A state estimation method for unmanned vehicle on disturbed surface based on interval observer

Abstract

The present invention provides a state estimation method for an unmanned boat on a disturbed water surface based on an interval observer, which relates to the field of ship state perception. First, the state space expression of the asymmetric motion of the unmanned boat under the interference of waves is modeled. Then, a two-point observer in the form of Lumberg is designed, and a two-point estimation error system is constructed based on this and a gain matrix is ​​designed to optimize the performance. Furthermore, by analyzing the state matrix of the error system, an interval observer based on a two-point observer is designed under different parameter matrices. This design effectively relaxes the non-negativity constraint of the interval observer, thereby improving its adaptability in practice. On this basis, the measurement output is used and a convex weighted sum is adopted to obtain a more accurate point estimate of the system state. Compared with the traditional state estimation method, the interval observer-based method proposed in the present invention can effectively utilize the bounded information of the disturbance to solve the estimation problem of the unmanned boat in complex waters, and has significant practical research value.

Description

Technical Field

[0001] The present invention belongs to the technical field of ship state perception, and particularly designs a state estimation method for an unmanned boat on a disturbed water surface based on an interval observer. Background Art

[0002] Unmanned boats (UAVs) can communicate remotely using advanced information technologies like the internet, and they can autonomously complete surface missions in aquatic environments like oceans and lakes using technologies like autonomous driving. Furthermore, UAVs can replace humans in more dangerous aquatic environments, such as polluted waters and stormy oceans. Their small size and high flexibility have led to their widespread application in civilian applications such as water quality testing, exploration, and waste removal, as well as military applications such as reconnaissance and surveillance. To remotely control and achieve autonomy, obtaining state information is essential. While positional status information is typically readily available through technologies like satellite positioning, state information such as speed is more difficult to obtain and measure. Therefore, state estimation of UAV systems holds significant research value.

[0003] When completing tasks in a complex ocean environment, sea breezes, waves, etc. will bring unpredictable interference to the unmanned boat, thereby increasing the difficulty of state estimation. The main methods for state estimation under disturbances are filters and observers. For the commonly used filter method, the Kalman filter needs to restrict the disturbance to obey the Gaussian distribution and the statistical characteristics are known, but this is not always satisfied in the actual ocean environment. If the disturbance does not satisfy the statistical characteristics, there will be a large deviation between the obtained state estimate and the true value of the system state. At this time, a general unknown input observer can be considered, but it needs to meet the observer matching conditions and has a certain range of use restrictions. Therefore, for state estimation under disturbances, further research and design of a less restricted and more universal estimation method is needed. Summary of the Invention

[0004] The purpose of the present invention is to design a state estimation method for a surface unmanned boat, which can still accurately estimate the state of the unmanned boat when the unmanned boat is subject to unknown interference.

[0005] In order to achieve the above-mentioned invention objectives, the following technical solutions are adopted:

[0006] A state estimation method for an unmanned vehicle on a disturbed surface based on an interval observer comprises the following steps:

[0007] Step 1: Modeling and studying the dynamic behavior of the asymmetric motion of the surface unmanned vehicle to obtain the state space equation of the disturbed unmanned vehicle system under the influence of waves;

[0008] Step 2: Based on the state space equation of the asymmetric motion of the unmanned boat obtained in step 1, a two-point observer of the Romberg form is designed;

[0009] Step 3: Based on the two-point observer in step 2, construct a two-point estimation error system and give the design of the observer gain matrix that ensures the stability of the error system in the form of linear matrix inequality;

[0010] Step 4: Determine whether the error system state matrix in step 3 is a Metzler matrix. If so, treat the two-point observer as an interval observer and set its initial state. If not, introduce the coordinate transformation matrix obtained by solving the nonlinear inequality group, construct an interval observer based on the two-point observer, and construct the error system under the coordinate transformation, and then set the initial state for the interval observer.

[0011] Step 5: Based on the upper and lower interval estimates generated by the interval observer in step 4, a convex weighted sum processing method is used to use the measurement output to obtain a more accurate system state point estimate.

[0012] The process of constructing the state space equation of the asymmetric motion of the disturbed surface unmanned vehicle in step 1 is as follows:

[0013] The overall motion of the unmanned surface vehicle includes six degrees of freedom (surge, sway, pitch, roll, heave, and pitch). Considering the asymmetric motion of the unmanned vehicle with components in the direction of the center of gravity pointing to the ship's side, including sway, pitch, and roll, its dynamic model is:

[0014]

[0015] Where, the heading angle ψ t , yaw speed r t 、Roll angle φ t , roll angular velocity p t , sway velocity v t and rudder deflection angle δ t are the physical variables of the system; ζ and ω n are the damping coefficient and undamped natural frequency, respectively; and They represent the heading angle ψ caused by the waves t and roll angle φ t Interference; time constant t r , t v and gain k rv 、k rd 、k vd 、k pv 、k pd These are all known system parameters.

[0016] Define the state vector x t =[ψ t r t φ t pt v t ] T and joint interference The above dynamic model is transformed into a standard state space equation:

[0017]

[0018] y t =Cx t

[0019] Among them, y t is the obtainable measurement output, C is the measurement constant matrix with known suitable dimension,

[0020] System state matrix

[0021] System input matrix

[0022] State perturbation matrix

[0023] The rudder is easy to operate, and the rudder deflection angle δ t is selected as the known control input of the system, which does not need to be estimated. In the subsequent design of the observer structure, δ t Information. Disturbance caused by wavesω t Although it is uncontrollable and unknown, its impact on the heading angle and rudder angle can be estimated within a range, that is, the interference ω t The upper and lower bounds of are known.

[0024] In step 2, the construction process of a two-point observer in the classic Lumberg form is as follows:

[0025] The disturbance-related terms in the two-point observer are designed as follows:

[0026] For any matrix Q, the following holds true

[0027] QD=(QD) + -(QD) -

[0028] Among them, (QD) + The matrix product QD is obtained by retaining all elements greater than or equal to 0 and setting all elements less than 0 to 0. (QD)- is obtained by setting all elements greater than or equal to 0 and setting all elements less than 0 to their opposites.

[0029] The upper and lower bounds of the known interference are and ω t , the following formula holds

[0030]

[0031] QDω t An upper bound of As QDω t can be introduced into the design of two-point observers as disturbance-related terms in the observer structure.

[0032] Based on the above disturbance-related terms, the following two-point observer in the classic Lumberg form is constructed:

[0033]

[0034] Among them, L is the two-point observer gain matrix to be designed, which is used to ensure the stability of the observer error system and thus ensure the boundedness of the estimated value; Q is the parameter matrix to be selected and designed, and The two-point observer provides a two-point estimate of the system state x. The two-point estimate values ​​generated by the two-point observer can provide a rough point estimate of the system state and is the basis for the subsequent construction of the interval observer.

[0035] The process of constructing the two-point observer error system and designing the gain matrix in step 3 is as follows:

[0036] Considering two-point estimation errors and From the state equation of the original system and the state equation of the two-point observer, the error dynamic system of the two-point observer is obtained as follows:

[0037]

[0038] To achieve the stability of the two-point observer error system and thus ensure that the two-point estimates are bounded, the error system matrix A-LC needs to be a Hurwitz matrix, that is, all eigenvalues ​​of A-LC have non-negative real parts. Considering this, the gain matrix L is designed to satisfy the following linear matrix inequality:

[0039]

[0040] R<0

[0041] in, refer to is a negative definite matrix; L R and R are matrices to be solved. By solving the above inequalities, the gain matrix is ​​designed to be L=R -1 L R .

[0042] In step 4, when the error system state matrix is ​​a Metzler matrix, the process of treating the two-point observer as an interval observer and setting the initial state for it is as follows:

[0043] The system state matrix of the error system is A-LC. If the gain matrix obtained by the above solution can simultaneously ensure that A-LC is a Metzler matrix, then the parameter matrix Q to be designed in the two-point observer structure is selected as the unit matrix. At this time, the two-point observer is also an interval observer, and the specific structure is as follows

[0044]

[0045] The two estimates provided and are the upper interval estimate and the lower interval estimate, respectively.

[0046] At this time, the error system is

[0047]

[0048] Integrating this error system yields

[0049]

[0050] From the above integral, we can see that as long as the error at the initial moment is and It can be guaranteed at any time and This also realizes the non-negativity of the two-point observer as an interval observer, that is, at any time Therefore, the initial state of the two-point observer is set to

[0051]

[0052] in, and x0 are the upper and lower bounds of the system initial state, respectively. For the system initial state x0, even if they are unknown, their upper bounds are usually and the lower bound x0 are known and can be obtained for use in observer initialization.

[0053] It is worth noting that the above interval estimates and It can be directly used for subsequent more accurate convex weighted estimation of the system state.

[0054] In step 4, when the error system state matrix is ​​not a Metzler matrix, a coordinate transformation matrix is ​​introduced to construct an interval observer based on a two-point observer, and an error system under coordinate transformation is constructed. The process of setting the initial state for the interval observer is as follows:

[0055] When the error system state matrix A-LC is not a Metzler matrix, the two-point observer can ensure that the error is bounded but cannot be guaranteed to be non-negative. In order to achieve interval estimation of the state, the goal is to convert it into a Metzler matrix without changing the stability of A-LC. Considering similarity transformation, the coordinate transformation matrix H is introduced so that H(A-LC)H -1 It is a Metzler matrix, and it is similar to the original matrix A-LC, so the eigenvalues ​​are the same and stability is maintained.

[0056] The coordinate transformation matrix H that transforms A-LC into the Metzler matrix is ​​obtained by solving the following nonlinear inequality system:

[0057]

[0058] where l i is a column vector whose i-th component is 1 and the rest are 0.

[0059] After the coordinate transformation matrix is ​​designed, the parameter matrix Q to be designed in the two-point observer structure is selected as the coordinate transformation matrix H. At this time, the state matrix of the two-point observer error system is still an A-LC non-Metzler matrix, and it cannot be guaranteed that the two-point estimation value satisfies In order to achieve interval estimation, the following interval observer based on two-point observer is constructed

[0060]

[0061] in, and X t are upper and lower interval estimates, respectively.

[0062] In order to construct the H(A-LC)H -1 is the error dynamic system of the system state matrix, considering the upper estimation error under the action of the coordinate transformation matrix and the lower estimation error The error dynamic characteristics are as follows:

[0063]

[0064] Integrating the transformed estimation error system, we can get the solution of the error system under transformation:

[0065]

[0066] When the initial error under coordinate transformation is non-negative, that is, When E0≥0, the above formula can be obtained at any time and That is to say

[0067]

[0068] At the same time, according to the above formula, we can get

[0069]

[0070] Therefore, the upper and lower intervals are estimated to be the upper and lower bounds of the system state, and we have

[0071]

[0072] Based on the above analysis and the linear algebraic relationship between the upper and lower interval estimates and the two-point estimates in the interval observer, in order to achieve the non-negative initial error under coordinate transformation and thus ensure the correctness of the interval estimate, the initial state of the two-point observer is and The setup process is:

[0073] Consider the initial state under coordinate transformation to satisfy

[0074]

[0075] and are the upper and lower bounds of Hx0, and according to x0=H -1 Hx0, set the initial state of the two-point observer in the interval observer to

[0076]

[0077] The design of the interval observer depends on the state estimation value provided by the two-point observer. The two-point observer can provide a point estimate of the state of the unmanned boat system. The significance of considering the subsequent state estimation based on the interval observer is that: although the two-point observer can provide a point estimate of the system state, the processing item for unknown interference in the observer structure is designed to be and When the estimated disturbance bound is larger than the actual difference, the error in the state estimate is also larger. The stability of the error system guaranteed by the A-LC Hurwitz matrix is ​​that the input is stable to the state. Only in the absence of disturbance can the error converge to 0 asymptotically. In the presence of bounded disturbance, it can only be guaranteed to be bounded. Therefore, a more accurate state estimation method is needed.

[0078] Furthermore, based on the upper and lower bounds of the system state generated by the interval observer, a convex weighted sum processing method is adopted to obtain a more accurate system state point estimate using the measurement output:

[0079]

[0080] in is the weight factor;

[0081] When the measured value is equal to the lower interval estimate, that is, when α = 1, the lower estimate provided by the interval observer is an accurate point estimate;

[0082] When the measured value is equal to the upper interval estimate, that is, when α = 0, the upper estimate provided by the interval observer is an accurate point estimate.

[0083] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0084] (1) The present invention solves the state estimation problem of the disturbed underwater unmanned vehicle system. The interval observer not only provides interval estimation, but also realizes more accurate weighted point estimation, which relaxes the restriction of the existing technology that the strict observer matching conditions must be met to deal with the interference system.

[0085] (2) The interval observer constructed in the present invention is based on a two-point observer. The two-point observer can provide a simple and rough point estimate of the system state. It can also be introduced into the design of the interval observer to relax the general interval observer's restriction on the non-negativity of the upper and lower interval estimation errors. This allows the interval observer to focus more on other performance characteristics such as stability, and also makes the structure of the interval observer more flexible.

[0086] (3) The present invention uses an interval observer to achieve the final weighted point estimate, effectively utilizing the good and universal property of bounded perturbations. Furthermore, when designing the interval observer, there is no need to consider complex estimation performance optimization issues. As long as the upper and lower bounds of the system state can be given through the interval observer using the upper and lower bounds of the perturbation and initial values, the output can be used to weight and ensure the accuracy of the point estimate. The method of the present invention is not only applicable to unmanned surface watercraft systems, but can also be extended to any system with bounded unknown inputs. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 This is a flow chart of the principle of state estimation of disturbed surface unmanned vehicle based on interval observer designed by the present invention. DETAILED DESCRIPTION

[0088] The following will refer to the attached Figure 1 , the key to the specific implementation details of the present invention is generally explained.

[0089] The present invention proposes a method for estimating the state of an unmanned vehicle on a disturbed surface based on an interval observer, comprising the following steps:

[0090] Step 1: Modeling and studying the dynamic behavior of the asymmetric motion of the surface unmanned vehicle to obtain the state space equation of the disturbed unmanned vehicle system under the influence of waves;

[0091] Select the motion variable heading angle ψ of the unmanned boat's asymmetric motion t, yaw speed r t , roll angle φ t , roll angular velocity p t and the sway velocity v t As the system state component; controllable rudder deflection angle δ t As the control input, considering the influence of waves on the unmanned boat, the state space equation for modeling the asymmetric motion of the unmanned boat is:

[0092]

[0093] y t =Cx t

[0094] Among them, x t =[ψ t r t φ t p t v t ] T is the system state vector,

[0095] System state matrix

[0096] System input matrix State perturbation matrix

[0097] interference in and They represent the heading angle ψ caused by the waves t and roll angle φ t The impact of t is the obtainable measurement output, C is a known constant matrix of suitable dimension, ζ and ω n are the damping coefficient and undamped natural frequency respectively; k rv 、k rd 、k vd k pv 、k pd and time constant t r , t v These are all known system parameters.

[0098] Step 2: Based on the state space equation of the unmanned boat motion obtained in the above steps, a two-point observer of the Romberg form is designed as

[0099]

[0100] Among them, L is the two-point observer gain matrix to be designed, Q is the parameter matrix to be selected, and is a two-point estimate of the system state produced by the observer.

[0101] Step 3: Based on the two-point observer obtained in the above steps, a two-point estimation error system is constructed, and the design of the observer gain matrix that ensures the stability of the error system is given in the form of linear matrix inequality;

[0102] Defining two-point estimation error

[0103]

[0104] Construct the following error dynamic system

[0105]

[0106] To obtain the gain matrix, construct the following linear matrix inequality:

[0107]

[0108] R<0

[0109] in, Expressed as is a negative definite matrix; L R and R are matrices to be solved;

[0110] Then, solving the above linear matrix inequality, the gain matrix is ​​designed to be L=R -1 L R .

[0111] Step 4: Based on the error system constructed in the above steps, determine whether the error system state matrix is ​​a Metzler matrix. If so, treat the two-point observer as an interval observer and set its initial state. If not, introduce the coordinate transformation matrix obtained by solving the nonlinear inequality group, construct an interval observer based on the two-point observer, and construct the error system under the coordinate transformation, and then set the initial state for the interval observer.

[0112] After designing the gain matrix in the above steps, the system state matrix A-LC of the error system can be determined.

[0113] The first case: its non-diagonal elements are all non-negative, then A-LC is a Metzler matrix. At this time, the parameter matrix to be designed in the two-point observer structure is selected as the unit matrix, and the two-point observer is also an interval observer.

[0114]

[0115] in, and X t They are upper and lower interval estimates, and point estimates generated by two-point observers Hewei are upper interval estimation and lower interval estimation respectively. In order to estimate the The initial state of the two-point observer is set to

[0116]

[0117] in, is the upper bound of the known initial state of the system, and x0 is the lower bound of the known initial state of the system.

[0118] The second case: If its non-diagonal elements have elements less than 0, then A-LC is not a Metzler matrix, and a coordinate transformation matrix needs to be introduced.

[0119] The coordinate transformation matrix H required to be introduced is solved by the following nonlinear inequality group:

[0120]

[0121] where l i is a column vector whose i-th component is 1 and the rest are 0.

[0122] Then, this coordinate transformation matrix is ​​introduced into the two-point observer structure, and the following interval observer based on the two-point observer is designed:

[0123]

[0124] in, and X t are upper and lower interval estimates, respectively.

[0125] In order to construct the H(A-LC)H -1 is the error dynamic system of the system state matrix, considering the estimation error under the action of the coordinate transformation matrix.

[0126] Define the upper and lower estimation errors after coordinate transformation

[0127]

[0128] The error dynamic characteristics are as follows:

[0129]

[0130] In order to ensure the accuracy of the interval observer, that is, the upper interval estimate is the upper bound of the system state, and the lower interval estimate is the lower bound of the system, the initial states of the two-point observer in the interval observer are set to

[0131]

[0132] After the initial state of the two-point observer is determined, the initial state of the interval observer can be determined as

[0133]

[0134] Step 5: Based on the interval observer constructed in the above steps, a convex weighted sum processing method is used to obtain a more accurate system state point estimate using the measurement output;

[0135] The designed weighted point estimate is

[0136]

[0137] in is the weight factor.

[0138] The above implementation process is intended to clearly and intuitively illustrate the technical concept of the present invention, rather than to impose any restrictive definition thereon. Persons skilled in the relevant art may still make further adjustments or replace or derive some or all of the technologies described herein. These potential adjustments do not change the essential attributes of the corresponding technical solution and remain within the scope of the technical solution of the present invention.

Claims

1. A state estimation method for an unmanned vehicle on a disturbed surface based on an interval observer, characterized in that: Includes the following: Modeling research is conducted on the dynamic behavior of the asymmetric motion of the surface unmanned vehicle, and the state space equation of the disturbed unmanned vehicle system under the influence of waves is obtained; Based on the state space equation of the asymmetric motion of the disturbed unmanned boat, a two-point observer of the Romberg form is designed. Based on the two-point observer, a two-point estimation error system is constructed, and the design of the observer gain matrix that ensures the stability of the error system is given in the form of linear matrix inequality; Determine whether the error system state matrix is ​​a Metzler matrix. If so, treat the two-point observer as an interval observer and set an initial state for it. If not, introduce the coordinate transformation matrix obtained by solving the nonlinear inequality group to construct an interval observer based on the two-point observer. Construct the error dynamic system under coordinate transformation, and further set the initial states for the two-point observers in the interval observer to ensure that the upper and lower interval estimates provided by the interval observer are the upper and lower bounds of the state; Based on the upper and lower bounds of the system state generated by the interval observer, a convex weighted sum processing method is adopted to utilize the measurement output to obtain a more accurate point estimate of the system state.

2. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 1 is characterized in that: The asymmetric motion characteristics of the surface unmanned boat under wave disturbance are studied and analyzed, and then the state space equation of the unmanned boat system is constructed as follows: By applying Newton's theorem to analyze the asymmetric motion of the unmanned boat with sway, bow pitch and roll in the direction of the boat's center of gravity pointing to the ship's side, the following mathematical expression is derived: in, and They are heading angle, yaw rate, roll angle, roll angular rate, sway rate and rudder deflection angle respectively; and are the damping coefficient and the undamped natural frequency, and are the heading angles caused by the waves and roll angle The disturbance effect of time constant and gain 、 、 All are known; Select variables To describe the current dynamic behavior of the unmanned boat, the rudder deflection angle As a known external input, the unknown disturbance caused by the waves is combined and recorded as = , further, transform the above expression into the state space equation of the unmanned boat system in, is the system measurement output, is a known dimensionally appropriate output matrix, The other system parameter matrices are , 。 3. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 2 is characterized in that: According to the state space equation of the modeled unmanned vehicle system, the construction process of a classic Romberg form two-point observer is as follows: For any matrix ,definition in, is the matrix product No. i Rank j Elements of the column; Based on the above definition, and taking into account the disturbance of the waves Although unknown, its effects can be bounded and Known limits The characteristics of the prediction are given in the disturbance related terms A lower and upper bound as follows Disturbance in the system , according to part of the disturbance term The upper and lower bounds of , construct the following two-point observer of the Lumberg form in, L is the two-point observer gain matrix to be designed, is the parameter matrix of the design to be selected, and is a two-point estimate of the system state produced by the observer.

4. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 3 is characterized in that: Construct a two-point observer error system and design the observer gain matrix to ensure the stability of the error system: Considering two-point estimation errors and , construct the following error dynamic system To ensure the stability of the error system and thus achieve the boundedness of the estimate, the state matrix It needs to be a Hurwitz matrix. To achieve this, the gain matrix is ​​designed L make sure The eigenvalues ​​of are all located in the left half of the complex plane, which is further converted into the following linear matrix inequality in, Expressed as is a negative definite matrix; and is the matrix to be solved, Restricted to positive definite matrices; Then, solving the above linear matrix inequality, the gain matrix is ​​designed as L= .

5. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 4 is characterized in that: When the error system state matrix is ​​a Metzler matrix, the two-point observer is regarded as an interval observer and the initial state is set as follows: The system state matrix of the error system is , if the gain matrix obtained by the above solution can ensure The off-diagonal elements of are non-negative, that is, is a Metzler matrix, then the parameter matrix to be designed in the two-point observer structure is selected as the unit matrix. At this time, the two-point observer is also an interval observer, and the form is as follows Among them, the point estimate produced by the two-point observer is and Upper interval estimates and lower interval estimates , in order to make any moment, The initial state of the two-point observer is set to ， in, is the upper bound of the system’s initial state, is the lower bound of the system initial state, For example, even if they are unknown, their upper bounds and the lower bound is known and can be directly used in setting the initial value of the observer; it is further worth noting that the above interval estimation and It can be directly used for subsequent more accurate convex weighted estimation of the system state.

6. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 5 is characterized in that: When the error system state matrix is ​​not a Metzler matrix, the coordinate transformation matrix is ​​introduced to construct an interval observer based on a two-point observer as follows: Error system state matrix When it is not a Metzler matrix, considering the characteristics that similarity transformation can change matrix elements but not matrix eigenvalues, the coordinate transformation matrix is ​​introduced H , making is the Metzler matrix, and this coordinate transformation matrix is ​​obtained by solving the following nonlinear inequality system , i, j = 1, 2, 3, 4, 5 in is a column vector whose i-th component is 1 and the rest are 0; Furthermore, using this coordinate transformation matrix, the following interval observer based on the two-point observer is designed: in, and are upper and lower interval estimates, respectively.

7. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 6, characterized in that: Construct the error dynamic system under coordinate transformation and set the initial state for the interval observer to ensure that the upper and lower interval estimates it provides are the upper and lower bounds of the system state. Specifically: In order to achieve non-negative error, it is necessary to construct a Metzler matrix is the error dynamic system of the system state matrix, considering the estimation error under the action of the coordinate transformation matrix and , and its error dynamic characteristics are as follows By ensuring the initial error and Non-negative, to achieve any time and Non-negative, thus realizing the upper and lower interval estimates as the upper and lower bounds of the state; the initial value setting of the interval observer is to set the initial value of the two-point observer in its structure, first considering based on And the upper and lower bounds of the initial state under the above coordinate transformation, the initial state of the two-point observer is set to 。 8. The state estimation method of an unmanned vehicle on a disturbed surface based on an interval observer according to claim 7 is characterized in that: Based on the upper and lower bounds of the system state generated by the interval observer, a convex weighted sum processing method is used to use the measurement value to obtain a more accurate system state point estimate: in ; When the measured value is equal to the lower interval estimate, that is, When , the lower estimate provided by the interval observer is an accurate point estimate; when the measured value is equal to the upper interval estimate, that is, When , the upper estimate provided by the interval observer is an exact point estimate.

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