A sky wave radar long time accumulation doppler compensation method

Abstract

The application belongs to the technical field of sky wave radar target detection, and provides a sky wave radar long-time accumulation Doppler compensation method, which is based on measurement sequence to initialize a covariance matrix and adaptively estimate the number of frequency modulation modes contained in a signal; the initial amplitude and initial frequency of each mode are estimated through a weighted covariance fitting method; a state vector is constructed for each mode, which includes the amplitude, current phase and historical amplitude and phase of the current time; a state transition equation is constructed based on a polynomial prediction model, and the state vector is recursively predicted and updated by using an unscented Kalman filter (UKF); the instantaneous amplitude and instantaneous frequency of each mode are extracted according to the updated state vector; the radar echo is compensated based on the instantaneous amplitude and instantaneous frequency, and the compensated signal is subjected to long-time coherent accumulation, and a distance-Doppler spectrum after compensation is output, which has low calculation complexity, good real-time performance and high resolution.

Description

Technical Field

[0001] This invention pertains to skywave radar target detection technology, specifically skywave radar long-term accumulation Doppler compensation technology. Background Technology

[0002] Over-the-Horizon Radar (OTHR) is an advanced radar system that utilizes the physical property of the ionosphere reflecting high-frequency (HF) electromagnetic waves to detect targets beyond the curvature of the Earth. Unlike conventional line-of-sight radars, OTHR can detect targets thousands of kilometers away, offering unique advantages such as wide-area surveillance, early warning, and low-altitude target detection.

[0003] However, the signal propagation mechanism of skywave over-the-horizon radar presents it with unprecedented challenges: high-frequency signals are affected by natural factors such as the space environment, solar activity, and changes in ionospheric density during propagation through the ionosphere, leading to complex and variable propagation paths, uncertain propagation delays, and severe random disturbances in signal phase. Simultaneously, due to multiple reflections, attenuation, and phase disturbances of the target echo, strong clutter (such as sea clutter, ground clutter, atmospheric noise, and background radio frequency interference) severely overwhelms weak target signals, greatly affecting the accuracy and stability of target detection.

[0004] Therefore, researching and developing high-performance weak target detection technologies, especially algorithms that can adapt to complex propagation environments and effectively improve the signal-to-noise ratio (SNR), has become a key direction for enhancing the effectiveness of OTHR operations.

[0005] Long-Time Coherent Integration (LTCI) is a core technology for improving the detection performance of weak targets and is widely used in skywave radar systems. Its basic principle is to phase-align and accumulate the target echo over a relatively long time window, thereby suppressing noise, increasing signal energy, and enhancing detection capabilities.

[0006] For OTHR (Over-the-Air Detection), the target is far away and the echo intensity is low. Traditional short-time accumulation methods are difficult to achieve effective detection in high-noise backgrounds. LTCI (Long-Term Coherent Accumulation), however, performs multi-pulse coherent accumulation of the target signal over a long observation window, enabling the target's energy to be stably aggregated over time, thus significantly improving the signal-to-noise ratio (SNR). Theoretically, the SNR improvement of LTCI is proportional to the number of accumulated pulses; therefore, under the premise of meeting the coherence condition, it can greatly enhance the detectability of the target signal.

[0007] However, LTCI also faces two main challenges: First, the target's motion state changes significantly over a long period (such as changes in acceleration and jerk), leading to nonlinear changes in its echo phase, which cannot be compensated for by a simple constant velocity model; second, the background clutter is complex and has non-Gaussian characteristics, easily interfering with the accumulation process. Therefore, how to achieve effective Doppler compensation and target motion modeling has become the core of LTCI technology research.

[0008] LTCI requires maintaining the phase consistency of the target signal over a long time window, which necessitates accurate estimation and compensation of the target's Doppler frequency and its variation trend. For targets with different motion patterns, various Doppler compensation methods and signal processing techniques have been proposed, mainly including:

[0009] Parametric search methods are based on a parameter grid search of the target's possible motion states, selecting the compensation parameters that concentrate the energy to achieve phase alignment. Typical examples include the Keystone transform, Radon transform, and the generalized Radon transform (GRadon). The Keystone transform is a linear correction technique for the range-Doppler motion problem of uniformly moving targets, decoupling the range-Doppler coupling to achieve energy compression on the range axis. This method works well for uniformly moving linear targets, but errors accumulate and fail when dealing with targets with acceleration or higher-order motion. The Radon transform / generalized Radon transform searches for the target's acceleration parameters in the time-frequency plane through energy trajectory search to achieve nonlinear Doppler trajectory compensation. Its advantage is that it can handle a certain degree of higher-order motion, but the computational complexity increases exponentially with higher parameter dimensions, placing high demands on real-time performance and resource consumption. Furthermore, its trajectory recognition capability decreases significantly in the presence of multiple targets or strong interference, making matching errors more likely.

[0010] The Fractional Fourier Transform (FRFT) can be viewed as a generalized form of the Fourier Transform, suitable for phase rotation compensation in processing linear frequency modulated (LFM) signals. When the target exhibits linear acceleration, FRFT can compress the target energy into a point-concentrated representation at a certain angle in the transform domain, achieving high time-frequency concentration. However, this method relies on accurate estimation of the target's frequency modulation (FM), and its performance degrades significantly in cases of nonlinear frequency changes or non-LFM targets. Furthermore, its ability to separate multi-target scenarios remains insufficient.

[0011] Time-frequency analysis methods, such as Short-Time Fourier Transform (STFT), Wigner-Ville Distribution (WVD), S-Transform, and wavelet analysis, vividly depict the frequency variation trend over time by expanding the signal in the time-frequency domain. These methods are suitable for preliminary observation and estimation of complex non-stationary signals and can reveal the frequency drift caused by target motion. STFT performs a sliding Fourier transform under a fixed window function, and its time-frequency resolution is limited by the choice of window length; WVD has high theoretical resolution but suffers from severe cross-terms, which can cause serious interference, especially in multi-target environments; S-Transform balances time and frequency resolution to some extent, but has a large computational cost and is suitable for offline analysis rather than real-time processing.

[0012] Although the above methods can characterize the changes in target frequency to some extent, they generally suffer from problems such as energy diffusion, poor concentration, and weak noise immunity, making them difficult to use directly for high-gain accumulation.

[0013] Adaptive phase compensation methods utilize prior or estimated motion models to construct phase compensation templates and perform pulse-by-pulse phase alignment. These templates include those for uniform acceleration and uniformly variable acceleration. This method is effective for known or modelable targets, but it is extremely sensitive to the motion model. Once the actual target motion deviates from the assumed model, the compensation effect drops sharply, leading to severe signal diffusion. Therefore, it faces practical limitations in moving target detection.

[0014] Filtering and estimation methods, based on the idea of ​​state estimation, such as Kalman filter (KF), extended Kalman filter (EKF), and particle filter (PF), recursively estimate the target state using measurement sequences and perform phase compensation accordingly. The target state includes position, velocity, and acceleration. Although these methods have been widely used in navigation and tracking, they face the following problems in OTHR:

[0015] (1) The system is required to have an accurate target motion and observation model, but the target motion height is uncertain in OTHR and the ionospheric propagation leads to strong measurement nonlinearity, making it difficult to establish a model;

[0016] (2) It performs poorly against non-Gaussian clutter and abrupt noise, and its filtering performance is prone to divergence;

[0017] (3) It is difficult to directly drive the filter in the time-frequency domain, resulting in the processing link not being closed.

[0018] Based on the analysis of the advantages and disadvantages of the above methods, the current OTHR system faces the following bottlenecks and research trends in the development of LTCI technology:

[0019] (1) Poor model adaptability: Most traditional methods are based on fixed or simplified target motion assumptions and lack generalization ability in the face of complex maneuver trajectories in actual combat.

[0020] (2) Difficult to handle multi-target interference: In multi-target scenarios, time-frequency crossover is severe and trajectory overlap is frequent, resulting in low energy accumulation efficiency and chaotic compensation path.

[0021] (3) High computational complexity: Methods such as Radon search and FRFT face high-dimensional parameter spaces when implementing high-order compensation, and real-time computing capability becomes a limiting factor.

[0022] (4) Noise and clutter interference: The non-Gaussian strong interference environment of OTHR poses a great challenge to most linear processing methods, and the traditional SNR criterion is no longer applicable.

[0023] (5) The rise of data-driven methods: In recent years, deep learning and data-driven detection methods have gradually emerged, attempting to introduce neural networks to learn the trajectory patterns of targets and realize complex motion modeling and phase compensation. However, they are still in the exploratory stage and have problems such as generalization, security and physical consistency.

[0024] Overall, the detection technology of skywave over-the-horizon radar, especially the long-term coherent accumulation method for long-range weak targets, is still under continuous development and optimization. Faced with complex propagation environments and target motion characteristics, single algorithms are insufficient to meet practical combat needs, necessitating the integration of multiple technologies and cross-domain collaboration. Future research directions can focus on the following aspects:

[0025] (1) Construct a more flexible and adaptable unified motion modeling framework for multiple types of targets;

[0026] (2) Develop a high-resolution, low-complexity multi-target trajectory extraction algorithm;

[0027] (3) Deeply integrate physical modeling and artificial intelligence to achieve robust prediction of target state;

[0028] (4) Enhance the radar-ionosphere joint modeling capability to compensate for the impact of channel uncertainty on detection performance.

[0029] Through continuous research in the aforementioned areas, it is hoped that the existing LTCI technology bottlenecks can be overcome, significantly improving the detection efficiency of skywave radar systems. Summary of the Invention

[0030] To address the challenge of detecting weak targets in complex propagation environments, this invention proposes a long-term accumulation Doppler compensation solution for skywave radar based on unscented Kalman filtering.

[0031] The technical solution adopted by this invention to solve the above-mentioned technical problems is a long-term accumulation Doppler compensation method for skywave radar, comprising the following steps:

[0032] System data input: Measurement sequence of received radar echoes;

[0033] Initialize covariance estimation and mode number estimation: Based on the measurement sequence, initialize the covariance matrix and adaptively estimate the number of frequency modulation modes contained in the signal;

[0034] Initial amplitude and frequency estimation: The initial amplitude and initial frequency of each mode are estimated by weighted covariance fitting method;

[0035] Initial state vector setting: Construct a state vector for each mode, which includes the amplitude and phase at the current moment, as well as the amplitude and phase at historical moments;

[0036] Filtering loop and state update: The state transition equation is constructed based on the multinomial prediction model, and the state vector is recursively predicted and updated using the unscented Kalman filter (UKF).

[0037] Results extraction and output: Based on the updated state vector, extract the instantaneous amplitude and instantaneous frequency of each mode;

[0038] Doppler compensation and accumulation: Doppler compensation is performed on the radar echo based on the instantaneous amplitude and instantaneous frequency, and the compensated signal is coherently accumulated over a long period of time to output the range-Doppler spectrum after compensation.

[0039] This invention models the amplitude and phase of each mode as predictable state variables and recursively updates them using an unscented Kalman filter, achieving accurate time-frequency estimation of multiple closely spaced or intersecting components. Given the known variance of the measurement noise, this invention offers low computational complexity, good real-time performance, and high resolution.

[0040] The filtering loop and state update steps specifically include:

[0041] Filtering update loop: For each sampling time, based on the state vector and state covariance matrix of the previous time, the prior state estimate and prior state covariance matrix of the current time are predicted using the state transition matrix F;

[0042] Unscented Transformation Point Generation: Based on the prior state estimate and the prior state covariance matrix, a set of unscented transformation points is generated;

[0043] Nonlinear observation propagation: The unscented transformation points are mapped to predicted observations through a nonlinear observation function h(⋅);

[0044] Calculation of observation statistics: Calculate the mean and covariance of the predicted observations, and calculate the cross-covariance between the state and the observations;

[0045] State update: Based on the Kalman gain and the difference between the actual observed value and the predicted observed mean, update the state vector and the state covariance matrix.

[0046] The more specific steps of this invention are as follows:

[0047] System data input: Received radar echo measurement sequence y n And Gaussian measurement noise variance R;

[0048] Initial covariance estimation: The initial covariance matrix R0 is calculated from the first N measurement samples using the sparse covariance estimation SPICE.

[0049] Mode number estimation: Based on the initial covariance matrix R0, the number of frequency modulation modes K in the signal is adaptively estimated using the SORTE criterion of eigenvalue statistics;

[0050] Initial amplitude and frequency estimation: For each mode k, k=1,…,K, the initial amplitude a is calculated using the weighted covariance fitting method. k,0 and initial frequency f k,0 ;

[0051] Initial state vector setup: Construct the initial state vector x for each pattern k. k,0 The state vector includes the current magnitude a. k,0 Current phase θ k,0 Its historical amplitude and phase values, and based on the initial frequency f k,0 Calculate the initial phase;

[0052] Filter update loop: For each sampling time n, based on the state vector of the previous time step... and state covariance matrix The prior state estimate at the current time step is predicted using the state transition matrix F. and prior state covariance matrix ;

[0053] Unscented Transformation Point Generation: Based on the aforementioned prior state estimation and prior state covariance matrix Generate a set of unscented transformation points;

[0054] Nonlinear observation propagation: The unscented transformation points are mapped to predicted observations through a nonlinear observation function h(⋅);

[0055] Calculation of observation statistics: Calculate the mean of the predicted observations. Covariance S n And calculate the cross-covariance C between the state and the observation. n ;

[0056] State update: based on Kalman gain C n Actual observed value y nCompared with the predicted observation mean The difference is used to update the state vector X. n and state covariance matrix P n ;

[0057] Result extraction and output: From the updated state vector X n Extract the instantaneous amplitude 'a' for each mode. k,n and instantaneous frequency f k,n ;

[0058] Doppler compensation and accumulation: The observations are compensated based on the instantaneous amplitude and instantaneous frequency, and the compensated observations are coherently accumulated over a long period of time to obtain the compensated range-Doppler spectrum.

[0059] This invention first initializes the covariance matrix using prior measurement samples and then adaptively estimates the number of frequency modulation modes in the signal using the SORTE criterion. Subsequently, the initial amplitude and frequency parameters of each mode are calculated using a weighted covariance fitting method. The key is to construct a state vector from the dynamic characteristics of each mode, such as instantaneous amplitude, current phase, and historical phase values, and to characterize the phase evolution using a multinomial prediction model. In the recursive filtering stage, state prediction and updating are performed using the UKF framework: a point set is generated to capture nonlinear characteristics, and after mapping by the observation model, the predicted mean and covariance are calculated. The state estimate and covariance matrix are then updated using Kalman gain. Finally, the instantaneous amplitude and instantaneous frequency trajectories of each mode are output in real time, thereby achieving real-time high-resolution tracking and compensation of multi-component frequency-modulated signals.

[0060] The beneficial effects of this invention are: the method has the advantage of breaking through the resolution limitation of traditional time-frequency analysis, and can directly output high-precision time-frequency ridges without post-processing; it can accurately separate and track multi-component signals with frequency intersections or close proximity; it avoids manual preset parameters through adaptive noise estimation and mode number determination; at the same time, it has low computational complexity, meets the real-time requirements of engineering, and significantly improves the ability of skywave radar to detect weak targets under strong clutter interference. Attached Figure Description

[0061] Figure 1 This is the result of MTD processing;

[0062] Figure 2 The result of STFT transformation before Doppler correction;

[0063] Figure 3 The result of STFT transformation after Doppler correction;

[0064] Figure 4 The MTD result after STFT processing;

[0065] Figure 5The result is the MTD after FrFT transformation;

[0066] Figure 6 The result of WVD transformation before Doppler correction according to the method of the present invention;

[0067] Figure 7 The result of WVD transformation after Doppler correction according to the method of the present invention;

[0068] Figure 8 The result is the MTD after processing by the method of the present invention. Detailed Implementation

[0069] In modern radar, communication, acoustics, and biomedical signal processing, the analysis and processing of non-stationary signals remains a core issue. Especially in applications such as target detection, target recognition, and spectrum sensing, the received signals often consist of multiple time-varying frequency components; these signals are commonly referred to as frequency-modulated (FM) signals. Accurately estimating the instantaneous frequency and amplitude of each component from a mixed observation signal, especially when multiple frequency components coexist and may be close to or even overlap with each other, becomes an extremely challenging task.

[0070] Traditional time-frequency analysis methods, such as Short-Time Fourier Transform (STFT), Wigner-Ville distribution (WVD), and wavelet transform, perform well in analyzing single linear frequency modulated signals. However, when multiple component frequencies are close or intersecting, these methods face significant resolution degradation and severe interference from cross-terms. Furthermore, sliding window-based algorithms suffer from an inherent trade-off between window width selection and time-frequency resolution, making it difficult to simultaneously handle rapid changes and high-precision estimation.

[0071] Therefore, in recent years, filter theory, especially Bayesian filtering methods, has emerged as a new approach to solving this problem. Within the framework of nonlinear system modeling and estimation, by modeling the instantaneous amplitude and phase of a signal as state variables and using filters to achieve recursive estimation, the time-frequency resolution limit of traditional methods can be overcome. Among these methods, the Unscented Kalman Filter (UKF), due to its excellent nonlinear processing capabilities and convergence performance, has gradually become the preferred tool for multi-signal estimation problems.

[0072] This invention proposes a UKF-based multi-mode amplitude and frequency estimation algorithm to achieve online estimation of multiple time-varying frequency signals without the need for prior frequency information or a sliding window. Its main advantages include strong adaptability, high resolution, ability to handle frequency overlap, and good real-time performance, making it a promising tool for broad engineering applications.

[0073] The object of this invention is a typical multimode signal, which has the following mathematical expression:

[0074] ;

[0075] in: n is the sampling point index variable. This represents the total number of sampling points; , For pattern number variables, The actual number of modes present in the signal; For the first Complex-valued observation signals at each sampling point; For the first The pattern in the first The amplitude of each sampling point may change over time; For the first The pattern in the first The phase of each sampling point; For the first Additive complex Gaussian white noise at each sampling point.

[0076] The core feature of this model is that the signal is a superposition of multiple frequency modulation modes, each of which may have a different frequency variation pattern. For example, mode 1 may be a linear rise, mode 2 a constant frequency sine wave, and mode 3 a quadratic frequency modulation. The observed signal is simply a complex superposition of these modes, accompanied by noise. The goal is to accurately recover the instantaneous amplitude of each mode from a single-channel observation sequence. With instantaneous frequency .

[0077] Under ideal conditions, if each mode has a significant frequency difference from the others, conventional methods such as spectral analysis or STFT can be used to estimate the frequency. However, in real-world signals, mode frequencies often overlap, cross over, or even interfere with each other, and the component amplitudes are not necessarily stable. In such cases, traditional methods struggle to effectively distinguish signal components.

[0078] Therefore, it is necessary to construct a framework capable of adaptive estimation under unknown component numbers, unknown frequency variation patterns, near-frequency conditions, and even crossover states. This invention utilizes the Bayesian filtering concept, modeling parameters (amplitude and phase) as state variables, and recursively estimating them using an unscented Kalman filter, thereby completing the component separation and frequency tracking tasks.

[0079] To achieve joint estimation of multiple components, this invention treats each mode in the signal as a subsystem in the state space. For each mode... Its state variables It is constructed as a combination of the amplitude at the current time (the nth sampling point in the time domain), the current phase, and its historical phase values, in the following form:

[0080] ;

[0081] in, For transpose, The prediction order used for modeling determines the model's ability to approximate frequency variation trends. By incorporating historical phase values, it is possible to capture the dynamic evolution of phase (i.e., frequency) and adapt to the frequency variation trends of both linear and nonlinear modes.

[0082] The state vectors of all modes at the nth sampling point are combined to form the overall system state vector. The state transition model uses a linear autoregressive structure (such as the AR model) to approximate the phase change, meaning that the phase at each time step (sampling point) can be approximated by the phase change from its previous value. The state is obtained through linear prediction of historical values. The corresponding state transition equation is:

[0083] ;

[0084] in Here is the state transition matrix. Let the process noise at the nth sampling point be used to describe the modeling error and system disturbance. The process noise is assumed to be a zero-mean Gaussian distribution, and the covariance matrix of the zero-mean Gaussian distribution is given by... .

[0085] The observation model is constructed based on the laws of physical signal synthesis, that is, the relationship between the system state and the observed values ​​is given by the following nonlinear function. definition:

[0086] ;

[0087] The nonlinear characteristics of this function mainly stem from the exponential form of the phase, making it difficult to directly apply conventional linear filtering methods. Therefore, this invention selects the Unscented Kalman Filter (UKF) as the core processing unit to solve the nonlinearity problem in observation modeling.

[0088] The Unscented Kalman Filter (UKF) is a high-precision nonlinear Bayesian filtering method that propagates the statistical properties of state variables under nonlinear mappings through an "unscented transformation" without requiring linearization of the function. Compared to the Extended Kalman Filter (EKF), the UKF offers higher accuracy and better stability when handling nonlinear systems, and is particularly suitable for the nonlinear observation function in this invention.

[0089] The core UKF process includes the following steps:

[0090] State prediction: Using the state transition equation, the prior state estimate is used to predict the current state vector at time n-1. and prior covariance ;

[0091] Point generation: estimation based on predicted prior states and prior covariance Generate a set of symmetrically distributed points;

[0092] Nonlinear propagation: Substituting points into a nonlinear observation model A set of predicted observations was obtained;

[0093] Observation mean and covariance: Calculate the weighted average of the predicted observations as the predicted mean, and calculate the covariance of the predicted observations;

[0094] State update: Calculate the actual observations The difference between the current value and the predicted mean is the new information, which is used to update the state vector. Covariance Matrix .

[0095] Observation function Defined as the superposition of multiple complex sine waves, its nonlinear form makes the UKF point propagation method a more reasonable estimation strategy. Each point reflects the changing trend under the nonlinear function after propagation, thus ensuring the stability and accuracy of state estimation in non-Gaussian and nonlinear environments.

[0096] The specific steps of the long-term accumulation Doppler compensation method for skywave radar based on UKF are as follows:

[0097] (1) System data input: Received radar echo measurement sequence Gaussian measurement noise variance ;

[0098] (2) Initialization of covariance estimation: SPICE is initialized using sparse covariance estimation. Measurement samples Calculate the initial covariance matrix ;

[0099] (3) Mode number estimation: using the initial covariance matrix Estimating the number of patterns using the SORTE criterion and eigenvalue statistics ;

[0100] ;

[0101] in, To obtain the eigenvalues, the SORTE is minimized. ;

[0102] (4) Initial amplitude and frequency estimation: For each frequency point The initial magnitude is estimated by weighted covariance fitting. and initial frequency , ;

[0103] (5) Initial state vector setting: for each mode Construct the initial state vector Initial state vector The initial states of K patterns Composition, state of each mode for:

[0104] ;

[0105] The phase is calculated from the frequency:

[0106] ;

[0107] in, For carrier frequency;

[0108] (6) Perform an update loop for the filter, updating... ,based on Time-state vector and state covariance matrix Using the state transition matrix Prior state estimate for predicting the current state vector at time n. and prior state covariance matrix :

[0109] ;

[0110] ;

[0111] The covariance matrix of a zero-mean Gaussian distribution; the initial values ​​of the state covariance matrix. It is the identity matrix;

[0112] (7) Generation of unscented transformation points: Generate the nth time point The unscented transformation point, i.e., the sigma point. Represents the nth time. The state vector of an unscented transformation point , The time is the initial value;

[0113] The generation of unscented transformation points is based on ;

[0114] in, As a scale factor, Represents the first of the matrix List;

[0115] (8) Using a nonlinear measurement model to... Transform into predictive observations , , It is a nonlinear observation function;

[0116] (9) Calculate the predicted observation mean: ; This represents the weighting coefficients used in the mean calculation;

[0117] (10) Calculate the observed covariance: ;* indicates conjugate transpose; These represent the weighting coefficients used in covariance calculation. Gaussian measures the noise variance;

[0118] (11) Calculate the cross-covariance between the state and the observation: ;

[0119] (12) Calculate the Kalman gain: ;

[0120] (13) Update the state vector at time n: ;

[0121] (14) Update the state covariance matrix at time n: ;

[0122] (15) Extract the estimation results from... Extract the amplitude of each mode. and frequency

[0123] (16) System output results: instantaneous amplitude of each mode Instantaneous frequency of each mode ;

[0124] (17) Based on the instantaneous amplitude of each mode Instantaneous frequency of each mode The compensated observations are then corrected, and the corrected observations are then subjected to long-term coherent accumulation (LTCI) to obtain a range-Doppler spectrum with a high signal-to-noise ratio and highly concentrated target energy.

[0125] Assuming the radar detects a moving target in a two-dimensional plane, and that the target undergoes uniformly accelerated linear motion, the simulation parameters of the long-term accumulation signal processing algorithm based on WVD transform are shown in Table 1.

[0126] Table 1

[0127] parameter Value Carrier frequency / MHz 12 Bandwidth / KHz 50 Time width / ms 5 Pulse repetition period / ms 10 Accumulated pulse count 1024 Number of distance units 2000 Signal-to-noise ratio (SNR) / dB 5 Target velocity / m / s 10 Target acceleration / m / s2 0.98 Target jerk / m / s3 1 Target distance / Km 375

[0128] like Figure 1 As shown, the MTD processing results exhibit significant broadening in the velocity dimension but no obvious broadening in the range dimension. This is because the target is in a low-velocity, high-acceleration state, thus not experiencing range migration, but Doppler broadening does occur. Figure 2 As shown, the STFT results before Doppler correction demonstrate the time-frequency distribution of the slow-time signal in the range cell where the target is located, with the signal frequency changing linearly with time. Figure 3 As shown, the WVD distribution map after Doppler correction illustrates the time-frequency distribution of the slow-time signal in the range cell where the target is located after Doppler correction. The signal frequency changes linearly with time, but the slope is significantly reduced compared to before correction. Figure 4 As shown, the MTD result after STFT processing of the target's range cell and adjacent range cells significantly reduces Doppler broadening compared to the original MTD result. However, due to the resolution limitations of STFT itself, the modulation frequency of the quadratic term is affected. The estimation is not precise enough, the energy cannot be fully accumulated, and there is still a certain degree of Doppler broadening. For example... Figure 5 As shown, the FrFT processing can effectively accumulate pulses exhibiting Doppler broadening, and the target's distance cell is the same as the preset initial distance, while the target's velocity cell is the same as the average velocity, verifying the effectiveness of the FrFT algorithm. Figure 6 As shown, the WVD distribution diagram before Doppler correction in the method proposed in this invention illustrates the time-frequency distribution of the slow-time signal in the range cell where the target is located, with the signal frequency changing linearly with time. Figure 7 As shown, the WVD distribution diagram after Doppler correction proposed in this invention illustrates the time-frequency distribution of the slow-time signal of the range cell where the target is located after Doppler correction, where the signal frequency is constant. Figure 8 As shown, the method proposed in this invention can effectively accumulate all pulses with Doppler broadening, and the target's distance unit is the same as the preset initial distance, and the target's velocity unit is the same as the target's initial velocity.

[0129] Table 2

[0130] method Gain (dB) MTD 0 STFT 6.0206 FrFT 4.0709 Method of the present invention 8.1230

[0131] The gains of different methods are shown in Table 2. With the MTD method as the benchmark, STFT has a gain of 6.0206 dB, FrFT has a gain of 4.0709 dB, while the method of the present invention has a gain of 8.1230 dB, which is better than the comparison algorithm, thus verifying the effectiveness of the method proposed in this invention.

[0132] The improvement of this invention over the prior art lies in:

[0133] (1) Breaking the limitations of the uncertainty principle: Through the polynomial prediction model, the phase evolution is approximated within a small time window through iterative updates. While maintaining the highest time resolution (sampling interval), the frequency resolution is constrained by state evolution.

[0134] (2) Direct output of time-frequency ridge: The state vector directly contains amplitude and phase, and the filtering result automatically forms a time-frequency trajectory. Compared with existing methods such as STFT / WVD that require post-processing, this invention does not require additional ridge extraction.

[0135] (3) Ability to handle cross modes: The state model constrains the phase evolution path of each mode, and can correctly correlate even if the frequency trajectories cross.

[0136] (4) Robust initialization: Combining sparse covariance estimation (SPICE) and eigenvalue statistics (SORTE) to adaptively estimate the number of modes. To avoid subjective settings.

[0137] In summary, this invention addresses the Doppler compensation challenge in weak target detection using skywave over-the-horizon radar (OTHR) by proposing a multi-component signal estimation algorithm based on unscented Kalman filtering. OTHR achieves long-range detection through ionospheric reflection, but traditional Doppler compensation methods suffer from inaccurate frequency estimation, severe energy diffusion, and poor real-time performance due to ionospheric disturbances, complex motion states, and strong clutter. This invention's algorithm utilizes a nonlinear Bayesian filtering framework, modeling the instantaneous amplitude and phase of multiple frequency-modulated components as state variables. Accurate estimation of the time-varying frequency signal is achieved through UKF recursion. The algorithm employs the SORTE criterion for adaptive estimation of the signal mode number, constructing a state vector containing amplitude and phase history. Combined with a multinomial prediction model, it accurately characterizes frequency evolution, ultimately outputting a high-resolution time-frequency ridge. Simulation results demonstrate that this method effectively suppresses Doppler broadening, achieves energy concentration, and outperforms traditional methods such as STFT and FrFT. It exhibits low computational complexity, good real-time performance, and strong robustness, making it suitable for weak target detection in complex OTHR environments.

Claims

1. A method for long-term accumulation Doppler compensation in skywave radar, characterized in that, Includes the following steps: System data input: Measurement sequence of received radar echoes; Initialize covariance estimation and mode number estimation: Based on the measurement sequence, initialize the covariance matrix and adaptively estimate the number of frequency modulation modes contained in the signal; Initial amplitude and frequency estimation: The initial amplitude and initial frequency of each mode are estimated by weighted covariance fitting method; Initial state vector setting: Construct a state vector for each mode, which includes the amplitude and phase at the current moment, as well as the amplitude and phase at historical moments; Filtering loop and state update: The state transition equation is constructed based on the multinomial prediction model, and the state vector is recursively predicted and updated using the unscented Kalman filter (UKF). Results extraction and output: Based on the updated state vector, extract the instantaneous amplitude and instantaneous frequency of each mode; Doppler compensation and accumulation: Doppler compensation is performed on the radar echo based on the instantaneous amplitude and instantaneous frequency, and the compensated signal is coherently accumulated over a long period of time to output the range-Doppler spectrum after compensation.

2. The method as described in claim 1, characterized in that, The filtering loop and state update specifically include: Filtering update loop: For each sampling time, based on the state vector and state covariance matrix of the previous time, the prior state estimate and prior state covariance matrix of the current time are predicted using the state transition matrix; Unscented Transformation Point Generation: Based on the prior state estimate and the prior state covariance matrix, a set of unscented transformation points is generated; Nonlinear observation propagation: The unscented transformation points are mapped to predicted observations through a nonlinear observation function; Calculation of observation statistics: Calculate the mean and covariance of the predicted observations, and calculate the cross-covariance between the state and the observations; State update: Based on the Kalman gain and the difference between the actual observed value and the predicted observed mean, update the state vector and the state covariance matrix.

3. The method according to claim 2, characterized in that, For each pattern k, the state variable at time n It is constructed as a combination of the amplitude at time n, the current phase, and its historical phase values: ； in, For transpose, M is the prediction order. k is the mode number variable, and K is the actual number of modes present in the signal. The amplitude of the k-th pattern at the n-th sampling point may vary over time; For the k-th pattern in the th... Phase of each sampling point , where n is the time sequence number and N is the total number of sampling points.

4. The method according to claim 3, characterized in that, The state transition equation is: ； in, The state vector of the system is formed by combining the state vectors of all modes at the nth sampling point. , Here is the state transition matrix. Let be the process noise at time n. The process noise is assumed to be a zero-mean Gaussian distribution, and the covariance matrix of the zero-mean Gaussian distribution is: ; The nonlinear observation function h(⋅) is: ； in, For the first Additive complex Gaussian white noise at each sampling point For the first The actual observed value at that moment.

5. The method according to claim 4, characterized in that, The method for generating the unscented transformation points is as follows: Prior state estimation using the state vector at time n and prior state covariance matrix Generate the nth time step A traceless transformation point, Represents the nth time. The state vector of an unscented transformation point, with superscript... Indicates the first The physical quantities corresponding to each unscented transformation point , The time is the initial value; The generation of unscented transformation points is based on ; in, As a scale factor, Represents the first of the matrix List.

6. The method according to claim 5, characterized in that, The method for generating the unscented transformation points is as follows: Using the state transition matrix Prior state estimate for predicting the current state vector at time n. and prior state covariance matrix : ； ； Wherein, the initial value of the state covariance matrix The identity matrix and the initial covariance matrix are given. It uses sparse covariance to estimate SPICE from the past Measurement samples It was calculated in the middle.

7. The method according to claim 6, characterized in that, Cross-covariance at time n ; in, To use a nonlinear measurement model to Transform into predictive observations To predict the observed mean, This represents the weighting coefficients used in covariance calculation; the superscript * indicates conjugate transpose. Kalman gain at time n: , The observation covariance at time n; , Gaussian measures the noise variance; Update the state vector at time n: ; Update the state covariance matrix at time n: .

Images