Low-angle fast target radar multipath effect compensation method based on time sequence characteristics

Abstract

The invention belongs to the technical field of new-generation information, and particularly relates to a low-angle fast target radar multipath effect compensation method based on time sequence characteristics. The method comprises the following steps: acquiring a three-dimensional measurement residual time sequence, performing continuous wavelet transform on a pitching residual sequence in the sequence, reconstructing a pitching multipath error term, and eliminating the pitching multipath error term from the pitching residual sequence to obtain a compensated pitching residual sequence; performing Gaussian test on the compensated pitch residual error sequence, calculating statistics, performing judgment according to an absolute difference between two adjacent statistics, and if iteration is not converged, starting next iteration; and if the iteration converges, outputting the current motion state estimation value and the compensated pitch measurement sequence, and realizing the compensation of the multipath effect of the low-angle fast target radar. According to the invention, effective compensation of the multipath error term of the low-angle fast target can be realized. Not only is front-end hardware modification not involved, but also good adaptability to the environment is achieved.

Description

Technical Field

[0001] This invention relates to the field of next-generation information technology, specifically to a method for compensating for multipath effects in low-angle fast target radar based on time-series characteristics. Background Technology

[0002] In this invention, "low angle" refers to the radar's elevation angle for detecting a target being less than 2°, and "fast" refers to the target's speed being greater than 100m / s.

[0003] Low-elevation target detection is a key challenge for radar equipment, one of the core difficulties being the severe impact of multipath effects. Multipath effects refer to the phenomenon where electromagnetic waves emitted by the radar, after being reflected from the ground or sea surface, reach the target, forming multiple non-linear propagation paths. With low-elevation targets, multipath effects cause distortions in the amplitude and phase of the radar signal, resulting in significant non-Gaussian multipath errors. Angle measurement accuracy can deteriorate to 5 to 6 times or more compared to conventional accuracy.

[0004] To address this issue, academic and engineering communities have conducted relevant research from both front-end hardware and back-end processing perspectives. On the hardware side, phase center stabilization and multipath suppression are achieved through hybrid choke coil antennas. On the processing side, angle measurement errors caused by multipath are suppressed by constructing a compensation factor for the time delay difference between direct and multipath signals.

[0005] However, existing radar multipath effect compensation methods are generally based on single-frame signals to compensate for multipath effects, without considering the continuity of target motion. Furthermore, the compensation factor is highly correlated with factors such as terrain, making it difficult to cover the multipath error compensation requirements of low-angle radar detection in various scenarios. Summary of the Invention

[0006] To address the problems in existing technologies and compensate for the multipath effect of low-angle fast target radar, this application provides a method for compensating for the multipath effect of low-angle fast target radar based on time-series characteristics.

[0007] The following plan will be adopted:

[0008] A method for compensating for multipath effects in low-angle, fast-target radar based on time-series characteristics includes the following steps:

[0009] S100. Obtain the three-dimensional measurement residual time series, including the distance residual series, azimuth residual series and pitch residual series;

[0010] S200. Perform continuous wavelet transform on the pitch residual sequence to reconstruct the pitch multipath error term, and subtract the pitch multipath error term from the pitch residual sequence to obtain the compensated pitch residual sequence.

[0011] S300. Perform a Gaussian test on the compensated pitch residual sequence, calculate the statistic, and compare the absolute difference between two adjacent statistics with the minimum allowable change threshold:

[0012] If the absolute difference between two consecutive statistics is less than the minimum allowable change threshold, the iteration converges, and the current motion state estimate and the compensated pitch measurement sequence are output.

[0013] If the absolute difference between two consecutive statistics is greater than or equal to the minimum allowable change threshold, the iteration has not converged. The next iteration is started, that is, after updating the weights of each measurement point, steps S100, S200 and S300 are executed again.

[0014] Further, step S100 includes the following sub-steps:

[0015] S110. Establish the target motion model:

[0016]

[0017] in, This is a discrete-time index, representing the current time. This indicates the target's motion state at the current moment, including the target's position information. With target speed information ,Right now ;when At time 1, it represents the initial motion state of the target; there is no previous moment. hour, Indicates the previous moment, This indicates the target's state of motion at the previous moment; Represents the state transition function;

[0018] S120. Obtain the target motion state estimate. ;

[0019] S130, Target Trajectory Extrapolation: Based on the target motion state estimate Based on the target motion model, the measurement sequence is obtained. Aligned target trajectory sequence ;in, A positive integer, representing the total number of measurements; Indicates the first Measurement data obtained at each sampling time; Indicates the first The estimated state of the target motion at each moment;

[0020] S140, Measurement Residual Sequence Calculation: Calculate the measurement sequence... With target trajectory sequence By subtracting the values, the measurement residual sequence is obtained. as follows:

[0021] .

[0022] Furthermore, the target motion model is a free-fall model in three-dimensional space, that is:

[0023]

[0024] in, This indicates the target's current location information. This indicates the target speed information at the current moment; This indicates the target's location information at the previous moment; This indicates the target velocity information at the previous moment; For the acceleration of the Earth's core, For discrete time intervals.

[0025] Furthermore, obtain the target motion state estimate. The method is as follows:

[0026] The weighted least squares method is used to obtain the estimated value of the target's motion state:

[0027]

[0028] in, This is an estimate of the target's motion state; The total number of measurements participating in the batch processing. It is an integer, and ; Represents discrete-time index, ; This represents the value of the independent variable that minimizes the function on the right. Represents the time series of the target's motion state; Indicates the transpose operation; For measurement equations; This indicates the target's state of motion at the current moment; For the first The weight matrix of the group measurement; For radar equipment, the measurement vector is... , These are measurement vectors The three components represent the measured values ​​of distance, azimuth, and elevation, respectively.

[0029] Further, step S200 includes the following sub-steps:

[0030] S210. Model the residuals in the measurement residual sequence and decompose them into multipath error terms and Gaussian noise terms;

[0031] S220. Perform continuous wavelet transform on the pitch measurement residual sequence to obtain the pitch measurement residual wavelet coefficients. :

[0032]

[0033] In the formula, It is the generating function of the wavelet transform; It represents the scaling factor, which controls the scaling of the mother wavelet and determines the analysis frequency; The translation factor controls the position of the mother wavelet along the time axis; These are wavelet coefficients, representing the signal at different scales. Translation Time-frequency energy distribution at the location; Indicates the first Time values ​​of each sampling point; In the pitch residual sequence Time residuals;

[0034] Pitch measurement residual wavelet coefficients Decomposed into:

[0035]

[0036] in, These are the wavelet coefficients of the multipath error term in the pitch measurement residuals; The wavelet coefficients of the Gaussian noise term in the pitch measurement residual;

[0037] S230, Reconstructing the pitch multipath error term This enables the estimation of the pitch multipath error term;

[0038]

[0039] in, The wavelet transform generating function is the multipath error term. Indicates time; Indicates the current decomposition level; Indicates the first The first multipath error term at the sampling point Layer wavelet coefficients; Indicates the number of decomposition levels in the wavelet transform;

[0040] S240. Subtract the pitch multipath error term from the pitch residual sequence to obtain the compensated pitch residual sequence:

[0041] The post-compensation pitch residual sequence is ,in,

[0042]

[0043] In the pitch residual sequence Time residuals; In the pitch residual sequence Multipath error term of time residual.

[0044] Furthermore, step S210 is as follows:

[0045] Decompose the residuals in the measurement residual sequence As shown below:

[0046]

[0047] in, This is the multipath error term; This is a Gaussian noise term;

[0048] The multipath error term The calculation is as follows:

[0049]

[0050] in, This is the distance multipath error term; This is the azimuth multipath error term; This is the pitch multipath error term;

[0051] make ;

[0052]

[0053] in, This indicates the magnitude of the pitch multipath error term. The angular frequency representing the pitch multipath error term. The phase of the pitch multipath error term is represented. Indicates the first The time value of each sampling point.

[0054] Further, step S300 includes the following sub-steps:

[0055] S310. Perform a Gaussian test on the compensated pitch residual sequence and calculate the statistic. ;

[0056] Index for iteration count, ;

[0057] when When steps S100 and S200 are executed for the first time, the statistic is calculated. After that, order Then it enters the iteration loop, that is, it executes steps S100, S200, and S300 again;

[0058] when At that time, the statistic was calculated. ;

[0059] S320. Compare the absolute difference between two consecutive statistics with the minimum permissible threshold for change:

[0060] (a) If the absolute difference between two consecutive statistics is less than or equal to the minimum permissible change threshold, i.e. If the iteration converges, proceed to step S330. It is the first The test statistic corresponding to the next iteration; It is the first The test statistic corresponding to the next iteration; It is the minimum allowable change threshold;

[0061] (b) If the absolute difference between two consecutive statistics is greater than or equal to the minimum permissible threshold for change, i.e. If the iteration does not converge, the weights of each measurement point in the batch processing are updated, and the next iteration is started, that is, steps S100, S200, and S300 are executed again.

[0062] S330, Output the current motion state estimate and the compensated pitch measurement sequence.

[0063] Output the current motion state estimate and compensated pitch measurement sequence :

[0064] ;

[0065] ;

[0066] in, For the first The estimated state of the target motion after the next iteration; To compensate for the pitch measurement sequence; For the first The pitch measurement vector estimate after the next iteration; For the first The post-compensation pitch residual sequence after each iteration.

[0067] Furthermore, when updating the weights of each measurement point during batch processing, the specific steps are as follows:

[0068] Initial weights Updated weights It is given by the following formula:

[0069]

[0070] in, Indicates the current decomposition level; Indicates the first The sampling point, the first Weighting step size of layer wavelet coefficients; Indicates the first In the sampling points, the multipath error term, after wavelet decomposition, is at the th sampling point. Wavelet coefficients of the layer; Indicates the first In the sampling points, the Gaussian noise term in the pitch measurement residual is decomposed by wavelet at the th sampling point. Wavelet coefficients of the layer; This indicates the number of decomposition levels in the wavelet transform.

[0071] The beneficial effects of this invention are as follows:

[0072] This application enables effective compensation for multipath error terms in low-angle, fast-moving targets, significantly improving target trajectory accuracy. Compensation for low-angle multipath error terms is achieved through back-end processing of target detection data, representing an optimization of radar system back-end processing methods without requiring modifications to front-end hardware. This results in low deployment costs and suitability for upgrading older and existing equipment. Utilizing the temporal motion characteristics of the fast-moving target itself for multipath error estimation and compensation eliminates reliance on modeling external factors such as terrain and environment, minimizing the impact of environmental changes. It exhibits good adaptability in complex environments such as maritime and urban environments. Attached Figure Description

[0073] Figure 1 This is a flowchart of the low-angle fast target radar multipath effect compensation method based on time-series characteristics in this embodiment;

[0074] Figure 2 This is a graph of low-angle fast target radar measurement data and its true value in this embodiment.

[0075] Figure 3 This is the initial measurement residual sequence of the low-angle fast target radar in this embodiment.

[0076] Figure 4 This is a comparison of the pitch residual sequences before and after removing pitch multipath errors in the first iteration of this embodiment.

[0077] Figure 5 These are the weights of each measurement point after the first iteration in this embodiment.

[0078] Figure 6 This is a comparison chart of the trajectory after multipath error compensation in this embodiment, the true trajectory, and the trajectory without this method.

[0079] Figure 7 This is a comparison chart of the trajectory accuracy after multipath error compensation in this embodiment and the trajectory accuracy without this method. Detailed Implementation

[0080] The present invention will now be described in further detail.

[0081] This invention provides a method for compensating for multipath effects in low-angle, fast-target radar based on time-series characteristics, such as... Figure 1 As shown, the steps include:

[0082] Step S100: Obtain the three-dimensional measurement residual time series, including the distance residual series, azimuth residual series and pitch residual series;

[0083] It includes the following sub-steps:

[0084] S110. Establish the target motion model.

[0085] For fast-moving targets, motion modeling methods such as uniform velocity, uniform acceleration, and two-body model are used to define the target motion model as follows:

[0086]

[0087] in, This is a discrete-time index, representing the current time. This indicates the target's motion state at the current moment, including the target's position information. With target speed information ,Right now ;when At time 1, it represents the initial motion state of the target; there is no previous moment. hour, Indicates the previous moment, This indicates the target's state of motion at the previous moment; Represents the state transition function;

[0088] By defining a target motion model, we can compensate for the information gaps in sensor sampling, transform discrete observations into continuous state trajectories, and predict future states.

[0089] In this embodiment, the target motion model is defined as a free-fall model in three-dimensional space, that is:

[0090]

[0091] in, This indicates the target's current location information. This indicates the target speed information at the current moment; This indicates the target's location information at the previous moment; This indicates the target velocity information at the previous moment; For the acceleration of the Earth's core, For discrete time intervals.

[0092] S120. Obtain the target motion state estimate.

[0093] Batch processing is employed, and the target motion state is estimated using weighted least squares based on the selected target motion model.

[0094]

[0095] in, This is an estimate of the target's motion state; The total number of measurements participating in the batch processing. It is an integer, and ; Represents discrete-time index, ; This represents the value of the independent variable that minimizes the function on the right. Represents the time series of the target's motion state; Indicates the transpose operation; For measurement equations; This indicates the target's state of motion at the current moment; For the first The weight matrix of the group measurement; For radar equipment, the measurement vector is... , These are measurement vectors The three components represent the measured values ​​of distance, azimuth, and pitch, respectively, with the pitch measurement being most affected by multipath effects.

[0096] In this embodiment, the radar measurement data of low-angle fast targets measured by radar and its true value are as follows: Figure 2 As shown, where Figure 2 (a) in the figure represents the distance measurement value; Figure 2 (b) in the figure represents the azimuth measurement value; Figure 2 In the figure, (c) represents the measured elevation angle. The black curve represents the radar's measured data, and the green curve represents the true value. The radar site is located at 100° longitude, 40° latitude, and 0m altitude in the WGS84 coordinate system.

[0097] S130, Target Trajectory Extrapolation

[0098] Based on the target motion state estimate obtained in step S120 Combined with equation (1), the target trajectory is extrapolated to obtain the result relative to the measurement sequence. Aligned target trajectory sequence .in, A positive integer, representing the total number of measurements; Indicates the first Measurement data obtained at each sampling time; Indicates the first The estimated state of the target motion at each moment;

[0099] S140, Measurement Residual Sequence Calculation

[0100] Measurement sequence With target trajectory sequence By subtracting the values, the measurement residual sequence is obtained. as follows:

[0101]

[0102] The measurement residual sequence is a three-dimensional sequence, including the range residual sequence, azimuth residual sequence, and pitch residual sequence, such as... Figure 3 As shown, where Figure 3 (a) in the table represents the distance residual sequence; Figure 3 (b) in the table represents the azimuth residual sequence; Figure 3 (c) in the equation represents the pitch residual sequence.

[0103] Step S200: Perform continuous wavelet transform on the pitch residual sequence to reconstruct the pitch multipath error term, and subtract the pitch multipath error term from the pitch residual sequence to obtain the compensated pitch residual sequence.

[0104] Includes the following sub-steps:

[0105] S210, Residuals in the measurement residual sequence The model is decomposed into a multipath error term and a Gaussian noise term.

[0106] break down As shown below:

[0107]

[0108] in This is the multipath error term; This is a Gaussian noise term;

[0109] Among them, the multipath error term Includes distance multipath error term Azimuth multipath error term and pitch multipath error term ,Right now:

[0110]

[0111] about and Calculation:

[0112] Since multipath reflections primarily occur in the vertical plane where the target and radar line of sight lie, they interfere with measurements in that vertical plane (i.e., elevation angle), while their impact on horizontal measurements (i.e., azimuth angle) is negligible. Range information can remain relatively accurate through techniques such as time-domain filtering. Therefore, the range multipath error term and the azimuth multipath error term can be ignored.

[0113]

[0114] in, This represents the distance multipath error term. Represents the distance dimension. This represents the multipath error term. It is a discrete time series; This represents the azimuth multipath error term. Indicates the azimuth dimension.

[0115] about Calculation:

[0116] Due to pitch multipath error term The modulation characteristics originate from the periodic variation of the geometric path difference with the target motion. A simplified model of the pitch multipath error is derived, and the error model can be approximated in a short time as follows:

[0117]

[0118] in This indicates the magnitude of the pitch multipath error term. The angular frequency representing the pitch multipath error term. The phase of the pitch multipath error term is represented. Indicates the first The time values ​​of each sampling point, these parameters will change with the target's movement, and in the time domain they will exhibit non-stationary oscillations with local characteristics.

[0119] S220. Perform continuous wavelet transform on the pitch measurement residual sequence to obtain the pitch measurement residual wavelet coefficients. :

[0120]

[0121] In the formula, It is the generating function of the wavelet transform; It represents the scaling factor, which controls the scaling of the mother wavelet and determines the analysis frequency; The translation factor controls the position of the mother wavelet along the time axis; These are wavelet coefficients, representing the signal at different scales. Translation Time-frequency energy distribution at the location; Indicates the first Time values ​​of each sampling point; In the pitch residual sequence The residual of time.

[0122] Pitch measurement residual wavelet coefficients Decomposed into:

[0123]

[0124] in The wavelet coefficients are used to represent the multipath error term in the elevation measurement residual. Due to the modulation properties of multipath signals, their energy is concentrated at specific scales and times. The wavelet coefficients of the Gaussian noise term in the pitch measurement residual are used to disperse the energy across the entire time-frequency plane, with relatively low amplitude and uniform distribution.

[0125] S230, Reconstructing the pitch multipath error term This enables the estimation of the pitch multipath error term.

[0126] Based on equation (8), reconstruct the pitch multipath error term in the pitch measurement residual sequence. This allows for the estimation of the pitch multipath error term, where... Generally, 2 to 3 is used.

[0127]

[0128] in, The wavelet transform generating function is the multipath error term. Represents time; in this embodiment, Daubechies wavelet coefficients (a type of wavelet basis function with orthogonality and compact support properties) are used. Indicates the current decomposition level; Indicates the first The first multipath error term at the sampling point Layer wavelet coefficients; This indicates the number of decomposition levels in the wavelet transform.

[0129] S240. Remove pitch multipath error terms from the pitch residual sequence.

[0130] Elimination refers to subtracting the pitch multipath error term from the pitch residual sequence to obtain the compensated pitch residual sequence. ,in,

[0131]

[0132] In the pitch residual sequence Time residuals; In the pitch residual sequence Multipath error term in the time residual. In this embodiment, the pitch residual sequence before and after removing the pitch multipath error in the first iteration is compared as follows: Figure 4 As shown.

[0133] Step S300, pitch multipath error term iterative compensation, is as follows:

[0134] Perform a Gaussian test on the compensated pitch residual sequence, calculate the statistic, and judge based on the absolute difference between two consecutive statistic test results:

[0135] If the absolute difference between two consecutive statistics is less than the minimum allowable change threshold, the iteration converges, and the current motion state estimate and the final compensated pitch measurement sequence are output.

[0136] If the absolute difference between two consecutive statistics is greater than or equal to the minimum allowable change threshold, the iteration has not converged. The next iteration is started, that is, after updating the weights of each measurement point, steps S100, S200 and S300 are executed again.

[0137] Step S300 includes the following sub-steps:

[0138] S310. Perform a Gaussian test on the compensated pitch residual sequence and calculate the statistic. .

[0139] Index for iteration count, It is the first The test statistic corresponding to each iteration is used to quantify the degree of agreement between the pitch residual sequence after compensation and the Gaussian distribution. It is the first The test statistic corresponding to the next iteration;

[0140] The current iteration is in the [number]th iteration. Step, if That is, after executing steps S100 and S200 for the first time, the target state estimate for the current step is obtained. Compensated pitch residual sequence .right Perform a Gaussian test and calculate the statistic. After calculating the statistic Afterwards, order Then it enters the iterative loop, that is, it executes steps S100, S200, and S300 again.

[0141] The current iteration is in the [number]th iteration. Step, if Obtain the target state estimate for the current step. Compensated pitch residual sequence .right Perform a Gaussian test and calculate the statistic. Common Gaussian test methods include the Shapiro-Wilk method, etc.

[0142] S320. Compare the absolute difference between two consecutive statistics with the minimum permissible change threshold (in this step) ):

[0143] (a) If the absolute difference between two consecutive statistics is less than or equal to the minimum permissible change threshold, i.e. If the iteration converges, proceed to step S330. Index for iteration count, It is the first The test statistic corresponding to the next iteration; It is the first The test statistic corresponding to the iteration. This represents the minimum permissible threshold for change between two consecutive statistics. In this embodiment, .

[0144] (b) If the absolute difference between two consecutive statistics is greater than or equal to the minimum permissible threshold for change, i.e. If the iteration fails to converge, the current multipath error estimate is used to assess the degree to which the measurement points are affected by multipath error. Based on this assessment, the weights of each measurement point in the batch processing are updated, and the next iteration begins, i.e., steps S100, S200, and S300 are executed again. Initial weights. Updated weights It is given by the following formula:

[0145]

[0146] in, Indicates the current decomposition level; Indicates the first The sampling point, the first The weight adjustment step size for the layer wavelet coefficients is set to 0.2 in this embodiment. Indicates the first In the sampling points, the multipath error term, after wavelet decomposition, is at the th sampling point. Wavelet coefficients of the layer; Indicates the first In the sampling points, the Gaussian noise term in the pitch measurement residual is decomposed by wavelet at the th sampling point. Wavelet coefficients of the layer; This indicates the number of decomposition levels in the wavelet transform.

[0147] In this embodiment, the weight adjustment of each measurement point after the first iteration is as follows: Figure 5 As shown.

[0148] S330, Output the current motion state estimate and the compensated pitch measurement sequence.

[0149] Output the current motion state estimate and compensated pitch measurement sequence :

[0150]

[0151]

[0152] in, For the first The estimated state of the target motion after the next iteration; To compensate for the pitch measurement sequence; For the first The pitch measurement vector estimate after the next iteration; For the first The post-compensation pitch residual sequence after each iteration.

[0153] Figure 6 This is a comparison chart of the trajectory after multipath error compensation in this embodiment, the true trajectory, and the trajectory without this method. The target trajectory is described using the station-centered coordinate system. The origin is the radar station site (100°E, 40°N, 0m). The X (East), Y (North), and Z (Sky) axes are defined. The green line is the true trajectory, the blue line is the trajectory with this method applied, and the red line is the trajectory without this method applied. Figure 7 The image shows a comparison between the trajectory accuracy after multipath error compensation in this embodiment and the trajectory accuracy without this method. It can be seen that the target trajectory accuracy (root mean square) is improved by 45.2% after compensation.

[0154] While the present invention has been disclosed above with reference to preferred embodiments, these embodiments are not intended to limit the invention. Any equivalent changes or modifications made without departing from the spirit and scope of the invention are also within the scope of protection of the invention. Therefore, the scope of protection of the present invention should be determined by the claims of this application.

Claims

1. A method for compensating for multipath effects in low-angle, fast-target radar based on time-series characteristics, characterized in that, Includes the following steps: S100. Obtain the three-dimensional measurement residual time series, including the distance residual series, azimuth residual series and pitch residual series; S200. Perform continuous wavelet transform on the pitch residual sequence to reconstruct the pitch multipath error term, and subtract the pitch multipath error term from the pitch residual sequence to obtain the compensated pitch residual sequence. S300. Perform a Gaussian test on the compensated pitch residual sequence, calculate the statistic, and compare the absolute difference between two consecutive statistics with the minimum allowable change threshold: If the absolute difference between two consecutive statistics is less than the minimum allowable change threshold, the iteration converges, and the current motion state estimate and the compensated pitch measurement sequence are output. If the absolute difference between two consecutive statistics is greater than or equal to the minimum allowable change threshold, the iteration has not converged. The next iteration is started, that is, after updating the weights of each measurement point, steps S100, S200 and S300 are executed again.

2. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 1, characterized in that, Step S100 includes the following sub-steps: S110. Establish the target motion model: in, This is a discrete-time index, representing the current time. This indicates the target's motion state at the current moment, including the target's position information. With target speed information ,Right now ;when At time 1, it represents the initial motion state of the target; there is no previous moment. hour, Indicates the previous moment, This indicates the target's state of motion at the previous moment; Represents the state transition function; S120. Obtain the target motion state estimate. ; S130, Target Trajectory Extrapolation: Based on the target motion state estimate Based on the target motion model, the measurement sequence is obtained. Aligned target trajectory sequence ;in, A positive integer, representing the total number of measurements; Indicates the first Measurement data obtained at each sampling time; Indicates the first The estimated state of the target motion at each moment; S140, Measurement Residual Sequence Calculation: Calculate the measurement sequence... With target trajectory sequence By subtracting the values, the measurement residual sequence is obtained. as follows: 。 3. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 2, characterized in that, The target motion model is a free-fall model in three-dimensional space, that is: in, This indicates the target's current location information. This indicates the target speed information at the current moment; This indicates the target's location information at the previous moment; This indicates the target velocity information at the previous moment; For the acceleration of the Earth's core, For discrete time intervals.

4. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 3, characterized in that, Obtain the target motion state estimate The method is as follows: The weighted least squares method is used to obtain the estimated value of the target's motion state: in, This is an estimate of the target's motion state; The total number of measurements participating in the batch processing. It is an integer, and ; Represents discrete-time index, ; This represents the value of the independent variable that minimizes the function on the right. Represents the time series of the target's motion state; Indicates the transpose operation; For measurement equations; This indicates the target's state of motion at the current moment; For the first The weight matrix of the group measurement; For radar equipment, the measurement vector is... , These are measurement vectors The three components represent the measured values ​​of distance, azimuth, and elevation, respectively.

5. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 1, characterized in that, Step S200 includes the following sub-steps: S210. Model the residuals in the measurement residual sequence and decompose them into multipath error terms and Gaussian noise terms; S220. Perform continuous wavelet transform on the pitch measurement residual sequence to obtain the pitch measurement residual wavelet coefficients. : In the formula, It is the generating function of the wavelet transform; It represents the scaling factor, which controls the scaling of the mother wavelet and determines the analysis frequency; The translation factor controls the position of the mother wavelet along the time axis; These are wavelet coefficients, representing the signal at different scales. Translation Time-frequency energy distribution at the location; Indicates the first Time values ​​of each sampling point; In the pitch residual sequence Time residuals; Pitch measurement residual wavelet coefficients Decomposed into: in, These are the wavelet coefficients of the multipath error term in the pitch measurement residuals; The wavelet coefficients of the Gaussian noise term in the pitch measurement residual; S230, Reconstructing the pitch multipath error term This enables the estimation of the pitch multipath error term; in, The wavelet transform generating function for the multipath error term. Indicates time; Indicates the current decomposition level; Indicates the first The first multipath error term at the sampling point Layer wavelet coefficients; Indicates the number of decomposition levels in the wavelet transform; S240. Subtract the pitch multipath error term from the pitch residual sequence to obtain the compensated pitch residual sequence: The post-compensation pitch residual sequence is ,in, In the pitch residual sequence Time residuals; In the pitch residual sequence Multipath error term of time residual.

6. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 5, characterized in that, Step S210 is as follows: Decompose the residuals in the measurement residual sequence As shown below: in, This is the multipath error term; This is a Gaussian noise term; The multipath error term The calculation is as follows: in, This is the distance multipath error term; This is the azimuth multipath error term; This is the pitch multipath error term; make ; in, This indicates the magnitude of the pitch multipath error term. The angular frequency representing the pitch multipath error term. The phase of the pitch multipath error term is represented. Indicates the first The time value of each sampling point.

7. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 1, characterized in that, Step S300 includes the following sub-steps: S310. Perform a Gaussian test on the compensated pitch residual sequence and calculate the statistic. ; Index for iteration count, ; when When steps S100 and S200 are executed for the first time, the statistic is calculated. After that, order Then it enters the iteration loop, that is, it executes steps S100, S200, and S300 again; when At that time, the statistic was calculated. ; S320. Compare the absolute difference between two consecutive statistics with the minimum permissible threshold for change: (a) If the absolute difference between two consecutive statistics is less than or equal to the minimum permissible change threshold, i.e. If the iteration converges, proceed to step S330. It is the first The test statistic corresponding to the next iteration; It is the first The test statistic corresponding to the next iteration; It is the minimum allowable change threshold; (b) If the absolute difference between two consecutive statistics is greater than or equal to the minimum permissible change threshold, i.e. If the iteration does not converge, the weights of each measurement point in the batch processing are updated, and the next iteration is started, that is, steps S100, S200, and S300 are executed again. S330, Output the current motion state estimate and the compensated pitch measurement sequence. Output the current motion state estimate and compensated pitch measurement sequence : ； ； in, For the first The estimated state of the target motion after the next iteration; To compensate for the pitch measurement sequence; For the first The pitch measurement vector estimate after the next iteration; For the first The post-compensation pitch residual sequence after each iteration.

8. The method for compensating for multipath effects of low-angle fast target radar based on time-series characteristics according to claim 7, characterized in that, When updating the weights of each measurement point during batch processing, the specific steps are as follows: Initial weights Updated weights It is given by the following formula: in, Indicates the current decomposition level; Indicates the first The sampling point, the first Weighting step size of layer wavelet coefficients; Indicates the first In the sampling points, the multipath error term, after wavelet decomposition, is at the th sampling point. Wavelet coefficients of the layer; Indicates the first In the sampling points, the Gaussian noise term in the pitch measurement residual is decomposed by wavelet at the th sampling point. Wavelet coefficients of the layer; This indicates the number of decomposition levels in the wavelet transform.

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