Method and system for unscented Kalman filter sight tracking based on detrending term

Abstract

The present invention discloses an unscented Kalman filter sight tracking algorithm based on a detrending term, which belongs to the field of automated guidance technology. In the target sight tracking problem based on the unscented Kalman filter, the requirement that the noise in the system is Gaussian white noise must be met, but the actual noise data generally contains a trend term, which does not meet this requirement. To this end, the present invention proposes an algorithm that uses a clamped B-spline function to remove the trend term of the measurement equation noise, thereby whitening the measurement equation noise in the unscented Kalman filter sight tracking system. Simulation results show that the position deviation of the unscented Kalman filter sight tracking algorithm based on the detrending term is less than 1.0m. Compared with the direct use of the unscented Kalman filter algorithm, the unscented Kalman filter sight tracking algorithm based on the detrending term has better filtering result robustness in non-Gaussian white noise systems and has higher filtering accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of automated guidance technology, and more particularly, relates to an unscented Kalman filter sight tracking method and system based on a detrending term. Background Art

[0002] In recent years, target tracking has been an important research topic. In the real world, the tracker can only obtain its own position information with disturbances. Figure 1 The measurement information, such as gaze angle and gaze angular velocity, is used to correct the perturbed information. This type of filter system for gaze tracking is highly nonlinear. Both the Extended Kalman Filter (EKF) and the Cubic Kalman Filter (CKF) can be used for gaze tracking. In gaze tracking using gaze angle and gaze angular velocity as the measurement information, the Unscented Kalman Filter (UKF) achieves better tracking results than the EKF and CKF.

[0003] However, when applying the UKF, the noise in the system must be Gaussian white noise. Therefore, when applying the UKF to systems containing colored noise, the state augmentation method or the dynamic modification of the noise covariance matrix is ​​often used to address the issue of colored noise, in the hope of reducing the impact of colored noise on the filter estimate. However, because the state augmentation method expands the state dimension, the numerical integration results during the filtering process are unstable. When dealing with non-Gaussian noise contamination, the dynamic modification of the noise covariance matrix treats non-Gaussian distributed colored noise as Gaussian white noise with a large covariance. This makes the covariance of the filter state estimate overly conservative, resulting in reduced filtering accuracy.

[0004] It can be seen that the strict constraints on noise limit the application of the UKF algorithm. The present invention provides a method for whitening noise based on removing the trend term, which improves the robustness and application range of the UKF algorithm. Summary of the Invention

[0005] To address the shortcomings and improvements of existing UKF techniques applied to colored noise, the present invention provides a method and system for UKF gaze tracking based on a detrended term. The key to this approach is to address the problem that the UKF can only be applied to gaze tracking when the measurement equation noise is Gaussian white noise. This invention can apply the UKF to general practical problems involving colored noise in the measurement equation.

[0006] The present invention provides a UKF gaze tracking method based on a detrended term, comprising:

[0007] S1. Obtain the measurement equation noise sequence based on UKF gaze tracking;

[0008] S2. Fitting the measurement equation noise mean sequence using a clamped B-spline function to remove the trend term; wherein the node sequence of the clamped B-spline function is non-uniform and is determined according to the following process:

[0009] The noise mean sequence of the measurement equation is used as the control point, and the sharpness index and steepness index of each control point are calculated; the larger value of the sharpness index and the steepness index is used to form a new sequence, and after normalization, the new sequence is multiplied by the number of nodes required to be set between the beginning and the end of the control point sequence to obtain the node number index set between adjacent control points; the sharpness index represents the sharpness of the curve, and the smaller the value, the smoother the curve, and the larger the value, the sharper the curve; the steepness index represents the steepness of the curve, and the smaller the value, the flatter the curve, and the larger the value, the steeper the curve;

[0010] The node sequence is determined based on the node number index set between adjacent control points.

[0011] Furthermore, when the node number index set between adjacent control points is greater than a set threshold m, the node number index is set to m.

[0012] Furthermore, the node sequence is determined according to the node number index set between adjacent control points. The specific process is as follows:

[0013] According to the inequality Determine node u i The integer part of the value (k i -1);

[0014] Calculate (ip) relative to The offset and interval of The ratio of the lengths of u i The decimal part of the value

[0015] a k is the number of nodes that should be set between the (k-1)th control point and the kth control point, k i is used to calculate u i Parameters, p represents the order of the Clamped B-spline function.

[0016] The present invention also provides a UKF gaze tracking system based on a detrended term, comprising:

[0017] The measurement equation noise sequence acquisition module obtains the measurement equation noise sequence based on UKF line of sight tracking;

[0018] A clamped B-spline fitting module is used to fit the noise mean sequence of the measurement equation using a clamped B-spline function to remove the trend term therein; the clamped B-spline fitting module includes a sharpness index calculation unit for calculating the sharpness of each control point;

[0019] Steepness index calculation unit, used to calculate the steepness of each control point;

[0020] A node number index obtaining unit is used to form a new sequence using the larger value of the sharp index and the steep index, normalize the new sequence, and then multiply it by the number of nodes required to be set between the beginning and the end of the control point sequence to obtain the node number index set between adjacent control points;

[0021] The node sequence calculation unit is used to determine the node sequence according to the node number index set between adjacent control points.

[0022] In general, the above solutions conceived by the present invention can achieve the following beneficial effects compared with the existing technical solutions.

[0023] (1) The non-uniform node setting method provided by the present invention can achieve a better fitting effect of the Clamped B-spline curve. In existing studies on fitting of Clamped B-spline curves, a uniform node sequence is generally directly used. The resulting Clamped B-spline function often has a poor fitting effect in areas where the sharpness index or steepness index is large, which in turn leads to poor filtering results. The present invention introduces an index sequence that comprehensively considers the influence of the sharpness index and steepness index of the control point. The Clamped B-spline function with a non-uniform node sequence that combines the sharpness index and steepness index is used to remove the trend term, resulting in higher filtering accuracy of the UKF.

[0024] (2) The present invention provides a method for whitening noise by removing the trend term, which improves the robustness and application range of the UKF algorithm. The classic UKF method requires that the noise is Gaussian white noise. When the measurement equation noise is colored noise, the state amplification method and dynamic correction noise covariance in the existing mainstream solutions have their own limitations. The present invention removes the trend term of the measurement equation noise by using the Clamped B spline function of the non-uniform node sequence with a comprehensive sharp index and steep index, which can better eliminate the influence of colored measurement equation noise on UKF, reduce filtering deviation, and have higher robustness and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The following is a schematic diagram of the aircraft tracking the target. qf represents the altitude angle of the line of sight during the line of sight tracking, and qh represents the azimuth angle of the line of sight during the line of sight tracking.

[0026] Figure 2 This is a scatter plot of the measurement noise before trend removal. The green line represents the mean of the measurement noise, and the red horizontal line represents the zero-value measurement noise line. Sub-figure (a) shows the measurement noise for the line-of-sight azimuth (qh), sub-figure (b) shows the measurement noise for the line-of-sight elevation (qf), sub-figure (c) shows the measurement noise for the line-of-sight azimuth velocity (Vqh), and sub-figure (d) shows the measurement noise for the line-of-sight elevation velocity (Vqf). The lower right corner of each figure shows a zoomed-in view at time 5.0s.

[0027] Figure 3 is the control point qh k Schematic diagram of the calculation method of the sharpness index and steepness index. The selected trajectory is the measurement equation trajectory with the trend term foresight angle (qh) removed. where the angle θ k It represents the control point qh k-1 、qh k 、qh k+1 The vertex qh in the triangle with k The corresponding interior angle. Steepness index ρ k =|sinα k |, where the angle α k It represents the control point qh k-1 and qh k+1 The angle between the connecting line and the horizontal line. At this point, the values ​​of the sharpness index and the steepness index are both between 0 and 1. Sub-graph (a) shows the case where the sharpness index is large and the steepness index is small. Sub-graph (b) shows the case where the steepness index is large and the sharpness index is small.

[0028] Figure 4 Schematic diagrams of a uniform node sequence and a non-uniform node sequence with a combination of sharpness and steepness. The red horizontal line represents the zero-value line. The dark red short dashed lines pointing downward are uniform nodes with uniform spacing. The blue short solid lines pointing upward are non-uniform nodes with a combination of sharpness and steepness, with varying spacing. Sub-figure (a) shows that when the sharpness and steepness indices are small, the non-uniform node sequence (blue short solid line) is sparser than the uniform node sequence (dark red short dashed line), with the spacing between the blue short solid lines approximately twice that of the dark red short dashed lines. Sub-figure (b) shows that when the sharpness and steepness indices are large, the non-uniform node sequence (blue short solid line) is denser than the uniform node sequence (dark red short dashed line), with the spacing between the blue short solid lines approximately half that of the dark red short dashed lines.

[0029] Figure 5This is a scatter plot of the measurement noise after removing the trend term. The green line represents the mean of the measurement noise, and the red horizontal line represents the zero-value measurement noise line. After removing the trend term, the trend of the measurement noise is removed to a certain extent, and the fluctuation of the measurement noise is around 0. Sub-figure (a) shows the measurement noise of the line of sight azimuth (qh); sub-figure (b) shows the measurement noise of the line of sight elevation (qf); sub-figure (c) shows the measurement noise of the line of sight azimuth angular velocity (Vqh); and sub-figure (d) shows the measurement noise of the line of sight elevation angular velocity (Vqf).

[0030] Figure 6 The following is a graph of the autocorrelation coefficients of the noise mean series of the measurement equations of the sight angle and sight angular velocity before and after detrending. The blue line represents the connection of the autocorrelation coefficients at each lag distance. The red horizontal line represents the zero value line. The part of the autocorrelation coefficient within the green shaded area (with the upper and lower limits of T is the sequence length) means that at a 95% confidence level, the noise mean sequence of the measurement equation can be considered to have no autocorrelation at the corresponding lag distance. Figure 6 After removing the trend term, the autocorrelation coefficient of the measurement equation noise has a smaller lag distance into the green shaded area, and the interval length within the green shaded area is longer. Subfigure (a) shows the autocorrelation coefficient of the measurement equation noise for the line of sight azimuth (qh) before and after removing the trend term; subfigure (b) shows the autocorrelation coefficient of the measurement equation noise for the line of sight elevation (qf) before and after removing the trend term; subfigure (c) shows the autocorrelation coefficient of the measurement equation noise for the line of sight azimuth angular velocity (Vqh) before and after removing the trend term; and subfigure (d) shows the autocorrelation coefficient of the measurement equation noise for the line of sight elevation angular velocity (Vqf) before and after removing the trend term.

[0031] Figure 7 Figure 2 shows the filtering results (i.e., the difference between the true position value and the filtered estimate) of the UKF algorithm for 200 simulations under each condition. Subfigure (a) shows the filtering results without any processing, subfigure (b) shows the filtering results after removing the trend term using the clamped B-spline function with a uniform knot sequence, and subfigure (c) shows the filtering results after removing the trend term using the clamped B-spline function with a non-uniform knot sequence that combines both sharpness and steepness indicators. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0033] refer to Figure 1, a UKF gaze tracking method based on detrended terms, comprising:

[0034] (1) First, the state equation and measurement equation based on UKF line of sight tracking are established by the state space description method, and the noise sequence of the measurement equation {r k+1}:

[0035]

[0036] Among them, X k Represents the state quantity at the kth moment, Z k+1 represents the quantity measurement at the (k+1)th moment, f(·) and h(·) represent the state equation function and measurement equation function in the filter system, q k represents the state equation noise at time k, r k+1 Represents the measurement equation noise at time (k+1).

[0037] The state equation noise sequence and the measurement equation noise sequence should meet the following conditions:

[0038]

[0039] Among them, Q k represents the covariance matrix of the state equation noise at time k, R k represents the covariance matrix of the measurement equation noise at time k, δ kj represents the Kronecker symbol, O6 represents a 6-dimensional zero vector, O4 represents a 4-dimensional zero vector, and O 6×4 Represents a zero matrix with 6 rows and 4 columns.

[0040] The state quantities in this model include the position and velocity in the xyz directions, and the quantity measurements include the line of sight azimuth (qh) and line of sight altitude (qf), as well as the line of sight azimuth velocity (Vqh) and line of sight altitude velocity (Vqf).

[0041] (2) Use the Clamped B-spline function to fit the trend of the measurement equation noise;

[0042] After 200 sets of trajectory simulation experiments, the noise scatter plot of the measurement equation is obtained as follows: Figure 2 As shown in (a)-(d) in the figure, the present invention obtains 200 sets of measurement equation noise sequences through simulation experiments, calculates the mean of the measurement equation noise at each moment, uses the measurement equation noise mean sequence as the control point sequence, and then uses the clamped B-spline function to fit the measurement equation noise trend term to remove the trend term.

[0043] The recursive calculation form of the p-order Clamped B-spline function C(u) is as follows:

[0044]

[0045]

[0046]

[0047] Where C(u) represents the p-order Clamped B-spline function, u represents the independent variable of C(u), It corresponds to the node sequence defined in The p-order Clamped B-spline basis function on , is with The corresponding control point sequence.

[0048] In order to make the p-order Clamped B-spline function curve and the measurement equation noise mean line tangent at both ends, (p+1) nodes need to be set at the beginning and end of the line. In addition to the (2p+2) nodes set at the beginning and end, (np) nodes need to be set in the middle to form a node sequence.

[0049] The following describes a method based on the indicator sequence {a k} to set (np) intermediate nodes. k Describes the number of nodes that should be set between the (k-1)th control point and the kth control point. The sharpness index η of the control point k and steepness index ρ k Calculation method is as follows Figure 3 shown. Figure 3 The sharpness index η is shown in k Large steepness index ρ k Small, and sharp index η k Small steepness index ρ k There are two major situations.

[0050] Depend on Figure 2 From (a) to (d), we can see that the change of the measurement equation noise mean sequence over time is not uniform. Therefore, in order to make the clamped B-spline curve fit the measurement equation noise mean sequence (i.e., the control point sequence) more closely, the intermediate nodes should be set so that the nodes are denser where the changes are drastic and sparser where the changes are gentle.

[0051] In order to get a better fitting effect at the control points with larger sharpness index or steepness index, when setting the nodes, first follow Figure 3 The calculation method shown in (a)-(b) calculates the sharpness index η at the kth control point in turn k and steepness index ρ k Then the sharp index η kand the steepness index ρ k The larger value in the new sequence {β k}, where β k =max(η k , ρ k ). Then for the sequence {β k} is normalized to obtain the ratio of the change intensity between the (k-1)th control point and the kth control point to the change intensity of the entire curve segment. Then multiply it by the number of nodes (np) that need to be set between the beginning and the end to obtain the index sequence {a describing the number of nodes that should be set between the (k-1)th control point and the kth control point k},in

[0052] Directly follow the indicator sequence {a k} to set the intermediate nodes, which can meet the conditions that the nodes are denser where the changes are drastic and sparser where the changes are gentle. However, when the sharp index or steep index at some control points is too large, too many nodes will be concentrated near this control point, making the nodes at some control points too sparse. Therefore, it is necessary to set a k Adjustments are made to avoid the problem of excessive concentration of nodes at certain control points. To this end, the present invention converts the index sequence {a k} whose value is greater than the threshold m k Set the value to m, and distribute the extra value to other sequence values ​​in proportion, keeping {a k} is still (np). Then check {a k}, for values ​​of a greater than m k Repeat the above steps until all a k All are within the range of (0, m].

[0053] Get the adjusted indicator sequence {a k}After that, if you want to k Get node sequence u i , first according to the inequality Determine node u i The integer part of the value (k i -1), then calculate (ip) relative to The offset and interval of The ratio of the lengths of u i The decimal part of the value The calculation formula is as follows:

[0054]

[0055] Among them, u i represents the i-th node, a jRepresents the jth indicator sequence value, where a0 is defined as 0, k i is used to calculate u i Parameters. Specifically, traverse from 1 to n and find a positive integer k i , so that the index sequence {a k The first k of} i The sum of the values ​​is less than (ip), the first k i +1 value added is greater than or equal to (ip). The formula is as follows:

[0056]

[0057] The node sequence set by the above method is as follows Figure 4 As shown in (a)-(b), the obtained Clamped B-spline function can better fit the trend of the measurement equation noise.

[0058] At this time, after adding the clamped B-spline function in each dimension to the measurement equation, the form of the measurement equation is as follows:

[0059]

[0060] in, is a four-dimensional function composed of the clamped B-spline functions of each dimension of the measurement equation, u k+1 is a four-dimensional vector consisting of the independent variables of the Clamped B-spline function of each dimension of the measurement equation at time (k+1), Represents the four-dimensional vector composed of noise in each dimension of the measurement equation at time (k+1) after removing the trend term.

[0061] The effectiveness of the method of the present invention in removing the trend term of the noise in the measurement equation can be verified by the noise scatter plot of the measurement equation after removing the trend term, the autocorrelation coefficient plot, and the simulation experiment filtering results. The noise scatter plot of the measurement equation after removing the trend term using the Clamped B spline function of the non-uniform node sequence with the combined sharp index and steep index is as follows: Figure 5 As shown in (a)-(d) in the figure. The autocorrelation coefficients of the noise in the measurement equations of sight angle and sight angular velocity before and after detrending are as follows: Figure 6 As shown in (a)-(d) in the figure. Before and after detrending, the filtering results of the UKF algorithm in the simulation experiment are as follows: Figure 7 As shown in (a)-(c).

[0062] Depend on Figure 5 From (a) to (d), we can see that after removing the trend term, the trend of the measurement equation noise is removed to a certain extent, and the fluctuation of the measurement equation noise is around 0.

[0063] When the lag distance is k, the autocorrelation coefficient w of the noise mean series of the measurement equation before removing the trend term is k , and the autocorrelation coefficient of the noise mean series of the measurement equation after removing the trend term The calculation formula is as follows:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Among them, r t represents the noise mean of the measurement equation before removing the trend term at time t, It represents the noise mean of the measurement equation after removing the trend term at time t, Represents r t mean, express The mean of , T represents the length of the noise mean sequence of the measurement equation.

[0070] The closer the autocorrelation coefficient is to 0, the more it can be considered as white noise. Figure 6 As can be seen from (a) to (d), after removing the trend term, the noise in the measurement equation can be considered to have no autocorrelation at a smaller lag distance. The filtering effect after removing the trend term of the noise in the measurement equation using the Clamped B-spline function of the uniform node sequence is as follows: Figure 7 As shown in (b), the position deviation in the xyz direction in the filtering result accuracy is less than 1.0m. After the ClampedB spline function of the non-uniform node sequence with the sharp index and steep index is used to remove the trend term, the UKF filtering accuracy is higher. The filtering results are shown in Figure 7 As shown in (c).

[0071] Figure 7 The filtering results in (a)-(c) show that compared with the Clamped B-spline function using a uniform knot sequence, the filtering deviation of the Clamped B-spline function using a non-uniform knot sequence with a comprehensive sharp index and steep index is improved after removing the trend term.

[0072] By comparing the measurement equation noise before and after removing the trend term, the autocorrelation coefficient of the measurement equation noise mean sequence and the filtering results, it is shown that this method is effective in noise whitening.

[0073] Simulation experiment:

[0074] 1 In order to verify that the filtering effect and accuracy of UKF are improved to a certain extent after removing the noise trend term of the measurement equation, the present invention uses Matlab programming to design the following simulation experimental data:

[0075] The initial x-axis (horizontal and vertical) position deviation is 100m, the initial y-axis (height) deviation is 100m, the initial z-axis (horizontal and horizontal) deviation is 100m, and the line of sight angle superposition N (0, 0.1 2 )deg noise, the line of sight angular velocity superimposed N(0, 0.1 2 )deg / s noise.

[0076] 2 According to the method proposed in the present invention, the following comparative experiments were designed.

[0077] Simulation experiments were conducted using UKF without removing the trend term, using the Clamped B-spline function of a uniform knot sequence to remove the trend term, and using the Clamped B-spline function of a non-uniform knot sequence with a comprehensive sharpness index and steepness index to remove the trend term. The filtering results are shown in Figure 2. Figure 7 As shown in (a)-(c), the filtering results are compared and analyzed as follows.

[0078] The filtering results (i.e., the difference between the true position value and the filtered estimate) of the UKF algorithm were calculated for 200 simulations under each condition. The filtering deviations in each condition were compared and analyzed. The maximum difference between the true position value and the filtered estimate in the xyz direction is shown in Table 1.

[0079] Without trend removal, the maximum filtering deviations in the xyz directions were 2385m, 636.7m, and 375.5m, respectively. After removing the trend using the clamped B-spline function with a uniform knot sequence, the maximum filtering deviations in the xyz directions were 1.824m, 1.914m, and 3.251m, respectively. After removing the trend using the clamped B-spline function with a non-uniform knot sequence that combines both sharpness and steepness, the maximum filtering deviations in the xyz directions were 0.247m, 0.233m, and 0.344m, respectively. After removing the noise trend using the clamped B-spline function with a non-uniform knot sequence that combines both sharpness and steepness, the filtering accuracy in the xyz directions was less than 1.0m. This reduction in filtering deviation was at least 96% compared to the uniform knot sequence clamped B-spline function after removing the noise trend, and was significantly lower than the filtering deviation without trend removal. This demonstrates that the UKF gaze tracking algorithm based on trend removal exhibits robustness and higher accuracy.

[0080] Table 1 Differences between true values ​​and filtered estimates

[0081]

[0082] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A UKF gaze tracking method based on detrending term, characterized in that: include: S1. Obtain the measurement equation noise sequence based on UKF gaze tracking; S2. Fitting the measurement equation noise mean sequence using a clamped B-spline function to remove the trend term; wherein the node sequence of the clamped B-spline function is non-uniform and is determined according to the following process: The noise mean sequence of the measurement equation is used as the control point, and the sharpness index and steepness index of each control point are calculated; the larger value of the sharpness index and the steepness index is used to form a new sequence, and after normalization, the new sequence is multiplied by the number of nodes required to be set between the beginning and the end of the control point sequence to obtain the node number index set between adjacent control points; the sharpness index represents the sharpness of the curve, and the smaller the value, the smoother the curve, and the larger the value, the sharper the curve; the steepness index represents the steepness of the curve, and the smaller the value, the flatter the curve, and the larger the value, the steeper the curve; The node sequence is determined based on the node number index set between adjacent control points.

2. The UKF gaze tracking method based on detrending term according to claim 1, characterized in that: When the node number index set between adjacent control points is greater than the set threshold m, the node number index is set to m.

3. The UKF gaze tracking method based on detrending term according to claim 1, characterized in that: The node sequence is determined based on the node number index set between adjacent control points. The specific process is as follows: According to the inequality Determine node u i The integer part k of the value i -1; Calculate the IP relative to The offset and interval of The ratio of the lengths of u i The decimal part of the value a k is the index of the number of nodes that should be set between the k-1th control point and the kth control point, k i is used to calculate u i Parameters, p represents the order of the Clamped B-spline function.

4. A UKF gaze tracking system based on detrending term, characterized in that: include: The measurement equation noise sequence acquisition module obtains the measurement equation noise sequence based on UKF line of sight tracking; a clamped B-spline fitting module for fitting the noise mean sequence of the measurement equation using a clamped B-spline function to remove the trend term therein, wherein the node sequence of the clamped B-spline function is non-uniform; the clamped B-spline fitting module includes a sharpness index calculation unit for calculating the sharpness of each control point; A steepness index calculation unit, configured to calculate the steepness of each control point, wherein the control point is a noise mean sequence of a measurement equation; A node number index obtaining unit is used to form a new sequence using the larger value of the sharp index and the steep index, normalize the new sequence, and then multiply it by the number of nodes required to be set between the beginning and the end of the control point sequence to obtain the node number index set between adjacent control points; The node sequence calculation unit is used to determine the node sequence according to the node number index set between adjacent control points.

5. The UKF gaze tracking system based on detrending term according to claim 4, characterized in that: When the node number index set between adjacent control points is greater than the set threshold m, the node number index is set to m.

6. A UKF gaze tracking system based on detrending term according to claim 4, characterized in that: The node sequence is determined based on the node number index set between adjacent control points. The specific process is as follows: According to the inequality Determine node u i The integer part k of the value i -1; Calculate the IP relative to The offset and interval of The ratio of the lengths of u i The decimal part of the value a k is the index of the number of nodes that should be set between the k-1th control point and the kth control point, k i is used to calculate u i Parameters, p represents the order of the Clamped B-spline function.

7. A UKF gaze tracking device based on detrending term, characterized in that: include: processor; The processor is coupled to a memory, the memory is used to store computer programs or instructions, and the processor is used to execute the computer programs or instructions in the memory, so that the UKF sight tracking method based on detrending items described in any one of claims 1-3 is executed.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the UKF sight tracking method based on detrending items according to any one of claims 1 to 3.

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