Target motion modeling and filtering method based on infrared fisheye warning system

Abstract

The application provides a target motion model simplification method and filtering algorithm based on an infrared fisheye warning system, and specifically comprises the following steps: by virtue of the short sampling period of the infrared fisheye warning system and with the aid of the Maclaurin formula, the state transition matrix and the system process noise covariance matrix of a current statistical model are simplified to obtain a simplified current statistical model; meanwhile, the weak maneuverability of a target on an image plane in the infrared fisheye warning system is utilized to simplify the one-step prediction formula of the target state in the Kalman filtering algorithm. Through the above model simplification method and filtering algorithm, the calculation amount in the target tracking process can be greatly reduced, the calculation time consumption is shortened, the real-time processing of the system is facilitated, and the simulation verification can meet the target tracking precision requirement.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, specifically to a method for simplifying and filtering a target motion model based on an infrared fisheye warning system. Background Technology

[0002] Infrared fisheye detection and warning systems are developed based on ultra-wide-angle fisheye lens technology and infrared focal plane array technology. They cleverly combine the omnidirectional staring characteristics of fisheye lenses with the all-weather operation of infrared systems, enabling them to track and warn of threatening targets in the hemispherical airspace from all directions and in all weather conditions. Target tracking is a crucial aspect of the warning system's intelligence, and target motion modeling is one of the fundamental problems that needs to be solved in target tracking.

[0003] The Current Statistics Model (CS model) uses a non-zero mean and a modified Rayleigh distribution to characterize the properties of maneuvering acceleration, thus better reflecting the actual maneuvering of targets and making it a better practical model for describing the motion of maneuvering targets. Currently, the common practice in existing technologies is to combine the CS model with the standard Kalman filter method to perform a one-step prediction of acceleration. Viewed as "current" acceleration The mean value of random maneuver acceleration is used to obtain a Kalman filter method based on the CS model that adaptively adjusts the variance of maneuver acceleration. Numerous experiments have shown that the Kalman filter method based on the CS model has good tracking results when tracking maneuvering targets.

[0004] Nevertheless, due to the introduction of the relatively complex CS model, the above-mentioned Kalman filtering method based on the CS model has the problem of large computational load. If the computational load can be reduced while ensuring its tracking accuracy, it will be beneficial to the real-time processing and engineering implementation of the system. Summary of the Invention

[0005] To address the issue of high computational complexity in the Kalman filtering method based on the CS model mentioned above, this invention provides a target motion model simplification method and filtering method based on an infrared fisheye alarm system. By utilizing the characteristics of the infrared fisheye alarm system, the aforementioned Kalman filtering method based on the CS model is simplified, reducing the computational load and facilitating real-time processing and engineering implementation of the system.

[0006] The first aspect of this invention provides a method for simplifying a target motion model based on an infrared fisheye warning system. The technical solution is as follows: A method for simplifying a target motion model based on an infrared fisheye warning system includes the following steps:

[0007] S11, determine the discrete form of the current statistical model;

[0008] S12, based on the short sampling period of the infrared fisheye alarm system, adjust the state transition matrix of the current statistical model. and system process noise covariance matrix After simplification, we obtain the simplified state transition matrix. and system process noise covariance matrix ;

[0009] S13, the simplified state transition matrix and system process noise covariance matrix Substitute back into the current statistical model to obtain the simplified model of the current statistical model.

[0010] Furthermore, S12 also includes the following steps:

[0011] S121, It is determined that the sampling period value T of the infrared fisheye alarm system is much less than 1 second;

[0012] S122, According to the Maclaurin formula, the state transition matrix of the current statistical model... and system process noise covariance matrix Simplify the exponential operations involved in the process;

[0013] S123, Substitute the simplified result of the exponential operation in S122 into the state transition matrix of the current statistical model. and system process noise covariance matrix Simplify;

[0014] S124. Based on the characteristic that the sampling period T is much less than 1 second, the simplified result of S123 is further simplified to obtain the simplified state transition matrix. and system process noise covariance matrix .

[0015] Furthermore, the state transition matrix of the current statistical model and system process noise covariance matrix The simplified result of the exponential operations involved is as follows:

[0016] ,

[0017] ;

[0018] The result of further simplification of the simplified result of S123 is as follows:

[0019] , .

[0020] A second aspect of this invention provides a target motion model filtering method based on an infrared fisheye warning system. The technical solution is as follows: a target motion model filtering method based on an infrared fisheye warning system, characterized by comprising the following steps:

[0021] S21, combine the current statistical model with the standard Kalman filter equation to obtain a Kalman filter method based on the current statistical model;

[0022] S22, based on the weak maneuverability characteristics of the target moving on the image plane in the infrared fisheye warning system, the one-step prediction formula of the target state in the Kalman filter method based on the current statistical model is simplified.

[0023] S23, the state transition matrix in the Kalman filtering method based on the current statistical model is... and system process noise covariance matrix Replace it with the simplified state transition matrix obtained by any one of the first aspects of the present invention. and system process noise covariance matrix ;

[0024] S24 yields the simplified Kalman filter method.

[0025] Furthermore, S22 also includes:

[0026] S221: Based on the weak maneuverability of the target's movement on the image plane in the infrared fisheye warning system, we obtain... ,in Let be the mean acceleration at time k+1. The acceleration estimate at time k+1 is the predicted value. This is the estimated acceleration value at time k;

[0027] S222: Will Substituting the target state prediction formula into the Kalman filter method based on the current statistical model, and simplifying it, we get... ,in ;

[0028] S223, according to The simplified Kalman filter method yields the one-step prediction formula for the target state. .

[0029] The above-mentioned technical solution of the present invention has the following beneficial effects: Utilizing the characteristic of a very short sampling period in the infrared fisheye alarm system, and with the aid of the McLaurin formula, the state transition matrix in the discrete form of the current statistical model is... and system process noise covariance matrix To simplify the process, the exponential operations involved are not only converted into simpler addition, subtraction, multiplication, and division using the McLaurin formula, but the short sampling period of the infrared fisheye alarm system is also utilized to further simplify the terms with higher powers of T in the polynomial, resulting in a simplified state transition matrix. and system process noise covariance matrix Simultaneously, it also utilizes the weak maneuverability of the target's movement on the image plane in the infrared fisheye warning system, through formula... The one-step prediction formula for the target state in the Kalman filter method is simplified. The simplified filtering method significantly reduces computational complexity, and simulation results demonstrate that it meets the target tracking accuracy requirements. Attached Figure Description

[0030] To more clearly illustrate the technical solutions 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.

[0031] Figure 1 This is a flowchart of a target motion model simplification method based on an infrared fisheye alarm system according to the present invention;

[0032] Figure 2 This invention addresses the state transition matrix in the current statistical model. and system process noise covariance matrix Simplified flowchart;

[0033] Figure 3 This is a flowchart of a target motion model filtering method based on an infrared fisheye alarm system according to the present invention;

[0034] Figure 4 This is a simplified flowchart of the one-step prediction formula for the target state in the Kalman filter method according to the present invention;

[0035] Figure 5 Block diagram of an infrared fisheye alarm system;

[0036] Figure 6 Comparison of the target's motion trajectory and actual trajectory as seen by the infrared fisheye system.

[0037] Figure 7 The filtering method of this invention and the Kalman filtering method based on the CS model have different RMSE values ​​in the x-direction.

[0038] Figure 8 The y-direction position RMSE of the filtering method of the present invention and the Kalman filtering method based on the CS model are compared.

[0039] Figure 9 The difference in RMSE of the x-direction position between the filtering method of this invention and the Kalman filtering method based on the CS model (T=0.02 s);

[0040] Figure 10 The difference in y-direction position RMSE between the filtering method of this invention and the Kalman filtering method based on the CS model (T=0.02 s);

[0041] Figure 11 The difference in RMSE (T=0.1 s) between the filtering method of this invention and the Kalman filtering method based on the CS model in the x-direction position.

[0042] Figure 12 The difference in RMSE of the x-direction position between the filtering method of this invention and the Kalman filtering method based on the CS model (T=0.5 s);

[0043] Figure 13 The difference in RMSE (T=1 s) between the filtering method of this invention and the Kalman filtering method based on the CS model is the position in the x-direction. Detailed Implementation

[0044] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0045] Since the target motion model simplification method and filtering method provided by this invention are based on the current statistical model (hereinafter referred to as CS model) and the Kalman filtering method based on the CS model, and combined with the characteristics of the infrared fisheye alarm system itself, in order to clearly and completely describe the simplification method and filtering method of this invention, the CS model, the Kalman filtering method based on the CS model, and the characteristics of the infrared fisheye alarm system itself will be explained first.

[0046] (a) CS model

[0047] The CS model uses a modified Rayleigh distribution to describe the "current" probability density of maneuver acceleration, with the mean being the predicted "current" acceleration value. Random acceleration still conforms to a first-order time-dependent process on the time axis. Let the state vector be... , For the maneuver frequency, under ideal conditions, Considering that the actual velocity cannot be an absolutely precise constant, its slight variations are described using zero-mean white noise. The state equation of the CS model for a continuous-time system is:

[0048] (1)

[0049] The discrete form of the model is:

[0050] (2)

[0051] in,

[0052] (3)

[0053] (4)

[0054] (5)

[0055] In the formula, W(k) is a discrete-time white noise sequence, and

[0056] (6)

[0057] Its variance is

[0058] (7)

[0059] in,

[0060] (8)

[0061] (9)

[0062] (10)

[0063] (11)

[0064] (12)

[0065] (13)

[0066] (II) Kalman Filtering Method Based on CS Model

[0067] Combining the CS model with the standard Kalman filter method, the one-step prediction of acceleration is improved. Viewed as "current" acceleration This is the mean of the random maneuver acceleration, thus yielding a Kalman filter method based on the CS model for adaptive adjustment of the maneuver acceleration variance. The specific process is as follows:

[0068] (14)

[0069] (15)

[0070] (16)

[0071] (17)

[0072] (18)

[0073] in,

[0074] (19)

[0075] (20)

[0076] The CS model assumes that the maneuvering acceleration at any time follows a modified Rayleigh distribution, from which the variance of the target maneuvering acceleration can be obtained as (21).

[0077] in and These are the known upper positive limit and lower negative limit of the target acceleration, respectively.

[0078] It is evident that the Kalman filter method based on the CS model already possesses the ability to adaptively adjust to process noise based on the acceleration estimate from the previous moment. Since the CS model more realistically reflects the changes in the target's maneuver range and intensity, it is currently a superior practical model. Extensive experiments demonstrate that the Kalman filter method based on the CS model achieves good tracking results when tracking maneuvering targets. However, due to the introduction of the CS model, its form is relatively complex, and the computational load is also significant.

[0079] (III) Inherent characteristics of infrared fisheye alarm systems

[0080] The infrared fisheye alarm system consists of the following components: Figure 1 As shown, the first part of the system is a mid-wave infrared bionic fisheye optical system, which mainly images all infrared radiation in the hemispherical space onto the system's infrared focal plane array; the second part is the data acquisition part, which mainly consists of a cooled tellurium-chromium-mercury infrared focal plane array, whose function is to convert infrared images into electrical signals; the third part is the signal processing unit, which consists of two high-performance DSP processors to complete the relevant methods for target tracking and alarm, and outputs the processed data to the display unit, alarm unit and tracking unit respectively.

[0081] 1. Sampling Period Characteristics of Infrared Fisheye Alarm System. Infrared fisheye systems have a high sampling rate. The embodiments of this invention select a sampling rate typically achievable by infrared fisheye systems, 50 frames / second, i.e., a sampling period T = 0.02 seconds, a value much less than 1. In reality, the sampling period of infrared fisheye systems is generally no greater than 0.04 seconds. According to mathematical principles, if T < 0.04, then... Where n≥1. Therefore, based on the short sampling period characteristic of infrared fisheye alarm systems, while simultaneously containing and The polynomial contains The terms have little impact on the overall result of the polynomial operation and can be omitted or simplified depending on the application.

[0082] 2. Target Motion Characteristics on the Image Plane under an Infrared Fisheye Warning System. The magnitude of the target's motion speed on the image plane depends on the target's own speed, the relative angle between the target's motion direction and the warning system, and the resolution of the infrared warning system. Given a fixed motion angle between the target and the infrared fisheye warning system, the target's motion speed on the image plane is proportional to the spatial resolution of a single detector element. Because the infrared fisheye warning system images infrared image information from a hemispherical spatial domain onto a finite detector array, the spatial resolution of a single detector element is relatively low, thus the target's motion speed on the image plane is relatively slow. For this system, the staring field of view of the infrared fisheye lens is... The actual staring field of view of the system depends on the size of the detector array, which is... The image quality is as follows: The unit staring field of view is 4.363 milliradians, and the system sampling rate is 50 frames per second. Assuming the target is flying at a lateral velocity of 1000 m / s at a warning distance of 10 km, the corresponding angular velocity is 100 milliradians / s. Calculated at a system sampling rate of 50 frames per second, the target's velocity on the image plane is only 0.4584 pixels / frame, meaning the target's velocity on the image plane is extremely slow. If the target were flying at 100 m / s... 2 During acceleration maneuvers, the target's acceleration on the image plane is only 0.0458 pixels / frame, indicating very weak maneuverability. In summary, the target's slow speed and weak maneuverability on the image plane inspire us to use simplified target motion models in target tracking to reduce computational load and thus improve system real-time performance. One-step prediction estimate It can be considered as the mean of the "current" maneuver acceleration at time k+1. That is, the above equation (20) holds true.

[0083] (iv) Simplifying the CS model based on the characteristics of the infrared fisheye alarm system

[0084] Based on the above CS model and the formula for the Kalman filter method based on the CS model, it can be seen that the state transition matrix... and system process noise covariance matrix It contains many , Exponential operations, especially excessive ones, will undoubtedly increase the overall computational load. We can start simplifying the model from this point. The specific steps are as follows:

[0085] S11, Determine the discrete form of the current statistical model, including its state transition matrix. and system process noise covariance matrix ;

[0086] S12, based on the short sampling period of the infrared fisheye alarm system, adjust the state transition matrix of the current statistical model. and system process noise covariance matrix After simplification, we obtain the simplified state transition matrix. and system process noise covariance matrix ;

[0087] S13, the simplified state transition matrix and system process noise covariance matrix Substituting back into the current statistical model, we obtain a simplified model of the target motion model, namely the simplified current statistical model (SCS model).

[0088] Of the above steps, S12 includes the following steps:

[0089] S121, It is determined that the sampling period T of the infrared fisheye alarm system is much less than 1 second. In this embodiment, T=0.02 seconds.

[0090] S122 utilizes the McLaurin formula to expand the exponential operation into a polynomial. Simultaneously considering the short sampling period of the infrared fisheye alarm system, it also includes... and The polynomial contains The terms have little impact on the overall result of the polynomial operation, thus allowing for some simplification of the expanded polynomial. The specific results are as follows:

[0091] (twenty two)

[0092] (twenty three)

[0093] Substituting equations (22) and (23) into equation (8) and rearranging, we get

[0094] (twenty four)

[0095] Similarly:

[0096]

[0097] Right now

[0098] (25)

[0099] Meanwhile, since the sampling period T is very small, following a similar idea, we have

[0100] (26)

[0101] (v) Kalman filtering method based on the characteristics of infrared fisheye alarm system

[0102] In the above simplification of the CS model, the simplified state transition matrix is ​​obtained. and system process noise covariance matrix Based on this, and by combining the motion characteristics of the target on the image plane under the infrared fisheye warning system, a simpler Kalman filtering method can be constructed. The specific steps are as follows:

[0103] S21, combine the current statistical model with the standard Kalman filter equation to obtain the Kalman filter method based on the current statistical model, namely equation (14)-equation (18).

[0104] S22, based on the weak maneuverability characteristics of the target moving on the image plane in the infrared fisheye warning system, the one-step prediction formula of the target state in the Kalman filter method based on the current statistical model is simplified, that is, equation (14) is simplified. The specific steps are as follows:

[0105] S221, Based on the weak maneuverability of the target's movement on the image plane in the infrared fisheye warning system, equation (20) holds. Substituting equation (20) into equation (14) yields...

[0106]

[0107] (27)

[0108] Simplifying the above equation yields

[0109] (28)

[0110] (29)

[0111] (30)

[0112] Written in matrix form as

[0113] (31)

[0114] in, .

[0115] As can be seen from equation (31), under the condition that equation (20) holds, the one-step prediction formula of the target state of the filtering method is greatly simplified.

[0116] S23, adjust the state transition matrix of the Kalman filtering method based on the current statistical model, i.e., equations (14)-(18). and system process noise covariance matrix Replace it with the simplified state transition matrix from equations (25) and (26). and system process noise covariance matrix ;

[0117] S24, the simplified Kalman filter method is obtained as follows:

[0118] (33)

[0119] (34)

[0120] (35)

[0121] (36)

[0122] (37)

[0123] (vi) Simulation experiment verification

[0124] To verify the tracking accuracy and computational time of the proposed method, computer simulation experiments were conducted on several typical target motions (uniform velocity, uniform acceleration, variable acceleration, and circular maneuver), and compared with the Kalman filter method based on the CS model. It was assumed that the target moves laterally in the field of view, the system sampling frequency is 50 frames / second, the distance between the target and the system is 5 kilometers, the target undergoes uniform linear motion with an initial velocity of 10 pixels / second, and variable acceleration motion from T51 to T200 (where the acceleration increment is 0.5 pixels / second from T51 to T100). 3 Between 101T and 150T, the acceleration increment is 1 pixel / s. 3 Between 151T and 200T, the acceleration increment is 1.5 pixels / s. 3From T201 to T800, the motion is uniform circular motion with a centripetal acceleration of 3.5 pixels / s². 2 From T801 to T950, the motion is uniformly accelerated with an acceleration of -3 pixels / s². 2 From T951 to T1000, the motion reverts to uniform linear motion at a velocity of 4.5 pixels / s. In a two-dimensional Cartesian coordinate system, the measurement noise on the X and Y axes is a Gaussian white noise sequence with a mean of zero and an error of 1 pixel, with an observation variance of 0.25 pixels. In the CS model, we take... , Because infrared fisheye systems employ a dissimilar imaging principle, the trajectory of a target in the air will be distorted after being imaged by the infrared fisheye lens. Therefore, the trajectory used for tracking in this simulation experiment is a modified version of the aforementioned trajectory based on the infrared fisheye imaging principle, thus making the experimental results more realistic. Figure 6 As shown in the figure, this diagram illustrates the actual trajectory of the target during its aerial motion and its trajectory on the infrared focal plane after imaging by an infrared fisheye system. The simulation was run 100 times, and the experimental results are as follows: Figures 7-10 As shown, Figure 7 and Figure 8 The root mean square errors (RMSE) of position estimation in the x and y directions of the proposed method and the Kalman filter method based on the CS model are given respectively. Figure 9 and Figure 10 The differences in RMSE between the two methods in the x and y directions are presented separately. Analysis of the simulation results shows that, for an infrared fisheye alarm system with a sampling rate of 50 frames / second, the proposed method achieves tracking accuracy comparable to the Kalman filter method based on the CS model.

[0125] Furthermore, it should be emphasized that the Kalman filtering method based on the SCS model, i.e., the method proposed in this invention, is a simplification of the CS model-based filtering method when the sampling period is small. If the system sampling period becomes larger or becomes large enough, its tracking performance will deteriorate or even become unusable. Therefore, understanding the applicable scope of the SCS model is essential. Figure 9 as well as Figures 11-13The differences in x-direction position RMSE between the proposed method and the Kalman filter-based method using the CS model are presented for sampling periods of 0.02 seconds, 0.1 seconds, 0.5 seconds, and 1 second. Comparative analysis of these four figures shows that the tracking accuracy of both methods decreases with increasing sampling period. Furthermore, the tracking accuracy of the proposed method gradually deteriorates compared to the CS model-based Kalman filter method, becoming more pronounced at a sampling period of 1 second. Therefore, when the sampling period is less than 0.5 seconds, the proposed method achieves tracking accuracy similar to or comparable to the CS model-based Kalman filter method. Since the actual sampling period of an infrared fisheye alarm system is generally no greater than 0.04 seconds, the proposed method fully meets the system's tracking accuracy requirements. Because the proposed method is simpler in form than the CS model filtering method, its computational complexity is reduced.

[0126] Table 1 shows the computation time of the two methods in the process of tracking the above trajectory. As can be seen from the experimental data in the table, the method proposed in this invention reduces the amount of computation and the computation time is reduced by more than 17% while ensuring the tracking accuracy. This is beneficial to the real-time processing of the system.

[0127] Table 1. Comparison of time consumption between the proposed method and the Kalman filter method based on the CS model.

[0128] Methods based on the CS model 0.126618 0.018540 0.003602 0.001793 The method of the present invention 0.104565 0.015287 0.002975 0.001476 Time saved percentage / % 17.42 17.55 17.41 17.68

[0129] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for simplifying the target motion model based on an infrared fisheye alarm system, characterized in that, Includes the following steps: S11, determine the discrete form of the current statistical model; S12, based on the short sampling period of the infrared fisheye alarm system, adjust the state transition matrix of the current statistical model. and system process noise covariance matrix After simplification, we obtain the simplified state transition matrix. and system process noise covariance matrix ; S13, the simplified state transition matrix and system process noise covariance matrix Substitute back into the current statistical model to obtain the simplified model of the current statistical model; S12 further includes the following steps: S121, It is determined that the sampling period value T of the infrared fisheye alarm system is much less than 1 second; S122, According to the Maclaurin formula, the state transition matrix of the current statistical model... and system process noise covariance matrix Simplify the exponential operations involved in the process; S123, Substitute the simplified result of the exponential operation in S122 into the state transition matrix of the current statistical model. and system process noise covariance matrix Simplify; S124. Based on the characteristic that the sampling period T is much less than 1 second, the simplified result of S123 is further simplified to obtain the simplified state transition matrix. and system process noise covariance matrix .

2. The simplification method according to claim 1, characterized in that, The state transition matrix of the current statistical model and system process noise covariance matrix The simplified result of the exponential operations involved is as follows: ， ； The result of further simplification of the simplified result of S123 is as follows: ， 。 3. A target motion model filtering method based on an infrared fisheye alarm system, characterized in that, Includes the following steps: S21, combine the current statistical model with the standard Kalman filter equation to obtain a Kalman filter method based on the current statistical model; S22, Based on the weak maneuverability characteristics of the target moving on the image plane in the infrared fisheye warning system, the one-step prediction formula of the target state in the Kalman filter method based on the current statistical model is simplified. S23. The state transition matrix adjusted using the Kalman filtering method based on the current statistical model. and system process noise covariance matrix Replace it with the simplified state transition matrix obtained by claim 1 or 2. and system process noise covariance matrix ; S24 yields the simplified Kalman filter method.

4. The filtering method according to claim 3, characterized in that, S22 further includes: S221: Based on the weak maneuverability of the target's movement on the image plane in the infrared fisheye warning system, we obtain... ,in Let be the mean acceleration at time k+1. The acceleration estimate at time k+1 is the predicted value. This is the estimated acceleration value at time k; S222: Will Substituting the state one-step prediction formula into the Kalman filter method based on the current statistical model, and simplifying, we obtain the target state one-step prediction formula. ,in ; S223, according to The simplified Kalman filter method yields the one-step prediction formula for the target state. .

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