A secondary radar track filtering method based on improved least square method

Abstract

The application relates to the technical field of secondary radar monitoring, and discloses a secondary radar track filtering method based on an improved least square method, which comprises the following steps: firstly, measuring the azimuth and distance of a target through a secondary radar; converting the coordinates of the target from polar coordinates into plane rectangular coordinates; filtering the track of the target through the improved least square filtering algorithm; converting the coordinates of the target from the plane rectangular coordinates into polar coordinates; and outputting the track of the target. The application can effectively improve the track filtering effect of the secondary radar.

Description

Technical Field

[0001] This invention relates to the field of secondary radar surveillance technology. Background Technology

[0002] Secondary radar monitors the flight paths of military and civilian aircraft using an interrogation-response mechanism, acquiring information such as target location, distance, and target code to provide data support for air traffic control. However, in real-world environments, secondary radar measurement systems are susceptible to random noise generated by external environmental factors and the equipment's own condition, affecting the accuracy of target trajectory measurements. Furthermore, the complex flight maneuvers of military and civilian aircraft can also degrade the accuracy of secondary radar trajectory measurements. Therefore, trajectory processing is necessary for secondary radar measurement systems to improve their accuracy.

[0003] Track filtering plays a crucial role in secondary radar track processing. It uses filtering algorithms to optimally estimate the target's detected position and updates the target's position based on this estimate. By employing filtering algorithms, the influence of random noise can be reduced, resulting in a more accurate target location.

[0004] Currently, there are three main algorithms for secondary radar track filtering: least squares filtering, α-β filtering, and Kalman filtering. For the least squares filtering algorithm, the secondary radar track filtering method found in publicly available literature is as follows: The coordinate system of the detected and tracked target is transformed from cylindrical coordinates to Cartesian coordinates. Then, each component in the Cartesian coordinate system is combined with time to form three sets of two-dimensional data. Next, each set of two-dimensional data is filtered to obtain the filtered values ​​in three directions. Finally, the filtered values ​​in the three directions are synthesized to obtain the filtered track. For the α-β filtering algorithm, the secondary radar track filtering method found in publicly available literature is as follows: The radial distance and detection time of the target are acquired for three consecutive detection cycles. The radial velocity of the target in the third detection cycle is calculated based on the radial distance and detection time of the first three detection cycles. The change in radial velocity is calculated based on the radial velocity in the second and third detection cycles. The α-filter coefficient is set to adaptively filter non-maneuvering and maneuvering targets by judging whether the change in radial velocity and the radial velocity in the second and third detection cycles meet preset conditions. Regarding the Kalman filter algorithm, the secondary radar track filtering method currently available in publicly available literature is as follows: First, the target's coordinate system is converted from polar coordinates to a Cartesian coordinate system. Then, each component in the Cartesian coordinate system is combined with time to form two sets of two-dimensional data. Next, the state equation and observation equation for the secondary radar track filtering are established, and track filtering is performed according to the recursive process of Kalman filtering. Finally, the filtered values ​​in the two directions are synthesized to obtain the filtered track.

[0005] The interactive multiple model algorithm proposed by Bolm and Bar-Shalom features Markov transition probabilities and involves multiple models operating in parallel. It obtains target state estimates through the interaction of multiple filters, exhibiting good adaptability and typically achieving better filtering results than a single filter. Based on the retrieved public literature, it has not yet been applied to the field of secondary radar surveillance technology.

[0006] In existing technologies, the least squares method is suitable for tracking maneuvering targets within a small range, and its tracking accuracy is superior to other filtering algorithms when the target is maneuvering and turning. However, its filtering effect is poor when the target is in linear motion. The α-β filtering algorithm is suitable for filtering non-maneuvering targets, but its error is relatively large when used for filtering maneuvering targets. The linear Kalman filter algorithm is suitable for targets in uniform linear motion or uniformly accelerated linear motion. If the moving target needs to be described by multiple maneuvering target models, it is difficult to achieve good filtering results by using only the linear Kalman filter algorithm, which is suitable for a single motion model, to filter the target track. Summary of the Invention

[0007] To address the issue that filtering algorithms in secondary radar track processing cannot simultaneously consider the accuracy of track filtering when the target is maneuvering and turning within a small range and is in multiple motion modes, this invention proposes a secondary radar track filtering method based on an improved least squares method, which can improve the filtering effect of secondary radar tracks.

[0008] To achieve the above objectives, the technical solution of the present invention includes:

[0009] Step 1: Measure the target's azimuth and distance using secondary radar;

[0010] Step 2: Convert the target's coordinates from polar coordinates to Cartesian coordinates;

[0011] Step 3: Filter the target track using the proposed improved least squares filtering algorithm;

[0012] Step 4: Convert the target's coordinates from Cartesian coordinates to polar coordinates;

[0013] Step 5: Output the target's trajectory.

[0014] The beneficial effects of this invention are as follows: the improved least squares filtering algorithm uses multiple maneuvering target models to describe the motion state of the maneuvering target, which to some extent overcomes the problem of large estimation errors when describing the target motion state using a single model. Furthermore, weighting the quadratic curve fitting values ​​with the linear curve fitting values ​​improves the trajectory filtering effect when the target is making small-range turns; weighting the filtering results of multiple maneuvering target models with the filtering results of the curve fitting least squares filtering algorithm also gives the proposed trajectory filtering algorithm good robustness. Attached Figure Description

[0015] Figure 1 This is a flowchart of the invention;

[0016] Figure 2 This is a flowchart of the improved least squares filtering algorithm. Detailed Implementation

[0017] The technical solution of the present invention will now be clearly and completely described in conjunction with the accompanying drawings and embodiments thereof.

[0018] The preferred implementation process and flow of the present invention are as follows: Figure 1 As shown, the specific steps are as follows:

[0019] Step 1: Measure the target's azimuth and distance using secondary radar;

[0020] Step 2: Convert the target's coordinates from polar coordinates to Cartesian coordinates. The specific calculation formula is as follows:

[0021]

[0022] In the formula, d1(k) is the distance of the target relative to the secondary radar at time k, and az1(k) is the azimuth of the target relative to the secondary radar at time k;

[0023] Step 3: Filter the target track using the proposed improved least squares filtering algorithm. Refer to the detailed procedure below. Figure 2 The observation equations and measurement equations for the uniform linear motion model and the uniformly accelerated linear motion model are as follows:

[0024]

[0025] Among them B i (k) is the state vector of the i-th model at time k; W i (k) is the process noise of the i-th model at time k; C i (k) is the observation vector at time k, C i (k)=[x1(k),y1(k)] T V i(k) is the observation noise of the i-th model at time k; g and f are nonlinear functions.

[0026] The improved least squares filtering algorithm proposed in step 3 includes the following steps:

[0027] Step 3-1: Perform curve fitting using the current x-axis observation x(k) and A previous historical observations, and the current y-axis observation y(k) and A previous historical observations, respectively, to obtain the fitted value S. x2 (k), S x1 (k), S y2 (k), S y1 (k), where S x2 (k) represents the quadratic curve fitting value of the x-axis observation at the current time, S x1 (k) represents the first-order curve fitting value of the x-axis observation at the current time, S y2 (k) represents the quadratic curve fitting value of the current y-axis observation, S y1 (k) is the first-order curve fitting value of the y-axis observation at the current time;

[0028] Step 3-2: Calculate the filtered value of the x-axis observation obtained by curve fitting at the current time. Filtered value of the y-axis observation obtained by curve fitting at the current time. The formula is as follows:

[0029]

[0030] Where α is the proportion of observed values ​​and β is the proportion of values ​​fitted to the first-order curve.

[0031] Step 3-3: Initialize the parameters of the filtering model, including: the scanning period T of the secondary radar. SSR Secondary radar ranging standard deviation Secondary radar direction finding standard deviation Covariance of process noise Covariance of observation noise Posterior estimation of the initial state vector Posterior estimate of error covariance P i (1|1)(i=1,2); Model probability v; Transition probability p from model i to model j ij ;

[0032] Steps 3-4: Estimating the state of the target Compared with the model probability v of each model in the previous step i (k-1) yields the mixed state estimate Covariance estimation P j(k-1|k-1), using the mixed-state estimate as the initial state of the model, the following parameters are obtained:

[0033]

[0034] in Predict the probability (normalization constant) for model j; v ij (k-1|k-1) represents the mixture probability from model i to model j;

[0035] Steps 3-5: Multi-model filtering, including the following sub-steps:

[0036] Step 3-5-1: Obtain 2D+1 Sigma points and their corresponding weights λ through transformation, where D is the dimension of the state vector.

[0037]

[0038] The weights corresponding to the sample points are:

[0039]

[0040] in It is the weight of the mean of the d-th sampling point. It is the weight of the covariance of the d-th sampling point;

[0041] Step 3-5-2: Perform one-step prediction on the Sigma point set, state vector, and covariance matrix:

[0042]

[0043] Step 3-5-3: Predict the Sigma point set again:

[0044]

[0045] Steps 3-5-4: Calculate the predicted observations:

[0046]

[0047] Step 3-5-5: Calculate the observation prediction, information covariance matrix, and cross covariance matrix:

[0048]

[0049] Steps 3-5-6: Calculate the gain:

[0050]

[0051] Step 3-5-7: Update the state and error covariance estimates:

[0052]

[0053] Steps 3-6: Calculate the likelihood function of model j:

[0054]

[0055] in:

[0056]

[0057] Steps 3-7: Update model probabilities v j (k):

[0058]

[0059] in:

[0060]

[0061] Steps 3-8: Calculate the overall state estimate and the overall covariance estimate:

[0062]

[0063] in:

[0064]

[0065] Let x be the x-axis filtered value obtained at time k through multi-model filtering. The y-axis filtered value obtained at time k through multi-model filtering;

[0066] Steps 3-9: Through The final x-axis filtered value x2(k) and y-axis filtered value y2(k) are obtained using the following formulas:

[0067]

[0068] Where η is the proportion of multi-model filter values;

[0069] Step 4: Convert the target's coordinates from Cartesian coordinates to polar coordinates. The specific calculation formula is as follows:

[0070]

[0071]

[0072] Where d2(k) is the distance of the target relative to the secondary radar at the current time after processing by the improved least squares filtering algorithm, and az2(k) is the azimuth of the target relative to the secondary radar at the current time after processing by the improved least squares filtering algorithm.

[0073] Step 5: Output the target's trajectory.

Claims

1. A quadratic radar track filtering method based on an improved least squares method, characterized in that: Step 1: Measure the target's azimuth and distance using secondary radar; Step 2: Convert the target's coordinates from polar coordinates to Cartesian coordinates; Step 3: Filter the target trajectory using the proposed improved least squares filtering algorithm. This algorithm includes two motion models: Model 1 is a uniform linear motion model, and Model 2 is a uniformly accelerated linear motion model. The observation and measurement equations for the uniform linear motion model and the uniformly accelerated linear motion model are as follows: Among them B i (k) is the state vector of the i-th model at time k; W i (k) is the process noise of the i-th model at time k; C i (k) is the observation vector at time k, C i (k)=[x1(k),y1(k)] T V i (k) is the observation noise of the i-th model at time k; g and f are nonlinear functions; the proposed improved least squares filtering algorithm includes: Step 3-1: Perform curve fitting using the observed x(k) at time k and A previous historical observations, and the observed y(k) at time k and A previous historical observations, to obtain the fitted value S. x2 (k), S x1 (k), S y2 (k), S y1 (k), where S x2 (k) is the quadratic curve fitting value of the x-axis observation at time k, S x1 (k) is the first-order curve fitting value of the x-axis observation at time k, S y2 (k) is the quadratic curve fitting value of the y-axis observation at time k, S y1 (k) is the first-order curve fitting value of the y-axis observation at time k; Step 3-2: Calculate the filtered value of the x-axis observation obtained by curve fitting at time k. Filtered value of the y-axis observation obtained by curve fitting at time k. The formula includes: Where α is the proportion of observed values ​​and β is the proportion of values ​​fitted to the first-order curve. Step 3-3: Initialize the parameters of the filtering model, including: the scanning period T of the secondary radar. SSR Secondary radar ranging standard deviation Secondary radar direction finding standard deviation Covariance of process noise Covariance of observation noise Posterior estimation of the initial state vector Posterior estimate of error covariance P i (1|1)(i=1,2); Model probability v; Transition probability p from model i to model j ij ; Steps 3-4: Estimating the state of the target Compared with the model probability v of each model in the previous step i (k-1) yields the mixed state estimate Covariance estimation P j (k-1|k-1), using the mixed-state estimate as the initial state of the model, the following parameters are obtained: in Let v be the predicted probability for model j, and v be the normalization constant. ij (k-1|k-1) represents the mixture probability from model i to model j; Steps 3-5: Multi-model filtering, including: Step 3-5-1: Obtain 2D+1 Sigma points and their corresponding weights λ through transformation, where D is the dimension of the state vector. The weights corresponding to the sample points are: in It is the weight of the mean of the d-th sampling point. It is the weight of the covariance of the d-th sampling point; Step 3-5-2: Perform one-step prediction on the Sigma point set, state vector, and covariance matrix: Step 3-5-3: Predict the Sigma point set again: Steps 3-5-4: Calculate the predicted observations: Step 3-5-5: Calculate the observation prediction, information covariance matrix, and cross covariance matrix: Steps 3-5-6: Calculate the gain: Step 3-5-7: Update the state and error covariance estimates: Steps 3-6: Calculate the likelihood function of model j: in: Steps 3-7: Update model probabilities v j (k): in: Steps 3-8: Calculate the overall state estimate and the overall covariance estimate: in Let x be the x-axis filtered value obtained at time k through multi-model filtering. The y-axis filtered value obtained at time k through multi-model filtering; Steps 3-9: Through The final x-axis filtered value x2(k) and y-axis filtered value y2(k) are obtained using the following formula: Where η is the proportion of multi-model filter values; Step 4: Convert the target's coordinates from Cartesian coordinates to polar coordinates; Step 5: Output the target's trajectory.

2. The quadratic radar track filtering method based on the improved least squares method according to claim 1, characterized in that: The formula for converting the target's coordinates from polar coordinates to Cartesian coordinates in step 2 is as follows: In the formula, d1(k) is the distance of the target relative to the secondary radar at time k, and az1(k) is the azimuth of the target relative to the secondary radar at time k.

3. The quadratic radar track filtering method based on the improved least squares method according to claim 1, characterized in that: The formula for converting the target's coordinates from Cartesian coordinates to polar coordinates in step 4 is as follows: Where d2(k) is the distance of the target relative to the secondary radar at the current time after processing by the improved least squares filtering algorithm, and az2(k) is the azimuth of the target relative to the secondary radar at the current time after processing by the improved least squares filtering algorithm.

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