ADAPTIVE ROBUST ESTIMATION METHOD AND SYSTEM FOR PARAMETERS OF UNMANNED SURFACE VESSEL

Abstract

An adaptive robust estimation method and system for parameters of an unmanned surface vessel belongs to the field of automatic control. First, an augmented state estimation problem considering an external disturbance for the unmanned surface vessel is constructed; augmented state vectors include a state vector of the unmanned surface vessel, a parameter vector, and an unknown input vector; and then, depending on a real-time input vector and a measurement vector of a system, a designed adaptive robust unscented Kalman filtering method is employed to obtain model parameters of the unmanned surface vessel.

Claims

1. An adaptive robust estimation method for parameters of an unmanned surface vessel, comprising the following steps: step 1: constructing an augmented state estimation problem considering an external disturbance for the unmanned surface vessel; augmented state vectors comprising a state vector of the unmanned surface vessel, a parameter vector of an unmanned surface vessel model, and an unknown input vector representing a modeling error of an unmanned surface vessel system and the external disturbance; step 2: depending on a real-time input vector and a measurement vector of the unmanned surface vessel system, employing an adaptive robust unscented Kalman filtering method having process noise covariance matrix constraints and based on the combination of a maximum cross entropy criterion and a minimum mean square error criterion to obtain model parameters of the unmanned surface vessel; the input vector comprising a control signal from a shipborne controller, and the measurement vector comprising data obtained by GPS and IMU measurement; a method for estimating the process noise covariance matrix comprising: firstly, employing an innovation-based adaptive method to estimate a noise covariance matrix .sub.k.sup.0; then, introducing covariance matrix constraints according to a known structure and dividing a process noise covariance matrix .sub.k to be estimated into a diagonal block without structure constraints and a diagonal block with structure constraints; and finally, employing KL divergence to construct and solve the following optimization problem: ${\stackrel{?}{Q}}_k^{1,j_1},{?}_k^{j_2}=\underset{{\stackrel{?}{Q}}_k^{1,j_1},{?}_k^{j_2}}{\min }{?}_{?}^{+?}p\left(x.Math.{\stackrel{?}{Q}}_k^0\right)\log \frac{p\left(x.Math.{\stackrel{?}{Q}}_k^0\right)}{p\left(x.Math.{\stackrel{?}{Q}}_k\right)}\mathrm{dx};$ wherein k represents the moment; .sub.k.sup.1,j.sup.1 represents the diagonal block without structure constraints; ?.sub.k.sup.j.sup.2 represents a coefficient of the diagonal block .sub.k.sup.2,j.sup.2 with structure constraints; .sub.k.sup.2,j.sup.2=?.sub.k.sup.j.sup.2.sub.k.sup.c,j.sup.2, .sub.k.sup.c,j.sup.2 is a known structure; j.sub.1=1, . . . , n.sub.1, j.sub.2=1, . . . , n.sub.2, n.sub.1 and n.sub.2 represent the number of the diagonal block without structure constraints and the number of the diagonal block with structure constraints, respectively; p(x|.sub.k.sup.0) and p(x|.sub.k) represent probability density functions of a random variable X with the covariance matrix being .sub.k.sup.0 and .sub.k respectively and obeying zero mean Gaussian distribution.

2. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 1, wherein the noise covariance matrix estimated by the innovation-based adaptive method is expressed as: ${\stackrel{?}{Q}}_k^0=\frac{1}{N}\underset{i=k_0}{\overset{k}{.Math.}}\left({\stackrel{?}{x}}_{i|i}-{\stackrel{?}{x}}_{i|i-1}\right){\left({\stackrel{?}{x}}_{i|i}-{\stackrel{?}{x}}_{i|i-1}\right)}^T,k_0=k-N+1,k?N$ wherein k.sub.0 represents an initial moment of a sample used for calculating the covariance matrix; N represents the quantity of the sample used; and {circumflex over (x)}.sub.i|i-1 and x.sub.i|i are a predicted value and an estimated value of the augmented state vector at an i th moment, respectively.

3. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 1, wherein the process noise covariance matrix to be estimated is expressed as: ${\stackrel{?}{Q}}_k=\mathrm{diag}\left[{\stackrel{?}{Q}}_k^{1,1},.Math.,{\stackrel{?}{Q}}_k^{1,n_1},{\stackrel{?}{Q}}_k^{2,1},.Math.,{\stackrel{?}{Q}}_k^{2,n_2}\right];$ in a case that .sup.c,j.sup.2=0 is present in an actual problem, this diagonal block is removed to ensure that .sub.k is positive definite, and .sup.2,j.sup.2=0 is directly given in an estimation result.

4. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 1, wherein an optimal solution for the optimization problem constructed by employing the KL divergence is: ${\stackrel{?}{Q}}_k^{1,j_1}={\stackrel{?}{Q}}_k^{3,j_1},{?}_k^{j_2}=\frac{1}{m_{j_2}}\mathrm{tr}\left[{\left({\stackrel{?}{Q}}_k^{c,j_2}\right)}^{-1}{\stackrel{?}{Q}}_k^{4,j_2}\right];$ wherein m.sub.j2 is the dimension of .sub.k.sup.c,j.sup.2; Q.sub.k.sup.3,j.sup.1 is a corresponding matrix block of .sub.k.sup.1,j.sup.i in .sub.k.sup.0 and .sub.k.sup.4,j.sup.2 is a corresponding matrix block of .sub.k.sup.2,j.sup.2 in .sub.k.sup.0.

5. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 1, wherein the augmented estimation problem constructed in step 1 employs a system equation as below: $x_k=\left[\begin{array}{c}{f}_{?}\left({?}_{k1},u_{k-1}\right)+G{d}_{k-1}\\ a_{k-1}\\ d_{k-1}\end{array}\right]+w_{k-1};$ $y_k=h_{?}\left({?}_k,u_k\right)+E{d}_k+v_k;$ wherein X.sub.k and y.sub.k are the augmented state vector and the measurement vector at a k th moment, respectively; ?.sub.k-1 and ?.sub.k are the state vectors of the unmanned surface vessel at a (k?1)th moment and the k th moment, respectively; u.sub.k-1 and u.sub.k are the input vectors at the (k?1)th moment and the k th moment, respectively; d.sub.k-1 and d.sub.k are the unknown input vectors at the (k?1)th moment and the k th moment, respectively; a.sub.k-1 is the parameter vector at the (k?1)th moment; f.sub.? represents nonlinear mapping from the state vector ?.sub.k-1 and the input vector u.sub.k-1 at the (k?1)th moment to the state vector ?.sub.k at the k th moment, without the consideration of noises and the unknown input vectors h.sub.? represents nonlinear mapping from the state vector ?.sub.k and the input vector u.sub.k at the k th moment to the measurement vector y.sub.k, without the consideration of the noises and the unknown input vectors; w.sub.k-1 is zero mean process noises at the (k?1)th moment; V.sub.k is zero mean measurement noises at the k th moment; and in a case that a system sampling period is T.sub.s, matrices G and E are expressed as: $G=T_s\left[\begin{array}{c}{0}_{3?3}\\ I_3\end{array}\right],E=\left[\begin{array}{cc}{0}_{6?2}& 0_{6?1}\\ I_2& 0_{2?1}\end{array}\right];$ I.sub.2 and I.sub.3 are 2?2 and 3?3 identity matrices, respectively.

6. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 5, wherein step 2 specifically comprises: step 21: initializing the adaptive robust unscented Kalman filtering, comprising an estimated value {circumflex over (x)}.sub.0|0 of the augmented state vector and a covariance matrix P.sub.0|0.sup.xx of an error thereof; step 22: acquiring the input vector u.sub.k and the measurement vector y.sub.k of the unmanned surface vessel system; step 23: predicating an augmented state vector {circumflex over (x)}.sub.k|k-1 at the k th moment and a covariance matrix P.sub.k|k-1.sup.xx of a prediction error of the augmented state vector; step 24: predicating a measurement vector ?.sub.k|k-1 at the k th moment, a covariance matrix P.sub.k|k-1.sup.yy of a prediction error of the measurement vector, and a cross covariance matrix P.sub.k|k-1.sup.yy; step 25: constructing an optimization problem employed by robust state estimation, comprising: linearizing a measurement equation for the unmanned surface vessel system by employing results of unscented transformation as follows: $y_k-{\stackrel{?}{y}}_{k|k-1}=H_k\left[x_k-{\stackrel{?}{x}}_{k|k-1}\right]+r_k;$ $H_k={\left(P_{k|k-1}^{xy}\right)}^T{\left(P_{k|k-1}^{xx}\right)}^{-1};$ wherein r.sub.k is noises of the linearized measurement equation, having a statistical property as below: $E\left[r_k\right]=0,{?}_k=E\left[r_k{r}_k^T\right]=P_{k|k-1}^{\mathrm{yy}}-{\left(P_{k|k-1}^{xy}\right)}^T{\left(P_{k|k-1}^{xx}\right)}^{-1}{P}_{k|k-1}^{xy};$ the system with the measurement equation linearized being written as: $\left[\begin{array}{c}{\stackrel{?}{x}}_{k|k-1}\\ y_k-{\stackrel{?}{y}}_{k|k-1}+H_k{\stackrel{?}{x}}_{k|k-1}\end{array}\right]=\left[\begin{array}{c}I\\ H_k\end{array}\right]x_k+{?}_k;$ wherein I is an identity matrix, and the vector ?.sub.k has the following properties: ${?}_k=\left[\begin{array}{c}{\stackrel{?}{x}}_{k|k-1}-x_k\\ r_k\end{array}\right];$ $E\left[{?}_k{?}_k^T\right]=\left[\begin{array}{cc}{P}_{k|k-1}^{\mathrm{xx}}& 0\\ 0& {?}_k\end{array}\right]=\left[\begin{array}{cc}{T_k^P\left(T_k^P\right)}^T& 0\\ 0& {T_k^{?}\left(T_k^{?}\right)}^T\end{array}\right]=T_k{T}_k^T;$ wherein T.sub.k.sup.P, T.sub.k.sup.?, and T.sub.k are Cholesky factors of P.sub.k|k-1.sup.xx, ?.sub.k, and E[?.sub.k?.sub.k.sup.T], respectively; further, the following equation being provided: $T_k^{-1}\left[\begin{array}{c}{\stackrel{?}{x}}_{k|k-1}\\ y_k-{\stackrel{?}{y}}_{k|k-1}+H_k{\stackrel{?}{x}}_{k|k-1}\end{array}\right]=T_k^{-1}\left[\begin{array}{c}I\\ H_k\end{array}\right]x_k+T_k^{-1}{?}_k;$ this equation being rewritten as: $Y_k=A_k{x}_k+e_k;$ wherein: $Y_k=T_k^{-1}\left[\begin{array}{c}{\stackrel{?}{x}}_{k|k-1}\\ y_k-{\stackrel{?}{y}}_{k|k-1}+H_k{\stackrel{?}{x}}_{k|k-1}\end{array}\right],A_k=T_k^{-1}\left[\begin{array}{c}I\\ H_k\end{array}\right],e_k=T_k^{-1}{?}_k;$ combining the maximum cross entropy criterion and the minimum mean square error criterion, the former being used for processing the process noises and the latter being used for processing the measurement noises; establishing and solving the following optimization problem to obtain optimal estimation {circumflex over (x)}.sub.k|k: ${\stackrel{?}{x}}_{k|k}=\arg \underset{x_k}{\min }\left\{\underset{i=1}{\overset{n}{.Math.}}\left[G_{?}\left(0\right)-G_{?}\left(e_k^i\right)\right]+w\underset{i=n+1}{\overset{n+m}{.Math.}}\left(e_k^i\right)\right\};$ wherein W is a weight coefficient; n is the dimension of the augmented state vector; m is the dimension of y.sub.k; e.sub.k.sup.i is an i th element of e.sub.k; ? is bandwidth; and G.sub.?(.Math.) is Gaussian kernel function; step 26: obtaining optimal estimation of the augmented state vector according to an iteration form of robust unscented Kalman filtering; step 27: estimating the process noise covariance matrix by employing an adaptive law having covariance matrix constraints; and step 28: determining whether to terminate the parameter estimation; if not, returning back to step 22.

7. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 1, wherein the state vector of the unmanned surface vessel comprises a center-of-mass position x, y and a yaw angle ? of the unmanned surface vessel under a world coordinate system, and a center-of-mass velocity u, v and a yaw velocity r of the unmanned surface vessel under a body coordinate system; and the parameter vector of the unmanned surface vessel model comprises an inertia-related parameter, a damping-related parameter, and a driving force-related parameter.

8. The adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 7, wherein in conjunction with kinematic and dynamical equations, state equations of a twin-propeller differential unmanned surface vessel system are obtained: $\stackrel{.}{x}=u\cos ?-v\sin ?;$ $\stackrel{.}{y}=u\sin ?+v\cos ?;$ $\stackrel{?}{?}=r;$ $\stackrel{.}{u}=a_{1}vr+a_2{r}^2+a_{5}u+a_6.Math.u.Math.u+a_{15}\left(.Math.{?}_1.Math.{?}_1+.Math.{?}_2.Math.{?}_2\right)-a_{16}\left(.Math.{?}_1.Math.+.Math.{?}_2.Math.\right)u;$ $\stackrel{.}{v}=a_{3}uv+a_{4}ur+a_{7}v+a_8.Math.v.Math.v+a_{9}r+a_{10}.Math.r.Math.r-a_{17}\left(.Math.{?}_1.Math.{?}_1-.Math.{?}_2.Math.{?}_2\right)+a_{18}\left(.Math.{?}_1.Math.-.Math.{?}_2.Math.\right)u;$ $\stackrel{.}{r}=-\frac{a_1{a}_3}{a_2}uv-a_{3}ur+a_{11}v+a_{12}.Math.v.Math.v+a_{13}r+a_{14}.Math.r.Math.r+\frac{a_1{a}_{17}}{a_2}\left(.Math.{?}_1.Math.{?}_1-.Math.{?}_2.Math.{?}_2\right)-\frac{a_1{a}_{18}}{a_2}\left(.Math.{?}_1.Math.-.Math.{?}_2.Math.\right)u;$ wherein a.sub.1, . . . , a.sub.4 are the inertia-related parameters, a.sub.5, . . . , a.sub.14 are the damping-related parameters, a.sub.15, . . . , a.sub.18 are the driving force-related parameters, and ?.sub.1 and ?.sub.2 are control signals used for controlling rotating speeds of two (sets of) motors.

9. An adaptive robust estimation system for parameters of an unmanned surface vessel, comprising: a problem construction module, configured to construct an augmented state estimation problem considering an external disturbance for the unmanned surface vessel; augmented state vectors comprising a state vector of the unmanned surface vessel, a parameter vector of an unmanned surface vessel model, and an unknown input vector representing a modeling error of an unmanned surface vessel system and the external disturbance; and an adaptive robust estimation module, configured to depending on a real-time input vector and a measurement vector of the unmanned surface vessel system, employ an adaptive robust unscented Kalman filtering method having process noise covariance matrix constraints and based on the combination of a maximum cross entropy criterion and a minimum mean square error criterion to obtain model parameters of the unmanned surface vessel; the input vector comprising a control signal from a shipborne controller, and the measurement vector comprising data obtained by GPS and IMU measurement; a method for estimating the process noise covariance matrix comprising: firstly, employing an innovation-based adaptive method to estimate a noise covariance matrix .sub.k.sup.0; then, introducing covariance matrix constraints according to a known structure and dividing a process noise covariance matrix .sub.k to be estimated into a diagonal block without structure constraints and a diagonal block with structure constraints; and finally, employing KL divergence to construct and solve the following optimization problem: ${\stackrel{?}{Q}}_k^{1,j_1},{?}_k^{j_2}=\underset{Q_k^{1,j_2},{?}_k^{j_2}}{\min }{?}_{-?}^{+?}p\left(x|{\stackrel{?}{Q}}_k^0\right)\log \frac{p\left(x|{\stackrel{?}{Q}}_k^0\right)}{p\left(x|{\stackrel{?}{Q}}_k\right)}\mathrm{dx};$ wherein k represents the moment; .sub.k.sup.1,j.sup.1 represents the diagonal block without structure constraints; ?.sub.k.sup.j.sup.2 represents a coefficient of the diagonal block .sub.k.sup.2,j.sup.2 with structure constraints; .sub.k.sup.2,j.sup.2=?.sub.k.sup.j.sup.2.sub.k.sup.c,j2, .sub.k.sup.c,j.sup.2 is a known structure; j.sub.1=, . . . , n.sub.1, j.sub.2=1, . . . , n.sub.2 n.sub.1 and n.sub.2 represent the number of the diagonal block without structure constraints and the number of the diagonal block with structure constraints, respectively; p(x|.sub.k.sup.0) and p(x|.sub.k) represent probability density functions of a random variable X with the covariance matrix being .sub.k.sup.0 and .sub.krespectively and obeying zero mean Gaussian distribution.

10. A computer system, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein when the computer program is loaded to the processor, the steps of the adaptive robust estimation method for parameters of an unmanned surface vessel according to claim 1 are implemented.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0043] FIG. 1 is a general flowchart of a method according to an embodiment of the present invention.

[0044] FIG. 2 is a flowchart of an adaptive robust unscented Kalman filtering method according to an embodiment of the present invention.

[0045] FIG. 3 is an error curve graph of parameters of a twin-propeller differential unmanned surface vessel estimated according to an embodiment of the present invention.

DETAILED DESCRIPTION

[0046] The technical solutions in embodiments of the present invention will be described below clearly and completely with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are merely a part rather than all of the embodiments of the present invention. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] As shown in FIG. 1, an adaptive robust estimation method for parameters of an unmanned surface vessel disclosed by the embodiments of the present invention includes: firstly, an augmented state estimation problem considering an external disturbance for the unmanned surface vessel is constructed, specifically, a system state equation is established according to kinematic and dynamical equations of the unmanned surface vessel, a system measurement equation is established according to real-time kinematic global positioning system and inertial measurement units, an unknown input of a system is introduced, and system parameters and the unknown input are augmented into a state, so as to transform a parameter estimation problem of the unmanned surface vessel into an augmented state estimation problem; then, depending on a real-time input vector and a measurement vector of an unmanned surface vessel system, an adaptive robust unscented Kalman filtering method having process noise covariance matrix constraints and based on the combination of a maximum cross entropy criterion and a minimum mean square error criterion is employed to obtain model parameters of the unmanned surface vessel. Specifically, considering that the state of the unmanned surface vessel system may be disturbed by outlier noises, a robust Kalman filtering method is designed based on the maximum cross entropy criterion and the minimum mean square error criterion; and considering that statistical characteristics of process noises of the unmanned surface vessel system are unknown and the system state dimension is relatively high, an adaptive law having process noise covariance matrix constraints is introduced to precisely estimate the process noise covariance matrix.

[0048] The implementation process of the embodiments of the present invention will be described in detail below by taking estimation for model parameters of a twin-propeller differential unmanned surface vessel as an example, which includes the following specific steps: [0049] S1: construction of an augmented state estimation problem considering an external disturbance for the unmanned surface vessel.

[0050] When it is assumed that a water flow rate is zero, an unmanned surface vessel model may be expressed with kinematic and dynamical equations, respectively:

[00016]$\stackrel{.}{?}=R?;$$M\stackrel{.}{?}+C?+D?=?;$ [0051] where ?=[x, y, ?].sup.T, X, Y represents a center-of-mass position of the unmanned surface vessel under a world coordinate system and ? represents a yaw angle of the unmanned surface vessel under the world coordinate system; v=[u, v, r].sup.T, u, v represents a center-of-mass velocity of the unmanned surface vessel under a body coordinate system and r represents a yaw velocity of the unmanned surface vessel under the body coordinate system; R represents a rotation matrix; M is an inertial matrix; C is a Coriolis force matrix; D is a damping matrix; ? is a force borne by the unmanned surface vessel; when ambient disturbances are not considered, ? is composed of a forward thrust ?.sub.u generated by a driving motor and a torque ?.sub.r that is, ?=?.sub.u, 0, ?.sub.r].sup.T: [0052] the rotation matrix R, the inertial matrix M, the Coriolis force matrix C, and the damping matrix D are expressed as follows, respectively:

[00017]$R=\left[\begin{array}{ccc}\cos ?& -s\mathrm{in}?& 0\\ \sin ?& \cos ?& 0\\ 0& 0& 1\end{array}\right];M=\left[\begin{array}{ccc}m-X_{\stackrel{.}{u}}& 0& 0\\ 0& m-Y_{\stackrel{.}{v}}& {\mathrm{mx}}_g-Y_{\stackrel{.}{r}}\\ 0& {\mathrm{mx}}_g-Y_{\stackrel{.}{r}}& I_z-N_{\stackrel{.}{r}}\end{array}\right];$$C=\left[\begin{array}{ccc}0& 0& -c_{31}\\ 0& 0& -c_{32}\\ c_{31}& c_{32}& 0\end{array}\right];D=\left[\begin{array}{ccc}{d}_{11}& 0& 0\\ 0& d_{22}& d_{23}\\ 0& d_{32}& d_{33}\end{array}\right];$ [0053] where m is a mass of the unmanned surface vessel; I.sub.z is a moment of inertia of the unmanned surface vessel; x.sub.g is a center-of-mass coordinate; and X.sub.{dot over (u)}, Y.sub.{dot over (v)}, and N.sub.{dot over (r)} are hydrodynamic force derivatives; [0054] c.sub.31, c.sub.32, d.sub.11, d.sub.22, d.sub.23, d.sub.32 and d.sub.33 in the Coriolis force matrix C and the damping matrix D are as follows, respectively:

[00018]$c_{31}=\left(m-Y_{\stackrel{.}{v}}\right)v+\left({\mathrm{mx}}_g-Y_{\stackrel{.}{r}}\right)r;c_{32}=-\left(m-X_{\stackrel{.}{u}}\right)u;$$d_{11}=-X_u-X_{.Math.u.Math.u}.Math.u.Math.;d_{22}=-Y_v-Y_{.Math.v.Math.v}.Math.v.Math.;d_{23}=-Y_r-Y_{.Math.r.Math.r}.Math.r.Math.;$$d_{32}=-N_v-N_{.Math.v.Math.v}.Math.v.Math.;d_{33}=-N_r-N_{.Math.r.Math.r}.Math.r.Math.;$ [0055] where X.sub.u, X.sub.|u|u, Y.sub.v, Y.sub.|v|v, Y.sub.r, Y.sub.|r|r, N.sub.v, N.sub.|v|v, N.sub.r and N.sub.|r|r are different types of hydrodynamic force derivatives.

[0056] With respect to a twin-propeller differential unmanned surface vessel system, a driving force thereof is generated by two (sets of) motors. Under an assumption that rotating speeds of the two (sets of) motors are in direct proportion to control signals ?.sub.1 and ?.sub.2 of a shipborne controller, ?.sub.u and ?.sub.r have the following relational expressions with respect to the control signals ?.sub.1 and ?.sub.2:

[00019]${?}_u=k_1\left(.Math.{?}_1.Math.{?}_1+.Math.{?}_2.Math.{?}_2\right)-k_2\left(.Math.{?}_1.Math.+.Math.{?}_2.Math.\right)u;$${?}_r=k_{1}l\left(.Math.{?}_1.Math.{?}_1-.Math.{?}_2.Math.{?}_2\right)-k_{2}l\left(.Math.{?}_1.Math.-.Math.{?}_2.Math.\right)u;$ [0057] where k.sub.1 and k.sub.2 are coefficients, and l is a moment arm of a torque generated by each one of the two (sets of) motors. In conjunction with the above expressions, by properly rearranging the kinematic and dynamical equations of the unmanned surface vessel, state equations of the twin-propeller differential unmanned surface vessel system may be obtained:

[00020]$\stackrel{.}{x}=u\cos ?-v\sin ?;$$\stackrel{.}{y}=u\sin ?+v\cos ?;$$\stackrel{.}{?}=r;$$\stackrel{.}{u}=a_1\mathrm{vr}+a_2{r}^2+a_{5}u+a_6.Math.u.Math.u+a_{15}\left(.Math.{?}_1.Math.{?}_1+.Math.{?}_2.Math.{?}_2\right)-a_{16}\left(.Math.{?}_1.Math.+.Math.{?}_2.Math.\right)u;$$\stackrel{.}{v}=a_3\mathrm{uv}+a_4\mathrm{ur}+a_{7}v+a_8.Math.v.Math.v+a_{9}r+a_{10}.Math.r.Math.r-a_{17}\left(.Math.{?}_1.Math.{?}_1-.Math.{?}_2.Math.{?}_2\right)+a_{18}\left(.Math.{?}_1.Math.-.Math.{?}_2.Math.\right)u;$$\stackrel{.}{r}=\frac{a_1{a}_3}{a_2}\mathrm{uv}-a_3\mathrm{ur}+a_{11}v+a_{12}.Math.v.Math.v+a_{13}r+a_{14}.Math.r.Math.r+\frac{a_1{a}_{17}}{a_2}\left(.Math.{?}_1.Math.{?}_1-.Math.{?}_2.Math.{?}_2\right)-\frac{a_1{a}_{18}}{a_2}\left(.Math.{?}_1.Math.-.Math.{?}_2.Math.\right)u;$ [0058] where a.sub.1, . . . , a.sub.4 are inertia-related parameters, a.sub.5, . . . ,a.sub.14 are damping-related parameters, and a.sub.15 . . . a.sub.18 are driving force-related parameters. Assuming that a vector a=[a.sub.1, . . . , a.sub.18].sup.T represents a parameter vector to be identified, the state vector of the twin-propeller differential unmanned surface vessel is selected as ?=[x, y, ?, u, v, r].sup.T and the input vector thereof is selected as u=?.sub.1,?.sub.2].sup.T the above equations may be denoted as a discrete state equation below:

[00021]${?}_k=f_{?}\left({?}_{k-1},u_{k-1}\right).$

[0059] It is assumed that the unmanned surface vessel has been equipped with a global positioning system (GPS) and an inertial measurement unit (IMU), the former is used for measuring a position X, Y and a velocity u, v of the unmanned surface vessel and the latter is used for measuring a yaw angle ?, a yaw velocity r, and an acceleration {dot over (u)}, {dot over (v)} of the unmanned surface vessel, then the measurement equation of the system is expressed as below:

[00022]$y_k=h_{?}\left({?}_{k,}{u}_k\right)={\left[x_k,y_k,{?}_k,u_k,v_k,r_k,{\stackrel{.}{u}}_k,{\stackrel{.}{v}}_k\right]}^T.$

[0060] In addition, considering influences caused by unknown inputs such as a modeling error of the unmanned surface vessel system and the external disturbance to dynamics characteristics of the unmanned surface vessel, an unknown input vector d.sub.k ?.sup.3 is introduced. To transform the parameter estimation problem of the unmanned surface vessel into the augmented state estimation problem, the following augmented state vector is selected:

[00023]$x_k={\left[\begin{array}{ccc}{?}_k^T& a_k^T& d_k^T\end{array}\right]}^T.$

[0061] In this case, a system equation employed by the augmented state estimation problem may be written as:

[00024]$x_k=f\left(x_{k-1},u_{k-1}\right)+w_{k-1}=\left[\begin{array}{c}{f}_{?}\left({?}_{k-1},u_{k-1}\right)+{\mathrm{Gd}}_{k-1}\\ a_{k-1}\\ d_{k-1}\end{array}\right]+w_{k-1};$$y_k=h\left(x_k,u_k\right)+v_k=h_{?}\left({?}_k,u_k\right)+{\mathrm{Ed}}_k+v_k;$ [0062] where f represents nonlinear mapping from an augmented state vector x.sub.k-1 and an input vector u.sub.k-1 at a (k?1)th moment to an augmented state vector x.sub.k at a k th moment, without the consideration of noises; h represents nonlinear mapping from the augmented state vector x.sub.k and an input vector U.sub.k at the k th moment to a measurement vector y.sub.k, without the consideration of noises; W.sub.k-1 and V.sub.k are zero mean process noises and zero mean measurement noises of covariance matrices .sub.k-1 and R.sub.k at the (k?1)th moment and the k th moment, respectively; and in a case that a system sampling period is T.sub.s, matrices G and E are expressed as:

[00025]$G=T_s\left[\begin{array}{c}{0}_{3?3}\\ I_3\end{array}\right],E=\left[\begin{array}{cc}{0}_{6?2}& 0_{6?1}\\ I_2& 0_{2?1}\end{array}\right];$

[0063] S2: adaptive robust unscented Kalman filtering having process noise covariance matrix constraints is employed to obtain model parameters of the unmanned surface vessel.

[0064] S21: the adaptive robust unscented Kalman filtering is initialized.

[0065] An initial augmented state vector estimated value {circumflex over (X)}.sub.0|0 is selected and the value should be approximate to actual initial augmented state vector, parameters and unknown input of the unmanned surface vessel. At the same time, a covariance matrix P.sub.0|0.sup.xx of an error of the initial augmented state vector estimated value is given.

[0066] S22: the input vector and the measurement vector of the unmanned surface vessel system are acquired.

[0067] An input vector u.sub.k of the unmanned surface vessel system may be directly obtained from a controller, whereas a measurement vector y.sub.k may be obtained from measurement results of the GPS and the IMU.

[0068] S23: an augmented state vector and a covariance matrix of a prediction error of the augmented state vector are predicted.

[0069] Firstly, a set of ? sample points X.sub.k-1|k-1.sup.(i) at the (k?1)th moment are generated:

[00026]${?}_{k-1.Math.k-1}^{\left(0\right)}={\hat{x}}_{k-1.Math.k-1};$${?}_{k-1.Math.k-1}^{\left(i\right)}={\hat{x}}_{k-1.Math.k-1}+{\left(\sqrt{{\mathrm{cP}}_{k-1.Math.k-1}^{\mathrm{xx}}}\right)}_i,i=1,...,n;$${?}_{k-1.Math.k-1}^{\left(i\right)}={\hat{x}}_{k-1.Math.k-1}-{\left(\sqrt{{\mathrm{cP}}_{k-1.Math.k-1}^{\mathrm{xx}}}\right)}_{i-n},i=n+1,...,2n;$ [0070] where {circumflex over (x)}.sub.k-1|k-1 is the augmented state vector estimated at the (k?1)th moment; P.sub.k-1|k-1.sup.xx is a covariance matrix of an error of this augmented state vector estimated value; n is the dimension of the augmented state vector; c is a constant; and (?{square root over (cP.sub.k-1|k-1.sup.xx)}).sub.i represents a vector composed of an i th column of a Cholesky factor of cP.sub.k-1|k-1.sup.xx. Then, a predicted value X.sub.k|k-1.sup.(i) of each ? point is mapped by means of the state equation of the unmanned surface vessel system:

[00027]${?}_{k.Math.k-1}^{\left(i\right)}=f\left({?}_{k-1.Math.k-1}^{\left(i\right)},u_{k-1}\right);$ [0071] an augmented state vector {circumflex over (x)}.sub.k|k-1 at the (k)th moment is predicted according to the predicted value X.sub.k|k-1.sup.(i) of the ? point:

[00028]${\hat{x}}_{k.Math.k-1}=\underset{i=0}{\overset{2n}{.Math.}}{W}^{\left(i\right)}{?}_{k.Math.k-1}^{\left(i\right)};$ [0072] where W is the weight.

[0073] Secondly, the covariance matrix P.sub.k|k-1.sup.xx of the error of the predicted value of the augmented state vector is calculated:

[00029]$P_{k.Math.k-1}^{\mathrm{xx}}=\underset{i=0}{\overset{2n}{.Math.}}{W}^{\left(i\right)}\left({?}_{k.Math.k-1}^{\left(i\right)}-{\hat{x}}_{k+1.Math.k}\right){\left({?}_{k.Math.k-1}^{\left(i\right)}-{\hat{x}}_{k+1.Math.k}\right)}^T+Q_k.$

[0074] S24: a measurement vector, a covariance matrix of a prediction error of the measurement vector and a cross covariance matrix are predicted: [0075] ? point X.sub.k|k-1.sup.(i) is regenerated:

[00030]${?}_{k.Math.k-1}^{\left(0\right)}={\hat{x}}_{k.Math.k-1};$${?}_{k.Math.k-1}^{\left(i\right)}={\hat{x}}_{k.Math.k-1}+{\left(\sqrt{{\mathrm{cP}}_{k.Math.k-1}^{\mathrm{xx}}}\right)}_i,i=1,...,n;$${?}_{k.Math.k-1}^{\left(i\right)}={\hat{x}}_{k.Math.k-1}-{\left(\sqrt{{\mathrm{cP}}_{k.Math.k-1}^{\mathrm{xx}}}\right)}_{i-n},i=n+1,...,2n;$ [0076] a measurement vector ?.sub.k|k-1.sup.(i) predicted by each ? point X.sub.k|k-1.sup.(i) is calculated:

[00031]${?}_{k.Math.k-1}^{\left(i\right)}=h\left({?}_{k.Math.k-1}^{\left(i\right)},u_k\right);$ [0077] a measurement vector ?.sub.k|k-1 predicted at the k th moment is calculated:

[00032]${\hat{y}}_{k.Math.k-1}=\underset{i=0}{\overset{2n}{.Math.}}{W}^{\left(i\right)}{?}_{k.Math.k-1}^{\left(i\right)};$ [0078] a covariance matrix P.sub.k|k-1.sup.yy of the prediction error of the measurement vector is calculated:

[00033]$P_{k|k-1}^{\mathrm{yy}}=\underset{i=0}{\overset{2n}{.Math.}}{W}^{\left(i\right)}\left({?}_{k|k-1}^{\left(i\right)}-{\hat{y}}_{k|k-1}\right){\left({?}_{k|k-1}^{\left(i\right)}-{\hat{y}}_{k|k-1}\right)}^T+R_k;$ [0079] an cross covariance matrix P.sub.k|k-1.sup.yy between {circumflex over (x)}.sub.k|k-1.sup.xy and ?.sub.k|k-1 is calculated:

[00034]$P_{k|k-1}^{\mathrm{xy}}=\underset{i=0}{\overset{2n}{.Math.}}{W}^{\left(i\right)}\left({?}_{k|k-1}^{\left(i\right)}-{\hat{x}}_{k|k-1}\right){\left({?}_{k|k-1}^{\left(i\right)}-{\hat{y}}_{k|k-1}\right)}^T.$

[0080] S25: an optimization problem employed by robust state estimation is constructed.

[0081] A measurement equation for the unmanned surface vessel system may be linearized by employing results of unscented transformation as follows:

[00035]$y_k-{\hat{y}}_{k|k-1}=H_k\left[x_k-{\hat{x}}_{k|k-1}\right]+r_k;$$H_k={\left(P_{k|k-1}^{\mathrm{xy}}\right)}^T{\left(P_{k|k-1}^{\mathrm{xx}}\right)}^{-1};$ [0082] where r.sub.k is noises of the linearized measurement equation, which have a statistical property as below:

[00036]$E\left[r_k\right]=0,{?}_k=E\left[r_k{r}_k^T\right]=P_{k|k-1}^{\mathrm{yy}}-{\left(P_{k|k-1}^{\mathrm{xy}}\right)}^T{\left(P_{k|k-1}^{\mathrm{xx}}\right)}^{-1}{P}_{k|k-1}^{\mathrm{xy}}.$

[0083] The system with the measurement equation linearized may be written as:

[00037]$\left[\begin{array}{c}{\hat{x}}_{k|k-1}\\ y_k-{\hat{y}}_{k|k-1}+H_k{\hat{x}}_{k|k-1}\end{array}\right]=\left[\begin{array}{c}I\\ H_k\end{array}\right]x_k+{?}_k;$ [0084] where:

[00038]${?}_k=\left[\begin{array}{c}{\tilde{x}}_{k|k-1}\\ r_k\end{array}\right]=\left[\begin{array}{c}{\hat{x}}_{k|k-1}-x_k\\ r_k\end{array}\right].$

[0085] It may be verified that, the desire E?.sub.k] of ?.sub.k has zero mean, and a covariance matric E[?.sub.k?.sub.k.sup.T] thereof may be transformed as:

[00039]$E\left[{?}_k{?}_k^T\right]=\left[\begin{array}{cc}{P}_{k|k-1}^{\mathrm{xx}}& 0\\ 0& {?}_k\end{array}\right]=\left[\begin{array}{cc}{T_k^P\left(T_k^P\right)}^T& 0\\ 0& T_k^{?}{\left(T_k^{?}\right)}^T\end{array}\right]=T_k{T}_k^T;$ [0086] where T.sub.k.sup.P, T.sub.k.sup.?, T.sub.k are Cholesky factors of P.sub.k|k-1.sup.xx, ?.sub.k, and E[?.sub.k ?.sub.k.sup.T], respectively.

[0087] Further, the following equation is provided:

[00040]$T_k^{-1}\left[\begin{array}{c}{\hat{x}}_{k|k-1}\\ y_k-{\hat{y}}_{k|k-1}+H_k{\hat{x}}_{k|k-1}\end{array}\right]=T_k^{-1}\left[\begin{array}{c}I\\ H_k\end{array}\right]x_k+T_k^{-1}{?}_k;$

[0088] This equation is rewritten as:

[00041]$Y_k=A_k{x}_k+e_k;$ [0089] where:

[00042]$Y_k=T_k^{-1}\left[\begin{array}{c}{\hat{x}}_{k|k-1}\\ y_k-{\hat{y}}_{k|k-1}+H_k{\hat{x}}_{k|k-1}\end{array}\right],A_k=T_k^{-1}\left[\begin{array}{c}I\\ H_k\end{array}\right],e_k=T_k^{-1}{?}_k.$

[0090] In addition, it may be verified that the mean value of a vector e.sub.k is 0, and a covariance matrix thereof is an identity matrix. The maximum cross entropy criterion with good robustness is introduced as an optimal criterion, and is combined with the minimum mean square error criterion employed by conventional Kalman filtering. The former is used for processing the process noises possibly having outliers and the latter is used for processing the measurement noises, that is, the former is modeled with respect to the state equation and the latter is modeled with respect to the measurement equation. An optimal estimation {circumflex over (x)}.sub.k|k integrating the robustness and accuracy may be obtained by establishing and solving the following optimization problem:

[00043]${\hat{x}}_{k|k}=\arg \underset{x_k}{\min }\left\{\underset{i=1}{\overset{n}{.Math.}}\left[G_{?}\left(0\right)-G_{?}\left(e_k^i\right)\right]+w\underset{i=n+1}{\overset{n+m}{.Math.}}{\left(e_k^i\right)}^2\right\};$ [0091] where W is a manually set weight coefficient and is used for balancing two optimal criteria; M is the dimension of the measurement vector y.sub.k; e.sub.k.sup.i is an i th element of e.sub.k; ? is bandwidth; and G.sub.?(.Math.) is Gaussian kernel function:

[00044]$G_{?}\left(e\right)=\exp \left(-\frac{e^2}{2{?}^2}\right).$

[0092] S26: optimal estimation of the augmented state is obtained according to an iteration form of robust unscented Kalman filtering.

[0093] The optimal solution in S25 satisfies a fixed point equation below and needs to be iteratively solved:

[00045]${\stackrel{?}{x}}_{k|k}={\left(A_k^T{W}_k{A}_k\right)}^{-1}{A}_k^T{W}_k{Y}_k;$ [0094] where W.sub.k=diag (W.sub.k.sup.x,I.sub.m), I.sub.m is an m-dimensional identity matrix, and:

[00046]$W_k^x=\frac{1}{2w{?}^2}\mathrm{diag}\left[G_{?}\left(e_k^1\right),.Math.,G_{?}\left(e_k^n\right)\right].$

[0095] A robust unscented Kalman filter iterative equation as below may be obtained by matrix inversion lemma and properly rearranging the optimal solution:

[00047]${\hat{x}}_{k|k}^{\left(t\right)}={\hat{x}}_{k|k-1}+K_k^{\left(t\right)}\left(y_k-{\hat{y}}_{k|k-1}\right);$$K_k^{\left(t\right)}={\stackrel{\_}{P}}_{k|k-1}^{\mathrm{xx},\left(t\right)}{H_k^T\left(H_k{\stackrel{\_}{P}}_{k|k-1}^{\mathrm{xx},\left(t\right)}{H}_k^T+{\stackrel{\_}{?}}_k^{\left(t\right)}\right)}^{-1};$${\stackrel{\_}{P}}_{k|k-1}^{\mathrm{xx},\left(t\right)}-{T_k^P\left(W_k^{x,\left(t\right)}\right)}^{-1}{\left(T_k^P\right)}^T;$${\stackrel{\_}{?}}_k^{\left(t\right)}={?}_k;$$e_k^{\left(t\right)}=Y_k-A_k{\hat{x}}_{k|k}^{\left(t-1\right)};$ [0096] where the superscript (t) represents a t th iteration; {circumflex over (x)}.sub.k|k.sup.(0)={circumflex over (x)}.sub.k|k-1; and in a case that the following conditions are satisfied, let {circumflex over (x)}.sub.k|k={circumflex over (x)}.sub.k|k.sup.(t) and K.sub.k=K.sup.t):

[00048]$\frac{.Math.{\hat{x}}_{k.Math.k}^{\left(t\right)}-{\hat{x}}_{k.Math.k}^{\left(t-1\right)}.Math.}{.Math.{\hat{x}}_{k.Math.k}^{\left(t-1\right)}.Math.}??;$ [0097] where ? is a threshold. After that, a covariance matrix of a state prediction error is:

[00049]$P_{k.Math.k}^{\mathrm{xx}}=\left(I-K_k{H}_k\right){P_{k.Math.k-1}^{\mathrm{xx}}\left(I-K_k{H}_k\right)}^T+K_k{?}_k{K}_k^T.$

[0098] S27: the process noise covariance matrix is estimated by employing an adaptive law having covariance matrix constraints.

[0099] On the premise of slow change of the noise covariance matrix and in order to ensure the positive definiteness of the noise covariance matrix, the innovation-based adaptive method may be employed to perform primary estimation of the noise covariance matrix:

[00050]${\stackrel{?}{Q}}_k^0=\frac{1}{N}\underset{i=k_0}{\overset{k}{.Math.}}\left({\hat{x}}_{i.Math.i}-{\hat{x}}_{i.Math.i-1}\right){\left({\hat{x}}_{i.Math.i}-{\hat{x}}_{i.Math.i-1}\right)}^T,k_0=k-N+1,k?N;$ [0100] where .sub.k.sup.0 is a covariance matrix estimated by the innovation-based adaptive method; k.sub.0 represents an initial moment of a sample used for calculating the covariance matrix; N represents the quantity of the sample used; x?.sub.i|i-1 is a predicted value of the augmented state vector at an i th moment; and {circumflex over (x)}.sub.i|i is an estimated value of the augmented state vector at the i th moment. An augmentation system for the unmanned surface vessel is a high-dimensional system and contains 27 dimensions of state variables. Since high-dimensional process noise covariance matrices directly calculated by using the above equation have greater errors, introducing covariance matrix constraints according to a known structure on the premise that the structure of the process noise covariance matrix is known may reduce the estimation error of the covariance matrix. It is assumed that the process noise covariance matrix to be estimated is expressed as:

[00051]${\stackrel{?}{Q}}_k=\mathrm{diag}\left[{\stackrel{?}{Q}}_k^{1,1},.Math.,{\stackrel{?}{Q}}_k^{1,n_1},{\stackrel{?}{Q}}_k^{2,1},.Math.,{\stackrel{?}{Q}}_k^{2,n_2}\right];$ [0101] where .sub.k.sup.1,j.sup.1, j.sub.1=1, . . . ,n.sub.1 represents a diagonal block without structure constraints, which needs to be solved; the number of .sub.k.sup.1,j.sup.1 is n.sub.1; .sub.k.sup.2,j.sup.2 represents a diagonal block with structure constraints, that is, .sub.k.sup.2,j.sup.2=?.sub.k.sup.j.sup.2.sub.k.sup.c,j.sup.2,j.sub.2=1, . . . , n.sub.2, ?.sub.k.sup.j.sup.2<0; .sub.k.sup.c,j.sup.2 is a known structure; ?.sub.k.sup.j.sup.2 is a coefficient to be solved; and the number of .sub.k.sup.2,j.sup.2 is n.sub.2. In addition, in a case that .sub.k.sup.c,j.sup.2=0 is present in an actual problem, this diagonal block is removed to ensure that .sub.k is positive definite, and .sub.k.sup.2,j.sup.2=0 is directly given in an estimation result. Based on a starting point that enables .sub.k.sup.0 estimated by using an unconstrained method to be the closest to zero mean Gaussian distribution constituted of .sub.k considering constraints, the following optimization problem is constructed by employing KL divergence.

[0102] The following gives the optimization problem employed by the KL divergence-based covariance matrix constraints:

[00052]${\stackrel{?}{Q}}_k^{1,j_1},{?}_k^{j_2}=\underset{{\stackrel{?}{Q}}_k^{1,j_1},{?}_k^{j_2}}{\mathrm{argmin}}{?}_{-?}^{+?}p\left(x|{\stackrel{?}{Q}}_k^0\right)\log \frac{p\left(x.Math.{\stackrel{?}{Q}}_k^0\right)}{p\left(x.Math.{\stackrel{?}{Q}}_k\right)}\mathrm{dx};$ [0103] where p(x|.sub.k.sup.0) and p(x|.sub.k) represent probability density functions of a random variable x with the covariance matrix being .sub.k.sup.0 and .sub.k respectively and obeying zero mean Gaussian distribution:

[00053]$\begin{array}{c}p\left(x.Math.{\stackrel{?}{Q}}_k^0\right)=\frac{1}{{\left(2?\right)}^{n/2}{.Math.{\stackrel{?}{Q}}_k^0.Math.}^{1/2}}\exp \left(-\frac{1}{2}{x^T\left({\stackrel{?}{Q}}_k^0\right)}^{-1}x\right);\\ p\left(x.Math.{\stackrel{?}{Q}}_k\right)=\frac{1}{{\left(2?\right)}^{n/2}{.Math.{\stackrel{?}{Q}}_k.Math.}^{1/2}}\exp \left(-\frac{1}{2}{x}^T{\stackrel{?}{Q}}_k^{-1}x\right);\end{array}$

[0104] An optimal solution below may be obtained by solving the above optimization problem:

[00054]${\stackrel{?}{Q}}_k^{1,j_1}={\stackrel{?}{Q}}_k^{3,j_1},{?}_k^{j_2}=\frac{1}{m_{j_2}}\left[{\left({\stackrel{?}{Q}}_k^{c,j_2}\right)}^{-1}{\stackrel{?}{Q}}_k^{4,j_2}\right];$ [0105] where m.sub.j.sub.2 is the dimension of .sub.k.sup.c,j.sup.2; .sub.k.sup.3,j.sup.3 is a corresponding matrix block of .sub.k.sup.1,j.sup.1 in .sub.k.sup.0 and .sub.k.sup.4,j.sup.2 is a corresponding matrix block of .sub.k.sup.2,j.sup.2 in .sub.k.sup.0.

[0106] S28: whether to terminate parameter identification is determined; if not, return back to S22.

[0107] In this embodiment, MATLAB 2021b is used as a simulation software to compare the adaptive robust estimation method for parameters of an unmanned surface vessel of the present invention with a conventional unscented Kalman filtering method.

[0108] The settings of model parameters of a twin-propeller differential unmanned surface vessel used for simulation are shown in Table 1:

TABLE-US-00001 TABLE 1 Settings of Model Parameters of a Twin-propeller Differential Unmanned Surface Vessel Parameter Numerical Value a.sub.1 1.3101 a.sub.2 0.0424 a.sub.3 0.0951 a.sub.4 ?0.7602 a.sub.5 ?0.0280 a.sub.6 ?0.0514 a.sub.7 ?0.3124 a.sub.8 ?0.7753 a.sub.9 ?0.0106 a.sub.10 ?0.0945 a.sub.11 ?0.2765 a.sub.12 ?0.0707 a.sub.13 ?0.6842 a.sub.14 ?0.2343 a.sub.15 0.3876 a.sub.16 1.9380 a.sub.17 0.0238 a.sub.18 0.1189

[0109] Measurement noises used for simulation are zero mean Gaussian noises, with a covariance matrix as:

[00055]$R_k=\mathrm{diag}\left(1,1,0.7615,4,4,76.15,100,100\right)?10^{-4}.$

[0110] Noises experienced by the state vector of the unmanned surface vessel are composed of the zero mean Gaussian noises and outliers. A covariance matrix of the zero mean Gaussian noises is:

[00056]$Q_k^{?}=\mathrm{diag}\left(1,1,0.7615,25,25,3.046\right)?10^{-3}.$

[0111] The outliers are generated once every 10 seconds. The outliers also obey the zero mean Gaussian distribution and have a covariance matrix 10.sub.k.sup.?. The covariance of initial process noises of the adaptive robust unscented Kalman filtering and the unscented Kalman filtering is:

[00057]$Q_0=\mathrm{diag}\left(1,1,0.7615,25,25,3.046,0_{1?18},10,10,10\right)?10^{-4}.$

[0112] The system input is set as:

[00058]$u_k=\left[\begin{array}{c}0.5+0.6\sin 0.01k\\ 0.5+0.6\cos 0.01k\end{array}\right].$

[0113] The unknown input experienced by the system is set as:

[00059]$d_k=\left[\begin{array}{c}0.5\cos k-0.1\\ 0.5\sin 2k+0.1\\ 2r\mathrm{and}-1\end{array}\right];$ [0114] where rand represents a uniformly distributed random number in a range from 0 to 1.

[0115] The process noise covariance matrix to be estimated has the following known structure:

[00060]${\stackrel{?}{Q}}_k=\mathrm{diag}\left[{\stackrel{?}{Q}}_k^{2,1},{\stackrel{?}{Q}}_k^{2,2},{\stackrel{?}{Q}}_k^{1,1},{\stackrel{?}{Q}}_k^{2,3},{\stackrel{?}{Q}}_k^{1,2}\right]$ [0116] where .sub.k.sup.c,1 is a two-dimensional identity matrix, that is, .sub.k.sup.c,1=I.sub.2; .sub.k.sup.c,2 is a one-dimensional identity matrix, that is, .sub.k.sup.c,2=I.sub.1; and .sub.k.sup.c,3 is an 18?18-dimensional identity matrix, that is, .sub.k.sup.c,3=0.sub.18?18.

[0117] Parameter settings of the adaptive robust unscented Kalman filtering method are: ?=12, ?=10.sup.?6, w=3.5?10.sup.?4, and N=200. The sampling period is ?t=0.1. Initial estimations of the augmented state vectors of the two types of unscented Kalman filtering are identical, the initial estimations of the state vector and the unknown input are set as 0, the parameters a.sub.1, . . . , a.sub.4, a.sub.15, . . . , a.sub.18 are set as 1, and the parameters a.sub.5, . . . , a.sub.14 are set as ?1. The duration of simulation is 500 seconds, and 20 times of simulation are performed in total.

[0118] FIG. 3 shows an iteration curve of a parameter error ?a.sub.k, and ?a.sub.k is defined as:

[00061]$?a_k=\frac{1}{18}\underset{i=1}{\overset{18}{.Math.}}\sqrt{\frac{1}{20}\underset{t=1}{\overset{20}{.Math.}}{\left(?a_{i,k}^t\right)}^2};$ [0119] where ?a.sub.i,k.sup.t is an estimation error of an i th parameter at the k th moment in a t th simulation.

[0120] In FIG. 3, the solid line marked as UKF represents the error of the parameters estimated by means of the conventional unscented Kalman filtering, and the dotted line marked as ARUKF represents the error of the parameters estimated by means of the adaptive robust unscented Kalman filtering provided by the present invention. It can be seen that, the adaptive robust estimation method for parameters of an unmanned surface vessel of the present invention can implement a better estimation effect.

[0121] Based on the same inventive concept, an adaptive robust estimation system for parameters of an unmanned surface vessel provided by the embodiments of the present invention includes: a problem construction module, configured to construct an augmented state estimation problem considering an external disturbance for the unmanned surface vessel; augmented state vectors including a state vector of the unmanned surface vessel, a parameter vector of an unmanned surface vessel model, and an unknown input vector representing a modeling error of an unmanned surface vessel system and the external disturbance; and an adaptive robust estimation module, configured to depending on a real-time input vector and a measurement vector of the unmanned surface vessel system, employ an adaptive robust unscented Kalman filtering method having process noise covariance matrix constraints and based on the combination of a maximum cross entropy criterion and a minimum mean square error criterion to obtain model parameters of the unmanned surface vessel.

[0122] For a specific working process of each module described above, reference may be made to a corresponding process in the foregoing method embodiment. Details are not described herein again. The module division is merely logical function division and may be other division in actual implementation. For example, a plurality of modules may be combined or integrated into another system.

[0123] Based on the same inventive concept, a computer system disclosed by the embodiments of the present invention includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor; when the computer program is loaded to the processor, the steps of the adaptive robust estimation method for parameters of an unmanned surface vessel are implemented.

[0124] A person skilled in the art may understand that, the technical solution of the present invention is essentially or a part contributing to the prior art may be embodied in a form of software products, the computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer system (which may be a personal computer, a server, or a network device) to execute all or some steps of the method according to the embodiments of the present invention. The storage medium includes: various media that can store computer programs, such as a USB flash drive, a removable hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disc.

[0125] The above contents are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention shall be included in the scope of the present invention.