Maximum likelihood parameter estimation method for underwater vehicles with missing data

Abstract

This invention discloses a maximum likelihood recursive parameter estimation method for the output error autoregressive model of an underwater vehicle with missing data. Most control strategies are based on mathematical models, and establishing accurate mathematical models plays a crucial role in process control. Underwater vehicles operate in complex marine environments, capable of anticipating underwater conditions and autonomously completing specific tasks. Motion control is a critical aspect of underwater vehicle design; however, difficulties in obtaining observational data from sampling points due to sensor failures, hardware limitations, communication errors, or computer overload, coupled with colored noise interference, hinder the identification of parameters in the underwater vehicle's motion control system. To achieve online adjustment of the identification model and controller, this invention skips missing data by changing the sampling interval and combines a maximum likelihood recursive least squares algorithm to estimate system parameters. This invention includes steps such as constructing an output error autoregressive model with missing data, constructing a maximum likelihood recursive least squares parameter identification algorithm, and constructing the maximum likelihood recursive least squares algorithm itself. This invention is simple, efficient, and can be applied to parameter identification in the motion control system of underwater vehicles with missing data.

Description

Technical Field

[0001] This invention relates to a maximum likelihood recursive parameter estimation method for an autoregressive model of the output error of an underwater vehicle based on missing data. Background Technology

[0002] Underwater vehicles operate in complex marine environments, capable of anticipating underwater conditions and autonomously completing specific tasks. Motion control is a crucial aspect of underwater vehicle design; however, difficulties arise due to sensor malfunctions, hardware limitations, communication errors, or computer overload, making it challenging to obtain observational data from sampling points. Furthermore, colored noise interference hinders parameter identification of the underwater vehicle's motion control system. Therefore, parameter identification of underwater vehicles with reliable data despite colored noise interference is essential. System identification exhibits good robustness to model identification errors and sensor noise. By identifying the model, future outputs can be predicted based on historical information and future inputs of the controlled system, enabling online adjustments to the model and control system.

[0003] The maximum likelihood indirect recursive least squares algorithm can skip missing data by changing the sampling interval, enabling online identification of system parameters with missing data. The maximum likelihood indirect recursive least squares method can effectively estimate system parameters with a large amount of missing data. Therefore, this invention employs the maximum likelihood variable interval recursive least squares method to identify parameters of the underwater vehicle equation error autoregressive model with missing data.

[0004] The purpose of this invention is to identify the autoregressive model of underwater vehicle output error with missing data using the maximum likelihood recursive parameter estimation method.

[0005] The solution of the present invention is:

[0006] (1) Construct an identification model for the output error autoregressive model of an underwater vehicle based on missing data. The specific steps are as follows:

[0007] Step 1: Construct an autoregressive model based on output error (see attached structure). Figure 1 ;

[0008] Step 2: Based on this model, construct the following expression for the output error autoregressive model:

[0009]

[0010] The meanings of the symbols in the above formula are as follows: and It refers to the inputs and outputs of the system. It has a mean of zero and a variance of And it is white noise that follows a Gaussian distribution. , and It's about the unit shift operator. polynomials ( ), assuming , and It is known. When , , and .

[0011] Step 3: Construct intermediate variables for the autoregressive model of output error and The expression is as follows:

[0012]

[0013]

[0014] Step 4: Construct an autoregressive model for output error. The model identification is as follows:

[0015]

[0016] Step 5: When Define an integer sequence satisfy and Observation output and information vector available, It contains all observable data.

[0017] (2) The algorithm flow for maximum likelihood variable-margin recursive least squares parameter identification is constructed as follows:

[0018] Step 1: Start the recognition algorithm;

[0019] Step Two: Order Set initial values;

[0020] Step 3: Obtain input and output data, perform data preprocessing, and construct... and ;

[0021] Step 4: Calculate the gain vector Covariance Matrix ;

[0022] Step 5: Update the parameter estimation vector ;

[0023] Step 6: Calculation , , and filter variables , , ;

[0024] Step 7: Increment the value by 1 and repeat the above process.

[0025] The definitions of each variable are as follows:

[0026] Define the input quantity as The output is ;

[0027] definition It is a function with a mean of zero and a variance of . And it is white noise that satisfies a Gaussian distribution;

[0028] definition and For the relevant information vector;

[0029] definition , , For filtering variables;

[0030] definition and As an intermediate variable;

[0031] definition For parameter vectors;

[0032] definition for time The estimated value; for time The estimated value; for time The estimated value; for time The estimated value; , and They are respectively time , and The estimated value, , and They are respectively time , and The estimated value.

[0033] (3) Based on the maximum likelihood variable interval recursive least squares estimation algorithm flow, the maximum likelihood variable interval recursive least squares estimation algorithm is constructed.

[0034] The maximum likelihood variable-interval recursive least squares estimation algorithm described in step (3) is as follows:

[0035]

[0036]

[0037]

[0038] ,

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] The specific steps of the above algorithm

[0048] (1) Start the identification algorithm and let Set initial value , , , , , and ( ),in, It is an extremely large number;

[0049] (2) Calculate using equations (10) and (9) , ;

[0050] (3) Obtained through equations (7) and (8) respectively and ;

[0051] (4) Update the parameter estimate using equation (5). ;

[0052] (5) Calculate using equations (12)-(16) , , , , , ;

[0053] (6) Increment the value by 1 and repeat the above process;

[0054] The definitions of each variable are as follows:

[0055] Define the input quantity as The output is ;

[0056] definition It is a function with a mean of zero and a variance of . And it is white noise that satisfies a Gaussian distribution;

[0057] definition and For the relevant information vector;

[0058] definition , , For filtering variables;

[0059] definition and The intermediate vector;

[0060] definition For parameter vectors;

[0061] definition for time The estimated value; for time The estimated value; for time The estimated value; for time The estimated value; , and They are respectively time , and The estimated value, , and They are respectively time , and The estimated value. Attached Figure Description

[0062] The present invention will be further described below with reference to the accompanying drawings and examples.

[0063] The definitions of each variable are as follows:

[0064] Figure 1 This is the structure diagram of the autoregressive model for output error.

[0065] Figure 2 This is a flowchart of the maximum likelihood recursive parameter identification algorithm for this model.

[0066] Figures 3 to 5 This is a schematic diagram illustrating a specific example of the method of the present invention. Figure 3 Output missing diagram, Figure 4 for and The waveform diagram. Figure 5 parameter vector and estimated value The waveform diagram.

Claims

1. A maximum likelihood parameter estimation method for underwater vehicles with missing data, characterized by: Includes the following steps: (1) Construct an identification model for the output error autoregressive model of an underwater vehicle based on missing data. The specific steps are as follows: Step 1: Construct the structure of an autoregressive model based on output error: Step 2: Based on this model, construct the following expression for the output error autoregressive model: （1）； The meanings of the symbols in the above formula are as follows: and It refers to the inputs and outputs of the system. It has a mean of zero and a variance of . And it is white noise that follows a Gaussian distribution. and It's about the unit shift operator. polynomial Assuming and It is known that when and , Step 3: Construct intermediate variables for the autoregressive model of output error and The expression is as follows: ； Step 4: Construct an autoregressive model for output error and identify the model as follows: （2）； Step 5: When Define an integer sequence satisfy and Observation output and information vector available, Includes all observable data. (2) The algorithm flow for maximum likelihood variable-margin recursive least squares parameter identification is constructed as follows: Step 1: Start the recognition algorithm; Step 2: Command Set initial values; Step 3: Obtain input and output data, perform data preprocessing, and construct... and ; Step 4: Calculate the gain vector Covariance Matrix ; Step 5: Update the parameter estimation vector ; Step 6: Calculation and Step 7: Increment the value of t by 1 and repeat the above process. The definitions of each variable are as follows: Define the input quantity as u(t) s The output is y(t) s ); Define v(t) s () is a function with a mean of zero and a variance of . And it is white noise that satisfies a Gaussian distribution; definition For the relevant information vector; definition For filtering variables; definition As the intermediate vector; definition For parameter vectors; definition For t s time The estimated value; For t s time The estimated value; For t s time The estimated value; For t s time The estimated value; t s time The estimated value, and t s time Estimated value (3) Based on the maximum likelihood variable interval recursive least squares estimation algorithm flow, the maximum likelihood variable interval recursive least squares estimation algorithm is constructed.

2. As described in claim 1, characterized in that... The maximum likelihood variable-interval recursive least squares estimation algorithm described in step (3) is as follows: （3）； （4）； （5）； （6）； （7）； （8）； （9）； （10）； （11）； （12）； （13）； The specific steps of the above algorithm are as follows: (1) Start the identification algorithm, let t=1, and set the initial value. , ,in, It is an extremely large value; (2) Acquire input and output data, and perform data preprocessing; (3) Calculate using equations (7) and (6) ; (4) Obtained through equations (4) and (5) respectively ; (5) Update the parameter estimate using equation (3). ; (6) Calculate using Wu (8)-(13) ; (7) Increment the value of t by 1 and repeat the above process; The definitions of each variable are as follows: Define the input quantity as The output is ; definition It is a function with a mean of zero and a variance of . And it is white noise that follows a Gaussian distribution; definition and ; represents the relevant information vector; definition For filtering variables; definition As the intermediate vector; definition For parameter vectors; definition For t s time The estimated value; definition For t s time The estimated value; definition For t s time The estimated value; definition For t s time The estimated value; definition For t s time The estimated value; definition For t s time The estimated value.

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