CN114673488B - Adaptive tool face angle estimation method for dynamic pointing rotary steerable drilling tools - Google Patents

Abstract

The invention relates to a self-adaptive tool face angle estimation method of a dynamic directional rotary steering drilling tool, which comprises the following specific steps: s1, establishing a mathematical model of a tool face angle system; s2, setting a rolling time domain estimation algorithm parameter; s3, predicting parameters of prior probability distribution of the covariance matrix; s4, updating approximate posterior probability distribution of the covariance matrix; s5, updating approximate posterior probability distribution of states; s6, calculating a tool face angle estimated value. The tool face intersection estimation method can effectively estimate the tool face angle of the dynamic directional rotary steering drilling tool system in real time, and simultaneously realize estimation of the state and noise covariance matrix, thereby improving the drilling precision and efficiency and reducing the drilling cost.

Description

Adaptive tool face angle estimation method for dynamic pointing rotary steerable drilling tools

Technical Field

The invention belongs to the technical field of oilfield drilling, and relates to a drilling tool measurement technology, in particular to an adaptive tool face angle estimation method for a dynamic pointing rotary steering drilling tool.

Background technique

Oil and gas are important resources for national strategic development, and drilling technology is the key technology for oil and gas exploration and development. As one of the most advanced directional drilling technologies in the world today, rotary steerable drilling technology has the advantages of high mechanical drilling speed, high precision of wellbore trajectory control, good wellbore purification effect, strong displacement extension ability, etc., which greatly improves the recovery efficiency of oil and gas. Therefore, rotary steerable drilling technology plays an irreplaceable role in oil exploration and development in complex terrain. In the development process in recent decades, due to the differences in steering methods and drill collar rotation, four types of rotary steerable drilling tool systems have gradually been formed: static push, dynamic push, static pointing, and dynamic pointing.

The dynamic pointing rotary steerable drilling tool system is the most advanced rotary steerable drilling system, which consists of a drilling platform, a drill string and a rotary steerable drilling tool system. The tool face angle can accurately describe the drilling direction of the drilling tool. During the drilling process, the on-site drilling platform combines the previous seismic exploration data and real-time measurement data to analyze the location of the oil and gas reservoir and calculate the tool face angle setting value. The core task of the downhole drilling tool is to control the drill bit to drill along the tool face angle setting value. Therefore, the performance of the drilling tool is mainly determined by the estimation and control accuracy of the tool face angle.

Accelerometers and gyroscopes are the core sensors used to detect tool face angles. During the drilling process, the drill bit and the rock produce intense friction, which will inevitably cause severe vibrations. Therefore, the raw data collected by the sensor is mixed with a large amount of measurement noise. The vibration frequency and amplitude usually change with the changes in the drilling environment, which leads to the covariance matrix of the measurement noise being unknown and time-varying. Therefore, the estimation of the tool face angle is essentially the estimation of a random system with an unknown time-varying noise covariance matrix.

The paper "Dynamic Toolface Estimation for Rotary Steerable Drilling System" (Wang Weiliang, Geng Yanfeng, Wang Kai, etc. Sensors, 2018) takes into account the difficulty of accurately estimating the tool face angle under harsh downhole conditions, and proposes a new tool face angle estimator. The estimator integrates the measurement information of two accelerometers and one gyroscope, designs a dual accelerometer tool face angle measurement method to compensate for the rotational acceleration of the system, and uses a nonlinear complementary filter to suppress the influence of vibration and axial acceleration. The estimator has been verified on a prototype of a dynamic pointing rotary steering system in a typical drilling mode and has high robustness.

In the paper "Dynamic Measurement of Tool Face Angle of Dynamic Pointing Rotary Steering Drilling" (Geng Yanfeng, Song Zhiyong, Wang Weiliang, et al. Journal of Chinese Inertial Technology, 2020 (3)), a combined filtering scheme integrating dual triaxial accelerometers and single-axis gyroscopes was designed. This scheme adopts an extended Kalman filter with adaptive measurement noise, which reduces the influence of unstable factors such as vibration during drilling on the dynamic tool face angle measurement to a certain extent. Finally, tests are conducted on vibrations of different intensities to achieve accurate measurement of tool face angle in complex vibration drilling projects.

However, although the above methods take the vibration of the drilling process into account, they all assume that the system noise covariance matrix caused by the vibration is known. However, in the actual drilling process, due to the change of the geological environment, the noise covariance matrix is usually unknown and time-varying. Therefore, it is necessary to design a suitable adaptive estimation method for the system with an unknown time-varying noise covariance matrix to further improve the estimation accuracy of the tool face angle.

Summary of the invention

In view of the above-mentioned problems existing in the prior art, the present invention provides an adaptive tool face angle estimation method for a dynamic pointing rotary steerable drilling tool, which can effectively estimate the tool face angle of the dynamic pointing rotary steerable drilling tool system in real time. The estimation accuracy of the tool face angle is high, which further improves the accuracy of steerable drilling.

In order to achieve the above object, the present invention provides an adaptive tool face angle estimation method for a dynamic pointing rotary steerable drilling tool, the specific steps of which are as follows:

S1. Establishing a mathematical model of the tool face angle system;

The mechanical structure of the dynamic pointing rotary steerable drilling tool system is analyzed and the following measurement equation is established:

Where _y1 represents the measurement value of the accelerometer y-axis, _y2 represents the measurement value of the accelerometer z-axis, _y3 represents the measurement value of the gyroscope, _v1 represents the measurement noise corresponding to the accelerometer y-axis, _v2 represents the measurement noise corresponding to the accelerometer z-axis, and d represents the measurement noise corresponding to the gyroscope. represents the component of gravitational acceleration, assuming that it satisfies/> is the tool face angle;

make The sampling step is h>0, and the mathematical model of the tool face angle system is constructed as follows:

Wherein, x(k) = [ _x1 (k) _x2 (k)] ^T is the state variable of the dynamic pointing rotary steerable drilling tool system, y(k) = [ _y1 (k) _y2 (k)] ^T is the measured output of the dynamic pointing rotary steerable drilling tool system, w(k) = [-hd(k) _x2 (k) hd(k) _x1 (k)] ^T and v(k) = [ _v1 (k) _v2 (k)] ^T are mutually uncorrelated zero-mean Gaussian white noises, w(k) has an unknown, time-varying covariance matrix R(k), and v(k) has an unknown, time-varying covariance matrix Q(k). is the coefficient matrix;

Given the state x(j) and R(j) at time j, the state x(j+1) at time j+1 satisfies the following distribution:

p(x(j+1)|x(j),R(j))＝N _x(j+1) (A(j)x(j),R(j)) (3)

Given x(j) and Q(j), the output y(j) at time j satisfies the following distribution:

p(y(j)|x(j),Q(j))＝N _y(j) (Cx(j),Q(j)) (4)

A known Then x(kN) satisfies the following distribution:

In the formula, p(X|·) represents the conditional probability of event X, is the mean of x(kN), is the estimated error covariance matrix, E{·} represents the mathematical expectation,/> Indicates that it has a mean value/> and the multivariate Gaussian probability density function of the covariance matrix P;

Assume that R(j)≈R _k , j∈[kN,k-1], Q(j)≈Q _k , j∈[kN,k], and R _k , Q _k and satisfies the following inverse Wishart distribution:

Where λ _R (k) is the degree of freedom parameter corresponding to R _k , λ _Q (k) is the degree of freedom parameter corresponding to Q _k , yes The corresponding degrees of freedom parameter, /> is a symmetric positive definite inverse scaling matrix, p(X) represents the probability of event X, IW _P (λ,Λ) represents the probability density function of the inverse Wishart distribution with degrees of freedom λ and the inverse scaling matrix Λ;

S2, given rolling horizon estimation algorithm parameters;

Let μ _R ∈ [0.9, 1] be the forgetting factor used to describe the fluctuation of R _k , μ _Q ∈ [0.9, 1] be the forgetting factor used to describe the fluctuation of Q _k , given the scalar α ∈ [2, 6], given the number of cycles τ, given the estimated value at time N-1

S3, prior probability distribution parameters of the predicted covariance matrix;

S4, updating the approximate posterior probability distribution of the covariance matrix;

S5, update the approximate posterior probability distribution of the state, if the number of iterations i<τ, let i=i+1, go to step S4 to continue to cyclically calculate the approximate posterior probability distribution of the covariance matrix and the approximate posterior probability distribution of the state, if the number of iterations i≥τ, go to step S6;

S6. Calculate the estimated tool face angle

The estimated value obtained in the τth cycle is set as the optimal estimated value at time k, and the estimated value of the tool face angle at time k is obtained by solving the solution. Let time update k=k+1, go to step S3, repeat steps S3 to S6, and calculate the estimated value of the tool face angle at time k+1.

Preferably, in step S3, the specific steps of predicting the prior probability distribution parameters of the covariance matrix are:

At time k, the result at time k-1 is known Calculate the covariance matrix at time k/> The prior estimate of is:

In the formula, n=2 is the dimension of x(k);

At the moment k ≥ N, we get:

Where n _y = 2 is the dimension of y(k);

Set the parameters for iteration 0:

In the formula, each parameter matrix is defined as:

x(k ₁ :k ₂ ) represents the set of vectors {x(k)|k∈[k ₁ ,k ₂ ]}, represents a (N+1)×(N+1) block matrix, whose submatrix of the lth row and qth column is/> Represents the Kronecker product operation.

Preferably, in step S4, the specific steps of updating the approximate posterior probability distribution of the covariance matrix are:

Given the estimated state and covariance matrix after i iterations, at the i+1th iteration, the approximate posterior probability density function of R _k q ⁽ⁱ⁺¹⁾ (R _k ), the approximate posterior probability density function of Q _k q ⁽ⁱ⁺¹⁾ (Q _k ) and The approximate posterior probability density function of Calculated by the following formula:

In the formula,

Covariance matrix In the ith iteration, syms{A} represents the symmetric matrix A+ ^AT .

Preferably, in step S5, the specific steps of updating the approximate posterior probability distribution of the state are:

The approximate posterior probability density function q ⁽ⁱ⁺¹⁾ (x(kN:k)) of the i+1th state variable is calculated by the following formula:

In the formula,

I _N is the identity matrix of N×N dimensions, and I _N+1 is the identity matrix of (N+1)×(N+1) dimensions;

If i<τ, let i=i+1, go to step S4 and continue to loop to calculate the approximate posterior probability distribution of the covariance matrix and the approximate posterior probability distribution of the state. If the number of iterations i≥τ, go to step S6.

Preferably, in step S6, the specific steps of solving the estimated value of the tool face angle are:

The estimated value obtained in the τth cycle is set as the optimal estimated value at time k, and the variation of the posterior probability density function is approximately:

In the formula,

Pick The last two lines of /> The estimated value of the tool face angle is solved using the following equation:

In the formula, is the estimated value of the tool face angle, /> For/> The first element of represents the estimated value of state x ₁ (k) at time k,/> For/> The second element of represents the estimated value of state x ₂ (k) at time k;

Let time update k=k+1, go to step S3, repeat steps S3 to S6, and calculate the estimated value of the tool face angle at the k+1th moment.

Compared with the prior art, the advantages and positive effects of the present invention are:

The adaptive tool face angle estimation method for the dynamic pointing rotary steerable drilling tool provided by the present invention takes into account that the system has an unknown time-varying noise covariance matrix, models the influence of vibration on the gyroscope and accelerometer as measurement noise with an unknown time-varying covariance matrix, obtains a mathematical model of the tool face angle system, and realizes real-time and effective estimation of the tool face angle of the dynamic pointing rotary steerable drilling tool system based on the rolling time domain estimation algorithm of variational Bayes, and simultaneously realizes the estimation of the state and noise covariance matrix, thereby improving drilling efficiency and reducing drilling costs. Compared with the existing tool face intersection estimation method, the tool face angle estimation method provided by the present invention can still maintain a good estimation effect in a complex and changeable downhole environment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of an adaptive tool face angle estimation method for a dynamic pointing rotary steerable drilling tool according to an embodiment of the present invention;

FIG2 is a diagram showing the estimated trajectory of the state and tool face angle in the numerical simulation of an embodiment of the present invention;

FIG3 is a diagram showing the average mean square error trajectory in numerical simulation of an embodiment of the present invention;

FIG4 is a schematic diagram of an experimental platform of a dynamic pointing rotary steerable drilling tool system according to an embodiment of the present invention;

FIG5 is a schematic diagram of raw measurement data of a gyroscope and an accelerometer in an experiment according to an embodiment of the present invention;

FIG. 6 is a diagram showing the estimated trajectory of the state and tool face angle in the experiment of the embodiment of the present invention.

In the figure, 1. drive motor, 2. coupling, 3. conductive slip ring, 4. gyroscope, 5. accelerometer, 6. DSP, 7. vibration platform.

Detailed ways

The present invention is described in detail below by way of exemplary embodiments. However, it should be understood that elements, structures, and features in one embodiment may also be beneficially combined in other embodiments without further description.

Referring to FIG. 1 , an embodiment of the present invention provides an adaptive tool face angle estimation method for a dynamic pointing rotary steerable drilling tool, and the specific steps are as follows:

S 1. Establish a mathematical model of the tool face angle system. The specific steps are:

The mechanical structure of the dynamic pointing rotary steerable drilling tool system is analyzed and the following measurement equation is established:

Where _y1 represents the measurement value of the accelerometer y-axis, _y2 represents the measurement value of the accelerometer z-axis, _y3 represents the measurement value of the gyroscope, _v1 represents the measurement noise corresponding to the accelerometer y-axis, _v2 represents the measurement noise corresponding to the accelerometer z-axis, and d represents the measurement noise corresponding to the gyroscope. represents the component of gravitational acceleration, assuming that it satisfies/> is the tool face angle;

make The sampling step is h>0, and the mathematical model of the tool face angle system is constructed as follows:

Wherein, x(k) = [ _x1 (k) _x2 (k)] ^T is the state variable of the dynamic pointing rotary steerable drilling tool system, y(k) = [ _y1 (k) _y2 (k)] ^T is the measured output of the dynamic pointing rotary steerable drilling tool system, w(k) = [-hd(k) _x2 (k) hd(k) _x1 (k)] ^T and v(k) = [ _v1 (k) _v2 (k)] ^T are mutually uncorrelated zero-mean Gaussian white noises, w(k) has an unknown, time-varying covariance matrix R(k), and v(k) has an unknown, time-varying covariance matrix Q(k). is the coefficient matrix;

Given the state x(j) and R(j) at time j, the state x(j+1) at time j+1 satisfies the following distribution:

p(x(j+1)|x(j),R(j))＝N _x(j+1) (A(j)x(j),R(j)) (3)

Given x(j) and Q(j), the output y(j) at time j satisfies the following distribution:

p(y(j)|x(j),Q(j))＝N _y(j) (Cx(j),Q(j)) (4)

A known Then x(kN) satisfies the following distribution:

In the formula, p(X|·) represents the conditional probability of event X, is the mean of x(kN),

is the estimated error covariance matrix, E{·} represents the mathematical expectation,/> represents the multivariate Gaussian probability density function with mean x and covariance matrix P;

In practical applications, the covariance matrix of process noise and measurement noise fluctuates very slowly. To simplify the algorithm, we assume that R(j)≈R _k , j∈[kN,k-1], Q(j)≈Q _k , j∈[kN,k], and R _k , Q _k and satisfies the following inverse Wishart distribution:

Where λ _R (k) is the degree of freedom parameter corresponding to R _k , λ _Q (k) is the degree of freedom parameter corresponding to Q _k , yes The corresponding degrees of freedom parameter, /> is a symmetric positive definite inverse scaling matrix, p(X) represents the probability of event X, and _IWP (λ,Λ) represents the probability density function of the inverse Wishart distribution with degrees of freedom λ and the inverse scaling matrix Λ.

S2, given rolling horizon estimation algorithm parameters;

Let μ _R ∈ [0.9, 1] be the forgetting factor used to describe the fluctuation of R _k , μ _Q ∈ [0.9, 1] be the forgetting factor used to describe the fluctuation of Q _k , given the scalar α ∈ [2, 6], given the number of cycles τ, given the estimated value at time N-1 It should be noted that, since the rolling horizon estimation algorithm starts estimating from time N, an estimated value at time N-1 is given.

S3. Predict the prior probability distribution parameters of the covariance matrix. The specific steps are:

At time k, the result at time k-1 is known Calculate the covariance matrix at time k/> The prior estimate of is:

In the formula, n=2 is the dimension of x(k);

At the moment k ≥ N, we get:

Where n _y = 2 is the dimension of y(k);

Set the parameters for iteration 0:

In the formula, each parameter matrix is defined as:

x(k ₁ :k ₂ ) represents the set of vectors {x(k)|k∈[k ₁ ,k ₂ ]}, represents a (N+1)×(N+1) block matrix, whose submatrix of the lth row and qth column is/> Represents the Kronecker product operation.

S4, update the approximate posterior probability distribution of the covariance matrix. The specific steps are:

Given the estimated state and covariance matrix after i iterations, at the i+1th iteration, the approximate posterior probability density function of R _k q ⁽ⁱ⁺¹⁾ (R _k ), the approximate posterior probability density function of Q _k q ⁽ⁱ⁺¹⁾ (Q _k ) and The approximate posterior probability density function of Calculated by the following formula:

In the formula,

Covariance matrix In the ith iteration, syms{A} represents the symmetric matrix A+ ^AT .

S5. Update the approximate posterior probability distribution of the state. If the number of iterations i<τ, let i=i+1, and go to step S4 to continue to cyclically calculate the approximate posterior probability distribution of the covariance matrix and the approximate posterior probability distribution of the state. If the number of iterations i≥τ, go to step S6.

Specifically, the specific steps for updating the approximate posterior probability distribution of the state are:

The approximate posterior probability density function q ⁽ⁱ⁺¹⁾ (x(kN:k)) of the i+1th state variable is calculated by the following formula:

In the formula,

I _N is the identity matrix of N×N dimensions, and I _N+1 is the identity matrix of (N+1)×(N+1) dimensions;

If i<τ, let i=i+1, go to step S4 and continue to loop to calculate the approximate posterior probability distribution of the covariance matrix and the approximate posterior probability distribution of the state. If the number of iterations i≥τ, go to step S6.

S6. Calculate the estimated tool face angle

The estimated value obtained in the τth cycle is set as the optimal estimated value at time k, and the estimated value of the tool face angle at time k is obtained by solving the solution. Let time update k=k+1, go to step S3, repeat steps S3 to S6, and calculate the estimated value of the tool face angle at time k+1.

Specifically, the specific steps for solving the tool face angle estimation are:

The estimated value obtained in the τth cycle is set as the optimal estimated value at time k, and the variation of the posterior probability density function is approximately:

In the formula,

Pick The last two lines of /> The estimated value of the tool face angle is solved using the following equation:

In the formula, is the estimated value of the tool face angle, /> For/> The first element of represents the estimated value of state x ₁ (k) at time k,/> For/> The second element of represents the estimated value of state x ₂ (k) at time k;

Let time update k=k+1, go to step S3, repeat steps S3 to S6, and calculate the estimated value of the tool face angle at the k+1th moment.

The adaptive tool face angle estimation method of the above-mentioned dynamic pointing rotary steerable drilling tool in the embodiment of the present invention takes into account that the system has an unknown time-varying noise covariance matrix, models the influence of vibration on the gyroscope and accelerometer as measurement noise with an unknown time-varying covariance matrix, obtains a mathematical model of the tool face angle system, and based on the rolling time domain estimation algorithm of variational Bayes, realizes real-time and effective estimation of the tool face angle of the dynamic pointing rotary steerable drilling tool system, and simultaneously estimates the state and noise covariance matrix. Compared with the existing tool face angle estimation method, the tool face angle estimation method of the present invention can still maintain a good estimation effect in a complex and changeable downhole environment.

In order to illustrate the effect of the adaptive tool face angle estimation method of the dynamic pointing rotary steerable drilling tool of the present invention, the present invention is further described below in conjunction with a numerical simulation experiment of a rotary steerable drilling tool system.

Example 1: The parameters of the rotary steerable drilling tool system used are: d(k)～N _d(k) (0,D(k)),D(k)＝(0.2+0.0005k) ² ,v(k)～N _v(k) (0,Q(k)),Q(k)＝(2+0.001k) ² I,x(0)～N _x(0) (0,P(0)),P(0)＝5 ² I,h＝0.01s，μ _R ＝μ _Q ＝0.99，α＝6，N＝20，/>

The tool face angle estimation method of the present invention is used to estimate the tool face angle of the rotary steerable drilling tool system. The estimation result is shown in FIG2. FIG2 describes the state variables x _i (k), the state estimation value and tool face angle estimate , FIG3 describes the average mean square error of 100 Monte Carlo simulations, where KF represents the Kalman filter with known noise covariance matrix, VBKF represents the Kalman filter based on variational Bayes, VBKS represents the Kalman smoother based on variational Bayes, MHE (N = 20) represents the rolling time domain estimator with a window length of N = 20, VBMHE (N = 5), VBMHE (N = 8), VBMHE (N = 10), VBMHE (N = 15) and VBMHE (N = 20) represent the adaptive rolling time domain estimators with window lengths of N = 5, N = 8, N = 10, N = 15 and N = 20 respectively. It can be seen from the simulation diagram that the estimator proposed in this patent has better estimation accuracy than the existing rolling time domain estimator, the Kalman filter based on variational Bayes and the Kalman smoother, which shows the superiority of the algorithm of this patent from the perspective of numerical simulation.

Example 2: To further verify the feasibility of the tool face angle estimation method of the present invention, an experiment was conducted using a simplified model of a dynamic pointing rotary steerable drilling tool system as shown in FIG4 , and a vibration platform was used to simulate vibration interference during the drilling process.

The sampling interval in the experiment is h = 0.01s, and the speed is as follows:

Where rps represents revolutions per second, and the vibration frequency of the vibration platform is selected as 30 Hz.

Selecting the same algorithm parameters as the numerical simulation, the raw measurement data of the gyroscope and accelerometer are shown in Figure 5. Figure 6 gives and/> The estimated value directly using the original data of the sensor In comparison, the tool face angle estimated by the tool face angle estimation method of the present invention is very smooth. In addition, by calculating the number of revolutions of the tool face angle, the estimated value is consistent with the set value. Therefore, it is feasible and effective to estimate the tool face angle of the dynamic pointing rotary steerable drilling tool system using the tool face angle estimation method of the present invention.

The above embodiments are used to explain the present invention rather than to limit the present invention. Any modification and change made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims (3)

1. A self-adaptive tool face angle estimation method of a dynamic directional rotary steering drilling tool is characterized by comprising the following specific steps:

S1, establishing a mathematical model of a tool face angle system;

The mechanical structure of the dynamic directional rotary steerable drilling tool system is analyzed, and the following measurement equation is established:

（1）

In the method, in the process of the invention, Representing measurements on the y-axis of an accelerometer,/>Representing measurements of the z-axis of an accelerometer,/>Representing the measured value of a gyroscope,/>Representing the corresponding measurement noise of the y-axis of the accelerometer,/>Representing the corresponding measurement noise of the z-axis of the accelerometer, d representing the corresponding measurement noise of the gyroscope,/>A component representing gravitational acceleration, provided that it satisfies/>Phi is the tool face angle;

Order the 、/>The sampling step length is h >0, and the construction of a tool face angle system mathematical model is as follows:

（2）

In the method, in the process of the invention, For a dynamic directional rotary steerable drilling tool system state variable,For the measurement output of a dynamically directed rotary steerable drilling tool system,、/>Is uncorrelated zero-mean gaussian white noise,With unknown, time-varying covariance matrix/>，/>With unknown, time-varying covariance matrix/>，，/>Is a coefficient matrix;

Knowing the state at time j And/>State at time j+1/>The following distribution is satisfied:

（3）

Is known to be And/>Output at time j/>The following distribution is satisfied:

（4）

Is known to be ，/>Then/>The following distribution is satisfied:

（5）

In the method, in the process of the invention, Representing the conditional probability of event X,/>For/>Is used for the average value of (a),In order to estimate the error covariance matrix,Representing mathematical expectations,/>Representation with mean/>And a multivariate Gaussian probability density function of the covariance matrix P;

Assume that 、/>And/>、/>And/>The following inverse Wishart distribution is satisfied:

（6）

（7）

（8）

In the method, in the process of the invention, Is/>Corresponding degree of freedom parameter,/>Is/>Corresponding degree of freedom parameter,/>Is thatCorresponding degree of freedom parameter,/>Is a symmetric positive inverse scale matrix,/>Representing the probability of event X,/>Representing a matrix/>, with degrees of freedom λ and inverse dimensionsProbability density function of inverse Wishart distribution;

S2, setting a rolling time domain estimation algorithm parameter;

Setting up For purposes of description/>Forgetting factor of fluctuation,/>For purposes of description/>Forgetting factor of fluctuation, given scalar/>Given the number of loops τ, given the estimated value at time N-1/>、/>、、/>、/>；

S3, predicting prior probability distribution parameters of a covariance matrix, wherein the method comprises the following specific steps of:

At time k, the result at time k-1 is known 、/>、/>、/>、Calculating the covariance matrix/>, at the moment kIs:

（9）

In the method, in the process of the invention, N=2 is/>Dimension of (2);

At the moment k is more than or equal to N, obtaining:

（10）

（11）

（12）

（13）

（14）

（15）

In the method, in the process of the invention, =2 Is/>Dimension of (2);

setting parameters of the 0 th iteration:

（16）

（17）

（18）

（19）

Wherein each parameter matrix is defined as:

（20）

（21）

（22）

（23）

representing vector set/> ，/>Representation/>The subarray of the first row and the q-th column is/>，/>Representing a kronecker product operation;

s4, updating approximate posterior probability distribution of covariance matrix, which comprises the following specific steps:

known pass through The state estimation value and covariance matrix estimation value after the iteration are repeated, and in the (i+1) th iteration,/>Approximate posterior probability density function/>、/>Approximate posterior probability density function/>And/>Approximate posterior probability density function/>Calculated by the following formula:

（24）

（25）

（26）

In the method, in the process of the invention,

（27）

（28）

（29）

（30）

（31）

（32）

（33）

（34）

（35）

（36）

Covariance matrixObtained in the ith iteration,/>Representing a symmetric matrix/>；

S5, updating the approximate posterior probability distribution of the state, if the iteration number i is smaller than tau, enabling i=i+1, turning to the step S4, continuously circularly calculating the approximate posterior probability distribution of the covariance matrix and the approximate posterior probability distribution of the state, and if the iteration number i is larger than or equal to tau, turning to the step S6;

s6, calculating tool face angle estimated value

Setting the estimated value obtained in the τ cycle as the optimal estimated value at the k moment, calculating to obtain the estimated value of the tool face angle at the k moment, enabling the time to update k=k+1, turning to step S3, repeating steps S3 to S6, and calculating the estimated value of the tool face angle at the k+1 moment.

2. The method for estimating the face angle of a dynamically directed rotary steerable drilling tool according to claim 1, wherein in step S5, the specific step of updating the approximate posterior probability distribution of the state is:

approximation posterior probability Density function for the (i+1) th order State variable Calculated by the following formula:

（37）

In the method, in the process of the invention,

（38）

（39）

（40）

（41）

（42）

（43）

（44）

（45）

（46）

（47）

（48）

（49）

（50）

（51）

（52）

（53）

For/>Unit matrix of dimension,/>For/>A unit matrix of dimensions;

if i < τ, let i=i+1, go to step S4 to continue to circularly calculate the approximate posterior probability distribution of the covariance matrix and the approximate posterior probability distribution of the state, and if the iteration number i is not less than τ, go to step S6.

3. The method for estimating the toolface angle of the dynamic directional rotary steerable drilling tool according to claim 2, wherein the step of calculating the toolface angle estimate in step S6 comprises the specific steps of:

setting the estimated value obtained by the τ cycle as the optimal estimated value at the k moment, and approximating the posterior probability density function variation as follows:

（54）

（55）

（56）

（57）

In the method, in the process of the invention, ，，/>；

Taking outThe last two behaviors/>The estimate of the toolface angle is solved using the following equation:

（58）

In the method, in the process of the invention, Is an estimate of the tool face angle,/>For/>1 St element of (2) represents a state/>Estimated value at time k,/>For/>Is the 2 nd element of (2) representing the state/>An estimated value at time k;

Turning to step S3, repeating steps S3 to S6, and calculating the estimated value of the toolface angle at time k+1.