A method for AUV velocity estimation based on centrosymmetric multicellular Kalman filter

Abstract

This invention discloses an AUV velocity estimation method based on a centrosymmetric multicell Kalman filter. First, a systematic analysis of the state-space model of the autonomous underwater vehicle (AUV) is performed. Then, combining the properties of centrosymmetric multicells and the concept of Kalman filtering, the reachable set of the AUV system state is calculated and optimized. The velocity range of the AUV is calculated using the optimal reachable set, enabling effective velocity monitoring. This method is applicable to AUVs with various configurations and different motion states. Compared with existing technologies, the proposed method can not only accurately estimate the velocity of the AUV but also provide velocity range estimates, thereby achieving effective velocity state monitoring and significantly improving the reliability and stability of the AUV.

Description

Technical Field

[0001] This invention belongs to the field of autonomous underwater vehicle (AUV) state estimation, specifically involving an AUV velocity estimation method based on a centrosymmetric multicellular Kalman filter. Background Technology

[0002] The ocean is the most vast natural environment on Earth, nurturing abundant mineral resources, oil, and natural gas. However, the seabed environment is complex and variable, typically characterized by high pressure, low temperature, and strong corrosiveness. These extreme environments pose significant challenges to the exploration and exploitation of seabed resources. While traditional underwater robots have made some breakthroughs in shallow waters, their flexibility and stability in deep-sea exploration remain far from sufficient. To address these issues, autonomous underwater vehicles (AUVs) have emerged as a new generation of intelligent marine equipment. Relying on their high degree of autonomy, excellent environmental adaptability, and ability to conduct long-duration deep-sea missions, AUVs are gradually becoming key technological equipment for seabed resource exploration, environmental monitoring, and marine scientific research.

[0003] Operating unmanned and untethered in complex marine environments, AUVs must ensure their own safety, which necessitates continuous monitoring of their status. Since monitoring sensors are often expensive, state estimation techniques have been developed to reduce overall costs and make AUV status monitoring more economical. This advancement has not only significantly reduced hardware costs but also enhanced the economics and operability of equipment. However, real-world uncertainties can cause deviations between state estimation results and actual conditions. To mitigate the impact of these uncertainties, robust state estimation methods have been extensively studied. These methods are mainly divided into two types: stochastic methods and set-membership estimation methods. Traditional stochastic methods assume that the uncertainty follows a Gaussian distribution when estimating the AUV's state, but this assumption is often inapplicable in practice. In contrast, set-membership estimation methods only assume that the uncertainty is unknown but bounded, providing a more flexible and realistic solution.

[0004] Membership estimation methods estimate state values ​​by creating a set that includes all possible state values. Depending on the set, membership estimation methods can be categorized into many types. Among them, centrosymmetric multiple cells have attracted widespread attention due to the simplicity of obtaining linear mappings and Minkowski sums. In the field of AUV state estimation, Doppler velocimeters used for velocity measurement are not only expensive but also have limited measurement accuracy in certain environments. Summary of the Invention

[0005] The purpose of this invention is to provide an AUV velocity estimation method based on a centrosymmetric multicell Kalman filter. This method can not only accurately estimate the velocity of an underwater robot, but also provide interval estimates of the velocity, thereby achieving effective monitoring of the velocity state and significantly improving the reliability and stability of autonomous underwater robots.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] An AUV velocity estimation method based on a centrosymmetric multicell Kalman filter is described below:

[0008] Step 1: Analyze the state-space model of the autonomous underwater robot system;

[0009] Step 2: Based on the state-space model formula in Step 1, use the definition of a centrally symmetric multicell, the Minkowski sum property, and the linear mapping property to calculate the reachable set of the underwater robot system's state;

[0010] Step 3: Optimize the reachability set of the underwater robot system state from Step 2;

[0011] Step 4: Based on the optimal reachable set obtained in Step 3, and according to the properties of the minimum interval envelope and the state space model obtained in Step 1, calculate the velocity range of the underwater robot system;

[0012] Step 5: Based on the speed range of the underwater robot system obtained in Step 4, analyze the speed estimation results of the underwater robot system.

[0013] Further, step 1 specifically includes:

[0014] Based on the "UVIC-I" AUV platform, a systematic analysis of the AUV's state-space model was conducted, and the following state-space model was obtained through identification:

[0015]

[0016] Where x represents the state vector, u represents the control input vector, d represents the system identification error vector, y represents the measurement output vector, v represents the noise vector caused by sensor accuracy, C is a known constant matrix, and A, B, and D are obtained from experimental data through system identification.

[0017] Since the motion state of the AUV varies within a preset range, the system's state variables are also bounded throughout the entire operation; although the specific values ​​of the initial values, identification error, and measurement noise are unknown, they are all bounded variables, expressed in the following form:

[0018]

[0019] in, These represent the initial value x0, the identification error w, and the boundary of the measurement noise ν, respectively.

[0020] According to the definition of a centrosymmetric multicellular body, formula (2) is expressed as:

[0021]

[0022] in,

[0023] Furthermore, the centrosymmetric multicellular body is defined as follows:

[0024] s-order centrosymmetric multicell It is hypercube B s =[-1,+1] s The affine transformation can be written in the following form:

[0025]

[0026] in, This represents Minkowski symbols and operators, where c is... The center vector of G is... The generating matrix.

[0027] Furthermore, step 2 specifically includes:

[0028] Based on the properties of Minkowski sums, the properties of linear mappings, and x in the state-space model formula (1) + =Ax+Bu+d and in formula (3) The predictable reach set of “UVIC-I” AUV It can be represented in the following form:

[0029]

[0030] Predict reachability set Write it in the form of a centrally symmetric multicellular body:

[0031]

[0032] According to the definition of a centrosymmetric multicellular body, formula (6) is expressed as:

[0033]

[0034] Where δ is a one-dimensional unit vector;

[0035] Based on the properties of Minkowski sums, the properties of linear mappings, the state-space model formula (1) y=Cx+v and formula (3) Measurement strips for “UVIC-I” AUV It can be represented in the following form:

[0036]

[0037] There exists a one-dimensional unit vector Γ such that the measurement strip... It can be represented in the following form:

[0038] y-Cx=G v Γ (9)

[0039] Based on the order reduction algorithm, predict the reachable set. (7) and measurement strips (8) The reachable set of the system state is obtained by calculation. as follows:

[0040] c = Ac - +Bu - +Ly-LCAc - -LCBu - (10)

[0041]

[0042] Furthermore, the properties of the Minkowski sum are:

[0043] Two centrosymmetric multicells and The Minkowski atom is still a centrally symmetric multicellular atom and satisfies the following equation:

[0044]

[0045] The property of the linear mapping is:

[0046] Given a centrosymmetric multicell Given a matrix Π, whose linear transformation with respect to the matrix still results in a centrally symmetric polytope, and satisfies the following equation:

[0047] Π<c,G> =<Πc,ΠG> (14)

[0048] The order reduction algorithm is as follows:

[0049] For a centrosymmetric multicellular body Given an integer q such that n < q < s, rearrange the columns of matrix G in descending order of their Euclidean norms to form a new matrix. Make Among them, G a It is the first qn columns of G, and G b It is a diagonal matrix that satisfies

[0050] Furthermore, step 3 specifically includes:

[0051] According to the generation matrix (11) of the system state reachable set, the reachable set The set contains a correction matrix L that needs to be determined. In fact, different Ls will form reachability sets of different shapes and sizes. Therefore, choosing the most suitable correction matrix L is crucial. L directly affects the reachability set. The size of the reachable set affects the accuracy of velocity estimation; optimization of the reachable set... The size criterion J makes... To minimize the volume and obtain a precise velocity range, the following is a detailed analysis:

[0052] Define the dimensional criterion J = tr(G) T G), where G is the reachable set. The generating matrix is ​​obtained from the generating matrix (11) of the system state reachable set:

[0053] J = tr[(Q d -LCQ d (I-LC) T ]+tr(LQ v L T )+tr[(A-LCA)P - (A-LCA) T (15)

[0054] in,

[0055]

[0056]

[0057]

[0058] To optimize the size criterion J, based on matrix operation rules, we differentiate equation (15):

[0059]

[0060] According to formula (16), since the size criterion J is a convex function of the generating matrix G and also exhibits the form of a positive definite quadratic form, it must have a unique minimum value; let have to:

[0061] L = (AP - A T +Q d C T Y - -1(17)

[0062] in,

[0063] Y - =C(AP) - A T +Q d C T +Q v

[0064] Based on formula (17), the optimal correction matrix L is obtained. * Make reachable set The volume should be as small as possible, and the optimized reachable set as follows:

[0065] c = Ac - +Bu - +L * yL * CAc - -L * CBu - (18)

[0066]

[0067] Furthermore, step 4 specifically includes:

[0068] Based on the properties of the minimum interval envelope and the state-space model (1), the intervals of the system state are obtained as follows:

[0069]

[0070] Where, x - (i) and x + (i) represent the upper and lower boundaries of the i-th component of the system state x, respectively, and c(i) represents the optimal reachable set. middle

[0071] Heart c * The i-th component, G(i,j), represents the reachable set. Generating matrix G * The i-th row and j-th column.

[0072] Furthermore, the property of the minimum interval envelope is:

[0073] For an s-order centrosymmetric multicell Its minimum interval envelope It is obtained from the following formula:

[0074]

[0075] Among them, z - (i), z+ c(i) and c(i) represent z respectively - , z + Let G(i,j) represent the i-th row and j-th column of G, and c be the i-th component of G.

[0076] Furthermore, in step 4, we obtained the state interval formula (20) for the underwater robot system. When the state component is velocity, the velocity interval of the underwater robot system can be obtained. This velocity interval ensures that the actual velocity value of the underwater robot system must be within the estimated interval, because the ensemble estimation method is based on worst-case assumptions regarding the environment and noise. This method not only effectively reduces the dependence on high-cost sensors but also significantly enhances the robustness and stability of the system in complex marine environments. In summary, this method has broad application prospects and high practical value, and is suitable for various complex underwater operation scenarios.

[0077] The beneficial effects of this invention are as follows:

[0078] 1. This invention proposes an AUV velocity estimation method based on a centrosymmetric multicellular Kalman filter. This method is applicable to autonomous underwater vehicles with various configurations and motion conditions, and has wide applicability and versatility, greatly expanding the scope of application.

[0079] 2. Compared with traditional methods, the Kalman filter AUV velocity estimation method based on centrosymmetric multicells proposed in this invention can not only accurately estimate the velocity of the underwater robot, but also provide interval estimation of the velocity, thereby realizing effective monitoring of the velocity state and significantly improving the reliability and stability of autonomous underwater robots.

[0080] 3. The AUV velocity estimation method proposed in this invention can effectively cope with various environmental noises and uncertainties, and has high robustness. Whether in still water or in dynamic and complex marine environments, this method maintains high state estimation performance.

[0081] 4. The AUV velocity estimation method proposed in this invention provides a more cost-effective solution with higher measurement accuracy in various environments. Through advanced algorithm optimization, this method reduces reliance on expensive hardware, maintaining stable velocity estimation even when measurement accuracy is susceptible to environmental factors. This reduces overall system operating costs and significantly improves application flexibility. Attached Figure Description

[0082] Figure 1 Here is a flowchart of the Kalman filter AUV velocity estimation method based on centrosymmetric multicells;

[0083] Figure 2This is a structural diagram of the "UVIC-I" AUV system.

[0084] Figure 3 The estimated diving speed range for the "UVIC-I" AUV system;

[0085] Figure 4 The estimated results for the pitch angular velocity range of the "UVIC-I" AUV system. Detailed Implementation

[0086] The present invention will now be further described with reference to the accompanying drawings.

[0087] This invention provides an AUV velocity estimation method based on a centrosymmetric multicell Kalman filter, which requires the following relevant definitions and properties:

[0088] To simplify the notation, we omit the symbol k for discrete time, where the subscript + is used to represent time k+1 and the subscript - is used to represent time k-1.

[0089] Definition 1: Definition of a centrosymmetric multicell, s-order centrosymmetric multicell It is hypercube B s =[-1,+1] s The affine transformation can be written in the following form:

[0090]

[0091] in, This represents Minkowski symbols and operators, where c is... The center vector of G is... The generating matrix.

[0092] Property 1: Matrix operation rules. For matrices A, B, C, X with appropriate dimensions, the following equations hold:

[0093]

[0094] Property 2: Minkowski and two centrosymmetric multicellular bodies and The Minkowski atom is still a centrally symmetric multicellular atom and satisfies the following equation:

[0095]

[0096] Property 3: Linear mapping, given a centrally symmetric multicellular structure Given a matrix Π, whose linear transformation with respect to the matrix still results in a centrally symmetric polytope, and satisfies the following equation:

[0097]

[0098] Property 4: Order reduction algorithm, for a centrally symmetric multicell Given an integer q such that n < q < s, the columns of matrix G can be rearranged in descending order of their Euclidean norms to form a new matrix. Make Among them, G a It is the first qn columns of G, and G b It is a diagonal matrix that satisfies

[0099] Property 5: Minimal interval envelope, for a centrosymmetric multicell of order s. Its minimum interval envelope It can be obtained from the following formula:

[0100]

[0101] Among them, z - (i), z + c(i) and c(i) represent z respectively - , z + Let G(i,j) represent the i-th row and j-th column of G, and c be the i-th component of G.

[0102] The specific structure of the "UVIC-I" AUV of this invention is as follows: Figure 2 As shown, the electronics compartment is located on top of the "UVIC-I" AUV and houses various electronic components to ensure protection and stable operation in the underwater environment. A robotic arm for underwater operations is mounted at the front of the AUV, enabling it to perform delicate tasks such as underwater grasping and manipulation. Furthermore, the "UVIC-I" AUV is equipped with various sensors, such as depth gauges and digital compasses, ensuring the accuracy and stability of attitude control during diving, thereby guaranteeing efficient and safe operation. The specific implementation scheme of this invention is as follows:

[0103] Experiments were conducted on the "UVIC-I" AUV in a water tank. During the experiment, the "UVIC-I" AUV operated from startup to reaching a preset steady state and maintained that state, exhibiting stable speed and attitude. The diving depth Z, diving speed w, pitch angle θ, and pitch angular velocity q of the "UVIC-I" AUV in the vertical plane were mainly controlled and achieved by the thrust T1 and T2 generated by the vertical thrusters. Based on the experimental data, the state-space model of the "UVIC-I" AUV in the vertical plane was identified as follows:

[0104]

[0105] in,

[0106]

[0107] Given that the motion state of the AUV varies within a preset range, the system's state variables are also bounded throughout the entire operation. Although the specific values ​​of the initial values, identification error, and measurement noise are unknown, they are all bounded variables and can be expressed in the following form:

[0108]

[0109] in, Let x0 be the initial value, w be the identification error, and ν be the boundary of the measurement noise.

[0110] According to the definition of a centrosymmetric multicellular body, the assumption (28) can be expressed as:

[0111]

[0112] in

[0113] Based on Minkowski equation (24), linear mapping equation (25), and state-space model equation x + =Ax+Bu+d and the assumption in (29) The predictable reach set of “UVIC-I” AUV It can be represented in the following form:

[0114]

[0115] The predictable reachable set (30) is written in the form of a centrosymmetric polytope:

[0116]

[0117] According to the definition of a centrosymmetric multicellular body, (31) can be expressed as:

[0118]

[0119] Here, δ is a one-dimensional unit vector.

[0120] Based on Minkowski's formula (24), the linear mapping formula (25), the state-space model equation y=Cx+v, and the assumptions in (29) Measurement strips for “UVIC-I” AUV It can be represented in the following form:

[0121]

[0122] There exists a one-dimensional unit vector Γ such that the measurement strip... It can be represented in the following form:

[0123] y-Cx=G v Γ (34)

[0124] Based on predictable reachability set and measuring strips (33) We can obtain the reachable set of the system state by calculation. The specific steps are as follows:

[0125] Substituting (32) into (34), the following equation holds:

[0126] C[AG - G d ]δ=yG v Γ-CAc - -CBu - (35)

[0127] At the same time, (32) is expressed in the following form:

[0128] x = Ac - +Bu - +LC[AG - G d ]δ+(I-LC)[AG - G d ]δ (36)

[0129] Where L is the correction matrix to be determined.

[0130] Substituting (35) into (36), the following equation holds:

[0131] x = Ac - +Bu - +Ly-LG v Γ-LCAc - -LCBu - +(I-LC)[AG - G d ]δ (37)

[0132] Since δ and Γ are both unit vectors, then It is also a unit vector. According to the definition of a centrosymmetric polytope, Minkowski and formula (24), the order reduction algorithm and the linear mapping formula (25), formula (37) can be expressed in the following form:

[0133]

[0134] c = Ac - +Bu - +Ly-LCAc - -LCBu - (39)

[0135]

[0136] make This allows us to obtain the reachable set of the “UVIC-I” AUV system state.

[0137] Define the dimensional criterion J = tr(G) T G), where G is the reachable set. The generating matrix, according to (40), is:

[0138] J = tr[(Q d -LCQ d (I-LC) T ]+tr(LQ v L T )+tr[(A-LCA)P - (A-LCA) T (42)

[0139] in,

[0140]

[0141] To optimize the size criterion J, based on the matrix operation rules, we differentiate (42):

[0142]

[0143] According to formula (43), since the size criterion J is a convex function of the generating matrix G and also exhibits the form of a positive definite quadratic form, it must have a unique minimum value. Let We can obtain:

[0144] L = (AP - A T +Q d C T Y - -1 (44)

[0145] in,

[0146] Y - =C(AP) - A T +Q d C T +Q v

[0147] Based on formula (44), the optimal correction matrix L can be obtained. * Make reachable set The volume should be as small as possible, and the optimized reachable set as follows:

[0148] c = Ac - +Bu - +L * yL * CAc - -L * CBu - (45)

[0149]

[0150] Based on the minimum interval envelope property formula (26) and the state-space model (27), the intervals of the system state can be obtained as follows:

[0151]

[0152] Where, x - (i) and x + (i) represent the upper and lower boundaries of the i-th component of the system state x, respectively, and c(i) represents the optimal reachable set. Center C * The i-th component, G(i,j), represents the reachable set. Generating matrix G * The i-th row and j-th column.

[0153] For the state-space model (27), the target velocity corresponds to the first and second components of the system state x, i.e., i = 1, 2. According to formula (47), the velocity range can be expressed as:

[0154]

[0155]

[0156] Based on the speed range calculated by formulas (48) and (49), effective speed monitoring can be achieved.

[0157] The sampling process of the "UVIC-I" AUV begins at startup, with a sampling frequency of 5Hz, meaning data is collected every 0.2 seconds. Since both the diving depth Z and pitch angle θ can be measured, the measurement matrix... Through the identification and analysis of the experimental data, the parameter matrices A, B, and D are obtained as follows:

[0158]

[0159] Based on the feedback from the experimental data, the magnitudes of the identification error and measurement noise can be obtained as follows:

[0160]

[0161] Based on the above conditions, the estimation results of the diving speed and pitch rate of the "UVIC-I" AUV system are as follows: Figure 3-4 As shown, the black star-shaped broken line represents the true values ​​of the dive velocity and pitch velocity of the "UVIC-I" AUV at various times. The two red dashed lines represent the upper and lower boundaries of the intervals for dive velocity and pitch velocity determined by the calculation method used in this invention, respectively. The cyan area within the red boundaries shows the optimal reachable set of the "UVIC-I" AUV. The green star-shaped broken line represents the estimated values ​​of the dive velocity and pitch velocity of the "UVIC-I" AUV at various times calculated by the Kalman filter method. Figure 3-4 As can be seen, the Kalman filter method can only perform point estimation of velocity, that is, obtain a single estimate of velocity at each sampling time. This estimation method is difficult to fully express the range or uncertainty of velocity changes when facing scenarios with large noise or uncertainties. However, the calculation method adopted in this invention can provide interval estimation of velocity. It can not only give the optimal estimate of velocity, but also provide the upper and lower limits of its possible fluctuations. When the system state has large uncertainties, interval estimation can more comprehensively reflect the true range of velocity changes, thereby improving the adaptability and reliability of the system in complex environments.

[0162] In summary, this invention addresses the problems of high cost and limited accuracy of Doppler velocimeters in certain environments by proposing an AUV velocity estimation method based on a centrosymmetric multicell Kalman filter. First, a systematic analysis of the state-space model of the autonomous underwater vehicle (AUV) is conducted. Then, combining the properties of centrosymmetric multicells and the concept of Kalman filtering, the reachability set of the AUV system state is calculated and optimized. The velocity range of the AUV is then calculated using the optimal reachability set, enabling effective velocity monitoring and ensuring the stability and reliability of the AUV.

[0163] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for AUV velocity estimation based on a centrosymmetric multicell Kalman filter, characterized in that: The specific steps are as follows: Step 1: Analyze the state-space model of the autonomous underwater robot system, wherein the model is; Where x represents the state vector, u represents the control input vector, d represents the error vector of system identification, y represents a vector, v represents the noise vector caused by sensor accuracy, C is a known constant matrix, and A, B, and D are obtained from experimental data through system identification. Initial values, identification error, and measurement noise are all bounded variables, satisfying: in, These represent the initial value x0, the identification error d, and the boundary of the measurement noise ν, respectively. According to the definition of a centrosymmetric multicellular body, formula (2) is expressed as: in, Step 2: Based on the state-space model formula in Step 1, use the definition of a centrally symmetric multicell, the Minkowski sum property, and the linear mapping property to calculate the reachable set of the underwater robot system's state; Predictable reachable set Write it in the form of a centrally symmetric multicellular body: According to the definition of a centrosymmetric multicellular body, formula (6) is expressed as: Where δ is a one-dimensional unit vector; Measurement strip Represented as: Based on the order reduction algorithm, formulas (7) and (8) are used to calculate the reachable set of the system state. as follows: c=Ac - +Bu - +Ly-LCAc - -LCBu - (10) Step 3: Optimize the reachability set of the underwater robot system state from Step 2; Define the dimensional criterion J = tr(G) T G), where G is the reachable set. The generating matrix is ​​obtained from the generating matrix (11) of the system state reachable set: J=tr[(G d -LCG d )(I-LC) T ]+tr(LG v L T )+tr[(A-LCA)P - (A-LCA) T ] (15) Differentiate equation (15) and set it to zero: make AND - =C(AP - TO T +Q d )C T +Q v Based on formula (17), the optimal correction matrix L is obtained. * The optimized reachable set is obtained. in, c=Ac - +Bu - +L * yL * CAc - -L * CBu - (18) Step 4: Based on the optimal reachable set obtained in Step 3, and according to the properties of the minimum interval envelope and the state space model obtained in Step 1, calculate the velocity range of the underwater robot system; Where, x - (i) and x + (i) represent the upper and lower boundaries of the i-th component of the system state x, respectively, and c(i) represents the optimal reachable set. Center C * The i-th component, G(i,j), represents the reachable set. Generating matrix G * The i-th row and j-th column; Step 5: Based on the speed range of the underwater robot system obtained in Step 4, analyze the speed estimation results of the underwater robot system.

2. The AUV velocity estimation method based on a centrosymmetric multicell Kalman filter according to claim 1, characterized in that: The definition of a centrosymmetric multicellular body is: s-order centrosymmetric multicell It is hypercube B s =[-1,+1] s The affine transformation can be written in the following form: in, This represents Minkowski symbols and operators, where c is... The center vector of G is... The generating matrix.

3. The AUV velocity estimation method based on a centrosymmetric multicell Kalman filter according to claim 1, characterized in that: In step 2: Based on the properties of Minkowski sums, the properties of linear mappings, and x in the state-space model formula (1) + =Ax+Bu+d and in formula (3) UVIC-I AUV Prediction Reach Set It can be represented in the following form: 。 4. The AUV velocity estimation method based on a centrosymmetric multicell Kalman filter according to claim 1, characterized in that: In step 2: There exists a one-dimensional unit vector Γ such that the measurement strip... It can be represented in the following form: y-Cx=G v C (9).

5. The AUV velocity estimation method based on a centrosymmetric multicell Kalman filter according to claim 3, characterized in that: The properties of the Minkowski sum are: Two centrosymmetric multicells and The Minkowski atom is still a centrally symmetric multicellular atom and satisfies the following equation: The property of the linear mapping is: Given a centrosymmetric multicell Given a matrix Π, whose linear transformation with respect to the matrix still results in a centrally symmetric polytope, and satisfies the following equation: Π<c,G> =<Πc,ΠG> (14) The order reduction algorithm is as follows: For a centrosymmetric multicellular body Given an integer q such that n < q < s, rearrange the columns of matrix G in descending order of their Euclidean norms to form a new matrix. Make Among them, G a It is the first qn columns of G, and G b It is a diagonal matrix that satisfies 6. The AUV velocity estimation method based on a centrosymmetric multicell Kalman filter according to claim 1, characterized in that: The property of the minimum interval envelope is: For an s-order centrosymmetric multicell Its minimum interval envelope It is obtained from the following formula: Among them, z - (i), z + (i) and c(i) represent z respectively - , z + Let G(i,j) represent the i-th row and j-th column of G, and c be the i-th component of G.

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