Parameter estimation method of ship response model based on multi-innovation extended Kalman filter

Abstract

The present invention discloses a ship response model parameter estimation method based on a multi-information extended Kalman filter, comprising the following steps: 1, determining the parameter to be estimated; 2, arranging the intermediate variables; 3, constructing the ship motion state; 4, solving the intermediate variables using the multi-information extended Kalman filter; 4-1, selecting the innovation length; 4-2, establishing a k-time multi-information extended observation deviation model; 4-3, establishing a k-time multi-information extended state gain matrix; 4-4, defining a multi-information weight matrix; 4-5, establishing a k-time state matrix update equation; 4-6, solving the intermediate variables; and 5, solving the parameter to be estimated using the intermediate variables. The present invention expands useful historical single innovation into multiple innovations and assigns an adaptively changing matrix to the multiple innovations, thereby greatly improving the filtering accuracy and effectively solving the problem of low estimation accuracy of the standard EKF in a strongly nonlinear system.

Description

Technical Field

[0001] The present invention relates to the field of ship monitoring, and in particular to a ship response model parameter estimation method based on multi-innovation extended Kalman filtering. Background Art

[0002] The ship response model established using force analysis is highly nonlinear, making its parameters, namely the various hydrodynamic coefficients, difficult to obtain. Traditional methods include theoretical calculation and measurement using specialized instruments. Theoretical calculations rely on experience and can achieve a certain level of accuracy, but cannot calculate all parameters. Using specialized instruments also requires multiple tests, which is costly. The Kalman filter, assuming a linear system, uses the minimum mean square error criterion to obtain a dynamic estimate of the target. However, strictly speaking, all systems are nonlinear, sometimes strongly nonlinear. Therefore, state estimation of moving targets in nonlinear systems has important theoretical significance and broad application prospects.

[0003] The Extended Kalman Filter (EKF) is one of the most widely used filtering methods for estimating the state of moving targets in nonlinear systems. However, in a standard EKF, only a single new information is used for prediction. That is, after linearization, the prediction at a certain moment is based solely on the state at the previous moment, without fully utilizing past data information. This results in the loss of useful information implicit in the past data, resulting in low identification accuracy. Therefore, the EKF is only suitable for weakly nonlinear systems. For strongly nonlinear systems, the EKF's performance is extremely unstable, and even filter divergence may occur. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned existing technologies and to provide a ship response model parameter estimation method based on multi-information extended Kalman filtering. The ship response model parameter estimation method based on multi-information extended Kalman filtering expands the useful historical single information into multiple information, and assigns an adaptively changing matrix to the multiple information, thereby greatly improving the filtering accuracy and effectively solving the problem of low estimation accuracy of the standard EKF in strongly nonlinear systems.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0006] A method for estimating ship response model parameters based on multi-innovation extended Kalman filtering includes the following steps.

[0007] Step 1. Determine the parameters to be estimated: The ship response model parameters include the rudder gain coefficient K, the ship following coefficient time constant T and the nonlinear coefficient α; among them, the rudder gain coefficient K and the ship following coefficient time constant T are the parameters to be estimated.

[0008] Step 2: Arrange the intermediate variables α1, α2 and β: transform the second-order derivative of the heading angle in the ship response model into Arranged as the first-order derivative of the heading angle and the rudder angle δ, the expressions of α1, α2 and β are:

[0009]

[0010] Step 3: Construct the ship motion state: According to the ship response model organized in step 2, the ship motion state x at the current k moment is obtained k The expression is:

[0011]

[0012] Where, ψ k and are the ship heading angle and the first-order derivative of the heading angle at the current k moment respectively.

[0013] α 1k , α 2k and β k are the values ​​of the intermediate variables α1, α2 and β at the current time k.

[0014] Step 4: Multi-innovation extended Kalman filter to solve α 1k , α 2k and β k , specifically including the following steps:

[0015] Step 4-1. Select the innovation length p: Select the required innovation length p according to different ship motion scenarios; where p ≥ 2.

[0016] Step 4-2: Establish the k-time multi-innovation extended observation deviation model E p,k , the specific expression is:

[0017]

[0018] Where, e k 、e k-1 and e k-p+1 are the observation deviations at time k, time k-1 and time k-p+1 respectively.

[0019] Step 4-3: Establish the k-time multi-innovation extended state gain matrix G p,k , the specific expression is:

[0020] G p,k =[G k G k-1 ... G k-p+1 ] T

[0021] Where G k , G k-1 and G k-p+1 are the state gain matrices at time k, time k-1, and time k-p+1 respectively.

[0022] Step 4-4: Define the multi-innovation weight matrix λ. The specific expression is:

[0023]

[0024] in:

[0025]

[0026] Where η1, η2 and η p are the weight coefficients of the product of the observation deviation and the state gain matrix at time k, k-1 and k-p+1 respectively; η n is any factor in the multi-innovation weight matrix λ, where 1≤n≤p.

[0027] Step 4-5: Establish the state matrix update equation at time k The specific expression is:

[0028]

[0029] Steps 4-6: Solve for α 1k , α 2k and β k : For x in step 3 k function; is the state matrix update equation at time k-1, and is the ship motion state x at time k-1 k-1 function; obtained by prediction Thus, we can solve α 1k , α 2k and β k .

[0030] Step 5. Solve the parameters to be estimated K and T: According to the calculation formulas of α1, α2 and β in step 2, reverse the calculation to obtain the rudder gain coefficient K and the ship tracking coefficient time constant T.

[0031] In step 4-4, n n According to the input heading angle ψ at time k k The first derivative of The specific calculation method is:

[0032] A. When hour,

[0033] B. When or hour,

[0034] In step 4-1, when the ship is in the speed and direction maintaining scenario, the innovation length p=5.

[0035] In step 4-1, when the ship is in a maneuvering scenario, the innovation length p=2.

[0036] In step 4-5, the state matrix update equation at time k = 0 is

[0037] The present invention has the following beneficial effects:

[0038] The present invention expands useful historical single innovation into multiple innovations and assigns an adaptively changing matrix to the multiple innovations, thereby greatly improving the filtering accuracy, being able to adapt to strong and weak nonlinear environments and increasing the convergence speed of parameter identification, thereby effectively solving the problem of low estimation accuracy of the standard EKF in strong nonlinear systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The present invention is a flow chart of a method for estimating ship response model parameters based on multi-innovation extended Kalman filtering. DETAILED DESCRIPTION

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and specific preferred embodiments.

[0041] The specific dimensions or specific values ​​used in this embodiment are only for illustrating the technical solution and do not limit the scope of protection of the present invention.

[0042] like Figure 1 As shown, a method for estimating ship response model parameters based on multi-innovation extended Kalman filtering includes the following steps.

[0043] Step 1: Determine the parameters to be estimated

[0044] The commonly used expression of the existing nonlinear ship second-order response model is:

[0045]

[0046] Where ψ is the heading angle, is the first-order derivative of the heading angle, is the second-order derivative, δ is the rudder angle, K represents the rudder gain coefficient, T represents the time constant of the ship's following coefficient, and α is the nonlinear coefficient. Here, the rudder gain coefficient K and the time constant of the ship's following coefficient T are the parameters to be estimated.

[0047] Step 2: Arrange the intermediate variables α1, α2 and β

[0048] The ship response model is sorted out to obtain:

[0049]

[0050] Then there is

[0051]

[0052] Through the above formula, the expressions of α1, α2 and β are:

[0053]

[0054] Step 3: Construct the ship's motion state

[0055] The nonlinear model of ship heading (1) can be written as

[0056] x k+1 =f k (x k ,u k )+ξ k (2)

[0057] Where u k is the system input at time k, including the heading angle and rudder angle at time k.

[0058] The above k is the process noise at time k, with mean 0 and variance Q k Gaussian distribution; where Q k is the covariance matrix, a symmetric semi-positive matrix, and its specific expression is:

[0059] Q k ={ξ k ξ k T}

[0060] The above x k+1 and x k are the ship motion states at time k+1 and time k, respectively, where x k It can be expressed as:

[0061]

[0062] Where, ψ k and are the ship heading angle and the first-order derivative of the heading angle at the current k moment respectively.

[0063] α 1k , α 2k and β k are the values ​​of the intermediate variables α1, α2 and β at the current time k.

[0064] The above f k (x k ,u k ) is the state equation at time k, which is the nonlinear function of the state at the next moment after discretization with respect to the state quantity and control quantity at the previous moment, and can be expressed as

[0065]

[0066] Where h is the sampling period, and δ is the frequency of sensor output data; k is the value of the rudder angle δ at time k.

[0067] Where h is the sampling period, which is the frequency of sensor output data.

[0068] The above equation f k (x k ,u k ) is

[0069]

[0070] Where, is the state matrix at time k.

[0071] Since sensors are suitable for providing information about the ship's status at discrete moments, the measurement model is formulated at discrete moments.

[0072] The measurement model v at discrete time k k Can be written as

[0073] v k =g k (x k )+η k

[0074] The above η k is the sensor measurement noise, which has a mean of 0 and a variance of R k Gaussian distribution; where R k is the covariance matrix, symmetric semi-positive matrix, and the specific expression is:

[0075] R k ={η k η k T}

[0076] The above g k (x k ) is the output equation at time k, which is also the observed value of the system, which can be written as

[0077]

[0078] The above equation gk (x k ) is

[0079]

[0080] The measurement value v of the above measurement model k It can be expressed in column vector form

[0081]

[0082] Step 4: Multi-innovation extended Kalman filter to solve α 1k , α 2k and β k

[0083] Kalman filter algorithm (EKF) solves α 1k , α 2k and β k , which is a mature existing technology, the specific solution method is:

[0084] Establishing the state prediction equation

[0085]

[0086] in is the optimal estimate of the system state at time k, and is the optimal estimate of the system at time k-1. and the system input u at time k-1 k-1 Prediction of the system state at time k.

[0087] Parameter estimation: Correct the prediction of the system state at time k obtained in the previous step based on the actual observation value (system output) of the system at time k to obtain the optimal estimate of the system state at time k.

[0088]

[0089] Where G k is the extended Kalman gain matrix; e k is the observation deviation at time k.

[0090] is the observed value of the system at time k-1.

[0091] The prediction error covariance matrix P at time k k|k-1 , specifically:

[0092]

[0093] in, for The Jacobian matrix of .

[0094] Pk-1|k-2 is the k-time prediction error covariance matrix.

[0095] is the covariance matrix and symmetric semi-positive matrix at time k-1, specifically:

[0096]

[0097] Filter gain matrix update

[0098]

[0099] in, yes The Jacobian matrix of ;

[0100] R k is the covariance matrix at time k, a symmetric positive semidefinite matrix.

[0101] Update the error covariance matrix

[0102]

[0103] Where I is the identity matrix.

[0104] It can be seen from this that in the EKF solution process of the existing technology, each estimation only uses the new information at the current k moment. If the observation error is large or the initial Q 0|0 、R 0|0 Inaccurate estimation may cause the parameters to not converge or converge slowly, thus leading to inaccurate identification results. In order to improve the accuracy of identification and the speed of convergence, the present invention expands the single innovation into multiple innovations.

[0105] In the present invention, the multi-innovation extended Kalman filter algorithm is used to solve α 1k , α 2k and β k The method preferably specifically comprises the following steps.

[0106] Step 4-1. Select the innovation length p: Select the desired innovation length p based on the ship's different motion scenarios, where p ≥ 2. When the ship is maintaining speed and direction, the preferred innovation length is p = 5. When the ship is maneuvering, the preferred innovation length is p = 2.

[0107] Step 4-2: Establish the k-time multi-innovation extended observation deviation model E p,k , the specific expression is:

[0108]

[0109] Where, e k 、e k-1 and ek-p+1 are the observation deviations at time k, time k-1 and time k-p+1 respectively.

[0110] v k-1 and are the measured value and observed value at time k-1 respectively.

[0111] v k-p+1 and are the measured value and observed value at time k-p+1 respectively.

[0112] Step 4-3: Establish the k-time multi-innovation extended state gain matrix G p,k , the specific expression is:

[0113] G p,k =[G k G k-1 ... G k-p+1 ] T

[0114] Where G k , G k-1 and G k-p+1 are the state gain matrices at time k, time k-1, and time k-p+1 respectively.

[0115] Step 4-4: Define the multi-innovation weight matrix λ. The specific expression is:

[0116]

[0117] in:

[0118]

[0119] Where η1, η2 and η p are the weight coefficients of the product of the observation deviation and the state gain matrix at time k, k-1 and k-p+1 respectively; η n is any factor in the multi-innovation weight matrix λ, where 1≤n≤p.

[0120] The above η n According to the input heading angle ψ at time k k The first derivative of The specific calculation method is:

[0121] A. When hour,

[0122] B. When or hour,

[0123] Step 4-5: Establish the state matrix update equation at time k The specific expression is:

[0124]

[0125] Steps 4-6: Solve for α 1k , α 2k and β k : For x in step 3 k function; is the state matrix update equation at time k-1, and is the ship motion state x at time k-1 k-1 function; obtained by prediction Thus, we can solve α 1k , α 2k and β k .

[0126] To initialize the recursive process, you must first give and P 0|0 , the common way to deal with it is to P 0|0 =θI, I is related to P 0|0 The corresponding identity matrix, θ, is a positive number, and its value depends on the system.

[0127] In addition, before the algorithm reaches the set innovation length p, the traditional EKF method can be used to obtain the expansion matrix G k,p The initial value in the model is not only reduced, but also reduces the interference of invalid historical data.

[0128] Step 5. Solve the parameters to be estimated K and T: According to the calculation formulas of α1, α2 and β in step 2, reverse the rudder gain coefficient K and the ship tracking coefficient time constant T, which are specifically:

[0129]

[0130] The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the scope of protection of the present invention.

Claims

1. A ship response model parameter estimation method based on multi-innovation extended Kalman filtering is characterized by: The steps include: Step 1: Determine the parameters to be estimated: the ship response model parameters include the rudder gain coefficient K, the ship tracking coefficient time constant T and the nonlinear coefficient α; in; The rudder gain coefficient K and the ship tracking coefficient time constant T are the parameters to be estimated; Step 2: Arrange the intermediate variables α1, α2 and β: transform the second-order derivative of the heading angle in the ship response model into Arranged as the first-order derivative of the heading angle and the rudder angle δ, the expressions of α1, α2 and β are: Step 3: Construct the ship motion state: According to the ship response model organized in step 2, the ship motion state x at the current k moment is obtained k The expression is: Where, ψ k and are the ship heading angle and the first-order derivative of the heading angle at the current k moment respectively; α 1k , α 2k and β k are the values ​​of the intermediate variables α1, α2 and β at the current time k; Step 4: Multi-innovation extended Kalman filter to solve α 1k , α 2k and β k , specifically including the following steps: Step 4-1. Select the innovation length p: Select the required innovation length p according to different ship motion scenarios; where p ≥ 2; Step 4-2: Establish the k-time multi-innovation extended observation deviation model E p,k , the specific expression is: Where, e k 、e k-1 and e k-p+1 are the observation deviations at time k, time k-1 and time k-p+1 respectively; Step 4-3: Establish the k-time multi-innovation extended state gain matrix G p,k , the specific expression is: G p,k =[G k G k-1 ... G k-p+1 ]T Where G k , G k-1 and G k-p+1 are the state gain matrices at time k, time k-1, and time k-p+1 respectively; Step 4-4: Define the multi-innovation weight matrix λ. The specific expression is: in: Where η1, η2 and η p are the weight coefficients of the product of the observation deviation and the state gain matrix at time k, k-1 and k-p+1 respectively; η n is any factor in the multi-innovation weight matrix λ, where 1≤n≤p; Step 4-5: Establish the state matrix update equation at time k The specific expression is: Steps 4-6: Solve for α 1k , α 2k and β k : For x in step 3 k function; is the state matrix update equation at time k-1, and is the ship motion state x at time k-1 k-1 function; obtained by prediction Thus, we can solve α 1k , α 2k and β k ; Step 5. Solve the parameters to be estimated K and T: According to the calculation formulas of α1, α2 and β in step 2, reverse the calculation to obtain the rudder gain coefficient K and the ship tracking coefficient time constant T.

2. The method for estimating ship response model parameters based on multi-innovation extended Kalman filtering according to claim 1, characterized in that: In step 4-4, n n According to the input heading angle ψ at time k k The first derivative of The specific calculation method is: A. When hour, B. When or hour, 3. The method for estimating ship response model parameters based on multi-innovation extended Kalman filtering according to claim 1, characterized in that: In step 4-1, when the ship is in the speed and direction maintaining scenario, the innovation length p=5.

4. The method for estimating ship response model parameters based on multi-innovation extended Kalman filtering according to claim 1, wherein: In step 4-1, when the ship is in a maneuvering scenario, the innovation length p=2.

5. The method for estimating ship response model parameters based on multi-innovation extended Kalman filtering according to claim 1, characterized in that: In step 4-5, the state matrix update equation at time k = 0 is

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