A method for estimating rotational speed based on extended Kalman filter
By using an extended Kalman filter-based speed estimation method, the problems of poor spectral analysis performance and difficult installation of traditional tachometers in fault diagnosis of rotating machinery under non-stationary operating conditions are solved, achieving efficient and accurate speed estimation and fault diagnosis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- EAST CHINA UNIV OF SCI & TECH
- Filing Date
- 2022-10-14
- Publication Date
- 2026-05-29
AI Technical Summary
In the diagnosis of rotating machinery faults under non-stationary operating conditions, the spectrum analysis method is not effective, and the use of traditional tachometers increases economic costs and space occupation, making them difficult to install in certain application scenarios. Existing tachometer-less order tracking methods are computationally complex and difficult to use for vibration signal analysis with long-term sampling.
A rotational speed estimation method based on extended Kalman filtering is adopted. By establishing a frequency modulation model, the model parameters are regarded as system state vectors. Extended Kalman filtering is used to linearize the observation model, and instantaneous rotational speed is calculated iteratively to estimate the rotational speed of rotating machinery.
It achieves efficient speed estimation under long-term sampling vibration signals, reduces computational complexity, improves computational accuracy, and is suitable for fault diagnosis of rotating machinery.
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Figure CN115913033B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of speed estimation, and in particular to a speed estimation method based on extended Kalman filtering. Background Technology
[0002] Rotating machinery is widely used in industrial systems, such as electric motors, wind turbines, and generators. Instantaneous speed (IS) estimation is a crucial aspect of fault diagnosis for rotating machinery under non-stationary conditions. Fault diagnosis and condition monitoring technologies are of paramount importance for improving operational safety and reducing maintenance costs in rotating machinery.
[0003] Spectrum analysis is considered a useful tool for diagnosing faults in rotating machinery under steady-state conditions. However, some rotating machinery operates at different speeds, and due to frequency aliasing, the aforementioned spectrum analysis method is not effective under these non-steady-state conditions.
[0004] To address this issue, order tracking methods have been applied to fault diagnosis of rotating machinery under non-stationary conditions. In order tracking methods, the signal is resampled in the angular domain with the shaft velocity as a reference. Traditionally, shaft velocity is measured using a tachometer, but installing a tachometer increases economic costs and occupies additional space, making it difficult to meet this requirement in some practical applications. For example, tachometers are generally not allowed to be installed on aircraft engines. Bonnardot proposed a tachometer-free order tracking method, which estimates the shaft speed from vibration signals instead of tachometer signals. Compared to tachometers, vibration sensors are cheaper and easier to install. Since instantaneous velocity estimation is crucial in tachometer-free order tracking methods, most existing methods come at the cost of high computational time. Although they can achieve high-precision speed estimation results, these computationally complex algorithms are difficult to use for analyzing vibration signals sampled over long periods. Summary of the Invention
[0005] The purpose of this invention is to provide a rotational speed estimation method based on extended Kalman filtering, which can estimate the rotational speed of rotating machinery based on vibration signals sampled over a long period of time.
[0006] To achieve the above objectives, the present invention provides the following solution:
[0007] A speed estimation method based on extended Kalman filtering, the method comprising:
[0008] Acquire the vibration signal to be analyzed;
[0009] The initial value of the vibration signal is determined based on the vibration signal to be analyzed;
[0010] The initial state vector, initial state error, and initial noise variance are set based on the initial value of the vibration signal.
[0011] Determine the first estimated value of the state vector based on the initial state vector;
[0012] A first estimate of the state error is determined based on the initial state error and the initial noise variance.
[0013] Obtain the estimated value of the observation function at time n;
[0014] The prior state estimate is determined based on the vibration signal to be analyzed and the estimated value of the observation function at time n.
[0015] Obtain the Jacobian matrix at time n;
[0016] The state prior error matrix is determined based on the Jacobian matrix at time n and the first estimate of the state error.
[0017] The optimized Kalman gain is determined based on the Jacobian matrix at time n, the first estimate of the state error, and the state prior error matrix.
[0018] The second estimate of the state vector is determined based on the first estimate of the state vector, the prior state estimate, and the optimized Kalman gain.
[0019] The second estimate of the state error is determined based on the first estimate of the state error, the Jacobian matrix at time n, and the optimized Kalman gain.
[0020] The instantaneous rotational speed of the rotating machinery is determined based on the second estimated value of the state vector;
[0021] The second estimated value of the state vector is used as the initial state vector for the next moment, and the second estimated value of the state error is used as the initial state error for the next moment. The process then jumps to the step "determine the first estimated value of the state vector based on the initial state vector" until the instantaneous rotational speed estimation for all moments is completed.
[0022] Optionally, the first estimate of the state vector is calculated using the following formula:
[0023]
[0024] Where F is the state transition matrix, Let be the initial state vector. This is the first estimate of the state vector.
[0025] Optionally, the first estimate of the state error is calculated using the following formula:
[0026] P n|n-1 =FP n-1|n-1 F T +ΓQ w ΓT
[0027] Where F is the state transition matrix, Γ is the noise weight parameter matrix, and P n-1|n-1 Q is the initial state error. w Let P be the initial noise variance. n|n-1 Let T be the first estimate of the state error, and let T denote the transpose of the matrix.
[0028] Optionally, the estimated value of the observation function at time n is calculated using the following formula:
[0029]
[0030] in, Let g be the estimated value of the observation function at time n, where a1, a2, and g are all identity matrices. This is the first estimate of the state vector.
[0031] Optionally, the prior state estimate is calculated using the following formula:
[0032]
[0033] Among them, y n u is the prior estimate of the state. n The vibration signal to be analyzed is... This is the estimated value of the observation function at time n.
[0034] Optionally, the Jacobian matrix at time n is calculated using the following formula:
[0035]
[0036] Among them, H n Let g be the Jacobian matrix at time n, where a1, a2, and g are all identity matrices. x is the first estimate of the state vector. n This is the state vector.
[0037] Optionally, the state prior error matrix is calculated using the following formula:
[0038]
[0039] Among them, S n Let H be the state prior error matrix. n Let P be the Jacobian matrix at time n. n|n-1 R is the first estimate of the state error. n Let T be the noise matrix, and let T denote the transpose of the matrix.
[0040] Optionally, the optimized Kalman gain is calculated using the following formula:
[0041]
[0042] Among them, K n To optimize the Kalman gain, P n|n-1 H is the first estimate of the state error. n Let S be the Jacobian matrix at time n. n Let T be the state prior error matrix, and let T denote the transpose of the matrix.
[0043] Optionally, the second estimate of the state vector is calculated using the following formula:
[0044]
[0045] in, This is the second estimate of the state vector. K is the first estimate of the state vector. n To optimize Kalman gain, y n This is the prior estimate of the state.
[0046] Optionally, the second estimate of the state error is calculated using the following formula:
[0047] P n|n =(IK n H n )P n|n-1
[0048] Among them, P n|n Let I be the second estimate of the state error, and K be the identity matrix. n To optimize Kalman gain, H n Let P be the Jacobian matrix at time n. n|n-1 This is the first estimate of the state error.
[0049] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:
[0050] This invention proposes a rotational speed estimation method based on extended Kalman filtering. By establishing a frequency modulation model whose parameters are related to the instantaneous rotational speed and treating the model parameters as system state vectors, the frequency modulation model is transformed into an observation model function. Then, extended Kalman filtering is used to linearize the observation model function, thereby determining the relationship between the instantaneous rotational speed and the model parameters. The instantaneous rotational speed can then be calculated iteratively using a formula based on extended Kalman filtering, thus enabling the estimation of the rotational speed of rotating machinery with long-term sampled vibration signals, and facilitating fault diagnosis based on the rotational speed. Attached Figure Description
[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0052] Figure 1 This is a flowchart of the rotational speed estimation method based on extended Kalman filtering of the present invention;
[0053] Figure 2 This is a diagram of the apparatus for implementing the speed estimation method based on extended Kalman filtering according to the present invention. Detailed Implementation
[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0055] The purpose of this invention is to provide a rotational speed estimation method based on extended Kalman filtering, which can estimate the rotational speed of rotating machinery based on vibration signals sampled over a long period of time.
[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0057] Figure 1 This is a flowchart of the rotational speed estimation method based on extended Kalman filtering of the present invention, as shown below. Figure 1 As shown, a speed estimation method based on extended Kalman filtering is presented. Figure 2 The method, implemented by the apparatus shown, includes:
[0058] Step 101: Obtain the vibration signal to be analyzed.
[0059] This step involves inputting the vibration signal u to be analyzed. n .
[0060] Step 102: Determine the initial value of the vibration signal based on the vibration signal to be analyzed.
[0061] Specifically, the initial value of the vibration signal is the data near the initial moment of the vibration signal to be analyzed, and the initialization variables of the algorithm are determined through spectrum analysis and correlation analysis.
[0062] Step 103: Set the initial state vector, initial state error, and initial noise variance based on the initial value of the vibration signal.
[0063] The initialization variable state vector of the algorithm is set based on the initial value of the signal. State error P 1|1 State noise W n Sum of noise variance Q w Specifically, based on data near the initial moment of the vibration signal, the state vector is determined through spectral analysis, including instantaneous frequency, modulation factor, amplitude parameter, and phase parameter. The state noise is determined through correlation analysis, and the state noise is estimated based on the on-site data of the system under analysis. The noise variance Q is... w It is based on the state noise W n Calculated.
[0064] Step 104: Determine the first estimated value of the state vector based on the initial state vector.
[0065] Specifically, the first estimate of the state vector is calculated using the following formula:
[0066]
[0067] Where F is the state transition matrix, Let be the initial state vector. This is the first estimate of the state vector.
[0068] Step 105: Determine the first estimated value of the state error based on the initial state error and the initial noise variance.
[0069] Specifically, the first estimate of the state error is calculated using the following formula:
[0070] P n|n-1 =FP n-1|n-1 F T +ΓQ w Γ T
[0071] Where F is the state transition matrix, Γ is the parameter matrix, and P n-1|n-1 Q is the initial state error. w Let P be the initial noise variance. n|n-1 Let T be the first estimate of the state error, and let T denote the transpose of the matrix.
[0072] Step 106: Obtain the estimated value of the observation function at time n.
[0073] Specifically, the estimated value of the observation function at time n is calculated using the following formula:
[0074]
[0075] in, Let g be the estimated value of the observation function at time n, where a1, a2, and g are all identity matrices. This is the first estimate of the state vector.
[0076] Step 107: Determine the prior state estimate based on the vibration signal to be analyzed and the estimated value of the observation function at time n.
[0077] Specifically, the state prior estimate is calculated using the following formula:
[0078]
[0079] Among them, y n u is the prior estimate of the state. n The vibration signal to be analyzed is... This is the estimated value of the observation function at time n.
[0080] Step 108: Obtain the Jacobian matrix at time n.
[0081] Specifically, the Jacobian matrix at time n is calculated using the following formula:
[0082]
[0083] Among them, H n Let g be the Jacobian matrix at time n, where a1, a2, and g are all identity matrices. x is the first estimate of the state vector. n This is the state vector.
[0084] Step 109: Determine the state prior error matrix based on the Jacobian matrix at time n and the first estimate of the state error.
[0085] Specifically, the state prior error matrix is calculated using the following formula:
[0086]
[0087] Among them, S n Let H be the state prior error matrix, which is a priori estimate of the system error. n Let P be the Jacobian matrix at time n. n|n-1 R is the first estimate of the state error. n Let T be the noise matrix, and let T denote the transpose of the matrix.
[0088] Step 110: Determine the optimized Kalman gain based on the Jacobian matrix at time n, the first estimate of the state error, and the state prior error matrix.
[0089] Specifically, the optimized Kalman gain is calculated using the following formula:
[0090]
[0091] Among them, K n To optimize the Kalman gain, P n|n-1 H is the first estimate of the state error. n Let S be the Jacobian matrix at time n. n Let T be the state prior error matrix, and let T denote the transpose of the matrix.
[0092] Step 111: Determine the second estimate of the state vector based on the first estimate of the state vector, the prior estimate of the state, and the optimized Kalman gain.
[0093] Specifically, the second estimate of the state vector is calculated using the following formula:
[0094]
[0095] in, This is the second estimate of the state vector. K is the first estimate of the state vector. n To optimize Kalman gain, y n This is the prior estimate of the state.
[0096] Step 112: Determine the second estimate of the state error based on the first estimate of the state error, the Jacobian matrix at time n, and the optimized Kalman gain.
[0097] Specifically, the second estimate of the state error is calculated using the following formula:
[0098] P n|n =(IK n H n )P n|n-1
[0099] Among them, P n|n Let I be the second estimate of the state error, and K be the identity matrix. n To optimize Kalman gain, H n Let P be the Jacobian matrix at time n. n|n-1 This is the first estimate of the state error.
[0100] Step 113: Determine the instantaneous rotational speed of the rotating machinery based on the second estimated value of the state vector.
[0101] Specifically, the second estimate of the state vector is a 6×1 matrix composed of the instantaneous frequency, modulation factor, amplitude parameter, and phase parameter, as shown in formula x. n =[ω n ,β n ,a n ,bn ,φ n-1 ,φ n-1 -φ n-2 ] T As shown, the instantaneous frequency ω n It refers to the instantaneous rotational speed of rotating machinery.
[0102] Step 114: Use the second estimated value of the state vector as the initial state vector at the next moment, and use the second estimated value of the state error as the initial state error at the next moment. Jump to step "Determine the first estimated value of the state vector based on the initial state vector" until the instantaneous rotational speed estimation at all moments is completed.
[0103] The principle of this invention is as follows:
[0104] The Extended Kalman Filter (EKF) is a nonlinear version of the Kalman Filter, which linearizes the current state and error. In the EKF, the nonlinear dynamic response can be expressed as:
[0105] x n =f(x) n-1 ,u n )+w n
[0106] z n =h(x n )+v n
[0107] In the formula x n ,u n , and z n These are the system state, system input, and system observations, respectively. n and v n These are process noise and observation noise, both assumed to be zero-mean Gaussian noise. f and h are the state transition function and observation model function, respectively. These two functions are not necessarily linear functions, but they must be differentiable functions.
[0108] Then, the nonlinear functions f and h are linearized using the first-order Taylor demonstration:
[0109] f(x n-1 ,u n )≈f(x n|n-1 ,u n )+F n (x n-1 -x n-1|n-1 )
[0110] h(x n )≈h(x n|n-1 )+H n (x n -xn|n-1 )
[0111] In the formula F n and H n It is the Jacobian matrix of functions f and h.
[0112] The extended Kalman filter consists of two steps: a prediction step and an update step.
[0113] In the prediction step, the formula for calculating the predicted state is:
[0114]
[0115] In the formula It is x n The estimated value at time n.
[0116] The estimated value of the prediction error is calculated using the following formula:
[0117] P n|n-1 =F n P n-1|n-1 F n T +Q n
[0118] In the update step, the prior calculation formula is:
[0119]
[0120] The formula for calculating prior error is:
[0121]
[0122] In the formula, the noise matrix R n The calculation formula is:
[0123]
[0124] The formula for calculating the optimized Kalman gain is as follows:
[0125]
[0126] The formula for calculating the estimated value of the state update is:
[0127]
[0128] The formula for calculating the error update estimate is as follows:
[0129] P n|n =(IK n H n )P n|n-1
[0130] Then, by repeatedly executing the prediction and update steps of the extended Kalman filter described above, the state estimate is obtained.
[0131] This invention introduces a frequency modulation (FM) model into the extended Kalman filter, estimating instantaneous rotational speed by calculating model parameters. The FM model parameters are considered as the system state vector, transforming the FM model into an observation model function. Since the observation model function is nonlinear, a Taylor expansion-based linearization process is used for processing.
[0132] The method proposed in this invention mainly estimates the instantaneous rotational speed of a frequency-modulated amplitude-modulated (FMAM) signal. A typical FMAM signal can be modeled as follows:
[0133] u n =A n cos(φ n +φ0)+e n
[0134] In the formula A n and φ n These are the instantaneous amplitude and instantaneous phase, where φ0 is the initial phase, and e n It's noise. To avoid estimating the initial phase, the above formula is rewritten as follows:
[0135] un = a n cos(φ n )+b n sin(φ n )+e n
[0136] In the formula a n and b n It is the amplitude parameter.
[0137] The instantaneous phase is defined as:
[0138]
[0139] In the formula l n It is a first-order frequency factor, k n It is a second-order frequency factor. Correspondingly, the instantaneous frequency is defined as a linear frequency modulation model:
[0140] ω n =l n +k n n
[0141] The frequency modulation factor is defined as:
[0142] β n =k n
[0143] Based on the first-order difference formula and the second-order difference formula, the following formula exists:
[0144] φ n -φ n-1 =ω n
[0145] (φ n -φ n-1 )-(φ n-1 -φ n-2 )=β n
[0146] The above formula can be rewritten as:
[0147] φ n =φ n-1 +(φ n-1 -φ n-2 )+β n
[0148] Instantaneous frequency ω n Frequency modulation factor β n and a n Amplitude parameter b n Phase parameter φ n-1 and φ n-1 - φ n-2 Composition of state vector:
[0149] x n =[ω n ,β n ,a n ,b n ,φ n-1 ,φ n-1 -φ n-2 ] T
[0150] Meanwhile, assume that the fundamental frequency, modulation factor, and amplitude parameter satisfy a Markov chain process:
[0151] ω n =ω n-1 +w n,1
[0152] β n =β n-1 +w n,2
[0153] a n =a n-1 +w n,3
[0154] b n =b n-1 +w n,4
[0155] In the formula w n,1,w n,2 ,w n,3 , and w n,4 They are independent random variables that follow a Gaussian distribution:
[0156]
[0157] In the formula σ i This is the corresponding error.
[0158] Based on the above Markov chain process formula, the state formula of the extended filter under the frequency modulation model is defined as follows:
[0159] x n =Fx n-1 +Γw n
[0160] In the formula, the noise state vector w n The state transition matrix F and the noise weight parameter matrix Γ are defined as follows:
[0161] w n =[w n,1 ,w n,2 ,w n,3 ,w n,4 ] T
[0162]
[0163]
[0164] Wherein, the noise variance Q w It is the noise state vector w n The covariance matrix is calculated according to the definition of covariance operation in mathematical statistics.
[0165] Based on the state variable x n The amplitude and phase parameters can be written in matrix form:
[0166] a n =a1x n
[0167] b n =a2x n
[0168] φ n =gx n
[0169] The vector in the formula is defined as:
[0170] a1 = [0 0 1 0 0 0]
[0171] a2 = [0 0 0 1 0 0]
[0172] g = [0 1 0 0 1 1]
[0173] The signal to be analyzed can be considered as an observation model of the extended Kalman filter:
[0174] u n =h(x n )+e n
[0175] The observation function h is defined as follows:
[0176] h(x n )=a1x n cos gx n +a2x n sin gx n
[0177] Expand the observation function h using a first-order Taylor expansion:
[0178]
[0179] In the formula It is x n At time n, the estimated value of H n H is the Jacobian matrix of the observation function h. n The calculation formula is:
[0180]
[0181] Then, the extended Kalman filter is used to analyze the signal model. In the prediction step of the extended Kalman filter, the following formula exists:
[0182]
[0183] P n|n-1 =FP n-1|n-1 F T +ΓQ w Γ T
[0184] In the update step of the extended Kalman filter, the following formula exists:
[0185]
[0186]
[0187]
[0188]
[0189] P n|n =(IKn H n )P n|n-1
[0190] The following section verifies the computational complexity of the invention, theoretically demonstrating the computational efficiency of the method.
[0191] If the state vector x n Let the number be M, and the formula
[0192]
[0193] P n|n-1 =FP n-1|n-1 F T +ΓQ w Γ T
[0194] and
[0195]
[0196]
[0197]
[0198]
[0199] P n|n =(IK n H n )P n|n-1
[0200] The computational complexity is O(M). 3 ) and O(M 3 The state vector is estimated by repeatedly calculating the above formula. Assuming the number of signals is N, the computational complexity of the method in this invention is O(NM). 3 The computational complexity is much lower than that of other instantaneous speed estimation methods, and the computational accuracy is improved.
[0201] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0202] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A speed estimation method based on extended Kalman filtering, characterized in that, The method includes: Acquire the vibration signal to be analyzed; The initial value of the vibration signal is determined based on the vibration signal to be analyzed; The initial state vector, initial state error, and initial noise variance are set based on the initial value of the vibration signal. Determine the first estimated value of the state vector based on the initial state vector; A first estimate of the state error is determined based on the initial state error and the initial noise variance. Obtain the estimated value of the observation function at time n; The prior state estimate is determined based on the vibration signal to be analyzed and the estimated value of the observation function at time n. Obtain the Jacobian matrix at time n; The state prior error matrix is determined based on the Jacobian matrix at time n and the first estimate of the state error. The optimized Kalman gain is determined based on the Jacobian matrix at time n, the first estimate of the state error, and the state prior error matrix. The second estimate of the state vector is determined based on the first estimate of the state vector, the prior state estimate, and the optimized Kalman gain. The second estimate of the state error is determined based on the first estimate of the state error, the Jacobian matrix at time n, and the optimized Kalman gain. The instantaneous rotational speed of the rotating machinery is determined based on the second estimated value of the state vector; The second estimated value of the state vector is used as the initial state vector for the next moment, and the second estimated value of the state error is used as the initial state error for the next moment. The process then jumps to the step "determine the first estimated value of the state vector based on the initial state vector" until the instantaneous rotational speed estimation for all moments is completed.
2. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The first estimate of the state vector is calculated using the following formula: Where F is the state transition matrix, This is the initial state vector; This is the first estimate of the state vector.
3. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The first estimate of the state error is calculated using the following formula: P n|n-1 =FP n-1|n-1 F T +ΓQ w Γ T Where F is the state transition matrix, Γ is the noise weight parameter matrix, and P n-1|n-1 Q is the initial state error. w Let P be the initial noise variance. n|n-1 Let T be the first estimate of the state error, and let T denote the transpose of the matrix.
4. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The estimated value of the observation function at time n is calculated using the following formula: in, Let g be the estimated value of the observation function at time n, where a1, a2, and g are all identity matrices. This is the first estimate of the state vector.
5. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The prior state estimate is calculated using the following formula: Among them, y n u is the prior estimate of the state. n The vibration signal to be analyzed is... This is the estimated value of the observation function at time n.
6. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The Jacobian matrix at time n is calculated using the following formula: Among them, H n Let g be the Jacobian matrix at time n, where a1, a2, and g are all identity matrices. x is the first estimate of the state vector. n This is the state vector.
7. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The state prior error matrix is calculated using the following formula: Among them, S n Let H be the state prior error matrix. n Let P be the Jacobian matrix at time n. n|n-1 R is the first estimate of the state error. n Let T be the noise matrix, and let T denote the transpose of the matrix.
8. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The optimized Kalman gain is calculated using the following formula: Among them, K n To optimize the Kalman gain, P n|n-1 H is the first estimate of the state error. n Let S be the Jacobian matrix at time n. n Let T be the state prior error matrix, and let T denote the transpose of the matrix.
9. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The second estimate of the state vector is calculated using the following formula: in, This is the second estimate of the state vector. K is the first estimate of the state vector. n To optimize Kalman gain, y n This is the prior estimate of the state.
10. The rotational speed estimation method based on extended Kalman filtering according to claim 1, characterized in that, The second estimate of the state error is calculated using the following formula: P n|n =(I-K n H n )P n|n-1 Among them, P n|n Let I be the second estimate of the state error, and K be the identity matrix. n To optimize Kalman gain, H n Let P be the Jacobian matrix at time n. n|n-1 This is the first estimate of the state error.