agile waveform and the missing characteristics of pulse train, the distance-related phase term, Doppler-related phase term and indicator function are modeled as a whole, a distance-Doppler joint steering vector with pulse train missing characteristics is constructed, and a corresponding dictionary matrix is formed; Step 4, based on step 3, a two-dimensional sparse modeling framework matching the distance-Doppler joint dictionary is constructed, that is, a distance-Doppler joint sparse signal model based on the distance blind area effect is established; Step 5, use a sparse reconstruction algorithm to solve the distance-Doppler joint sparse signal model in step 4, output the target distance-Doppler scattering coefficient matrix, and realize the nonlinear parameter estimation for inter-pulse non-repeating waveform radar distance blind area.

2. The method according to claim 1, wherein, The step 2 is specifically as follows: Step 21, read the original echo data from the radar receiver; A single base pulse radar transmits a group of pulse train signals with pseudo-random hopping characteristics of inter-pulse parameters within a single CPI, and the corresponding baseband signal s(t) expression is as follows: wherein t represents a time variable; rect(·) represents a rectangular window function; x(t) represents an intra-pulse baseband signal; and the two together constitute an intra-pulse waveform s of the mth pulse m For the inter-pulse non-repeating waveform, the pulse repetition interval of the fixed parameter waveform is T p , and the offset of the pulse repetition interval of the mth pulse is δ m , then T pm = T p + δ m , and δ m obeys a uniform distribution; Suppose there are Q targets in the radar detection range, and consider the Doppler effect and noise effect caused by the targets where the real part a(t) and the imaginary part b(t) are both zero-mean real Gaussian white noise processes with variance σ 2 , and are independent of each other, denoted as The complex noise process ζ(t) obeys a zero-mean complex Gaussian distribution with variance denoted as The expression of the echo signal z(t) received by the radar is as follows: wherein, denotes the real field, i.i.d. denotes independent and identically distributed; σ k , τ dk , f dk denote the scattering coefficient, time delay, Doppler frequency of the kth target, respectively; Step 22, pulse train echo signal modeling considering the distance blind area; The distance-Doppler two-dimensional space is discretized into a sufficiently fine grid, and the target is assumed to be located at the grid points. Equation (2) is discretized and extended to vector superposition of all resolution cells in the two-dimensional space. The distance dimension and the Doppler dimension are assumed to include N f and N s discrete cells, respectively, and the distance blind zone effect caused by the monostatic pulse system is considered. The expression of the pulse train echo signal z(l) of the lth sampling sequence after discretization is as follows: z(l) = ΣΣa(k, m)ej2π(fD(k) + fR(m))lT where σ i,j represents the scattering coefficient corresponding to the resolution unit with Doppler frequency f di and time delay τ dj , which constitutes a two-dimensional scattering coefficient matrix represents the complex field; ζ(l) represents the sampling of the noise process ζ(t); l = l0, l1,..., l M-1 represents the sampling sequence, M represents the number of sampling points, l M-1 represents the Mth sampling point in the sampling sequence, T s represents the sampling interval, s(l) represents the baseband signal corresponding to the lth sampling sequence, and I[·] represents the indicator function, and the specific expression is as follows: Let us set the time delay of the nearest target and the farthest target in the observation interval as τ min and τ max Then the sampling sequence expressions of the leftmost and rightmost of the distance observation interval are as follows: wherein denotes rounding down.

3. The method according to claim 2, wherein, The step 3 is specifically as follows: First, set the intermediate variable expression as follows: where y(l; i, j) represents the 1th sample value corresponding to the resolution unit with Doppler frequency f di and time delay τ dj ; then the range-Doppler joint steering vector with the characteristics of pulse train truncation can be constructed, and the expression is as follows: wherein α i,j represents a steering vector corresponding to the Doppler frequency f di and the time delay τ dj , [·] T denotes the transpose operation of a matrix; Finally, the distance-Doppler joint dictionary A with pulse train missing characteristics can be constructed, and the expression is as follows:

4. The method according to claim 3, wherein, The step 4 is specifically as follows: According to the dictionary matrix A constructed in step 3 and the corresponding sparse signal model, formula (3) is further characterized, and the expression is as follows: Again, the equation (9) is constituted as a measurement vector The specific expression is as follows: Set variables Θ and ζ, and the expression is as follows: Wherein, Θ represents the scattering coefficient vector to be recovered, which is obtained by expanding the two-dimensional scattering coefficient matrix σ by column; ζ represents the observation noise vector; then the measurement vector Z expression is as follows: Z=AΘ+ζ (12).

5. The method of claim 4, wherein, In step 5, the sparse reconstruction algorithm uses the orthogonal matching pursuit algorithm, and when the distance blind area effect is not considered, the indicator function constraint I[s(l)=0] is removed in the derivation of step 22 considering the pulse train echo signal modeling of the distance blind area.

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