Kalman filter based radar anti-jamming parameter error state estimation and correction method

Abstract

This invention provides a method for estimating and correcting radar anti-jamming parameter errors based on Kalman filtering. Since radar tracking of targets involves certain observation errors, which can vary due to interference or experimental conditions, the magnitude of these errors directly determines the radar's anti-jamming performance during target locking. This application introduces the Kalman filtering method into the radar target tracking process. Using the acquired target position information and the predicted target position information for the next moment, the Kalman gain is calculated. This gain is then used to correct the predicted target position information for the next moment. By applying the target observation information with optimal weights to the position estimation, the radar obtains the target position estimate when both observation and prediction uncertainties are minimized. This makes radar target tracking more accurate.

Description

Technical Field

[0001] This invention belongs to the field of radar anti-jamming, and in particular relates to a method for estimating and correcting radar anti-jamming parameter error states based on Kalman filtering. Background Technology

[0002] In complex electromagnetic environments, electronic countermeasures against various types of interference require improved radar accuracy in locating targets. Accurate estimation of target status based on parameter error data is crucial for achieving this objective.

[0003] Kalman filtering theory has proven highly effective for target state estimation. Traditional target measurement data primarily focuses on a detection-then-track framework, where data correlation significantly impacts target localization accuracy. However, inaccurate radar ranging and angle measurement can affect target positioning. Multi-sensor fusion techniques require optimizing the weight distribution among sensors. Traditional Euclidean distance methods, considering only linear relationships, result in inaccurate target localization. Summary of the Invention

[0004] The main problem addressed by this invention is how to estimate the state of a radar-tracked target during interference and anti-interference processes. It provides a method for state estimation and correction of radar anti-interference parameter errors based on Kalman filtering.

[0005] To solve the above technical problems, the technical solution adopted is: A method for estimating and correcting radar anti-jamming parameter error states based on Kalman filtering includes the following steps: Step 1: Obtain target location information; Step 2: Predict the target location information at the next moment based on the acquired target location information; Step 3: Based on the acquired target position information and the predicted target position information at the next moment, and considering the uncertainty of observation error during radar interference and anti-interference, calculate the Kalman gain; Step 4: Use Kalman gain to correct the predicted target position information for the next moment during the interference and anti-interference process.

[0006] Furthermore, the method for predicting the target location information at the next moment based on the acquired target location information is as follows: ; This represents the position prediction information at step n. F represents the position information at step n-1, and F is the state transition matrix from step n-1 to step n.

[0007] Furthermore, based on the acquired target position information and the predicted target position information for the next moment, and considering the uncertainty of observation errors during radar interference and anti-interference processes, the method for calculating the Kalman gain is as follows: ; Let be the covariance matrix of the predicted target position at step n, used to describe the volatility of the target position estimation; H is the Jacobian matrix for the transformation between target position information and observation information. Due to the uncertainty of observation error, the observation error differs during interference and anti-interference processes. The observation error refers to the error generated by the measuring instrument during measurement. , Including distance error Direction angle error and pitch angle error It is measurable. This represents the matrix transpose, where K is the Kalman gain and S is the error covariance transition matrix; The probability density function is: ; in, for The mean; ; in, Let Q represent the covariance matrix of the target position at step n-1, and let Q be the uncertainty matrix of the prediction process error, which refers to the unmeasurable error generated during the target's movement due to weather or noise.

[0008] Furthermore, the method for correcting the predicted target position information at the next moment using Kalman gain is as follows: ; in, This represents the amount of change in the observed information of the target. This represents the target's position observation information at step n. This represents the predicted position observation information at step n; K is the Kalman gain. This represents the predicted target location information at the nth step of the prediction process. This represents the corrected target position value at step n. ; ; For the position observation information of the target at step n, This refers to the measurement error that occurs during position observation, according to... Sampling is performed according to a probability density function. , combined The distribution that it follows The probability density function is: ; in, ; Predicted location observation information at step n It refers to the position prediction information of the nth step, expressed in a Cartesian coordinate system. This is converted into position prediction observation information formed by the distance R between the target and the radar, the azimuth angle A, and the elevation angle E. ; in, , , These represent the position prediction information for the nth step, expressed in Cartesian coordinates. This is converted into the predicted range, predicted heading angle, and predicted elevation angle between the target and the radar. The method for correcting the predicted covariance matrix for the next time step using Kalman gain is as follows: .

[0009] Furthermore, for ground targets, the position status information of the ground targets is set as follows: , The covariance matrix Q of the prediction process error is ; The transition matrix F is: .

[0010] Furthermore, for aerial targets, the position status of the aerial targets is set as follows: , The covariance matrix of the prediction process error is: ; State transition matrix: .

[0011] The present invention also provides a radar anti-jamming parameter error state estimation and correction system based on Kalman filtering, which is implemented using the steps of a radar anti-jamming parameter error state estimation and correction method based on Kalman filtering.

[0012] By adopting the above technical solution, the present invention has the following beneficial effects: This invention provides a method for estimating and correcting radar anti-jamming parameter errors based on Kalman filtering. Since radar tracking of targets involves certain observation errors, which can vary due to interference or experimental conditions, the magnitude of these errors directly determines the radar's anti-jamming performance during target locking. This application introduces the Kalman filtering method into the radar target tracking process. Using the acquired target position information and the predicted target position information for the next moment, the Kalman gain is calculated. This gain is then used to correct the predicted target position information for the next moment. By applying the target observation information with optimal weights to the position estimation, the radar obtains the target position estimate when both observation and prediction uncertainties are minimized. This makes radar target tracking more accurate. Attached Figure Description

[0013] Figure 1 This is a system flowchart of the present invention; Figure 2 This is a schematic diagram illustrating the tracking effect; Figure 3 This is a diagram comparing the actual value and the predicted value. Figure 4 This is a diagram illustrating the target's movement trajectory at each stage. Detailed Implementation

[0014] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] The present invention will be further explained below with reference to specific embodiments.

[0016] Figures 1 to 4 This invention illustrates a specific embodiment of a radar anti-jamming parameter error state estimation and correction method based on Kalman filtering, comprising the following steps: Step 1: Obtain target location information.

[0017] In this embodiment, for radar target localization and tracking, the radar's measurement data of the target, including the target's current distance error, azimuth angle error, and elevation angle error, needs to be fused to achieve target state estimation during radar localization and tracking in the process of interference and anti-interference. The radar's measurement data of the target, i.e., the observation information, includes the distance R between the radar and the target, the target's azimuth angle A relative to the radar, and the target's elevation angle E relative to the radar. Since target trajectories are usually described using a Cartesian coordinate system, this application needs to convert the radar's observation information of the target into target position information expressed in a Cartesian coordinate system XYZ. Therefore, the target position information obtained in this embodiment is derived from the observation information.

[0018] Step 2: Predict the target location information at the next moment based on the obtained target location information.

[0019] In this embodiment, the method for predicting the target position prediction information at the next moment based on the acquired target position information is as follows: (1) This represents the position prediction information at step n. F represents the position information at step (n-1), and F is the state transition matrix from step (n-1) to step n; the position information at step (n-1) The initial value is obtained by transforming observation information, and in subsequent iterations, The value is the estimated position result obtained at step n-1, which is the position value corrected based on the position prediction information at step n-1.

[0020] For ground or sea targets, let the target's coordinates be... Its speed is Considering the maneuverability of ground targets, acceleration is not taken into account in the target's state. The Kalman filter principle is used for target position prediction. Assuming the target's motion model is ground-based, the target's current position is calculated based on actual measurement information, expressed as range R, direction angle A, and pitch angle E.

[0021] For ground targets, the position status information of the ground targets is set as follows: , Depend on The transition matrix F for ground or sea targets can be derived as follows: .

[0022] The time interval for observing the target's motion.

[0023] For the motion state of aerial targets, which may exhibit strong maneuverability, acceleration is considered, and the position information of the aerial target is set as follows: ,Depend on The state transition matrix F of the airborne target can be derived as follows: .

[0024] Step 3: Calculate the Kalman gain based on the acquired target position information and the predicted target position information at the next moment, and considering the uncertainty of observation error during radar interference and anti-interference.

[0025] In this embodiment, the method for calculating the Kalman gain is as follows: ; Let be the covariance matrix of the predicted target position at step n, used to describe the volatility of the target position estimation; H is the Jacobian matrix for the transformation between target position information and observation information. Due to the uncertainty of observation error, the observation error differs during interference and anti-interference processes. The observation error refers to the error generated by the measuring instrument during measurement. , Including distance error Direction angle error and pitch angle error It is measurable. This represents the matrix transpose, where K is the Kalman gain and S is the error covariance transition matrix; The probability density function is: ; in, for The mean.

[0026] Taking the distribution type Swerling I-II that the radar cross-section (RCS) follows as an example, let RCS be the variable r, then , for The mean value is derived from the relationship between RCS and the root mean square of parameter error. , Since it is a constant, substituting it into the equation yields... .

[0027] ; in, Let Q represent the covariance matrix of the target position at step n-1, and let Q be the uncertainty matrix of the prediction process error, which refers to the unmeasurable error generated during the target's movement due to weather or noise.

[0028] In this embodiment, for ground targets, the position status information of the ground targets is set as follows: , Q is the covariance matrix of the predicted process error displacement and velocity: that is... ; in, ; From the initial position At sampling interval The position after Indicates the initial velocity. For acceleration, For the initial velocity At sampling interval The speed after that, For speed exist Components on the axis, For speed exist Components on the axis, express and The covariance function.

[0029] The change in target position is related to the target's velocity and displacement. Starting from the angle at which the target changes position due to a certain force, the force acting on the object is related to the target's acceleration. The uncertainty of acceleration is the source of uncertainty in process error. In this embodiment, it is assumed that the variance of the process error (acceleration) is... , Let be the standard deviation of the process error. The process error refers to the unmeasurable error caused during the experiment due to weather conditions, noise, acceleration, deceleration, turning, etc., of the target's motion. Velocity and displacement follow a normal distribution with a mean of 0. Therefore, the velocity can be derived using probability theory. variance is displacement variance , and Displacement and velocity in different directions are independent. The covariance of velocity and displacement can be calculated using the formula... Calculations show that, yes The mean function.

[0030] by For example: ; Therefore, for ground targets, the covariance matrix of the prediction error is: .

[0031] In this embodiment, assuming the radar is at the origin in three-dimensional space, the target position is... Based on the target's observation information, including the distance R, azimuth angle A, and elevation angle E, as well as the relationship between the observation information and the position coordinates, we can obtain: ; The observation equation is then: ; Jacobian matrix for converting target location information into observation information H It can be represented as: .

[0032] In this embodiment, for aerial targets, the position state of the aerial target is set as follows: , The covariance matrix of the prediction process error is: .

[0033] The Jacobian matrix H of the aerial target is: .

[0034] Step 4: Use Kalman gain to correct the predicted target position information for the next moment during the interference and anti-interference process.

[0035] Taking radar equipment striking ground or sea targets as an example, the entire tracking process can be divided into three stages. In the first stage, the radar begins searching for and detecting the target; in the second stage, the radar is interfered with by the target and deviates from the target; in the third stage, the radar uses anti-jamming technology to search for and lock onto the target again.

[0036] Under interference conditions, the observation error refers to the error generated by the measuring instrument during measurement, including distance error, orientation angle error, and pitch angle error, which is measurable. Let's assume, without loss of generality, that the uncertainty of the measurement error... The radar tracking of the target during the jamming process is divided into three stages.

[0037] ; When calculating the Kalman gain, different measurement error uncertainties are used in three different stages. This makes position correction more accurate when using Kalman gain.

[0038] In this embodiment, the method for correcting the predicted target position information at the next moment using Kalman gain during the interference and anti-interference process is as follows: ; in, This represents the amount of change in the observed information of the target. This represents the actual position observation information of the target at step n. This represents the predicted position observation information at step n. The observation information consists of the distance R between the radar and the target, the target's azimuth angle A relative to the radar, and the target's elevation angle E relative to the radar. The position information is represented by coordinates XYZ in a Cartesian coordinate system; K is the Kalman gain. This represents the predicted target location information at the nth step of the prediction process. This represents the corrected target position value at step n. ; ; For the position observation information of the target at step n, This refers to the measurement error that occurs during position observation, according to... Sampling is performed according to a probability density function. , combined The distribution that it follows The probability density function is: ; in, .

[0039] Predicted location observation information at step n It refers to the position prediction information of the nth step, expressed in a Cartesian coordinate system. This is converted into position prediction observation information formed by the distance R between the target and the radar, the azimuth angle A, and the elevation angle E. .

[0040] in, , , These represent the position prediction information for the nth step, expressed in Cartesian coordinates. This is converted into the predicted distance, predicted azimuth angle, and predicted elevation angle between the target and the radar.

[0041] The updated location information is as follows: ; From the formula for calculating the Kalman gain coefficient K above, it can be seen that K is related to H, where H is the Jacobian matrix for the transformation between target position information and observation information. Therefore... Although it is a change in the target observation information, it is converted into position information in a Cartesian coordinate system after being multiplied by the Kalman gain coefficient.

[0042] The method for correcting the predicted covariance matrix for the next time step using Kalman gain is as follows: ; For ground targets, I is a 4th-order identity matrix, and for air targets, I is a 9th-order identity matrix.

[0043] The formula for calculating the next predicted location information is: ; The new covariance matrix for predicting the next location information can be obtained: .

[0044] In this embodiment, the inherent observation error during radar target tracking is considered. Generally, radar or radar equipment provides a reference value after leaving the factory, but in actual testing environments, the observation error can vary due to interference or testing conditions. During radar target locking, the magnitude of the observation error directly determines the radar's anti-jamming target tracking performance. Kalman filtering plays a crucial role in radar target tracking. By considering the uncertainty of measurement error in the Kalman gain and using different uncertainties of measurement error at different stages of radar tracking, it integrates range error, azimuth error, and elevation error from the radar measurement process, thereby making the position estimation information more accurate. The more precise the observation error, the more accurate the state estimation method based on Kalman filtering.

[0045] Taking radar equipment striking ground or sea targets as an example, such as a radar seeker striking a moving ship, the entire tracking process can be divided into three stages. In the first stage, the radar detects the target and begins flying towards it. In the second stage, the radar is interfered with by ship jammers and deviates from the target. In the third stage, the radar seeker uses anti-jamming measures to re-track the target and hit it. Under jamming conditions, the observation error will vary significantly. Let's assume that the uncertainty of the measurement error... Target tracking by radar is divided into three phases. The root mean square error in the initial search phase is... The root mean square error of the radar during the jamming phase is The root mean square of the radar during the successful anti-jamming phase is By incorporating the uncertainty of measurement error into the Kalman gain and using different measurement error uncertainties at different stages of radar tracking, the range error, azimuth error, and elevation error in the radar measurement process are integrated, thereby making the position estimation information more accurate.

[0046] This embodiment introduces the Kalman filtering method into the radar target tracking process. Using the acquired target position information and the predicted target position information for the next moment, the Kalman gain is calculated at different stages during interference and anti-interference processes. The Kalman gain is then used to correct the predicted target position information for the next moment. Target observation information is applied to the position estimation with optimal weights, thereby obtaining the radar's target position estimate when both observation and prediction uncertainties are minimized. This makes the radar's target tracking process more accurate.

[0047] Experimental verification When the radar is stationary, it is effective at tracking ground and air targets.

[0048] First, the nonlinear Kalman filtering process for ground targets is explained. Assume a total duration of t = 40 seconds, an initial covariance matrix of P = I * 100, and the standard deviation of the process error... =0.05, measurement error The standard deviations of distance, pitch angle, and azimuth angle in the data. =10, =0.0001 =0.0001.

[0049] According to the nonlinear Kalman filter algorithm, the tracking result is as follows: Figure 2 As shown, the predicted estimate is getting closer and closer to the actual target trajectory.

[0050] When dealing with an aerial target, assuming a total duration of t = 40 seconds, the target's motion is measured every 0.005 seconds, with an initial acceleration of 0 and an initial covariance matrix of P = I * 10. The standard deviation of the process error is... =0.1, measurement error The standard deviations of distance, pitch angle, and azimuth angle in the data. =10, =0.01, =0.01. According to the nonlinear Kalman filter algorithm, the tracking result is as follows: Figure 3 As shown, the predicted value of the aerial target is very close to the target's actual flight trajectory.

[0051] The process of tracking ground targets while the radar is in motion, during interference and anti-interference operations.

[0052] When a moving radar strikes a ground target, assuming the time from radar emission to target impact is 70 seconds, and the target's motion relative to the radar is measured every 0.005 seconds, where the radar initially tracks the target for t=20 seconds, the measurement error at this time is... The radar is interfered with for a period of t = 20s-40s; the measurement error during this time is... The radar finally regained control of the target after 40s-70s, and the measurement error at this point... The initial acceleration is 0, the initial covariance matrix is ​​P=I*10, and the standard deviation of the process error is... =0.1, measurement error The variance of distance, heading angle and pitch angle in , , .like Figure 4 The results of the radar and target trajectory are shown. When there is no interference, the radar predicts a trajectory that tracks the target. However, after interference, the radar deviates from the target, but with anti-jamming measures, it gradually tracks back to the target. It can be seen that the radar slowly flies towards the target, eventually successfully tracking and hitting it.

[0053] In the experiment, since radar observation data can only be obtained through simulation, the target position information in step 1 was calculated using the following method:

[0054] This indicates the preset position information for step n. Let F represent the target position after the correction at step n-1, and F be the state transition matrix from step n-1 to step n. Indicates process error, with 0 as the mean and... The random number is the standard deviation. Process error is the unmeasurable error caused by weather or noise, the acceleration, deceleration, turning, etc. of the target movement during the test.

[0055] The present invention also provides a radar anti-jamming parameter error state estimation and correction system based on Kalman filtering, which is implemented using the steps of a radar anti-jamming parameter error state estimation and correction method based on Kalman filtering.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating and correcting radar anti-jamming parameter error states based on Kalman filtering, characterized in that, Step 1: Obtain target location information; Step 2: Predict the target location information at the next moment based on the acquired target location information; Step 3: Based on the acquired target position information and the predicted target position information at the next moment, and considering the uncertainty of observation error during radar interference and anti-interference, calculate the Kalman gain; Step 4: Use Kalman gain to correct the predicted target position information for the next moment during the interference and anti-interference process.

2. The radar anti-jamming parameter error state estimation and correction method based on Kalman filtering according to claim 1, characterized in that, The method for predicting the target's position information at the next moment based on the acquired target position information is as follows: ； This represents the position prediction information at step n. F represents the position information at step n-1, and F is the state transition matrix from step n-1 to step n.

3. The radar anti-jamming parameter error state estimation and correction method based on Kalman filtering according to claim 2, characterized in that, Based on the acquired target position information and the predicted target position information for the next moment, and considering the uncertainty of observation errors during radar interference and anti-interference processes, the method for calculating the Kalman gain is as follows: ； in, Let be the covariance matrix of the predicted target position at step n, used to describe the volatility of the target position estimation; H is the Jacobian matrix for the transformation between target position information and observation information. Due to the uncertainty of observation error, the observation error differs during interference and anti-interference processes. The observation error refers to the error generated by the measuring instrument during measurement. , Including distance error Direction angle error and pitch angle error It is measurable. This represents the matrix transpose, where K is the Kalman gain and S is the error covariance transition matrix; The probability density function is: ; in, for The mean; ； in, This represents the covariance matrix of the target position corrected at step n-1, and Q is the uncertainty matrix of the prediction process error, which refers to the unmeasurable error generated when the target moves due to weather or noise.

4. The radar anti-jamming parameter error state estimation and correction method based on Kalman filtering according to claim 3, characterized in that, The method for correcting the predicted target position information at the next time step using Kalman gain is as follows: ； in, This represents the amount of change in the observed information of the target. This represents the target's position observation information at step n. This represents the predicted position observation information at step n; K is the Kalman gain. This represents the predicted target location information at the nth step of the prediction process. This represents the corrected target position value at step n. ； ； For the position observation information of the target at step n, This refers to the measurement error that occurs during position observation, according to... Sampling is performed according to a probability density function. , combined The distribution that it follows The probability density function is: ； in, ; Predicted location observation information at step n It refers to the position prediction information of the nth step, expressed in a Cartesian coordinate system. This is converted into position prediction observation information formed by the distance R between the target and the radar, the azimuth angle A, and the elevation angle E. ； in, , , These represent the position prediction information for the nth step, expressed in Cartesian coordinates. This is converted into the predicted range, predicted heading angle, and predicted elevation angle between the target and the radar. The method for correcting the predicted covariance matrix for the next time step using Kalman gain is as follows: .

5. The radar anti-jamming parameter error state estimation and correction method based on Kalman filtering according to claim 3, characterized in that, For ground targets, the position status information of the ground targets is set as follows: , The covariance matrix Q of the prediction process error is ； The transition matrix F is: 。 6. The radar anti-jamming parameter error state estimation and correction method based on Kalman filtering according to claim 3, characterized in that, For aerial targets, the position state of the aerial target is set as follows: , The covariance matrix of the prediction process error is: ； State transition matrix: 。 7. A radar anti-jamming parameter error state estimation and correction system based on Kalman filtering, characterized in that, The method is implemented using the steps of the radar anti-jamming parameter error state estimation and correction method based on Kalman filtering as described in any one of claims 1 to 6.

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