CN108920842B - Submarine kinetic model parameter online estimation method and device - Google Patents
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Abstract
The invention provides a submarine dynamic model parameter online estimation method and device, wherein the method comprises the following steps: establishing a submarine kinetic parameter estimation model based on the submarine kinetic model; and solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model. The submarine kinetic model parameter online estimation method and device can accurately estimate submarine kinetic model parameters, provide online correction mathematical models for submarine self-adaptive control, greatly improve the accuracy of submarine kinetic models, and further improve the control performance of submarines.
Description
Technical Field
The invention relates to the technical field of submarine parameter estimation, in particular to a submarine dynamics model parameter online estimation method and device.
Background
At present, the complexity of submarine dynamics and time-varying nonlinearity cause the difficulty of accurate modeling by using a traditional method, and an inaccurate mathematical model directly influences the operation control performance of the submarine. Therefore, in order to implement maneuvering control on the nuclear submarine under different working conditions, the dynamic model of the submarine motion needs to be identified and corrected on line.
While there are uncertain parameters in the submarine dynamics system model, one way to reduce the uncertainty of the parameters is by parameter estimation, i.e., inferring the value of the parameters from the measurements of the input and output signals of the submarine dynamics system. The parameter estimation can be performed either off-line or on-line. Offline estimation is preferable if there is sufficient time to estimate the parameters before control. However, for parameters that are slowly changing during submarine operation, online estimation is necessary to keep track of the parameter values.
Because submarine kinetic model parameters are time-varying characteristics, no mature method for online estimation of submarine kinetic model parameters exists at present.
Disclosure of Invention
In order to overcome the problems or at least partially solve the problems, the invention provides a submarine dynamics model parameter online estimation method and a submarine dynamics model parameter online estimation device.
According to a first aspect of the invention, a submarine dynamics model parameter online estimation method is provided, and comprises the following steps:
establishing a submarine kinetic parameter estimation model based on the submarine kinetic model;
solving the submarine dynamics parameter estimation model by using a bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine dynamics model.
The step of establishing the submarine kinetic parameter estimation model based on the submarine kinetic model specifically comprises the following steps:
determining parameters to be estimated of the submarine kinetic model according to the submarine kinetic model, and acquiring a state equation corresponding to the parameters to be estimated;
and carrying out filter transformation on the state equation, and sorting the equation obtained after the filter transformation to obtain a submarine kinetic parameter estimation model expressed in a linear equation form.
Wherein the bounded gain forgetting estimator is to have a forgetting factor
The least squares estimator of (a);
where P (t) is the gain matrix, λ 0 Is a preset maximum forgetting rate, k 0 A predetermined limit is set for the gain matrix.
The method comprises the following steps of solving a submarine dynamics parameter estimation model by using a bounded gain forgetting estimator to obtain an online estimation result of a parameter to be estimated of the submarine dynamics model, and specifically comprises the following steps:
based on the fact that the factor of forgetting is provided
Establishing a parameter updating equation of the submarine dynamics model by using the least square estimator and the submarine dynamics parameter estimation model;
obtaining multiple measurement data of output quantity and input quantity in the submarine dynamics model parameter estimation model;
and calculating to obtain an online estimation result of the parameter to be estimated of the submarine dynamic model according to the multiple measurement data and the parameter updating equation.
Wherein, the parameter updating equation of the submarine dynamic model is as follows:
wherein the content of the first and second substances,
and P (t) is a first derivative of the parameter to be estimated of the submarine kinetic model, P (t) is a gain matrix, W is the input quantity in the submarine kinetic model parameter estimation model, and e is the prediction error of the output quantity in the submarine kinetic model parameter estimation model.
According to a second aspect of the invention, there is provided an online submarine kinetic model parameter estimation device, comprising:
and the parameter estimation model establishing module is used for establishing a submarine dynamics parameter estimation model based on the submarine dynamics model.
And the parameter estimation module is used for solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator to obtain the online estimation result of the parameter to be estimated of the submarine kinetic model.
The parameter estimation model establishing module is specifically configured to:
determining parameters to be estimated of the submarine kinetic model according to the submarine kinetic model, and acquiring a state equation corresponding to the parameters to be estimated;
and carrying out filter transformation on the state equation, and sorting the equation obtained after the filter transformation to obtain a submarine kinetic parameter estimation model expressed in a linear equation form.
Wherein the parameter estimation module is specifically configured to:
based on the having a forgetting factor
Least squares estimation ofThe counter and the submarine kinetic parameter estimation model establish a parameter updating equation of the submarine kinetic model;
obtaining multiple measurement data of output quantity and input quantity in the submarine dynamics model parameter estimation model;
and calculating to obtain an online estimation result of the parameter to be estimated of the submarine dynamic model according to the multiple times of measurement data and the parameter updating equation.
According to a third aspect of the invention, there is provided a submarine kinetic model parameter online estimation device, comprising:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, and the processor calls the program instructions to perform the submarine dynamics model parameter online estimation method provided by any one of the various possible implementations of the first aspect.
According to a fourth aspect of the present invention, there is provided a non-transitory computer readable storage medium storing computer instructions for causing a computer to perform a method for on-line estimation of submarine dynamics model parameters, the method being capable of performing the method provided in any one of the various possible implementations of the first aspect.
The submarine dynamics model parameter online estimation method and device can accurately estimate submarine dynamics model parameters, provide online correction mathematical models for submarine self-adaptive control, and greatly improve the accuracy of the submarine dynamics model so as to improve the control performance of the submarine.
Drawings
FIG. 1 is a schematic flow chart of a submarine kinetic model parameter online estimation method according to another embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an online submarine kinetic model parameter estimation device according to another embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating an online estimation result under a jump condition of submarine dynamics model parameters according to another embodiment of the present invention;
FIG. 4 is a schematic diagram of an online estimation result under a gradual change of parameters of a submarine dynamics model according to another embodiment of the present invention;
FIG. 5 is a schematic structural diagram of an online submarine dynamics model parameter estimation device according to another embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, a schematic flow chart of an online submarine kinetic model parameter estimation method according to an embodiment of the present invention includes:
s101, establishing a submarine kinetic parameter estimation model based on the submarine kinetic model.
Specifically, the submarine dynamics model is as follows:
wherein the content of the first and second substances,
for the time derivative of the state variable, i =1,2, \8230, 6,
are respectively as
Respectively representing the longitudinal acceleration, the transverse acceleration, the vertical acceleration, the transverse inclination acceleration, the longitudinal inclination acceleration and the yaw angular speed of the submarine; b is a mixture of ij Is the coefficient of the equation of state, c j Is a combination term of the state variable and the control variable.
The submarine kinetic parameter estimation model is a linear model capable of reflecting the relationship between submarine kinetic model parameters and observable quantities. And analyzing the submarine kinetic model to obtain a state equation corresponding to each state variable, and processing the state equation to enable the processed equation to be represented by a linear model y (t) = W (t) a, wherein the obtained linear model y (t) = W (t) a is the established submarine kinetic parameter estimation model.
S102, solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model.
In particular, the nature of parameter estimation is to extract information about parameters from data relating to the system, thus requiring a model to relate the available data to the parameters. Since submarines are essentially continuous as non-linear physical systems and meaningful discretization is difficult, if the sampling frequency is high, the digital control system can also be considered as a continuous time system for analysis and synthesis, and the improvement of computer performance allows the use of high sampling frequencies, the continuous time system is used for online parameter estimation of the submarine dynamics model in the embodiment of the invention.
The most common method for parameter evaluation of continuous time systems is the least squares method, with a minimum of two multiplications fitting the mathematical model to the experimental data in the sense that the sum of the squared errors is minimal. In the process of parameter estimation, after a new set of observation data is introduced, in order to obtain a new parameter estimation result, the new data needs to be substituted into a formula together with old data in the past for calculation, so as to form a new estimation result. Because all data are required to participate in operation, the data amount required to be stored by a computer is increased along with the increase of measurement data, matrix inverse operation is required during least square estimation, in order to simplify the calculation, input and output information is considered to be contained in the previous operation result, and a new parameter estimation result can be calculated by using the previous parameter estimation result. However, due to the time-varying property of the submarine dynamics model parameters, in order to keep the submarine parameter tracking capability, a forgetting factor is introduced to form a bounded gain forgetting estimator, and by correcting the change of the forgetting factor, when the input quantity in the submarine dynamics parameter estimation model is continuously excited, forgetting data is activated, and when the input quantity in the submarine dynamics parameter estimation model is not continuously excited, the forgetting data is abandoned.
In order to utilize the bounded gain forgetting estimator to perform online evaluation on parameters of the submarine dynamics model, a model which is a submarine dynamics parameter estimation model and is used for linking observable data with the parameters of the submarine dynamics model needs to be obtained, wherein the submarine dynamics parameter estimation model is obtained on the basis of the submarine dynamics model and is expressed in a linear equation form.
The submarine kinetic model parameter online estimation method provided by the invention can accurately estimate submarine kinetic model parameters, provides an online correction mathematical model for submarine self-adaptive control, and can greatly improve the accuracy of submarine kinetic models and further improve the control performance of submarines.
Based on the content of the above embodiment, as an optional embodiment, the step of establishing the submarine dynamics parameter estimation model based on the submarine dynamics model specifically includes:
determining parameters to be estimated of the submarine kinetic model according to the submarine kinetic model, and acquiring a state equation corresponding to the parameters to be estimated;
and carrying out filtering transformation on the state equation, and sorting the equation obtained after filtering transformation to obtain a submarine kinetic parameter estimation model expressed in a linear equation form.
Specifically, according to a submarine kinetic model, determining parameters to be estimated of the submarine kinetic model, obtaining a state equation corresponding to the parameters to be estimated, explaining by taking an axial equation as an example, and obtaining, according to the submarine kinetic model:
c in the above equation 6 (i.e. r) 2 ) Parameter b of 16 Namely a parameter to be estimated of the submarine kinetic model. Initial assumption of estimation
I.e. without any a priori knowledge of the parameter.
Since the longitudinal acceleration cannot be measured directly and the noise is taken into account, it is not desirable to numerically differentiate the longitudinal velocity, which requires the parameter b to be estimated 16 The corresponding state equation, namely formula (2), is processed and transformed into a linear model.
This problem is solved by filtering on both sides of equation (2), resulting in:
where s is the Laplace variable, λ f Is the bandwidth of the filter.
The equation (3) obtained after the filtering transformation is further processed by:
wherein the content of the first and second substances,
the method comprises the following steps:
a submarine kinetic parameter estimation model expressed in the form of a linear equation is thus obtained:
y(t)＝W(t)a，
wherein the content of the first and second substances,
W(t)＝c 6f ，a＝b 16 。
and then
And c 6f Are all measurable, b 16 Are the submarine dynamic model parameters which need to be estimated on line.
The parameter estimation model of other parameters of the submarine dynamics model can be obtained by adopting the same method as the embodiment of the invention.
After the submarine dynamics parameter estimation model expressed in the form of the linear equation is obtained, the parameters of the submarine dynamics model can be estimated on line.
The least square method is usually adopted to solve the parameter estimation model expressed in the form of a linear equation, but due to the time-varying property of submarine model parameters, in order to still utilize the forgetting data (namely, to keep the submarine parameter tracking capability) when avoiding possible unbounded gains, the effective method is to correct the change of the forgetting factor, so that when W is continuously excited, the forgetting data is activated, and when W is not continuously excited, the forgetting data is abandoned.
Since the magnitude of the gain matrix P predicts the excitation level of W, the change in forgetting factor is naturally linked to | | P (t) |.
Based on the above description of the embodiments, as an alternative embodiment, the bounded gain forgetting estimator is a device with a forgetting factor
A least squares estimator of (a);
where P (t) is the gain matrix, λ 0 Is a preset maximum forgetting rate, k 0 A predefined limit for the gain matrix.
In particular, a forgetting factor
Meaning that when the norm of P is small (strong sustained excitation), forgetting is with a forgetting factor lambda 0 (ii) a When the norm of P increases, the forgetting speed is reduced and when the norm reaches some specified upper bound, forgetting is stopped. Due to lambda 0 Larger means faster forgetting implies not only a stronger ability to track parameter changes, but also more oscillation in the estimated parameters due to the short time averaging of noisy data points, so λ 0 Represents a trade-off between the speed of parameter tracking and the estimated parameter hunting. Boundary k of gain 0 Similar trade-offs exist, as the update speed of the parameters also affects the interference in the prediction error. To meet the intent of bounded gain, we choose P (0) | ≦ k | | | P (0) | ≦ k 0 (whereby P (0) ≦ k 0 I) .1. The Is said to have a forgetting factor
Is a Bounded Gain Forgetting (BGF) estimator. It can be shown that the level of continuous excitation is not the same, like
The forgetting factor change rate of (c) can ensure that the generated gain matrix P (t) is all with a predetermined constant k 0 Is the upper bound.
In a Bounded Gain Forgetting (BGF) estimator, the parameter error and gain matrix are always bounded. If W is continuously excited, the estimation error index converges and P (t) has its consistent upper and lower bounds, respectively, in two positive definite matrices. Also, for a given acceptable severity of oscillation of the estimated parameter, the Bounded Gain Forgetting (BGF) method can use a large margin of gain, making the parameter converge faster.
Based on the content of the above embodiments, as an optional embodiment, the bounded gain forgetting estimator is used to solve the submarine dynamics parameter estimation model to obtain the online estimation result of the parameter to be estimated of the submarine dynamics model, and the method specifically includes:
based on the having a forgetting factor
Establishing a parameter updating equation of the submarine dynamics model by using the least square estimator and the submarine dynamics parameter estimation model;
obtaining multiple measurement data of output quantity and input quantity in the submarine dynamics model parameter estimation model;
and calculating to obtain an online estimation result of the parameter to be estimated of the submarine dynamic model according to the multiple measurement data and the parameter updating equation.
In particular, a bounded gain forgetting estimator is known to have a forgetting factor
The least square estimator obtains a submarine dynamics parameter estimation model y (t) = W (t) a in the previous step, and a bounded gain forgetting method provided by the bounded gain forgetting estimator is used for deducing an expression of the parameter a to be evaluated, namely a parameter updating equation of the submarine dynamics model is established. After learning the parameter update equation of the parameter to be evaluated, several observations of the output quantity y (t) in the parameter estimation model y (t) = W (t) a are obtained, and several observations of the input quantity W (t) are obtained, for example, in the above-described embodiment
W(t)＝c 6f Is obtained immediately
And c 6f The measured data of (2). And directly calculating to obtain an online estimation result of the corresponding parameter according to the acquired measurement data and a parameter updating equation for establishing the submarine dynamic model.
The parameter updating equation of the submarine dynamic model is as follows:
wherein the content of the first and second substances,
in the formula (4), the first and second groups,
and P (t) is a first derivative of the parameter to be estimated of the submarine kinetic model, P (t) is a gain matrix, W is the input quantity in the submarine kinetic model parameter estimation model, and e is the prediction error of the output quantity in the submarine kinetic model parameter estimation model.
As shown in fig. 2, a schematic structural diagram of an online submarine kinetic model parameter estimation device according to another embodiment of the present invention includes: the method comprises the following steps: a parameter estimation model building module 201 and a parameter estimation module 202, wherein,
the parameter estimation model establishing module 201 is used for establishing a submarine dynamics parameter estimation model based on the submarine dynamics model.
The parameter estimation module 202 is configured to solve the submarine dynamics parameter estimation model by using the bounded gain forgetting estimator, and obtain an online estimation result of the parameter to be estimated of the submarine dynamics model.
The submarine kinetic model parameter online estimation device is used for realizing the submarine kinetic model parameter online estimation method in the embodiments. Therefore, the description and definition of the on-line estimation method for the parameters of the submarine dynamics model in the foregoing embodiments can be used for understanding the execution modules in the embodiments of the present invention.
Based on the above embodiment, the parameter estimation model establishing module 201 is specifically configured to:
determining parameters to be estimated of the submarine kinetic model according to the submarine kinetic model, and acquiring a state equation corresponding to the parameters to be estimated;
and carrying out filtering transformation on the state equation, and sorting the equation obtained after filtering transformation to obtain a submarine kinetic parameter estimation model expressed in a linear equation form.
Based on the above embodiment, the bounded gain forgetting estimator is provided with a forgetting factor
The least squares estimator of (a);
where P (t) is the gain matrix, λ 0 Is a preset maximum forgetting rate, k 0 A predetermined limit is set for the gain matrix.
Based on the foregoing embodiment, the parameter estimation module 202 is specifically configured to:
based on the fact that the factor of forgetting is provided
Establishing a parameter updating equation of the submarine dynamics model by the least square estimator and the submarine dynamics parameter estimation model;
obtaining multiple measurement data of output quantity and input quantity in the submarine dynamic model parameter estimation model;
and calculating to obtain an online estimation result of the parameter to be estimated of the submarine dynamic model according to the multiple measurement data and the parameter updating equation.
Based on the above embodiment, the parameter update equation of the submarine dynamics model:
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
p (t) is the first derivative of the parameter to be estimated of the submarine dynamics model, P (t) is a gain matrix, and W is the submarine dynamicsAnd e is the prediction error of the output quantity in the submarine dynamics model parameter estimation model.
The submarine kinetic model parameter online estimation device provided by the embodiments of the invention can accurately estimate submarine kinetic model parameters and provide an online correction mathematical model for submarine adaptive control.
The submarine dynamics model online parameter estimation simulation result is given below.
The actual value and the online estimated value of the submarine kinetic parameter can be obtained by applying the Simulink tool, so that the online estimation capability of the bounded gain forgetting method on the submarine kinetic model parameter is measured.
Estimate initial assumptions
I.e. without any a priori knowledge of the parameter. First, consider the case of a parameter jump, i.e., assuming that the true parameter a of the submarine dynamics model is 12.589 before t =100s, and suddenly jumps to 6.5 at t =100 s. FIG. 3 shows the online estimation result under the condition of parameter jump of the submarine dynamic model, wherein a dotted line represents an actual parameter value, and a solid line represents an online estimation value of the parameter. Then consider the case of parameter tapering, i.e. assuming that the true parameter a of the submarine dynamics model is 12.589 before t =30 π s, at t =30 π s parameter a oscillates: a =12.589+0.5sin (0.2 t). FIG. 4 shows the results of online estimation with gradual changes in submarine dynamics model parameters. As can be seen from the figures 3 and 4, when the submarine dynamics model parameters have jump and gradual change, the Bounded Gain Forgetting (BGF) method has good effect, and the parameter online estimation algorithm can accurately estimate the submarine dynamics model parameters and provide an online correction mathematical model for the adaptive control of the submarine.
As shown in fig. 5, a schematic structural diagram of an online submarine dynamics model parameter estimation apparatus according to another embodiment of the present invention includes: a processor (processor) 501, a memory (memory) 502, and a bus 503;
the processor 501 and the memory 502 respectively complete communication with each other through a bus 503; the processor 501 is used for calling the program instructions in the memory 502 to execute the method provided by the above embodiments, for example, including: establishing a submarine kinetic parameter estimation model based on the submarine kinetic model; and solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model.
In yet another embodiment of the present invention, a non-transitory computer-readable storage medium is provided, which stores computer instructions for causing a computer to perform a method for online estimation of submarine dynamics model parameters, as provided in the above embodiments, for example, comprising: establishing a submarine kinetic parameter estimation model based on the submarine kinetic model; and solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The embodiments of the apparatuses described above are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment may be implemented by software plus a necessary general hardware platform, and may also be implemented by hardware. Based on the understanding, the foregoing technical solutions or portions contributing to the prior art may be embodied in the form of software products, which may be stored in a computer-readable storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and include instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the various embodiments or some parts of the methods of the embodiments.
Finally, the method of the present invention is only a preferred embodiment and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A submarine dynamic model parameter online estimation method is characterized by comprising the following steps:
establishing a submarine kinetic parameter estimation model based on the submarine kinetic model;
solving the submarine kinetic parameter estimation model by using a bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model;
wherein the bounded gain forgetting estimator is to have a forgetting factor
The least-squares estimator of (a) is,
where P (t) is the gain matrix, λ 0 Is a preset maximum forgetting rate, k 0 A predefined limit for the gain matrix;
the method comprises the following steps of solving a submarine kinetic parameter estimation model by using a bounded gain forgetting estimator to obtain an online estimation result of a parameter to be estimated of the submarine kinetic model, wherein the step of solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator specifically comprises the following steps:
based on the having a forgetting factor
Establishing a parameter updating equation of the submarine dynamics model by the least square estimator and the submarine dynamics parameter estimation model;
obtaining multiple measurement data of output quantity and input quantity in the submarine kinetic parameter estimation model;
calculating to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model according to the multiple times of measurement data and the parameter updating equation;
wherein, the parameter updating equation of the submarine dynamic model is as follows:
wherein the content of the first and second substances,
and P (t) is a first derivative of the parameter to be estimated of the submarine kinetic model, P (t) is a gain matrix, W is the input quantity in the submarine kinetic parameter estimation model, and e is the prediction error of the output quantity in the submarine kinetic parameter estimation model.
2. The method of claim 1, wherein the step of building the submarine dynamics parameter estimation model based on the submarine dynamics model comprises:
determining parameters to be estimated of the submarine dynamic model according to the submarine dynamic model, and acquiring a state equation corresponding to the parameters to be estimated;
and carrying out filtering transformation on the state equation, and sorting the equation obtained after filtering transformation to obtain a submarine kinetic parameter estimation model expressed in a linear equation form.
3. A submarine dynamics model parameter online estimation device is characterized by comprising:
the parameter estimation model establishing module is used for establishing a submarine kinetic parameter estimation model based on the submarine kinetic model;
the parameter estimation module is used for solving the submarine kinetic parameter estimation model by using the bounded gain forgetting estimator to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model;
wherein the bounded gain forgetting estimator is to have a forgetting factor
The least-squares estimator of (a) is,
where P (t) is the gain matrix, λ 0 Is a preset maximum forgetting rate, k 0 A predefined limit for the gain matrix;
the method comprises the following steps of solving a submarine dynamics parameter estimation model by using a bounded gain forgetting estimator to obtain an online estimation result of a parameter to be estimated of the submarine dynamics model, and specifically comprises the following steps:
based on the having a forgetting factor
Establishing a parameter updating equation of the submarine dynamics model by the least square estimator and the submarine dynamics parameter estimation model;
obtaining multiple measurement data of output quantity and input quantity in the submarine kinetic parameter estimation model;
calculating to obtain an online estimation result of the parameter to be estimated of the submarine kinetic model according to the multiple times of measurement data and the parameter updating equation;
wherein, the parameter updating equation of the submarine dynamic model is as follows:
wherein the content of the first and second substances,
and P (t) is a first derivative of the parameter to be estimated of the submarine kinetic model, P (t) is a gain matrix, W is the input quantity in the submarine kinetic parameter estimation model, and e is the prediction error of the output quantity in the submarine kinetic parameter estimation model.
4. The apparatus of claim 3, wherein the parameter estimation model building module is specifically configured to:
determining parameters to be estimated of the submarine kinetic model according to the submarine kinetic model, and acquiring a state equation corresponding to the parameters to be estimated;
and carrying out filtering transformation on the state equation, and sorting the equation obtained after filtering transformation to obtain a submarine kinetic parameter estimation model expressed in a linear equation form.
5. An online submarine dynamics model parameter estimation device, comprising:
at least one processor; and
at least one memory communicatively coupled to the processor, wherein:
the memory stores program instructions executable by the processor, the processor invoking the program instructions to perform the method of any of claims 1 to 2.
6. A non-transitory computer-readable storage medium storing computer instructions that cause a computer to perform the method of any one of claims 1-2.
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| EP2123931A1 (en) * | 2008-05-21 | 2009-11-25 | KNORR-BREMSE Systeme für Nutzfahrzeuge GmbH | Parameter estimation method for self-energized brake mechanism |
| CN107505636A (en) * | 2017-07-17 | 2017-12-22 | 北京航空航天大学 | Sea base JPALS locator field MRCC method and devices |
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