WO2022088797A1 - Measurement abnormality-considered cooperative localization method for cluster type multi-deep-sea underwater vehicle - Google Patents

Measurement abnormality-considered cooperative localization method for cluster type multi-deep-sea underwater vehicle Download PDF

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WO2022088797A1
WO2022088797A1 PCT/CN2021/108864 CN2021108864W WO2022088797A1 WO 2022088797 A1 WO2022088797 A1 WO 2022088797A1 CN 2021108864 W CN2021108864 W CN 2021108864W WO 2022088797 A1 WO2022088797 A1 WO 2022088797A1
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matrix
submersible
uncertainty
measurement
deep
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陈熙源
王俊玮
马振
方琳
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东南大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/203—Specially adapted for sailing ships
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/30—Assessment of water resources

Definitions

  • the invention belongs to the technical field of navigation, and relates to a navigation and positioning method of a deep-sea submersible, in particular to a cooperative positioning method of a clustered multi-submarine submersible that considers measurement anomalies.
  • the WEINIG cluster multi-submersible cooperative working system has the characteristics of wide detection range, strong fault tolerance and high work efficiency, and can realize diverse and complex underwater tasks that are difficult for single submersibles to complete.
  • the co-location technology of multiple deep-sea submersibles has certain particularities, and there are inherent difficulties such as complex environment interference, sensor limitations, and communication technology. Therefore, the information acquisition and communication between multiple deep-sea submersibles can only be accomplished by ultrasonic waves.
  • the relative distance information between the master and slave deep-sea submersibles often contains multiplicative noise.
  • the underwater acoustic wave speed is affected by changes in seawater temperature and salinity, and its uncertainty will cause the master-slave deep sea.
  • the present invention aims at the problem that the measurement abnormality is prone to occur in the collaborative positioning process of the multi-deep sea submersibles of the power cluster, which causes the accuracy and reliability of the collaborative navigation system to decrease, thereby providing a power cluster that considers the measurement abnormality.
  • the present invention effectively solves the difficulty that the traditional H ⁇ filter is difficult to model when there are multiplicative noise and parameter uncertainty in the measurement by designing a new form of krein space filter, and reduces the time and space complexity of the filter.
  • an adaptive algorithm is designed to estimate and compensate the parameter uncertainty of filter modeling online, so as to improve the matching degree between the physical process of co-location and the established mathematical model.
  • S1 Establish the state error equation of the slave submersible in the local geographic coordinate system and the measurement equation considering the abnormality of the relative distance measurement information of the master and slave submersible;
  • S3 Design an adaptive algorithm to estimate and compensate the parameter uncertainty of filter modeling online, and improve the matching degree between the physical process of co-location and the established mathematical model.
  • the further improvement of the present invention is:
  • the step S1 specifically includes the following steps:
  • ⁇ , ⁇ , ⁇ represent the attitude angle error from the submersible
  • ⁇ v E , ⁇ v N , ⁇ v U represent the northeast sky speed error from the submersible
  • ⁇ L, ⁇ , ⁇ h represent From the latitude, longitude and altitude errors of the submersible, represents the constant offset from the inertial totalizer in the submersible, represents the constant offset from the inertial gyroscope in the submersible;
  • the discrete time error equation of the inertial navigation system from the submarine in the local geographic coordinate system is:
  • Z k ⁇ R m is the amount of external information
  • L m , ⁇ m , h m are the positions of the main submersibles
  • L s , ⁇ s , h s are the positions of the submerged submersibles
  • H k [ ⁇ 3x6 I 3x3 ⁇ 3x6 ] is the measurement matrix
  • ⁇ H k is the uncertain parameter matrix
  • ⁇ is the multiplicative noise adaptation matrix
  • v 1,k , v 2,k are the uncorrelated measurement white Gaussian noise respectively.
  • ⁇ R ⁇ , ⁇ R L , and ⁇ R h are mainly the relative eastward distance, northward relative distance and vertical relative distance from the deep-sea submersible;
  • ⁇ V represents the uncertainty of the underwater acoustic wave velocity V
  • ⁇ L , ⁇ ⁇ , and ⁇ h represent the underwater acoustic wave transmission time.
  • step S2 is specifically as follows:
  • ⁇ k is the system noise, which is Gaussian white noise obeying zero mean
  • Y k is the estimation matrix
  • L k is the linear combination of the system state variables, usually the identity matrix I
  • ⁇ is the multiplicative noise adaptation matrix
  • ⁇ H k is an uncertain parameter matrix, and it satisfies:
  • ⁇ k is the unknown uncertainty matrix
  • Matrices A and E k are adaptation matrices of known dimensions, which describe the process of ⁇ k uncertainty matrix affecting ⁇ H k uncertain parameter matrix
  • Sk and ⁇ k are perturbation parameters, and have:
  • X 0 is the initial state quantity of the system
  • P 0 is the initial covariance
  • Q k , R k are the covariance matrix of the system state noise ⁇ k and the measurement noise v 2,k respectively
  • ⁇ is the H ⁇ filter in the Design threshold
  • ⁇ is a finite constant
  • R E is the adaptive noise variance
  • the ⁇ -level robust H ⁇ posterior filtering equation based on the new form of krein space system is:
  • step S3 specifically includes the following steps:
  • the adaptation matrix is estimated online according to the difference between the actual innovation covariance and the theoretical innovation covariance
  • the uncertain parameter array can improve the matching degree between the physical process of co-location and the established mathematical model, suppress the influence of the uncertainty of the underwater acoustic wave speed on the filter, and finally realize the overall high precision, High reliability collaborative navigation and positioning.
  • the present invention estimates and compensates the uncertainty of modeling parameters caused by the influence of changes in seawater temperature and salinity on the underwater acoustic wave speed by designing a new form of krein space filter, thereby improving the multi-deep sea vehicle. Accuracy of co-location. Secondly, it effectively solves the difficulty of modeling the traditional H ⁇ filter when there is multiplicative noise in the measurement, and reduces the time and space complexity of the filter while ensuring the high reliability of the multi-submarine co-location system.
  • Fig. 1 is the power cluster multi-deep sea submersible system in the embodiment of the present invention
  • FIG. 2 is a block diagram of the co-location of the WEINIG cluster type multi-deep-sea submersible system in the embodiment of the present invention.
  • this embodiment provides a method for co-locating clustered multi-submersible submersibles that considers measurement anomalies, including the following steps:
  • S1 Establish the state error equation of the slave submersible in the local geographic coordinate system and the measurement equation considering the abnormality of the relative distance measurement information of the master and slave submersibles, which are as follows:
  • ⁇ , ⁇ , ⁇ represent the attitude angle error from the submersible
  • ⁇ v E , ⁇ v N , ⁇ v U represent the northeast sky speed error from the submersible
  • ⁇ L, ⁇ , ⁇ h represent From the latitude, longitude and altitude errors of the submersible, represents the constant offset from the inertial totalizer in the submersible, represents the constant offset from the inertial gyroscope in the submersible;
  • the discrete time error equation of the inertial navigation system from the submarine in the local geographic coordinate system is:
  • Z k ⁇ R m is the amount of external information
  • L m , ⁇ m , h m are the positions of the main submersibles
  • L s , ⁇ s , h s are the positions of the submerged submersibles
  • H k [ ⁇ 3x6 I 3x3 ⁇ 3x6 ] is the measurement matrix
  • ⁇ H k is the uncertain parameter matrix
  • ⁇ is the multiplicative noise adaptation matrix
  • v 1,k , v 2,k are the uncorrelated measurement white Gaussian noise respectively.
  • ⁇ R ⁇ , ⁇ R L , and ⁇ R h are mainly the relative eastward distance, northward relative distance and vertical relative distance from the deep-sea submersible.
  • ⁇ V represents the uncertainty of the underwater acoustic wave velocity V
  • ⁇ L , ⁇ ⁇ , and ⁇ h represent the underwater acoustic wave transmission time.
  • ⁇ k is the system noise, which is Gaussian white noise obeying zero mean
  • Y k is the estimation matrix
  • L k is the linear combination of the system state variables, usually the identity matrix I
  • ⁇ is the multiplicative noise adaptation matrix
  • ⁇ H k is an uncertain parameter matrix, and it satisfies:
  • ⁇ k is the unknown uncertainty matrix
  • Matrices A and E k are adaptation matrices of known dimensions, which describe the process of ⁇ k uncertainty matrix affecting ⁇ H k uncertain parameter matrix
  • Sk and ⁇ k are perturbation parameters, and have:
  • X 0 is the initial state quantity of the system
  • P 0 is the initial covariance
  • Q k , R k are the covariance matrix of the system state noise ⁇ k and the measurement noise v 2,k respectively
  • ⁇ is the H ⁇ filter in the Design threshold
  • ⁇ is a finite constant.
  • the energy-constrained SQC inequality can only give an elliptical set, which is not suitable for describing the results of uncertain systems, the energy-constrained SQC inequality is transformed into an equivalent objective quadratic form:
  • R E is the adaptive noise variance
  • the adaptation matrix is estimated online according to the difference between the actual innovation covariance and the theoretical innovation covariance.
  • the uncertain parameter array can improve the matching degree between the physical process of co-location and the established mathematical model, suppress the influence of the uncertainty of the underwater acoustic wave speed on the filter, and finally realize the overall high precision, High reliability collaborative navigation and positioning.

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Abstract

A measurement abnormality-considered cooperative localization method for a powerful cluster type multi-deep-sea underwater vehicle. A state error equation and a measurement equation considering an abnormality of relative distance measurement information between master and slave deep-sea underwater vehicles are constructed in a local geographic coordinate system, thus providing a mathematical model for the implementation of cooperative localization of multiple deep-sea underwater vehicles.Then, according to the features of cooperative localization of multiple deep-sea underwater vehicles and the Krein space linear estimation theory, multiplicative noise and a parameter uncertainty are introduced, and a robust posteriori filtering equation for collaborative navigation of a new-form Krein space is designed under the condition of taking a measurement abnormality into consideration.Moreover, an adaptive algorithm is designed to perform on-line estimation and compensation on a parameter uncertainty of filter modeling, so as to improve the matching degree between a cooperative localization physical process and the constructed mathematical model.Finally, high-precision and high-reliability cooperative navigation and localization of the whole powerful cluster type multi-deep-sea underwater vehicle is implemented.

Description

考虑量测异常的集群式多深海潜航器的协同定位方法Co-location method for clustered multi-submersible submersibles considering measurement anomalies 技术领域technical field
本发明属于导航技术领域，涉及了深海潜航器的导航定位方法，具体是一种考虑量测异常的集群式多深海潜航器的协同定位方法。The invention belongs to the technical field of navigation, and relates to a navigation and positioning method of a deep-sea submersible, in particular to a cooperative positioning method of a clustered multi-submarine submersible that considers measurement anomalies.
背景技术Background technique
威力集群多深海潜航器协同工作***具有探测范围广、容错能力强、工作效率高的特点，能够实现单体深海潜航器难以完成的多样化、复杂化水下任务。The WEINIG cluster multi-submersible cooperative working system has the characteristics of wide detection range, strong fault tolerance and high work efficiency, and can realize diverse and complex underwater tasks that are difficult for single submersibles to complete.
多深海潜航器的协同定位技术与空中多无人机、陆地多机器人协同工作***的协同定位技术相比有着一定的特殊性，存在着复杂环境干扰、传感器限制、通信技术等固有难点。因此多深海潜航器间的信息获取和交流只能靠超声波来完成。Compared with the cooperative positioning technology of multi-unmanned aerial vehicles and land-based multi-robot cooperative working systems, the co-location technology of multiple deep-sea submersibles has certain particularities, and there are inherent difficulties such as complex environment interference, sensor limitations, and communication technology. Therefore, the information acquisition and communication between multiple deep-sea submersibles can only be accomplished by ultrasonic waves.
但由于超声波距离传感器的信号相关特性，主从深海潜航器间的相对距离信息中往往含有乘性噪声，同时水下声波波速受海水温度、盐度变化影响，其不确定性会造成主从深海潜航器的相对距离建模中的参数存在不确定性。这两种情况统称为量测异常，会造成主从潜航器协同导航***的定位精度降低，甚至于失效。However, due to the signal-related characteristics of the ultrasonic distance sensor, the relative distance information between the master and slave deep-sea submersibles often contains multiplicative noise. At the same time, the underwater acoustic wave speed is affected by changes in seawater temperature and salinity, and its uncertainty will cause the master-slave deep sea. There is uncertainty about the parameters in the relative distance modeling of the submarine. These two situations are collectively referred to as measurement anomalies, which will reduce the positioning accuracy of the master-slave submersible cooperative navigation system, or even fail.
因此在海洋复杂的环境中，考虑量测异常情况下实现主从式深海潜航器的精准协同定位是目前多深海潜航器研究的一个热门方向。Therefore, in the complex marine environment, it is a popular direction in the current research on multi-submersible submersibles to realize the precise co-location of master-slave submersibles considering measurement anomalies.
发明内容SUMMARY OF THE INVENTION
为解决上述问题，本发明针对威力集群多深海潜航器在协同定位过程中容易出现量测异常情况，造成协同导航***的精度和可靠性下降的问题，从而提供一种考虑量测异常的威力集群式多深海潜航器协同定位方法。In order to solve the above problems, the present invention aims at the problem that the measurement abnormality is prone to occur in the collaborative positioning process of the multi-deep sea submersibles of the power cluster, which causes the accuracy and reliability of the collaborative navigation system to decrease, thereby providing a power cluster that considers the measurement abnormality. A method for co-location of multi-submersible submersibles.
本发明通过设计新形式krein空间滤波器来有效解决量测中存在乘性噪声和参数不确定性时传统H∞滤波器难以建模的困难，降低滤波器的时空复杂度。同时，设计自适应算法对滤波器建模的参数不确定性进行在线估计和补偿，提高协同定位物理过程与所建数学模型的匹配度。最终实现威力集群多深海潜航器整体的高精度、高可靠性协同导航定位。The present invention effectively solves the difficulty that the traditional H∞ filter is difficult to model when there are multiplicative noise and parameter uncertainty in the measurement by designing a new form of krein space filter, and reduces the time and space complexity of the filter. At the same time, an adaptive algorithm is designed to estimate and compensate the parameter uncertainty of filter modeling online, so as to improve the matching degree between the physical process of co-location and the established mathematical model. Finally, the high-precision and high-reliability cooperative navigation and positioning of the multi-deep-sea submersibles of the Weinig cluster will be realized.
技术方案：为实现上述发明目的，本发明采用的技术方案，包括如下步骤：Technical scheme: In order to realize the above-mentioned purpose of the invention, the technical scheme adopted in the present invention includes the following steps:
S1：建立从深海潜航器在当地地理坐标系下的状态误差方程和考虑主从深海潜航器的相对距离测量信息异常的量测方程；S1: Establish the state error equation of the slave submersible in the local geographic coordinate system and the measurement equation considering the abnormality of the relative distance measurement information of the master and slave submersible;
S2：根据多深海潜航器协同定位的特点以及Krein空间线性估计理论，引入乘性噪声和参数不确定性，在考虑量测异常的情况下设计新形式Krein空间的协同导航的鲁棒后验滤波方程；S2: According to the characteristics of multi-submersible co-location and the linear estimation theory of Krein space, multiplicative noise and parameter uncertainty are introduced, and a new form of robust posterior filtering for cooperative navigation in Krein space is designed while considering measurement anomalies equation;
S3：设计自适应算法对滤波器建模的参数不确定性进行在线估计和补偿，提高协同定位物理过程与所建数学模型的匹配度。S3: Design an adaptive algorithm to estimate and compensate the parameter uncertainty of filter modeling online, and improve the matching degree between the physical process of co-location and the established mathematical model.
本发明进一步改进在于：The further improvement of the present invention is:
所述步骤S1具体包括如下步骤：The step S1 specifically includes the following steps:
S1-1:考虑一个15维***状态量的主从潜航器协同定位离散系 统：S1-1: Consider a master-slave submersible co-location discrete system with a 15-dimensional system state quantity:
Figure PCTCN2021108864-appb-000001
Figure PCTCN2021108864-appb-000001
其中，△θ,△φ,△ω表示从潜航器的姿态角误差，△v E,△v N,△v U代表从潜航器的东北天向速度误差，△L,△λ,△h表示从潜航器的纬度、经度、高度误差，
Figure PCTCN2021108864-appb-000002
代表从潜航器中惯性加计的常值偏移，
Figure PCTCN2021108864-appb-000003
代表从潜航器中惯性陀螺仪的常值偏移； Among them, △θ, △φ, △ω represent the attitude angle error from the submersible, △v E , △v N , △v U represent the northeast sky speed error from the submersible, △L, △λ, △h represent From the latitude, longitude and altitude errors of the submersible,
Figure PCTCN2021108864-appb-000002
represents the constant offset from the inertial totalizer in the submersible,
Figure PCTCN2021108864-appb-000003
represents the constant offset from the inertial gyroscope in the submersible;
从潜航器惯导***在当地地理坐标系下的离散时间误差方程为：The discrete time error equation of the inertial navigation system from the submarine in the local geographic coordinate system is:
Figure PCTCN2021108864-appb-000004
Figure PCTCN2021108864-appb-000004
其中，
Figure PCTCN2021108864-appb-000005
为状态转移矩阵，X k∈R n是为状态量，k是滤波时刻，τ s是离散时间间隔，
Figure PCTCN2021108864-appb-000006
是从载体坐标系到导航坐标系的转换矩阵。且
Figure PCTCN2021108864-appb-000007
为捷联惯导***连续时间误差方程中相应的***矩阵； in,
Figure PCTCN2021108864-appb-000005
is the state transition matrix, X k ∈ R n is the state quantity, k is the filtering moment, τ s is the discrete time interval,
Figure PCTCN2021108864-appb-000006
is the transformation matrix from the carrier coordinate system to the navigation coordinate system. and
Figure PCTCN2021108864-appb-000007
is the corresponding system matrix in the continuous time error equation of the strapdown inertial navigation system;
S1-2:考虑主从深海潜航器的相对距离测量信息异常的量测方程为：S1-2: The measurement equation considering the abnormality of the relative distance measurement information of the master-slave submersible is:
Figure PCTCN2021108864-appb-000008
Figure PCTCN2021108864-appb-000008
其中，Z k∈R m是为外信息量，L m、λ m、h m为主深海潜航器的位置，L s、λ s、h s为从深海潜航器的位置，H k＝[Ο 3x6 I 3x3 Ο 3x6]为量测矩阵，△H k为不确定参数阵，Γ为乘性噪声适配矩阵，v 1,k、v 2,k分别为互不相关的量测高斯白噪声。△R λ、△R L、△R h为主从深海潜航器的东向相对距离、北向相对距离、垂向相对距离； Among them, Z k ∈ R m is the amount of external information, L m , λ m , h m are the positions of the main submersibles, L s , λ s , h s are the positions of the submerged submersibles, H k = [Ο 3x6 I 3x3 Ο 3x6 ] is the measurement matrix, ΔH k is the uncertain parameter matrix, Γ is the multiplicative noise adaptation matrix, v 1,k , v 2,k are the uncorrelated measurement white Gaussian noise respectively. △R λ , △R L , and △R h are mainly the relative eastward distance, northward relative distance and vertical relative distance from the deep-sea submersible;
由于水下声波波速V的不确定性问题，会导致主从深海潜航器间 相对距离测量的不确定：Due to the uncertainty of the underwater acoustic wave velocity V, it will lead to the uncertainty of the relative distance measurement between the master and slave submersibles:
Figure PCTCN2021108864-appb-000009
Figure PCTCN2021108864-appb-000009
其中，△V表示水下声波波速V的不确定，τ L、τ λ、τ h表示水下声波传输时间。 Among them, ΔV represents the uncertainty of the underwater acoustic wave velocity V, and τ L , τ λ , and τ h represent the underwater acoustic wave transmission time.
本发明进一步改进在于：所述步骤S2其具体如下：A further improvement of the present invention is: the step S2 is specifically as follows:
S2-1：建立目标二次型S2-1: Establish the target quadratic form
考虑乘性噪声和参数不确定性的情况下一个线性离散***：Consider a linear discrete system with multiplicative noise and parametric uncertainty:
Figure PCTCN2021108864-appb-000010
Figure PCTCN2021108864-appb-000010
其中，μ k为***噪声，是服从零均值的高斯白噪声；Y k为估计矩阵；L k表示对***状态变量的线性组合，通常为单位阵I；Γ为乘性噪声适配矩阵；△H k为不确定参数阵，并且使其满足： Among them, μ k is the system noise, which is Gaussian white noise obeying zero mean; Y k is the estimation matrix; L k is the linear combination of the system state variables, usually the identity matrix I; Γ is the multiplicative noise adaptation matrix; △ H k is an uncertain parameter matrix, and it satisfies:
△HX k＝A△ kE kX k＝A△ kS k＝Aξ k △HX k =A△ k E k X k =A△ k S k =Aξ k
其中，△ k是未知的不确定性矩阵，且
Figure PCTCN2021108864-appb-000011
矩阵A、E k为已知维度的适配矩阵，它描述了△ k不确定性矩阵影响△H k不确定参数阵的过程；S k、ξ k为摄动参数，且有： where Δk is the unknown uncertainty matrix, and
Figure PCTCN2021108864-appb-000011
Matrices A and E k are adaptation matrices of known dimensions, which describe the process of △ k uncertainty matrix affecting △ H k uncertain parameter matrix; Sk and ξ k are perturbation parameters, and have:
||ξ k|| 2≤||S k|| 2 ||ξ k || 2 ≤||S k || 2
其中，||·||表示向量H 2范数； Among them, || · || represents the vector H 2 norm;
令v 1,kX k＝η k，将
Figure PCTCN2021108864-appb-000012
以及
Figure PCTCN2021108864-appb-000013
引入传统能量约束SQC不等式，建立新型的鲁棒H∞***的不确定性可用能量约束SQC不等式： Let v 1,k X k =η k , set
Figure PCTCN2021108864-appb-000012
as well as
Figure PCTCN2021108864-appb-000013
Introducing the traditional energy-constrained SQC inequality, a new type of robust H∞ system's uncertainty-available energy-constrained SQC inequality is established:
Figure PCTCN2021108864-appb-000014
Figure PCTCN2021108864-appb-000014
其中，X 0为***初始状态量；P 0为初始协方差；Q k、R k分别为***状态噪声μ k和量测噪声v 2,k的协方差阵；γ为H∞滤波器中的设计的阈值；
Figure PCTCN2021108864-appb-000015
表示状态量线性组合估计量Y k的误差；ε为一限定常数； Among them, X 0 is the initial state quantity of the system; P 0 is the initial covariance; Q k , R k are the covariance matrix of the system state noise μ k and the measurement noise v 2,k respectively; γ is the H∞ filter in the Design threshold;
Figure PCTCN2021108864-appb-000015
Represents the error of the state quantity linear combination estimator Y k ; ε is a finite constant;
将能量约束SQC不等式转换为等价目标二次型：Transform the energy-constrained SQC inequality into an equivalent objective quadratic form:
Figure PCTCN2021108864-appb-000016
Figure PCTCN2021108864-appb-000016
S2-2：建立新形式krein空间***模型和滤波方程S2-2: Establish a new form of krein space system model and filter equations
考虑乘性噪声和参数不确定性的情况下建立新形式krein空间***：A new form of krein space system is established considering multiplicative noise and parameter uncertainty:
Figure PCTCN2021108864-appb-000017
Figure PCTCN2021108864-appb-000017
其中，
Figure PCTCN2021108864-appb-000018
Figure PCTCN2021108864-appb-000019
in,
Figure PCTCN2021108864-appb-000018
Figure PCTCN2021108864-appb-000019
且具有形式噪声方差阵：and has the form noise variance matrix:
Figure PCTCN2021108864-appb-000020
Figure PCTCN2021108864-appb-000020
其中，
Figure PCTCN2021108864-appb-000021
R E为适配噪声方差；
Figure PCTCN2021108864-appb-000022
基于新形式krein空间***的γ水平鲁棒H∞后验滤波方程为： in,
Figure PCTCN2021108864-appb-000021
R E is the adaptive noise variance;
Figure PCTCN2021108864-appb-000022
The γ-level robust H∞ posterior filtering equation based on the new form of krein space system is:
Figure PCTCN2021108864-appb-000023
Figure PCTCN2021108864-appb-000023
Figure PCTCN2021108864-appb-000024
Figure PCTCN2021108864-appb-000024
Figure PCTCN2021108864-appb-000025
Figure PCTCN2021108864-appb-000025
其中，
Figure PCTCN2021108864-appb-000026
in,
Figure PCTCN2021108864-appb-000026
本发明进一步改进在于：所述步骤S3具体包括如下步骤：A further improvement of the present invention is that: the step S3 specifically includes the following steps:
理想情况中新形式krein空间***的γ水平鲁棒H∞后验滤波器的新息
Figure PCTCN2021108864-appb-000027
为： INNOVATIONS OF γ-Horizontal Robust H∞ Posterior Filters for New Form Krein Space Systems in Ideal Cases
Figure PCTCN2021108864-appb-000027
for:
Figure PCTCN2021108864-appb-000028
Figure PCTCN2021108864-appb-000028
则理论情况中
Figure PCTCN2021108864-appb-000029
而实际情况滤波器中估计的状态量
Figure PCTCN2021108864-appb-000030
受参数不确定性干扰成为有偏估计，其新息期望和协方差分别有
Figure PCTCN2021108864-appb-000031
且有： in the theoretical case
Figure PCTCN2021108864-appb-000029
While the actual state quantity estimated in the filter
Figure PCTCN2021108864-appb-000030
Affected by parameter uncertainty, it becomes a biased estimate, and its innovation expectation and covariance are respectively
Figure PCTCN2021108864-appb-000031
and have:
Figure PCTCN2021108864-appb-000032
Figure PCTCN2021108864-appb-000032
参数不确定性会反映在滤波器新息中，不确定性干扰越大，实际新息协方差与理论新息协方差越大。因此可以新息协方差入手，在线估计
Figure PCTCN2021108864-appb-000033
适配矩阵： The parameter uncertainty will be reflected in the filter innovation. The larger the uncertainty interference, the larger the actual innovation covariance and the theoretical innovation covariance. Therefore, we can start with the innovation covariance and estimate it online.
Figure PCTCN2021108864-appb-000033
Adaptation matrix:
Figure PCTCN2021108864-appb-000034
Figure PCTCN2021108864-appb-000034
即：which is:
Figure PCTCN2021108864-appb-000035
Figure PCTCN2021108864-appb-000035
当且仅当适配矩阵
Figure PCTCN2021108864-appb-000036
被正确估计时，上式取等号；于是在滤波器迭代过程，根据实际新息协方差与理论新息协方差的差异，在线估计适配矩阵
Figure PCTCN2021108864-appb-000037
if and only if the adaptation matrix
Figure PCTCN2021108864-appb-000036
When it is correctly estimated, the above formula takes the equal sign; then in the filter iteration process, the adaptation matrix is estimated online according to the difference between the actual innovation covariance and the theoretical innovation covariance
Figure PCTCN2021108864-appb-000037
Figure PCTCN2021108864-appb-000038
Figure PCTCN2021108864-appb-000038
将正确估计的适配矩阵
Figure PCTCN2021108864-appb-000039
带入△H k+1不确定参数阵，得到： will correctly estimate the adaptation matrix
Figure PCTCN2021108864-appb-000039
Bringing in the ΔH k+1 uncertain parameter matrix, we get:
Figure PCTCN2021108864-appb-000040
Figure PCTCN2021108864-appb-000040
正确估计的
Figure PCTCN2021108864-appb-000041
不确定参数阵能够提高协同定位物理过程与所建数学模型的匹配度，抑制水下声波波速的不确定性所给滤波器带来的影响，最终实现威力集群多深海潜航器整体的高精度、高可靠性协同导航定位。 correctly estimated
Figure PCTCN2021108864-appb-000041
The uncertain parameter array can improve the matching degree between the physical process of co-location and the established mathematical model, suppress the influence of the uncertainty of the underwater acoustic wave speed on the filter, and finally realize the overall high precision, High reliability collaborative navigation and positioning.
有益效果：Beneficial effects:
本发明与现有方法相比，通过设计新形式krein空间滤波器来估计和补偿了水下声波波速受海水温度、盐度变化影响而产生的建模参数不确定性，提高了多深海潜航器协同定位的精度。其次，有效解决了量测中存在乘性噪声时传统H∞滤波器难以建模的困难，在保证多深海潜航器协同定位***高可靠性的同时降低了滤波器的时空复杂度。Compared with the existing method, the present invention estimates and compensates the uncertainty of modeling parameters caused by the influence of changes in seawater temperature and salinity on the underwater acoustic wave speed by designing a new form of krein space filter, thereby improving the multi-deep sea vehicle. Accuracy of co-location. Secondly, it effectively solves the difficulty of modeling the traditional H∞ filter when there is multiplicative noise in the measurement, and reduces the time and space complexity of the filter while ensuring the high reliability of the multi-submarine co-location system.
附图说明Description of drawings
图1、是本发明实施例中威力集群多深海潜航器***；Fig. 1, is the power cluster multi-deep sea submersible system in the embodiment of the present invention;
图2是本发明实施例中考威力集群式多深海潜航器***协同定位框图。FIG. 2 is a block diagram of the co-location of the WEINIG cluster type multi-deep-sea submersible system in the embodiment of the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施方式，进一步阐明本发明，应理解下述 具体实施方式仅用于说明本发明而不用于限制本发明的范围。需要说明的是，下面描述中使用的词语“前”、“后”、“左”、“右”、“上”和“下”指的是附图中的方向，词语“内”和“外”分别指的是朝向或远离特定部件几何中心的方向。The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to the directions in the drawings, and the words "inner" and "outer" ” refer to directions towards or away from the geometric center of a particular part, respectively.
如图1、2所示，本实施例提供一种考虑量测异常的集群式多深海潜航器的协同定位方法，包括如下步骤：As shown in Figures 1 and 2, this embodiment provides a method for co-locating clustered multi-submersible submersibles that considers measurement anomalies, including the following steps:
S1：建立从深海潜航器在当地地理坐标系下的状态误差方程和考虑主从深海潜航器的相对距离测量信息异常的量测方程，其具体如下：S1: Establish the state error equation of the slave submersible in the local geographic coordinate system and the measurement equation considering the abnormality of the relative distance measurement information of the master and slave submersibles, which are as follows:
考虑一个15维***状态量的主从潜航器协同定位离散***：Consider a master-slave submersible co-located discrete system with a 15-dimensional system state:
Figure PCTCN2021108864-appb-000042
Figure PCTCN2021108864-appb-000042
其中，△θ,△φ,△ω表示从潜航器的姿态角误差，△v E,△v N,△v U代表从潜航器的东北天向速度误差，△L,△λ,△h表示从潜航器的纬度、经度、高度误差，
Figure PCTCN2021108864-appb-000043
代表从潜航器中惯性加计的常值偏移，
Figure PCTCN2021108864-appb-000044
代表从潜航器中惯性陀螺仪的常值偏移； Among them, △θ, △φ, △ω represent the attitude angle error from the submersible, △v E , △v N , △v U represent the northeast sky speed error from the submersible, △L, △λ, △h represent From the latitude, longitude and altitude errors of the submersible,
Figure PCTCN2021108864-appb-000043
represents the constant offset from the inertial totalizer in the submersible,
Figure PCTCN2021108864-appb-000044
represents the constant offset from the inertial gyroscope in the submersible;
从潜航器惯导***在当地地理坐标系下的离散时间误差方程为：The discrete time error equation of the inertial navigation system from the submarine in the local geographic coordinate system is:
Figure PCTCN2021108864-appb-000045
Figure PCTCN2021108864-appb-000045
其中，
Figure PCTCN2021108864-appb-000046
为状态转移矩阵，X k∈R n是为状态量，k是滤波时刻，τ s是离散时间间隔，
Figure PCTCN2021108864-appb-000047
是从载体坐标系到导航坐标系的转换矩阵。且
Figure PCTCN2021108864-appb-000048
为 捷联惯导***连续时间误差方程中相应的***矩阵。 in,
Figure PCTCN2021108864-appb-000046
is the state transition matrix, X k ∈ R n is the state quantity, k is the filtering moment, τ s is the discrete time interval,
Figure PCTCN2021108864-appb-000047
is the transformation matrix from the carrier coordinate system to the navigation coordinate system. and
Figure PCTCN2021108864-appb-000048
is the corresponding system matrix in the continuous-time error equation of the strapdown inertial navigation system.
考虑主从深海潜航器的相对距离测量信息异常的量测方程为：The measurement equation considering the abnormality of the relative distance measurement information of the master-slave submersible is:
Figure PCTCN2021108864-appb-000049
Figure PCTCN2021108864-appb-000049
其中，Z k∈R m是为外信息量，L m、λ m、h m为主深海潜航器的位置，L s、λ s、h s为从深海潜航器的位置，H k＝[Ο 3x6 I 3x3 Ο 3x6]为量测矩阵，△H k为不确定参数阵，Γ为乘性噪声适配矩阵，v 1,k、v 2,k分别为互不相关的量测高斯白噪声。△R λ、△R L、△R h为主从深海潜航器的东向相对距离、北向相对距离、垂向相对距离。 Among them, Z k ∈ R m is the amount of external information, L m , λ m , h m are the positions of the main submersibles, L s , λ s , h s are the positions of the submerged submersibles, H k = [Ο 3x6 I 3x3 Ο 3x6 ] is the measurement matrix, ΔH k is the uncertain parameter matrix, Γ is the multiplicative noise adaptation matrix, v 1,k , v 2,k are the uncorrelated measurement white Gaussian noise respectively. △R λ , △R L , and △R h are mainly the relative eastward distance, northward relative distance and vertical relative distance from the deep-sea submersible.
由于水下声波波速V的不确定性问题，会导致主从深海潜航器间相对距离测量的不确定：Due to the uncertainty of the underwater acoustic wave speed V, it will lead to the uncertainty of the relative distance measurement between the master and slave submersibles:
Figure PCTCN2021108864-appb-000050
Figure PCTCN2021108864-appb-000050
其中，△V表示水下声波波速V的不确定，τ L、τ λ、τ h表示水下声波传输时间。 Among them, ΔV represents the uncertainty of the underwater acoustic wave velocity V, and τ L , τ λ , and τ h represent the underwater acoustic wave transmission time.
S2：根据多深海潜航器协同定位的特点以及Krein空间线性估计理论，引入乘性噪声和参数不确定性，在考虑量测异常的情况下设计新形式Krein空间的协同导航的鲁棒滤波方程，其具体如下：S2: According to the characteristics of multi-submersible co-location and the linear estimation theory of Krein space, multiplicative noise and parameter uncertainty are introduced, and a robust filtering equation for cooperative navigation in a new form of Krein space is designed while considering measurement anomalies. The details are as follows:
S2-1：建立目标二次型S2-1: Establish the target quadratic form
考虑乘性噪声和参数不确定性的情况下一个线性离散***：Consider a linear discrete system with multiplicative noise and parametric uncertainty:
Figure PCTCN2021108864-appb-000051
Figure PCTCN2021108864-appb-000051
其中，μ k为***噪声，是服从零均值的高斯白噪声；Y k为估计矩阵；L k表示对***状态变量的线性组合，通常为单位阵I；Γ为乘性 噪声适配矩阵；△H k为不确定参数阵，并且使其满足： Among them, μ k is the system noise, which is Gaussian white noise obeying zero mean; Y k is the estimation matrix; L k is the linear combination of the system state variables, usually the identity matrix I; Γ is the multiplicative noise adaptation matrix; △ H k is an uncertain parameter matrix, and it satisfies:
△HX k＝A△ kE kX k＝A△ kS k＝Aξ k △HX k =A△ k E k X k =A△ k S k =Aξ k
其中，△ k是未知的不确定性矩阵，且
Figure PCTCN2021108864-appb-000052
矩阵A、E k为已知维度的适配矩阵，它描述了△ k不确定性矩阵影响△H k不确定参数阵的过程；S k、ξ k为摄动参数，且有： where Δk is the unknown uncertainty matrix, and
Figure PCTCN2021108864-appb-000052
Matrices A and E k are adaptation matrices of known dimensions, which describe the process of △ k uncertainty matrix affecting △ H k uncertain parameter matrix; Sk and ξ k are perturbation parameters, and have:
||ξ k|| 2≤||S k|| 2 ||ξ k || 2 ≤||S k || 2
其中，||·||表示向量H 2范数。 where ||·|| represents the vector H 2 norm.
令v 1,kX k＝η k，将
Figure PCTCN2021108864-appb-000053
以及
Figure PCTCN2021108864-appb-000054
引入传统能量约束SQC不等式，建立新型的鲁棒H∞***的不确定性可用能量约束SQC不等式： Let v 1,k X k =η k , set
Figure PCTCN2021108864-appb-000053
as well as
Figure PCTCN2021108864-appb-000054
Introducing the traditional energy-constrained SQC inequality, a new type of robust H∞ system's uncertainty-available energy-constrained SQC inequality is established:
Figure PCTCN2021108864-appb-000055
Figure PCTCN2021108864-appb-000055
其中，X 0为***初始状态量；P 0为初始协方差；Q k、R k分别为***状态噪声μ k和量测噪声v 2,k的协方差阵；γ为H∞滤波器中的设计的阈值；
Figure PCTCN2021108864-appb-000056
表示状态量线性组合估计量Y k的误差；ε为一限定常数。 Among them, X 0 is the initial state quantity of the system; P 0 is the initial covariance; Q k , R k are the covariance matrix of the system state noise μ k and the measurement noise v 2,k respectively; γ is the H∞ filter in the Design threshold;
Figure PCTCN2021108864-appb-000056
Represents the error of the state quantity linear combination estimator Y k ; ε is a finite constant.
由于能量约束SQC不等式只能给出椭圆集合，不适合描述不确定***的结果，因此将能量约束SQC不等式转换为等价目标二次型：Since the energy-constrained SQC inequality can only give an elliptical set, which is not suitable for describing the results of uncertain systems, the energy-constrained SQC inequality is transformed into an equivalent objective quadratic form:
Figure PCTCN2021108864-appb-000057
Figure PCTCN2021108864-appb-000057
S2-2：建立新形式krein空间***模型和滤波方程S2-2: Establish a new form of krein space system model and filter equations
考虑乘性噪声和参数不确定性的情况下建立新形式krein空间***：A new form of krein space system is established considering multiplicative noise and parameter uncertainty:
Figure PCTCN2021108864-appb-000058
Figure PCTCN2021108864-appb-000058
其中，
Figure PCTCN2021108864-appb-000059
Figure PCTCN2021108864-appb-000060
in,
Figure PCTCN2021108864-appb-000059
Figure PCTCN2021108864-appb-000060
且具有形式噪声方差阵：and has the form noise variance matrix:
Figure PCTCN2021108864-appb-000061
Figure PCTCN2021108864-appb-000061
其中，
Figure PCTCN2021108864-appb-000062
R E为适配噪声方差；
Figure PCTCN2021108864-appb-000063
in,
Figure PCTCN2021108864-appb-000062
R E is the adaptive noise variance;
Figure PCTCN2021108864-appb-000063
基于新形式krein空间***的γ水平鲁棒H∞后验滤波方程为：The γ-level robust H∞ posterior filtering equation based on the new form of krein space system is:
Figure PCTCN2021108864-appb-000064
Figure PCTCN2021108864-appb-000064
Figure PCTCN2021108864-appb-000065
Figure PCTCN2021108864-appb-000065
Figure PCTCN2021108864-appb-000066
Figure PCTCN2021108864-appb-000066
其中，
Figure PCTCN2021108864-appb-000067
值得注意的是，当且仅当
Figure PCTCN2021108864-appb-000068
成立时才能使用上述滤波方程。 in,
Figure PCTCN2021108864-appb-000067
Notably, if and only if
Figure PCTCN2021108864-appb-000068
The above filtering equation can only be used when it is established.
S3：由于水下声波波速的不确定性会造成主从深海潜航器的相对距离建模中的参数存在不确定性，最优滤波器估计的状态量
Figure PCTCN2021108864-appb-000069
无法满足精确的协同定位。设计自适应算法对滤波器建模的参数不确定性进行在线估计和补偿，提高协同定位物理过程与所建数学模型的匹配度，其具体如下： S3: Due to the uncertainty of the underwater acoustic wave velocity, the parameters in the relative distance modeling of the master-slave submersible will be uncertain, and the state quantity estimated by the optimal filter
Figure PCTCN2021108864-appb-000069
Accurate co-location cannot be satisfied. An adaptive algorithm is designed to estimate and compensate the parameter uncertainty of the filter modeling online, so as to improve the matching degree between the physical process of co-location and the established mathematical model. The details are as follows:
理想情况中新形式krein空间***的γ水平鲁棒H∞后验滤波器的新息
Figure PCTCN2021108864-appb-000070
为： INNOVATIONS OF γ-Horizontal Robust H∞ Posterior Filters for New Form Krein Space Systems in Ideal Cases
Figure PCTCN2021108864-appb-000070
for:
Figure PCTCN2021108864-appb-000071
Figure PCTCN2021108864-appb-000071
则理论情况中
Figure PCTCN2021108864-appb-000072
而实际情况滤波器中估计的状态量
Figure PCTCN2021108864-appb-000073
受参数不确定性干扰成为有偏估计，其新息期望和协方差分别有
Figure PCTCN2021108864-appb-000074
且有： in the theoretical case
Figure PCTCN2021108864-appb-000072
While the actual state quantity estimated in the filter
Figure PCTCN2021108864-appb-000073
Affected by parameter uncertainty, it becomes a biased estimate, and its innovation expectation and covariance are respectively
Figure PCTCN2021108864-appb-000074
and have:
Figure PCTCN2021108864-appb-000075
Figure PCTCN2021108864-appb-000075
参数不确定性会反映在滤波器新息中，不确定性干扰越大，实际新息协方差与理论新息协方差越大。因此可以新息协方差入手，在线估计
Figure PCTCN2021108864-appb-000076
适配矩阵： The parameter uncertainty will be reflected in the filter innovation. The larger the uncertainty interference, the larger the actual innovation covariance and the theoretical innovation covariance. Therefore, we can start with the innovation covariance and estimate it online.
Figure PCTCN2021108864-appb-000076
Adaptation matrix:
Figure PCTCN2021108864-appb-000077
Figure PCTCN2021108864-appb-000077
即：which is:
Figure PCTCN2021108864-appb-000078
Figure PCTCN2021108864-appb-000078
当且仅当适配矩阵
Figure PCTCN2021108864-appb-000079
被正确估计时，上式取等号。于是在滤波器迭代过程，根据实际新息协方差与理论新息协方差的差异，在线估计适配矩阵
Figure PCTCN2021108864-appb-000080
if and only if the adaptation matrix
Figure PCTCN2021108864-appb-000079
When correctly estimated, the above equation takes the equal sign. Therefore, in the filter iteration process, the adaptation matrix is estimated online according to the difference between the actual innovation covariance and the theoretical innovation covariance.
Figure PCTCN2021108864-appb-000080
Figure PCTCN2021108864-appb-000081
Figure PCTCN2021108864-appb-000081
将正确估计的适配矩阵
Figure PCTCN2021108864-appb-000082
带入△H k+1不确定参数阵，得到： will correctly estimate the adaptation matrix
Figure PCTCN2021108864-appb-000082
Bringing in the ΔH k+1 uncertain parameter matrix, we get:
Figure PCTCN2021108864-appb-000083
Figure PCTCN2021108864-appb-000083
正确估计的
Figure PCTCN2021108864-appb-000084
不确定参数阵能够提高协同定位物理过程与所建数学模型的匹配度，抑制水下声波波速的不确定性所给滤波器带来的影响，最终实现威力集群多深海潜航器整体的高精度、高可靠性协同导航定位。 correctly estimated
Figure PCTCN2021108864-appb-000084
The uncertain parameter array can improve the matching degree between the physical process of co-location and the established mathematical model, suppress the influence of the uncertainty of the underwater acoustic wave speed on the filter, and finally realize the overall high precision, High reliability collaborative navigation and positioning.
本发明方案所公开的技术手段不仅限于上述实施方式所公开的技术手段，还包括由以上技术特征任意组合所组成的技术方案。The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.

Claims (4)

  1. 一种考虑量测异常的威力集群式多深海潜航器协同定位方法，其特征在于：包括以下步骤：A powerful cluster-type multi-deep-sea submersible cooperative positioning method considering measurement anomalies, which is characterized by comprising the following steps:
    S1：建立从深海潜航器在当地地理坐标系下的状态误差方程和考虑主从深海潜航器的相对距离测量信息异常的量测方程；S1: Establish the state error equation of the slave submersible in the local geographic coordinate system and the measurement equation considering the abnormality of the relative distance measurement information of the master and slave submersible;
    S2：根据多深海潜航器协同定位的特点以及Krein空间线性估计理论，引入乘性噪声和参数不确定性，在考虑量测异常的情况下设计新形式Krein空间的协同导航的鲁棒后验滤波方程；S2: According to the characteristics of multi-submersible co-location and the linear estimation theory of Krein space, multiplicative noise and parameter uncertainty are introduced, and a new form of robust posterior filtering for cooperative navigation in Krein space is designed while considering measurement anomalies equation;
    S3：设计自适应算法对滤波器建模的参数不确定性进行在线估计和补偿，提高协同定位物理过程与所建数学模型的匹配度。S3: Design an adaptive algorithm to estimate and compensate the parameter uncertainty of filter modeling online, and improve the matching degree between the physical process of co-location and the established mathematical model.
  2. 如权利要求1所述的一种考虑量测异常的威力集群式多深海潜航器协同定位方法，其特征在于：所述步骤S1具体包括如下步骤：The method for co-locating multi-submersible submersibles in a power cluster type considering measurement anomalies according to claim 1, wherein the step S1 specifically includes the following steps:
    S1-1:考虑一个15维***状态量的主从潜航器协同定位离散***：S1-1: Consider a 15-dimensional system state quantity of the master-slave submersible co-location discrete system:
    Figure PCTCN2021108864-appb-100001
    Figure PCTCN2021108864-appb-100001
    其中，△θ,△φ,△ω表示从潜航器的姿态角误差，△v E,△v N,△v U代表从潜航器的东北天向速度误差，△L,△λ,△h表示从潜航器的纬度、经度、高度误差，
    Figure PCTCN2021108864-appb-100002
    代表从潜航器中惯性加计的常值偏移，
    Figure PCTCN2021108864-appb-100003
    代表从潜航器中惯性陀螺仪的常值偏移；     Among them, △θ, △φ, △ω represent the attitude angle error from the submersible, △v E , △v N , △v U represent the northeast sky speed error from the submersible, △L, △λ, △h represent From the latitude, longitude and altitude errors of the submersible,
    Figure PCTCN2021108864-appb-100002
    represents the constant offset from the inertial totalizer in the submersible,
    Figure PCTCN2021108864-appb-100003
    represents the constant offset from the inertial gyroscope in the submersible;
    从潜航器惯导***在当地地理坐标系下的离散时间误差方程为：The discrete time error equation of the inertial navigation system from the submarine in the local geographic coordinate system is:
    Figure PCTCN2021108864-appb-100004
    Figure PCTCN2021108864-appb-100004
    其中，
    Figure PCTCN2021108864-appb-100005
    为状态转移矩阵，X k∈R n是为状态量，k是滤波时刻，τ s是离散时间间隔，
    Figure PCTCN2021108864-appb-100006
    是从载体坐标系到导航坐标系的转换矩阵。且
    Figure PCTCN2021108864-appb-100007
    为捷联惯导***连续时间误差方程中相应的***矩阵；     in,
    Figure PCTCN2021108864-appb-100005
    is the state transition matrix, X k ∈ R n is the state quantity, k is the filtering moment, τ s is the discrete time interval,
    Figure PCTCN2021108864-appb-100006
    is the transformation matrix from the carrier coordinate system to the navigation coordinate system. and
    Figure PCTCN2021108864-appb-100007
    is the corresponding system matrix in the continuous time error equation of the strapdown inertial navigation system;
    S1-2:考虑主从深海潜航器的相对距离测量信息异常的量测方程为：S1-2: The measurement equation considering the abnormality of the relative distance measurement information of the master-slave submersible is:
    Figure PCTCN2021108864-appb-100008
    Figure PCTCN2021108864-appb-100008
    其中，Z k∈R m是为外信息量，L m、λ m、h m为主深海潜航器的位置，L s、λ s、h s为从深海潜航器的位置，H k＝[Ο 3x6 I 3x3 Ο 3x6]为量测矩阵，△H k为不确定参数阵，Γ为乘性噪声适配矩阵，v 1,k、v 2,k分别为互不相关的量测高斯白噪声。△R λ、△R L、△R h为主从深海潜航器的东向相对距离、北向相对距离、垂向相对距离； Among them, Z k ∈ R m is the amount of external information, L m , λ m , h m are the positions of the main submersibles, L s , λ s , h s are the positions of the submerged submersibles, H k = [Ο 3x6 I 3x3 Ο 3x6 ] is the measurement matrix, ΔH k is the uncertain parameter matrix, Γ is the multiplicative noise adaptation matrix, v 1,k , v 2,k are the uncorrelated measurement white Gaussian noise respectively. △R λ , △R L , and △R h are mainly the relative eastward distance, northward relative distance and vertical relative distance from the deep-sea submersible;
    由于水下声波波速V的不确定性问题，会导致主从深海潜航器间相对距离测量的不确定：Due to the uncertainty of the underwater acoustic wave speed V, it will lead to the uncertainty of the relative distance measurement between the master and slave submersibles:
    Figure PCTCN2021108864-appb-100009
    Figure PCTCN2021108864-appb-100009
    其中，△V表示水下声波波速V的不确定，τ L、τ λ、τ h表示水下声波传输时间。 Among them, ΔV represents the uncertainty of the underwater acoustic wave velocity V, and τ L , τ λ , and τ h represent the underwater acoustic wave transmission time.
  3. 根据权利要求1所述的一种考虑量测异常的威力集群式多深海潜航器协同定位方法，其特征在于：所述步骤S2其具体如下：A power cluster type multi-deep-sea submersible co-location method considering measurement anomalies according to claim 1, characterized in that: the step S2 is as follows:
    S2-1：建立目标二次型S2-1: Establish the target quadratic form
    考虑乘性噪声和参数不确定性的情况下一个线性离散***：Consider a linear discrete system with multiplicative noise and parametric uncertainty:
    Figure PCTCN2021108864-appb-100010
    Figure PCTCN2021108864-appb-100010
    其中，μ k为***噪声，是服从零均值的高斯白噪声；Y k为估计矩阵；L k表示对***状态变量的线性组合，通常为单位阵I；Γ为乘性噪声适配矩阵；△H k为不确定参数阵，并且使其满足： Among them, μ k is the system noise, which is Gaussian white noise obeying zero mean; Y k is the estimation matrix; L k is the linear combination of the system state variables, usually the identity matrix I; Γ is the multiplicative noise adaptation matrix; △ H k is an uncertain parameter matrix, and it satisfies:
    △HX k＝A△ kE kX k＝A△ kS k＝Aξ k △HX k =A△ k E k X k =A△ k S k =Aξ k
    其中，△ k是未知的不确定性矩阵，且
    Figure PCTCN2021108864-appb-100011
    矩阵A、E k为已知维度的适配矩阵，它描述了△ k不确定性矩阵影响△H k不确定参数阵的过程；S k、ξ k为摄动参数，且有：     where Δk is the unknown uncertainty matrix, and
    Figure PCTCN2021108864-appb-100011
    Matrices A and E k are adaptation matrices of known dimensions, which describe the process of △ k uncertainty matrix affecting △ H k uncertain parameter matrix; Sk and ξ k are perturbation parameters, and have:
    ||ξ k|| 2≤||S k|| 2 ||ξ k || 2 ≤||S k || 2
    其中，||·||表示向量H 2范数； Among them, || · || represents the vector H 2 norm;
    令v 1,kX k＝η k，将
    Figure PCTCN2021108864-appb-100012
    以及
    Figure PCTCN2021108864-appb-100013
    引入传统能量约束SQC不等式，建立新型的鲁棒H∞***的不确定性可用能量约束SQC不等式：     Let v 1,k X k =η k , set
    Figure PCTCN2021108864-appb-100012
    as well as
    Figure PCTCN2021108864-appb-100013
    Introducing the traditional energy-constrained SQC inequality, a new type of robust H∞ system's uncertainty-available energy-constrained SQC inequality is established:
    Figure PCTCN2021108864-appb-100014
    Figure PCTCN2021108864-appb-100014
    其中，X 0为***初始状态量；P 0为初始协方差；Q k、R k分别为***状态噪声μ k和量测噪声v 2,k的协方差阵；γ为H∞滤波器中的设计的阈值；
    Figure PCTCN2021108864-appb-100015
    表示状态量线性组合估计量Y k的误差；ε为一限定常数；     Among them, X 0 is the initial state quantity of the system; P 0 is the initial covariance; Q k , R k are the covariance matrix of the system state noise μ k and the measurement noise v 2,k respectively; γ is the H∞ filter in the Design threshold;
    Figure PCTCN2021108864-appb-100015
    Represents the error of the state quantity linear combination estimator Y k ; ε is a finite constant;
    将能量约束SQC不等式转换为等价目标二次型：Transform the energy-constrained SQC inequality into an equivalent objective quadratic form:
    Figure PCTCN2021108864-appb-100016
    Figure PCTCN2021108864-appb-100016
    S2-2：建立新形式krein空间***模型和滤波方程S2-2: Establish a new form of krein space system model and filter equations
    考虑乘性噪声和参数不确定性的情况下建立新形式krein空间***：A new form of krein space system is established considering multiplicative noise and parameter uncertainty:
    Figure PCTCN2021108864-appb-100017
    Figure PCTCN2021108864-appb-100017
    其中，
    Figure PCTCN2021108864-appb-100018
    Figure PCTCN2021108864-appb-100019
    in,
    Figure PCTCN2021108864-appb-100018
    Figure PCTCN2021108864-appb-100019
    且具有形式噪声方差阵：and has the form noise variance matrix:
    Figure PCTCN2021108864-appb-100020
    Figure PCTCN2021108864-appb-100020
    其中，
    Figure PCTCN2021108864-appb-100021
    R E为适配噪声方差；
    Figure PCTCN2021108864-appb-100022
    基于新形式krein空间***的γ水平鲁棒H∞后验滤波方程为：     in,
    Figure PCTCN2021108864-appb-100021
    R E is the adaptive noise variance;
    Figure PCTCN2021108864-appb-100022
    The γ-level robust H∞ posterior filtering equation based on the new form of krein space system is:
    Figure PCTCN2021108864-appb-100023
    Figure PCTCN2021108864-appb-100023
    Figure PCTCN2021108864-appb-100024
    Figure PCTCN2021108864-appb-100024
    Figure PCTCN2021108864-appb-100025
    Figure PCTCN2021108864-appb-100025
    其中，
    Figure PCTCN2021108864-appb-100026
    in,
    Figure PCTCN2021108864-appb-100026
  4. 根据权利要求1所述的一种考虑量测异常的威力集群式多深海潜航器协同定位方法，其特征在于：所述步骤S3具体包括如下步骤：理想情况中新形式krein空间***的γ水平鲁棒H∞后验滤波器的新息
    Figure PCTCN2021108864-appb-100027
    为：     The method for co-locating multi-deep-sea submersibles in a WEINIG cluster that considers measurement anomalies according to claim 1, wherein the step S3 specifically includes the following steps: ideally, the γ level of the new form of krein space system is robust The innovation of stick H∞ posterior filter
    Figure PCTCN2021108864-appb-100027
    for:
    Figure PCTCN2021108864-appb-100028
    Figure PCTCN2021108864-appb-100028
    则理论情况中
    Figure PCTCN2021108864-appb-100029
    而实际情况滤波器中估计的状态量
    Figure PCTCN2021108864-appb-100030
    受参数不确定性干扰成为有偏估计，其新息期望和协方差分别有
    Figure PCTCN2021108864-appb-100031
    且有：     in the theoretical case
    Figure PCTCN2021108864-appb-100029
    while the actual state quantity estimated in the filter
    Figure PCTCN2021108864-appb-100030
    Affected by parameter uncertainty, it becomes a biased estimate, and its innovation expectation and covariance are respectively
    Figure PCTCN2021108864-appb-100031
    and have:
    Figure PCTCN2021108864-appb-100032
    Figure PCTCN2021108864-appb-100032
    参数不确定性会反映在滤波器新息中，不确定性干扰越大，实际新息协方差与理论新息协方差越大。因此可以新息协方差入手，在线估计
    Figure PCTCN2021108864-appb-100033
    适配矩阵：     The parameter uncertainty will be reflected in the filter innovation. The larger the uncertainty interference, the larger the actual innovation covariance and the theoretical innovation covariance. Therefore, we can start with the innovation covariance and estimate it online.
    Figure PCTCN2021108864-appb-100033
    Adaptation matrix:
    Figure PCTCN2021108864-appb-100034
    Figure PCTCN2021108864-appb-100034
    即：which is:
    Figure PCTCN2021108864-appb-100035
    Figure PCTCN2021108864-appb-100035
    当且仅当适配矩阵
    Figure PCTCN2021108864-appb-100036
    被正确估计时，上式取等号；于是在滤波器迭代过程，根据实际新息协方差与理论新息协方差的差异，在线估计适配矩阵
    Figure PCTCN2021108864-appb-100037
    if and only if the adaptation matrix
    Figure PCTCN2021108864-appb-100036
    When it is correctly estimated, the above formula takes the equal sign; then in the filter iteration process, the adaptation matrix is estimated online according to the difference between the actual innovation covariance and the theoretical innovation covariance
    Figure PCTCN2021108864-appb-100037
    Figure PCTCN2021108864-appb-100038
    Figure PCTCN2021108864-appb-100038
    将正确估计的适配矩阵
    Figure PCTCN2021108864-appb-100039
    带入△H k+1不确定参数阵，得到：     will correctly estimate the adaptation matrix
    Figure PCTCN2021108864-appb-100039
    Bringing in the ΔH k+1 uncertain parameter matrix, we get:
    Figure PCTCN2021108864-appb-100040
    Figure PCTCN2021108864-appb-100040
    正确估计的
    Figure PCTCN2021108864-appb-100041
    不确定参数阵能够提高协同定位物理过程与所建数 学模型的匹配度，抑制水下声波波速的不确定性所给滤波器带来的影响，最终实现威力集群多深海潜航器整体的高精度、高可靠性协同导航定位。     correctly estimated
    Figure PCTCN2021108864-appb-100041
    The uncertain parameter array can improve the matching degree between the physical process of co-location and the established mathematical model, suppress the influence of the uncertainty of the underwater acoustic wave speed on the filter, and finally realize the overall high precision, High reliability collaborative navigation and positioning.
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