Low angle of attack multipath effect real-time compensation method, system, device and medium

Abstract

The present application relates to radar target detection technology field, specifically to low grazing angle multipath effect real-time compensation method, system, equipment and medium, wherein the method comprises: establishing an augmented state vector, including target motion state parameters and pitch angle error oscillation characteristic parameters; the state transition model and the nonlinear measurement model of the augmented state vector are established, wherein the nonlinear measurement model represents the pitch angle observation as the sum of the error term composed of the true pitch angle of the target and the pitch angle error oscillation characteristic parameters; according to the state transition model and the state estimation value at the last time, the state prediction vector and the prediction covariance matrix at the current time are predicted; based on the nonlinear measurement model and the actual observation of the radar at the current time, the state prediction vector and the prediction covariance matrix are updated, and the target state estimation value and the multipath oscillation characteristic parameter estimation value after the multipath error compensation are output. The purpose is to realize the low delay, high precision pitch angle error compensation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar target detection, in particular to a low-grazing-angle multipath effect real-time compensation method, system, device and medium. BACKGROUND

[0002] With the rapid development of low-altitude economy, efficient detection of unmanned aerial vehicles and other targets in low-altitude and ultra-low-altitude airspace has become a core requirement for ensuring airspace safety and promoting the construction of low-altitude transportation systems. As a detection equipment with all-weather and all-day working capability, radar has become a core technical means in the field of low-altitude target detection due to its advantage of continuous tracking of dynamic targets. In typical low-altitude detection scenarios such as urban near-ground airspace, deserts, and forests, radar often needs to observe targets at low grazing angles. At this time, significant multipath effects are likely to occur in the propagation process of radar electromagnetic waves. The direct wave emitted by the radar and the multipath reflected wave reflected by obstacles such as the ground, vegetation, and buildings will interfere in the spatial domain, thereby destroying the symmetry of the radar elevation beam pattern and causing the measured target elevation angle to have a nearly biased sinusoidal periodic oscillation error, which greatly reduces the target height detection accuracy and greatly restricts the application effectiveness of radar in key fields such as low-altitude surveillance and airspace control.

[0003] To address the problem of deterioration of elevation angle measurement accuracy caused by low-grazing-angle multipath effects, existing technologies mainly conduct multipath interference suppression research from two dimensions of electromagnetic environment modeling and signal processing. In the aspect of electromagnetic environment modeling, methods such as ray tracing and hybrid diffraction model are often used to construct electromagnetic wave propagation models in complex scenarios to achieve prediction and suppression of multipath signals. In the aspect of signal processing, techniques such as array antenna beamforming and environment matching filtering are used to weaken the influence of multipath interference on measurement results. However, the electromagnetic environment modeling method needs to construct a refined scene geometry and electromagnetic parameter model, which has extremely high computational complexity and poor model adaptability, and is difficult to meet the real-time detection requirements due to poor engineering portability. The array antenna beamforming scheme relies on specific multi-channel antenna hardware architecture and requires hardware modification of existing radar systems, increasing the technical implementation cost and complexity. The environment matching filtering method requires complex offline training and online matching operations on observation data, resulting in high processing delay and inability to adapt to the stable tracking requirements of high-speed dynamic targets. The existing elevation angle error compensation methods still have obvious deficiencies in real-time performance, system compatibility, and environmental adaptability. An effective technical approach that does not rely on complex modeling and special hardware and can achieve low-latency and high-precision compensation is urgently needed. SUMMARY

[0004] To achieve low-latency and high-precision elevation angle error compensation, the present application provides a low-grazing-angle multipath effect real-time compensation method and system, and the technical solutions adopted are as follows:

[0005] The technical solution of the first aspect of the application provides a low grazing angle multipath effect real-time compensation method, and the method comprises the following steps:

[0006] An augmented state vector is established, and the augmented state vector comprises target motion state parameters and pitch angle error oscillation characteristic parameters;

[0007] A state transition model of the augmented state vector and a nonlinear measurement model are established, wherein the nonlinear measurement model represents a pitch angle observation as a sum of a target true pitch angle and an error term formed by the pitch angle error oscillation characteristic parameters;

[0008] According to the state transition model and a state estimation value at a previous time, a state prediction vector and a prediction covariance matrix at a current time are predicted;

[0009] Based on the nonlinear measurement model and actual observation of the radar at the current time, the state prediction vector and the prediction covariance matrix are updated by filtering, and a target state estimation value after multipath error compensation and a multipath oscillation characteristic parameter estimation value are output.

[0010] Further, the target motion state parameters comprise position components and velocity components of the target in horizontal and vertical directions;

[0011] The pitch angle error oscillation characteristic parameters comprise an amplitude, an angular frequency and a phase angle of periodic oscillation of the pitch angle caused by the multipath effect.

[0012] Further, the establishment of the state transition model specifically comprises:

[0013] The position and velocity components of the target are predicted by time recursion according to a target kinematics relationship;

[0014] The phase angle is updated by linear accumulation based on the angular frequency;

[0015] Process noise models are respectively constructed for each state variable in the augmented state vector.

[0016] Further, the establishment of the nonlinear measurement model specifically comprises:

[0017] A target true pitch angle term is calculated according to a geometric projection relationship between the target and the radar;

[0018] A periodic oscillation error term representing the multipath effect is constructed according to the pitch angle error oscillation characteristic parameters;

[0019] The target true pitch angle term and the periodic oscillation error term are superimposed and integrated into radar measurement noise to form the nonlinear measurement model.

[0020] Further, the state prediction vector and the prediction covariance matrix are filtered and updated, specifically including:

[0021] By combining the prediction covariance matrix and the measurement noise covariance matrix, the inverse matrix of the covariance matrix of the measurement prediction residual is solved, and the optimal weighting matrix is calculated;

[0022] Based on the current state prediction value, the measurement prediction result is calculated through the nonlinear measurement model, and the deviation is obtained by comparing the measurement prediction result with the actually collected radar observation data;

[0023] The optimal weighting matrix is used to linearly weight the deviation, and the compensated value after weighting adjustment is applied to the state prediction vector to complete the estimation of the augmented state vector;

[0024] Based on the optimal weighting matrix, the partial derivative matrix of the measurement function and the prediction covariance matrix, the state estimation covariance matrix is updated.

[0025] Further, the method further includes noise covariance matrix initialization, specifically including:

[0026] The process noise covariance matrix in the state transition process is configured to represent the uncertainty of the state prediction model;

[0027] The measurement noise covariance matrix in the observation process is configured according to the measurement accuracy of the radar sensor, and is used to represent the uncertainty of the radar observation data;

[0028] Based on the process noise covariance matrix and the measurement noise covariance matrix, the confidence between the prediction value and the observation value is dynamically weighted and balanced in the filtering process.

[0029] Further, the filtering and updating of the state prediction vector and the prediction covariance matrix further include model linearization, specifically including:

[0030] The partial derivative matrix of the state transition function with respect to the augmented state vector is calculated to obtain the linear approximation representation of the state transition function;

[0031] The partial derivative matrix of the measurement function with respect to the augmented state vector is calculated to obtain the linear approximation representation of the measurement function;

[0032] The linear approximation representations of the state transition function and the measurement function are used for covariance matrix prediction and update calculation of the augmented state Kalman filter.

[0033] The technical scheme of the second aspect of the application provides a low-grazing-angle multipath effect real-time compensation system, which adopts the low-grazing-angle multipath effect real-time compensation method of the technical scheme of the first aspect of the application, and the system comprises:

[0034] The state vector construction module is configured to build an augmented state vector, which includes target motion state parameters and pitch angle error oscillation characteristic parameters.

[0035] The model building module is configured to build a state transition model and a nonlinear measurement model for the augmented state vector, wherein the nonlinear measurement model represents the pitch angle observation as the sum of the error terms consisting of the target's true pitch angle and the pitch angle error oscillation characteristic parameters;

[0036] The state prediction module is configured to predict the state prediction vector and the prediction covariance matrix at the current moment based on the state transition model and the state estimate at the previous moment.

[0037] The filtering update module is configured to filter and update the state prediction vector and prediction covariance matrix based on the nonlinear measurement model and the actual radar observations at the current time, and output the target state estimate and multipath oscillation characteristic parameter estimate after multipath error compensation.

[0038] The third aspect of the present invention provides an electronic device, the electronic device comprising: a processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to enable the processor to perform the steps of the real-time compensation method for low grazing angle multipath effect described in the first aspect of the present invention.

[0039] The fourth aspect of the present invention provides a computer-readable storage medium storing a program for implementing a real-time compensation method for low grazing angle multipath effects. The program for implementing the real-time compensation method for low grazing angle multipath effects is executed by a processor to implement the steps of the real-time compensation method for low grazing angle multipath effects described in the first aspect of the present invention.

[0040] The present invention has the following beneficial effects:

[0041] This invention provides a real-time compensation method for low-grazing-angle multipath effects. By establishing an augmented state vector containing parameters of the target motion state and the oscillation characteristics of the elevation angle error caused by multipath, and constructing corresponding state transition and nonlinear measurement models, the elevation angle observation is separated into the sum of the target's true elevation angle and the multipath error term. This achieves joint estimation of the target state and multipath error within a unified filtering framework. Based on this method, the periodic oscillation error of the elevation angle caused by multipath effects can be estimated and compensated online in real time and dynamically, significantly improving the accuracy of elevation angle measurement. Furthermore, this method is implemented solely based on signal processing, without relying on complex environment modeling or special hardware support. It boasts advantages such as high computational efficiency, good real-time performance, and easy engineering deployment, solving the core problem of insufficient radar elevation angle measurement accuracy in low-grazing-angle scenarios. Attached Figure Description

[0042] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart of a method for real-time compensation of low grazing angle multipath effect provided in an embodiment of the present invention;

[0044] Figure 2 A schematic diagram illustrating the multipath period and amplitude prediction effect provided in an embodiment of the present invention;

[0045] Figure 3 A comparison chart of the pitch angle estimation accuracy of different filtering methods provided in an embodiment of the present invention;

[0046] Figure 4 Provided as an embodiment of the present invention Figure 3 Comparison of pitch angle estimation accuracy for different matching filtering methods;

[0047] Figure 5 This is a schematic diagram of the structure of a real-time compensation system for low grazing angle multipath effect provided in an embodiment of the present invention. Detailed Implementation

[0048] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a real-time compensation method, system, device, and medium for low grazing angle multipath effects proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0050] The inventors discovered in their practical work that the pitch angle error caused by the low grazing angle multipath effect has a key and exploitable feature: its time-domain form approximately presents an error, expressed as follows:

[0051]

[0052] Where A is the oscillation amplitude, typically 1°-5°; T is the oscillation period, varying between 10-100 seconds. B is the initial phase; B is the bias. This formula provides a theoretical basis for suppressing errors from the perspective of signal processing.

[0053] However, existing solutions with fixed-parameter filters cannot adapt to dynamically changing multipath environments; while complex adaptive algorithms suffer from excessive computational burden (such as O(N³) complexity) or slow convergence speed.

[0054] Based on this, this invention utilizes the periodic oscillation characteristics of multipath errors, which can be parameterized, and incorporates the key parameters describing these periodic oscillations as augmented state variables. These parameters, along with the target's motion state, are introduced into the Kalman filter framework to construct a new joint estimation filtering model. This method abandons the traditional approach of complex physical modeling or requiring special hardware support, and instead transforms into a pure signal processing error compensation strategy.

[0055] The following description, in conjunction with the accompanying drawings, details the specific solutions for a real-time compensation method, system, device, and medium for low grazing angle multipath effects provided by this invention.

[0056] Please see Figure 1 The diagram illustrates a method flowchart for real-time compensation of low grazing angle multipath effects according to an embodiment of the present invention, the method comprising:

[0057] Step S100: Establish an augmented state vector, which includes target motion state parameters and pitch angle error oscillation characteristic parameters;

[0058] In some embodiments, the target motion state parameters include the target's position and velocity components in the horizontal and vertical directions;

[0059] In some embodiments, the pitch angle error oscillation characteristic parameters include the amplitude, angular frequency, and phase angle of the pitch angle periodic oscillation caused by the multipath effect;

[0060] The augmented state vector is represented as:

[0061]

[0062] Where k represents the time index, used to distinguish state quantities at different time points; This indicates the horizontal position component of the target, expressed in meters (m). This represents the vertical height component of the target, expressed in meters (m). This indicates the target's horizontal speed, measured in meters per second (m / s). This indicates the target's velocity in the vertical direction, expressed in meters per second (m / s). This represents the amplitude of pitch angle oscillation caused by multipath effect, in degrees (°). This represents the angular frequency of multipath oscillations, expressed in radians per second (rad / s). The phase angle of the multipath oscillation is expressed in radians (rad). This formula integrates the dynamic information of the target motion and the oscillation characteristics of the multipath error into the same vector space. By constructing an augmented state vector that integrates the target motion state and the oscillation characteristics of the pitch angle error caused by the multipath effect, it breaks through the limitation of traditional filtering that only focuses on the estimation of the target motion state. It incorporates the key characteristic parameters of the multipath effect into the unified framework of subsequent joint estimation, providing a basic state space description for real-time tracking of the multipath effect and accurate compensation of the pitch angle error. The subsequent filtering process can simultaneously and dynamically update the target motion state and multipath oscillation characteristics, thereby improving the accuracy of pitch angle measurement in low grazing angle scenarios.

[0063] Step S200: Establish the state transition model and nonlinear measurement model of the augmented state vector, wherein the nonlinear measurement model represents the pitch angle observation as the sum of the error terms composed of the target's true pitch angle and the pitch angle error oscillation characteristic parameters;

[0064] In some embodiments, the state transition model serves to recursively deduce the predicted state value at the current time based on the augmented state of the previous time step, and reflects the uncertainties in the actual environment through a process noise model. Establishing the state transition model specifically includes:

[0065] Step S210: Predict the target's position and velocity components using time recursion based on the target's kinematic relationships; specifically, for the target motion state parameters in the augmented state vector, a uniform kinematic model is used for time recursion; the radar system sampling time interval is... The unit is seconds, representing the time difference between two consecutive state updates. The horizontal position at the current time k is... From the horizontal position at the previous moment With horizontal speed Joint decision, that is Similarly, the current vertical height can be obtained. For the velocity component, since the motion state of the low-altitude target changes gradually in a short period of time, the recursive rule of maintaining the velocity of the previous moment is adopted. Through this process, the noiseless recursion of the target motion state from moment k-1 to moment k is completed.

[0066] Step S211: Perform linear cumulative update of the phase angle based on the angular frequency; this step is for the phase angle in the augmented state vector. That is, the phase angle of the multipath oscillation at time k-1, using angular frequency. Achieving linear cumulative updates; the physical meaning of the phase angle is the starting position of the sinusoidal oscillation, and its change over time is equal to the product of the angular frequency and the time interval. Through linear calculation, the dynamic evolution of the phase of multipath oscillations can be accurately characterized. At the same time, because the change of angular frequency is extremely small in a short time, the linear cumulative model can balance accuracy and computational complexity.

[0067] Step S212: Construct process noise models for each state variable in the augmented state vector. The state transition model is expressed as:

[0068]

[0069] In the formula, express The augmented state vector at time step; express The augmented state vector at time step; Represents the state transition function; This indicates the sampling time interval of the radar system, in seconds (s). Let represent the process noise vector at time k, a 7-dimensional column vector. Each component corresponds to the following noise levels in sequence: horizontal position noise, vertical height noise, horizontal velocity noise, vertical velocity noise, oscillation amplitude noise, angular frequency noise, and phase angle noise. Each component is modeled with a mean of 0 and a covariance of . Gaussian white noise; This is a 7×7 diagonal matrix, where the elements on the diagonal represent the variances of each noise component. This example uses, but is not limited to, the following parameter settings: standard deviation of position process noise. Speed ​​process noise standard deviation Standard deviation of noise during amplitude process - Standard deviation of frequency process noise Phase process noise standard deviation - ;

[0070] In some embodiments, the nonlinear measurement model serves to establish an augmented state vector. Compared with actual radar observations The mapping relationship between them is clarified, the impact of multipath error on pitch angle observation is defined, and a nonlinear measurement model is established, specifically including:

[0071] Step S220: Calculate the target's true pitch angle term based on the geometric projection relationship between the target and the radar; specifically, calculate the target's true pitch angle based on the geometric projection relationship using the target's position component in the horizontal direction and its height component in the vertical direction in the augmented state vector.

[0072] In some embodiments, the slant range between the radar and the target is calculated using the Pythagorean theorem. Then, through the arctangent function The ratio of altitude to horizontal distance is converted into an angle to obtain the target's true pitch angle, which is the pitch angle that the radar should observe when there is no multipath interference.

[0073] Step S221: Based on the pitch angle error oscillation characteristic parameters, construct a periodic oscillation error term characterizing the multipath effect; specifically, extract the pitch angle error oscillation characteristic parameters from the augmented state vector, including the pitch angle periodic oscillation amplitude caused by the multipath effect. Phase angle Based on these parameters, a periodic oscillation error term characterizing the multipath effect is constructed. This is used to simulate the periodic error caused by the interference between multipath reflected waves and direct waves. This error term reflects the degree of interference of the multipath effect on the elevation angle measurement.

[0074] Step S222: The true target elevation angle term and the periodic oscillation error term are superimposed and incorporated into the radar measurement noise to form a nonlinear measurement model. The nonlinear measurement transfer model is expressed as:

[0075]

[0076] in, Represents the radar measurement vector at time k; To measure noise, Represents the measurement transfer function. This represents the square root operation. This is represented by the arctangent operation; this example uses, but is not limited to, the following parameter settings: standard deviation of radar slant range measurement noise. Standard deviation of pitch angle measurement noise This example uses, but is not limited to, the oscillation amplitude. This nonlinear measurement model accurately correlates the target motion state with the physical essence of radar slant range and true elevation angle through geometric projection relationships. It uses an explicit sine model to characterize the periodic oscillation error of elevation angle caused by multipath interference at low grazing angles. It also incorporates measurement noise to reflect the measurement uncertainty of radar hardware. This provides an observation layer mapping that fits the actual detection scenario for subsequent augmented Kalman filtering, ensuring the physical rationality of the joint estimation of multipath oscillation parameters and target motion state. It also supports the effective separation of real signal, multipath error and measurement noise in the filtering process, ultimately improving the accuracy of radar elevation angle measurement in low grazing angle scenarios.

[0077] The state transition model and nonlinear measurement model established in step S200 accurately characterize the dynamic characteristics of the augmented state vector's evolution over time and its inherent nonlinear relationship with radar observations. The state transition model achieves joint prediction of target motion and multipath error characteristics through kinematic recursion and phase linear accumulation, while the nonlinear measurement model effectively separates and characterizes the influence mechanism of multipath error on pitch angle observations through geometric relationships and the superposition of oscillation terms. The establishment of the two models provides a rigorous mathematical foundation for the subsequent joint optimal estimation of multipath oscillation parameters and target motion state based on the Kalman filter framework.

[0078] Step S300: Based on the state transition model and the state estimate of the previous time step, predict the state prediction vector and prediction covariance matrix for the current time step;

[0079] In some embodiments, the one-step prediction of the state vector is represented as:

[0080]

[0081] in, It represents the optimal state estimate at time k-1 based on all observations at time k-1 and before, including target motion state parameters and multipath oscillation characteristic parameters; This represents the one-step prediction of the state at time k based on the observation at time k-1; This is the state transition function;

[0082] In some embodiments, the prediction covariance matrix is ​​calculated as follows:

[0083]

[0084] in, This represents the state estimation covariance matrix at time k-1, used to quantify the uncertainty of the state estimation at time k-1. This represents the covariance matrix of the predicted state in one step. This indicates the transpose operation; Represents the process noise covariance matrix; For the state transition function Jacobian matrix; for The transpose of the matrix;

[0085] This embodiment, based on the target's kinematic laws and the time-varying characteristics of multipath oscillations, ensures the physical rationality of the target's motion and multipath parameter state predictions. Furthermore, by combining the covariance matrix with the Jacobian matrix and process noise, it accurately quantifies the uncertainty of the prediction process. This provides prior state information with uncertainty measurement for subsequent filter updates, enabling the augmented Kalman filter to adaptively balance the prior constraints of the predicted values ​​and the posterior corrections of the observed values.

[0086] Step S400: Based on the nonlinear measurement model and the actual radar observations at the current moment, filter and update the state prediction vector and prediction covariance matrix, and output the target state estimate and multipath oscillation characteristic parameter estimate after multipath error compensation.

[0087] Step S400 specifically includes:

[0088] Step S410: By combining the prediction covariance matrix and the measurement noise covariance matrix, solve for the inverse matrix of the covariance matrix of the measurement prediction residual and calculate the optimal weighting matrix, which can be expressed as:

[0089]

[0090] in, This represents the Kalman gain matrix, also known as the optimal weighting matrix, which determines the extent to which new observations should be trusted relative to previous predictions during state updates. The state covariance matrix at time k is used to quantify the uncertainty of state prediction. The measurement noise covariance matrix is ​​represented as follows: ; First, calculate the sum of the state prediction uncertainty after propagation through the measurement model and the measurement noise uncertainty, then inversely calculate the confidence level of the measurement residual; the overall calculation logic is as follows: The linear approximation relationship between the uncertainty of the associated state prediction and the measurement model is then multiplied by the inverse matrix mentioned above to obtain the Kalman gain matrix. Its function is to control the correction weight of the measurement residual on the state estimation.

[0091] Step S420: Based on the current state prediction value, calculate the measurement prediction result using a nonlinear measurement model, and compare the measurement prediction result with the actual collected radar observation data to obtain the deviation; based on the current state prediction value The measurement prediction results are calculated using a nonlinear measurement model and then compared with actual radar observation data to obtain the deviation. , This represents the actual radar observation vector at the current moment; For state-based predicted values The obtained measurement prediction values; the deviation contains new information in the current observations that has not been explained by the prediction model, and is the basis for subsequent state corrections;

[0092] Step S430: Linearly weight the deviation using the optimal weighting matrix, and apply the weighted compensation value to the state prediction vector to complete the estimation of the augmented state vector, which can be expressed as:

[0093]

[0094] In the formula, This represents the updated state estimate; the formula uses Kalman gain to weight the deviation between the observed and predicted values, and applies the weighted correction to the state prediction vector to obtain the updated state estimate at time k.

[0095] Step S440: Based on the optimal weighting matrix, the partial derivative matrix of the measurement function, and the predicted covariance matrix, update the state estimation covariance matrix, which can be expressed as:

[0096]

[0097] in, This represents the updated state covariance matrix; Is with An identity matrix of the same dimension; this formula reflects that the uncertainty of state estimation is reduced after incorporating new observation information; This can be understood as the portion subtracted from the predicted covariance, representing the reduction in uncertainty due to this observation; the updated covariance matrix This will be used in the prediction step of the next time step, thus starting a new round of filtering recursion loop.

[0098] Through the filtering update process in step S400, the state prediction value is optimally corrected using the actual radar observations at the current moment. The confidence level between the state prediction and radar observation is dynamically balanced by calculating the Kalman gain matrix, and the new information in the observation data is fused into the augmented state estimation using the innovation vector (bias quantity). This process not only outputs a more accurate target motion state estimate after multipath error compensation, but also updates the latest estimates of the multipath oscillation characteristic parameters simultaneously. At the same time, by updating the state estimation covariance matrix, an accurate uncertainty measure is provided for the filtering recursion at the next moment, thereby ensuring the continuous stability and convergence of the entire augmented Kalman filtering process, and finally achieving high-precision, real-time compensation of the target elevation angle in a strong multipath interference environment.

[0099] In some embodiments, the real-time compensation method for low grazing angle multipath effects further includes noise covariance matrix initialization, specifically including:

[0100] In some embodiments, a process noise covariance matrix is ​​configured during the state transition process to characterize the uncertainty of the state prediction model; the augmented state vector includes target motion state parameters and multipath oscillation characteristic parameters, and a process noise variance needs to be configured for each component, i.e. Let represent the process noise covariance matrix, expressed as: , Represents a diagonal matrix. The process noise variance for the horizontal position. The process noise variance is the vertical height. The process noise variance for horizontal velocity. The process noise variance for vertical velocity. The process noise variance for the multipath oscillation amplitude. The process noise variance is the angular frequency. The process noise variance of the phase angle is used to characterize "random disturbances not accurately described by the state transition model";

[0101] In some embodiments, the measurement noise covariance matrix during the observation process is configured according to the measurement accuracy of the radar sensor to characterize the uncertainty of the radar observation data. The radar observation vector includes slant range and elevation angle, which can be configured separately according to the measurement accuracy of the radar sensor: Slant range component: The slant range measurement noise variance is determined according to the radar ranging accuracy index, through manufacturer technical parameters or actual measurements; Elevation angle component: The elevation angle measurement noise variance is determined according to the performance of the radar elevation angle measurement unit, such as the beam pointing accuracy of the phased array antenna, the influence of receiver noise on angle measurement, etc., through parameter documents or actual measurements.

[0102] In some embodiments, based on the process noise covariance matrix and the measurement noise covariance matrix, the confidence level between the predicted value and the observed value is dynamically weighted and balanced during the filtering process; prediction stage: predicting the covariance matrix. ;like As the number of states increases, the uncertainty of state transitions also increases. This will increase, indirectly reducing the confidence level of predictions that rely solely on state transition models.

[0103] Update phase: Kalman gain matrix ;like Large, with high forecast uncertainty. This will tend to increase, giving radar observations a higher proportion in status updates; if Large, with high observational uncertainty. This will tend to decrease, allowing the state prediction value to account for a larger proportion. In this way, the contribution weights of the model and observations to the final state estimation are adaptively adjusted based on the relative uncertainty of the model and observations.

[0104] In summary, the noise covariance matrix initialization, by precisely configuring the process noise covariance matrix (matching the random disturbance characteristics of target motion and multipath environment) and the measurement noise covariance matrix (matching the measurement accuracy limitations of radar hardware), provides a basis for quantifying model uncertainty and observation uncertainty in the prediction and update process of augmented Kalman filtering. Based on this, the filtering process can adaptively balance the confidence levels of the state prediction values ​​obtained from the prior model based on target motion and multipath characteristics and the radar observation values ​​reflecting real-time detection information. This avoids estimation drift caused by assumption bias in the state transition model and reduces the interference of radar observation noise on the estimation results. Ultimately, it ensures the accuracy and stability of the joint estimation of target motion state and multipath oscillation characteristic parameters in low grazing angle scenarios, achieving real-time, high-precision compensation for pitch angle errors.

[0105] In some embodiments, the filtering update of the state prediction vector and the prediction covariance matrix further includes model linearization, specifically including: calculating the partial derivative matrix of the state transition function with respect to the augmented state vector to obtain a linear approximation of the state transition function; calculating the partial derivative matrix of the measurement function with respect to the augmented state vector to obtain a linear approximation of the measurement function; and using the linear approximation of the state transition function and the measurement function to perform covariance matrix prediction and update calculation for the augmented state Kalman filter. Specifically, the state transition Jacobian matrix is ​​first calculated. This is used to describe the linear propagation relationship of small changes in state during the transition process, and is expressed as:

[0106]

[0107] in, Represents the augmented state vector Differentiation operation; This matrix realizes the first-order Taylor linear approximation of the nonlinear state transition process near the current state, providing a linear mapping relationship for subsequent covariance propagation;

[0108] Then, calculate the measurement Jacobian matrix. This is used to describe the linear effect of a small change in state on an observation, and is expressed as:

[0109]

[0110] in , representing the instantaneous slant range between the radar and the target; For measurement functions;

[0111] Then through and It is directly used in the covariance prediction and update formula of standard Kalman filtering to replace the state transition matrix and measurement matrix in a linear system, i.e., to predict the covariance matrix: Kalman gain matrix: And update the state estimation covariance matrix: By calculating the Jacobian matrix of the state transition function and the measurement function in real time, the model linearization process successfully approximates the nonlinear system describing the joint evolution of target motion and multipath error with a first-order linear approximation around the current state estimate or prediction value in each filtering cycle. This approximation allows the standard Kalman filter covariance prediction and update rule to be applied to highly nonlinear augmented state systems. Ultimately, this step ensures that the extended Kalman filter can effectively handle nonlinear problems caused by complex geometric relationships and multipath periodic oscillations, thereby guaranteeing stable convergence and high-precision output of the joint estimation process of target state and multipath parameters.

[0112] Please see Figure 2 As shown, Figure 2 The figure shows the real-time compensation method for low grazing angle multipath effect based on augmented state Kalman filtering in this application, as well as the prediction effect of system multipath period and amplitude. The figure contains three curves:

[0113] True oscillation component: represents the true trend of pitch angle periodic error caused by multipath effect under ideal conditions;

[0114] Estimated oscillation component: representing the multipath error estimated by the augmented state Kalman filter method proposed in this invention;

[0115] Oscillations in measurements: These refer to the multipath oscillation components contained in the actual radar observation data, and usually also include measurement noise and other interferences.

[0116] Where the horizontal axis represents time (in seconds) and the vertical axis represents the magnitude of the oscillation component (in degrees); according to Figure 2 The three curves in the middle can be understood as follows: after an initial iterative convergence process, the estimated oscillation component is in high agreement with the actual oscillation component, indicating that the method of the present invention can accurately and stably track the amplitude and periodic changes of multipath error. The method has dynamic adaptability to the amplitude and frequency of multipath oscillation and is suitable for time-varying multipath environments.

[0117] Please see Figure 3 and Figure 4 As shown, the performance of the method of this invention and the classical filtering method in pitch angle estimation is illustrated by comparison. Figure 3 and Figure 4 Includes:

[0118] True pitch angle, the trajectory of the target's true pitch angle change;

[0119] Noise-inclusive measurements: The elevation angle data actually observed by the radar, including multipath error and sensor noise;

[0120] Standard KF estimation, the pitch angle estimation result obtained using the classical Kalman filter method;

[0121] The augmented state KF estimation is based on the pitch angle estimation results obtained using the augmented state Kalman filtering method proposed in this invention.

[0122] By comparing the performance metrics of the standard Kalman filter (KF) and the augmented state KF, the root mean square error (RMSE) of the standard KF is 0.9266 degrees, with a maximum error of 4.0887 degrees; while the RMSE of the augmented state KF is 0.2772 degrees, with a maximum error of 1.2360 degrees. This shows that the augmented state Kalman filter method significantly improves the pitch angle estimation accuracy, reducing the RMSE by 70.08% and the maximum error by 69.77%.

[0123] according to Figure 3 and Figure 4 The curves show the pitch angle error of the standard KF and the amplified KF over time. It is understandable that the curves of the noisy measurements show obvious periodic oscillations, which verifies the error characteristics caused by the multipath effect. The standard KF estimation results still contain significant multipath errors, indicating that traditional methods are difficult to effectively suppress this type of structured error.

[0124] The augmented-state Kalman filtering (ADF) estimation results are closer to the true pitch angle, with a significant reduction in error, indicating that the method of this invention can significantly improve the accuracy of pitch angle measurement. The error curve shows that the method of this invention maintains a low error level throughout the entire time range, exhibiting good stability and consistency. Based on this, this invention successfully achieves real-time, high-precision modeling and compensation for low grazing angle multipath errors through the augmented-state Kalman filtering method. This method has good convergence and tracking capabilities and can adapt to changes in multipath characteristics. Compared with classical filtering methods, this invention significantly improves the accuracy of pitch angle estimation, with a substantial reduction in both the root mean square error and the maximum error.

[0125] In summary, this real-time compensation method for low-grazing-angle multipath effects constructs an augmented state vector containing the target's motion state and multipath oscillation characteristic parameters. Combining a state transition model and a nonlinear measurement model, and utilizing augmented Kalman filtering, it achieves joint estimation of multipath oscillation parameters and target motion state. This accurately removes multipath oscillation errors from the original pitch angle measurement, significantly improving the accuracy of pitch angle measurement. Furthermore, the algorithm is based on pure signal processing, requiring no modification to the radar hardware, thus reducing system modification costs. Its low computational latency meets the real-time requirements of high-speed target tracking. Through parameter self-initialization and other design features, it is adaptable to complex scenarios such as cities, deserts, and forests. It can also output multipath characteristic parameters to assist environmental perception, providing high-precision assurance for scenarios such as low-altitude UAV monitoring and low-altitude logistics navigation.

[0126] Please see Figure 5 The diagram illustrates a real-time compensation system for low grazing angle multipath effects according to an embodiment of the present invention. The system includes:

[0127] The state vector construction module is configured to build an augmented state vector, which includes target motion state parameters and pitch angle error oscillation characteristic parameters.

[0128] The model building module is configured to build a state transition model and a nonlinear measurement model for the augmented state vector, wherein the nonlinear measurement model represents the pitch angle observation as the sum of the error terms consisting of the target's true pitch angle and the pitch angle error oscillation characteristic parameters;

[0129] The state prediction module is configured to predict the state prediction vector and the prediction covariance matrix at the current moment based on the state transition model and the state estimate at the previous moment.

[0130] The filtering update module is configured to filter and update the state prediction vector and prediction covariance matrix based on the nonlinear measurement model and the actual radar observations at the current time, and output the target state estimate and multipath oscillation characteristic parameter estimate after multipath error compensation.

[0131] The third aspect of the present invention provides an electronic device, the electronic device comprising: a processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to enable the processor to perform the steps of the real-time compensation method for low grazing angle multipath effect described in the first aspect of the present invention.

[0132] The fourth aspect of the present invention provides a computer-readable storage medium storing a program for implementing a real-time compensation method for low grazing angle multipath effects. The program for implementing the real-time compensation method for low grazing angle multipath effects is executed by a processor to implement the steps of the real-time compensation method for low grazing angle multipath effects described in the first aspect of the present invention.

[0133] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0134] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A method for real-time compensation of low-grazing-angle multipath effects, characterized in that, The method comprises: establishing an augmented state vector, the augmented state vector comprising target motion state parameters and pitch angle error oscillation characteristic parameters; the target motion state parameters comprising position components and velocity components of the target in horizontal and vertical directions; the pitch angle error oscillation characteristic parameters comprising amplitude, angular frequency and phase angle of periodic oscillation of the pitch angle caused by multipath effect; establishing a state transition model and a nonlinear measurement model of the augmented state vector, wherein the nonlinear measurement model represents the pitch angle observation as a sum of a target true pitch angle and an error term composed of the pitch angle error oscillation characteristic parameters; establishing the state transition model comprises: time recursively predicting the position and velocity components of the target according to target kinematics; for the target motion state parameters in the augmented state vector, time recursively predicting using a uniform motion kinematics model; linearly cumulatively updating the phase angle based on the angular frequency; respectively constructing a process noise model for each state variable in the augmented state vector; establishing the nonlinear measurement model comprises: calculating a target true pitch angle term according to a geometric projection relationship between the target and the radar; constructing a periodic oscillation error term representing the multipath effect according to the pitch angle error oscillation characteristic parameters; superimposing and integrating the target true pitch angle term and the periodic oscillation error term into radar measurement noise to form the nonlinear measurement model, and the nonlinear measurement transition model is represented as: wherein represents the radar measurement vector at time k; is the measurement noise, represents the measurement transfer function, represents the square root operation, represents the inverse tangent operation; represents the augmented state vector at time k; represents the phase angle; represents the pitch angle periodic oscillation amplitude; represents the horizontal position; represents the vertical position; predicting a state prediction vector and a prediction covariance matrix at the current time according to the state transition model and the state estimation value at the previous time; filtering and updating the state prediction vector and the prediction covariance matrix based on the nonlinear measurement model and actual observation of the radar at the current time, and outputting a target state estimation value after multipath error compensation and a multipath oscillation characteristic parameter estimation value.

2. The low-grazing-angle multipath effect real-time compensation method of claim 1, wherein, The filtering and updating of the state prediction vector and the prediction covariance matrix specifically comprises: solving an inverse matrix of a covariance matrix of a measurement prediction residual by combining the prediction covariance matrix and a measurement noise covariance matrix, and calculating an optimal weighting matrix; calculating a measurement prediction result through the nonlinear measurement model based on the current state prediction value, and comparing the measurement prediction result with the actually collected radar observation data to obtain a deviation; linearly weighting the deviation using the optimal weighting matrix, and applying a compensation value after the weighting adjustment to the state prediction vector to complete the estimation of the augmented state vector; updating a state estimation covariance matrix based on the optimal weighting matrix, a partial derivative matrix of the measurement function and the prediction covariance matrix.

3. The low-grazing-angle multipath effect real-time compensation method of claim 1, wherein, The method further comprises noise covariance matrix initialization, specifically comprising: configuring a process noise covariance matrix in the state transition process to represent the uncertainty of the state prediction model; configuring a measurement noise covariance matrix in the observation process according to the measurement accuracy of the radar sensor to represent the uncertainty of the radar observation data; based on the process noise covariance matrix and the measurement noise covariance matrix, dynamically weighting and balancing the confidence between the prediction value and the observation value in the filtering process.

4. The low-grazing-angle multipath effect real-time compensation method of claim 1, wherein, The filtering and updating of the state prediction vector and the prediction covariance matrix further comprises model linearization, specifically comprising: A partial derivative matrix of the state transition function with respect to the augmented state vector is calculated to obtain a linear approximation of the state transition function; A partial derivative matrix of the measurement function with respect to the augmented state vector is calculated to obtain a linear approximation of the measurement function; The linear approximations of the state transition function and the measurement function are used to perform covariance matrix prediction and update calculation of the augmented state Kalman filter.

5. A low angle multipath effect real-time compensation system, characterized in that, The low-grazing-angle multipath effect real-time compensation method of any one of claims 1 to 4, wherein the system comprises: a state vector construction module configured to establish an augmented state vector, the augmented state vector comprising target motion state parameters and pitch angle error oscillation characteristic parameters; a model establishment module configured to establish a state transition model of the augmented state vector and a nonlinear measurement model, wherein the nonlinear measurement model represents a pitch angle observation as a sum of a true pitch angle of the target and an error term composed of the pitch angle error oscillation characteristic parameters; a state prediction module configured to predict a state prediction vector and a prediction covariance matrix at a current time according to the state transition model and a state estimation value at a previous time; a filter update module configured to perform filter update on the state prediction vector and the prediction covariance matrix based on the nonlinear measurement model and actual observation of the radar at the current time, and output a target state estimation value and a multipath oscillation characteristic parameter estimation value after multipath error compensation.

6. An electronic device, comprising: The electronic device comprises a processor and a memory connected with the processor in communication; wherein the memory stores instructions executable by the processor, and the instructions are executed by the processor to enable the processor to perform the steps of the low-grazing-angle multipath effect real-time compensation method of any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program for implementing the low-grazing-angle multipath effect real-time compensation method, and the program is executed by the processor to implement the steps of the low-grazing-angle multipath effect real-time compensation method of any one of claims 1 to 4.

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