State estimation method of proof mass based on adaptive extended Kalman filter
Through the combination of adaptive extended Kalman filtering and strong tracking filter, the lack of Kalman filtering in nonlinear model processing and noise adaptability is solved, and high-precision inspection mass block state estimation is achieved, which significantly reduces the estimation error and Improves the adaptability and stability of the method.
Patent Information
- Application Number
- CN202410400901.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-03
- Publication Date
- 2024-12-13
- Estimated Expiration
- 2044-04-03
AI Technical Summary
The existing model-based Kalman filtering method is not effective in processing the nonlinear characteristics of the model, and has a strong dependence on the model and noise prior information, which limits its adaptability under different environmental conditions, resulting in the inspection. Mass block state estimation accuracy and stability are insufficient.
Adopting the state estimation method based on adaptive extended Kalman filtering, by adjusting the covariance prediction value and Kalman gain, combining strong tracking filter and covariance matching technology, state estimation is optimized in real time, adapting to changes in noise environment, improving estimation accuracy and stability sex.
Achieve high-precision contactless state estimation, especially in charge mutation, unbias and stability, reducing the absolute root mean square error by nearly half, and improving the adaptability and robustness of the extended Kalman filter estimation method. .
Smart Images
Figure CN118244018B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of high-precision space inertial sensors. Background Art
[0002] Space inertial sensors are one of the core payloads of gravitational wave detection satellites and play a vital role. The proof mass block located inside the space inertial sensor serves as a reflector for the high-precision interstellar laser interferometer, providing an inertial reference for the laser interferometer. The gravitational wave detection mission requires the construction of an ultra-high-precision inertial reference, and the proof mass block needs to be in a free-fall state as much as possible, so there are strict requirements on the residual acceleration of the proof mass block. The source of the acceleration noise of the proof mass block is very complex. Factors such as Brownian noise, thermal gradient effect, light pressure fluctuation, magnetic field effect, and random charging noise will cause residual acceleration noise of the proof mass block. The charge of the proof mass block will generate Lorentz force under the influence of the cosmic electromagnetic field and the magnetic field inside the spacecraft, and will also generate electrostatic force when interacting with the surrounding plates, all of which will introduce additional acceleration noise.
[0003] The charge of the proof mass is mainly caused by some galactic cosmic rays (GCR) and solar energetic particles (SEP), which can penetrate the protection of the spacecraft, reach the inside of the inertial sensor, and interact with the proof mass, resulting in charge accumulation. To ensure that the acceleration noise caused by the charge meets the requirements, the charge must be controlled within an acceptable range.
[0004] Precise management of the charge of the proof mass is a key technology to ensure the accuracy of the inertial sensor. Accurate measurement of the charge of the proof mass is the basis for high-precision charge control and one of the core functions of the charge management system. The current mainstream charge measurement uses force modulation, which can achieve contactless charge measurement. This method generates electrostatic force by applying a voltage signal on the plate to make the proof mass move, and estimates the charge by analyzing its movement. At present, there are two main methods for proving the state estimation of the proof mass: the first is the orthogonal demodulation method based on frequency domain analysis, but its estimation accuracy is relatively low and its response speed is slow. The second is the model-based Kalman filter estimation method, which can achieve higher estimation accuracy. However, the classical Kalman filter is not effective in processing the nonlinear characteristics of the model, and has a strong dependence on the model and noise prior information, which limits its adaptability under different environmental conditions. Therefore, it is particularly important to design a high-precision state estimation method. Summary of the invention
[0005] The present invention aims to solve the problem that the existing model-based Kalman filter proof mass block state estimation method is not effective in processing the nonlinear characteristics of the model, and has a strong dependence on the model and noise prior information, which limits its adaptability under different environmental conditions. A proof mass block state estimation method based on adaptive extended Kalman filtering is now provided.
[0006] A method for estimating a state of a proof mass block based on an adaptive extended Kalman filter comprises:
[0007] Calculate the covariance prediction value of the test mass block at time k according to the classical Kalman filtering method
[0008] The covariance prediction value of the inspection mass block at time k is given by the following formula: Make adjustments:
[0009]
[0010] in, is the covariance prediction value of the inspection mass block at time k after adjustment, λ k is the adjustment function, and: κ k Adjust the parameters for the k moment, when R k / R0≤α,κ k = 0 and λ k =0, when R k / R0>α,κ k =κ k-1 +τ,R k To measure the noise covariance, R0 is the initial value of the process noise covariance, α is the set threshold, and τ is the sampling period;
[0011] Verify the covariance prediction of the mass block based on the adjusted k moment Calculate the Kalman gain K k ;
[0012] According to the Kalman gain K k Estimate the state of the proof mass at time k.
[0013] Furthermore, the above measurement noise covariance R k The methods of obtaining include:
[0014] Use recursion to calculate the mean square error D(ε k ):
[0015]
[0016] Among them, ε k , ε k-1 and εk-g are the innovations at time k, k-1 and kg respectively, g is the number of innovation memories, and D(·) represents the innovation variance function;
[0017] Using the k-time innovation mean square error D(ε k ) Calculate the measurement noise covariance R k :
[0018]
[0019] Among them, H k is the observation matrix at time k;
[0020] The measurement noise covariance R k The values of are as follows:
[0021]
[0022] λ1 and λ2 are both set parameters.
[0023] Furthermore, the new information ε at time k is k The expression is as follows:
[0024]
[0025] Among them, x k is the state of the inspection mass block at time k, v k is the observation noise at time k, is the predicted value of the state of the inspection mass block at time k.
[0026] Furthermore, the above covariance prediction value of the inspection mass block at time k is calculated according to the classical Kalman filter method include:
[0027]
[0028] in, is the covariance estimate at k-1 time, Q k-1 is the k-1 moment process noise covariance, A k-1 is the k-1 moment discrete state transfer matrix, B k-1 is the k-1 moment process noise transfer matrix.
[0029] Furthermore, the above k-1 discrete state transfer matrix A k-1 and k-1 moment process noise transfer matrix B k-1 The expression is as follows:
[0030]
[0031] Where I is the identity matrix, Φ k-1is the state transfer matrix at time k-1.
[0032] Furthermore, the state transfer matrix Φ at time k k To use f(x,u ts ) is used to derive the state quantity x of the proof mass, and the expression is:
[0033]
[0034] Among them, the expressions of intermediate variables Ψ1 and Ψ2 are:
[0035]
[0036] f(·) represents the state transfer function, m is the weight of the test mass block, ω is the electrostatic required stiffness of the suspension drive control system, x1 is the displacement of the test mass block, x2 is the velocity of the test mass block, x3 is the charge of the test mass block, x4 is the rate of change of the charge of the test mass block, and F ts is the resultant force of the four plates around the test mass block on the test mass block, S is the plate area, d0 is the distance between the test mass block and the plates on both sides when it is located at the center of the electrode cage, ε is the vacuum dielectric constant, C tot is the total capacitance between the test mass and the four plates, u ts It is the test voltage signal.
[0037] Furthermore, the above-mentioned adjusted k-time covariance prediction value Calculate the Kalman gain K k ,include:
[0038] The Kalman gain K is calculated according to the following formula: k :
[0039]
[0040] Among them, H k is the observation matrix at time k.
[0041] Furthermore, according to the Kalman gain K k Estimate the state of the proof mass at time k, including:
[0042] The estimated state value of the inspection mass block at time k is obtained according to the following formula
[0043]
[0044] in, is the predicted value of the state of the inspection mass block at time k, H k is the observation matrix at time k, y kis the state observation value of the inspection mass block at time k.
[0045] Furthermore, after obtaining the estimated value of the state of the proof mass block at time k, the state of the proof mass block at time k+1 is predicted by the following formula:
[0046]
[0047] in, is the predicted value of the state of the inspection mass block at time k+1, is the estimated value of the state of the inspection mass block at time k. The expressions of the intermediate variables k1, k2, k3, and k4 are as follows:
[0048]
[0049] f(·) represents the state transition function, u ts It is the test voltage signal.
[0050] Furthermore, the covariance estimate at time k is updated according to the following formula:
[0051]
[0052] Among them, H k is the observation matrix at time k, and I is the unit matrix.
[0053] The method for estimating the state of the proof mass block based on the adaptive extended Kalman filter described in the present invention can implement high-precision contactless state estimation of the proof mass block, especially in dealing with charge mutation, and can improve the unbiasedness and stability of the extended Kalman filter estimation method. The absolute root mean square error of the present invention in estimating the constant charge is 2.371×10 4 , while the absolute root mean square error of the extended Kalman filter estimation is 4.04×10 4 The present invention reduces the estimation error of the extended Kalman filter charge estimation method by nearly half. BRIEF DESCRIPTION OF THE DRAWINGS
[0054] Figure 1 Flowchart for the adaptive extended Kalman filter;
[0055] Figure 2 It is a schematic diagram of the relationship between the inspection mass block and the electrode plate of the inertial sensor;
[0056] Figure 3 For the inspection mass block with 10 6 Schematic diagram of the estimated results of the test mass block charge at e, (a) represents the extended Kalman filter estimation result, and (b) represents the adaptive extended Kalman filter estimation result. DETAILED DESCRIPTION
[0057] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.
[0058] Reference Figures 1 to 3 This embodiment will be described in detail.
[0059] The spatial inertial sensor uses electrostatic force to suspend a proof mass block and measures the acceleration and attitude of the object in the inertial coordinate system by detecting the displacement of the proof mass block. The sensitive probe of the inertial sensor consists of a plate frame, a proof mass block and 18 plates (6 injection electrodes and 12 sensing drive electrodes). Figure 2 As shown, this embodiment takes the X-axis translation as an example, the inspection mass block is a cube with a side length of a, the area of the four plates on the X-axis are all S, the center distance between the two plates on the same side is b, and when the inspection mass block is located at the center of the electrode cage, the distance between it and the two side plates is d0.
[0060] The basic steps of electrostatic suspension drive control are: position measurement, control force calculation, voltage signal conversion and application of electrostatic execution force. In this implementation, the suspension drive control system is simplified, and the electrostatic required stiffness ω is directly used as the actual stiffness to calculate the electrostatic control force F. cmd for:
[0061] F cmd =-mω 2 x tm (1)
[0062] Where m is the weight of the test mass, x tm To verify the displacement of the center of the mass offset plate.
[0063] When the modulation voltage signal u is applied to the i-th plate at time t i (t) is as shown below (i = 1, 2, 3, 4), which will cause the proof mass to produce translational motion:
[0064]
[0065] Among them, u ts (t) is the amplitude V at time t ts And the frequency is f ts The sinusoidal voltage signal is called the test voltage signal, and has the following expression:
[0066] u ts (t) = V ts sin(2πf ts t) (3).
[0067] The electrostatic force F of the i-th plate on the proof mass i It is expressed as:
[0068]
[0069] Among them, u tm To test the potential of the mass block, Represents the capacitance C of the i-th plate i The derivative of displacement x is expressed as follows:
[0070]
[0071] ε is the dielectric constant of vacuum.
[0072] The resultant force F of the four plates on the proof mass ts for:
[0073]
[0074] Among them, Q tm To test the charge of the mass block, C tot is the total capacitance between the test mass and the four plates.
[0075] In order to combine the charge model with the translational motion model, we define the state quantity x1 is the displacement of the test mass block, x2 is the velocity of the test mass block, x3 is the charge of the test mass block, and x4 is the charge change rate of the test mass block. According to the physical laws and control input, the following 4-dimensional state equation can be constructed:
[0076]
[0077] In the formula, represents the first-order derivative of x with respect to time t, w∈R n is the process noise, y is the state observation of the proof mass, H∈R m×n is the observation matrix, and v is the observation noise. Both w and v are Gaussian white noise and are uncorrelated, with covariance matrices Q0 and R0 respectively.
[0078] Based on the above foundation, the specific steps of the method for estimating the state of a proof mass block based on an adaptive extended Kalman filter described in this embodiment are as follows:
[0079] Step 1: State prediction.
[0080] The classical Kalman filter adopts the form of formula (8) in the state prediction stage of the proof mass block:
[0081]
[0082] in, is the predicted value of the state of the inspection mass block at time k, A k-1 is the discrete state transfer matrix at time k-1, is the estimated value of the state of the inspection mass block at time k-1.
[0083] For nonlinear continuous systems, if equation (8) is used directly, two steps of linearization and discretization are required. However, state prediction can actually be implemented directly in a nonlinear form, which can avoid the linearization step, thereby retaining more information of the original model and obtaining a more accurate estimate. To this end, this embodiment uses the fourth-order Runge-Kutta method to directly discretize equation (8), as shown below:
[0084]
[0085] Among them, τ is the sampling period, and the expressions of intermediate variables k1, k2, k3, and k4 are:
[0086]
[0087] Step 2: Covariance prediction.
[0088] In formula (7), f(·) represents the state transfer function, and it can be seen that the charge measurement system of this embodiment is a nonlinear system. The extended Kalman filter is an important variant of the classical Kalman filter, which is used to solve the state estimation problem of nonlinear systems. The basic method is to first linearize the nonlinear system appropriately to obtain a linearized state equation, as shown in formula (10), and then use the basic steps of the classical Kalman filter to achieve estimation.
[0089]
[0090] Among them, Φ is the continuous state transfer matrix, Φ k is the state transfer matrix at time k, that is, at time k, f(x,u ts ) is differentiated with respect to x, and the expression is:
[0091]
[0092] The expressions of intermediate variables Ψ1 and Ψ2 are:
[0093]
[0094] The discretized state space equation is expressed as:
[0095]
[0096] Among them, x k is the state of the inspection mass block at time k, y k is the observed value of the inspection mass block at time k, w k-1 is the process noise at time k, v k is the observation noise at time k, H k is the observation matrix at time k, A k-1 is the discrete state transfer matrix at time k-1, B k-1 is the process noise transfer matrix at time k-1 and has the following form:
[0097]
[0098] Where I is the identity matrix.
[0099] According to the basic steps of the classic Kalman filter, the covariance prediction formula is:
[0100]
[0101] in, is the covariance prediction value at time k, is the covariance estimate at time k-1, Q k-1 is the process noise covariance at time k-1, ignoring Q k-1 Adaptive time Q k-1 =Q0.
[0102] Step 3: New interest variance.
[0103] Define the difference between the actual observation and the state prediction as the new information ε k In this embodiment, the new information ε k For scalars:
[0104]
[0105] The innovation variance is:
[0106]
[0107] Among them, Cov(·) represents the covariance function, and D(·) represents the innovation variance function.
[0108] The measurement noise covariance can be obtained as:
[0109]
[0110] The algorithm remembers the new information of g-1 moments before moment k, that is, ε k-(g-1),ε k-(g-2) ,…,ε k-1 ,ε k . Calculate the mean square error of g moments at time k, and use this value as the new information variance D(ε k ):
[0111]
[0112] However, this method needs to calculate the mean square error every time, which has a great impact on the execution speed of the algorithm.
[0113] This implementation uses a recursive method to calculate the mean square error of the new information at time k, including improving the calculation formula of the mean square error and calculating the mean square error by an iterative method. Specifically:
[0114] The difference between the mean square error of the new information at time k and time k-1 is:
[0115]
[0116] Therefore, the mean square error of the innovation at time k is
[0117]
[0118] Taking D(ε in formula (21) k ) is taken as the mean square error of the new information at time k.
[0119] Step 4: Measurement noise covariance adjustment.
[0120] According to formula (18), the measurement noise covariance R k Can be based on D(ε k ) to make adjustments:
[0121]
[0122] But if R k Too large will seriously affect the stability of the system, so R k The following restrictions are imposed on the adjustments:
[0123]
[0124] Among them, R0 is the initial value of the process noise covariance, and λ1 and λ2 are both set parameters.
[0125] Step 5: State error covariance adjustment.
[0126] When the estimation process tends to be stable, R k tends to be equal to R0. k Ratio R to R0 kWhen / R0 is greater than a certain threshold α, it means that the estimation result is more inaccurate, so it is necessary to increase the state error covariance To make the estimate more stable, that is:
[0127]
[0128] in, is the state error covariance after the adjustment, λ k To adjust the parameters.
[0129] The choice of setting the threshold α will be affected by the number of new information memories g.
[0130] Increase the state error covariance The post-state error will not decrease immediately, there will be a certain time delay, but during this process R k When / R0 is still greater than the set threshold α, it is necessary to k As a gradually decreasing function. Adjust the function λ k The selection of will be affected by the set threshold α. In this embodiment, there are:
[0131] λ k =0.4e -κ +0.0004 (24),
[0132] Among them, when R k / R0≤α,κ k = 0 and λ k =0; when R k / R0>α,κ k =κ k-1 +τ.
[0133] Therefore, λ k The choice of and the number of new information memories g influence each other.
[0134] Step 6: Kalman gain K k calculate:
[0135]
[0136] Step 7: Status Update:
[0137]
[0138] Among them, y k is the state observation value of the inspection mass block at time k.
[0139] Step 8: Covariance update:
[0140]
[0141] In this implementation, the introduction of the strong tracking filter enhances the filter's adaptability to system dynamic changes and sudden noise, and improves the stability and robustness of state estimation. Secondly, the use of the covariance matching adaptive filter enables the filter to adjust the function in real time, and perform adaptive optimization according to the dynamic changes of the noise environment, thereby improving the accuracy and precision of state estimation. In addition, STCMEKF inherits the advantages of EKF, that is, it can effectively handle nonlinear systems and non-Gaussian noise, and is therefore suitable for state estimation problems in complex and changeable spatial environments.
[0142] The adaptive Kalman filter based on covariance matching technology is an advanced Kalman filter variant used to deal with the adaptive estimation problem of parameter uncertainty and model error in dynamic systems. It achieves a more accurate estimation of the system state by dynamically adjusting the state transfer matrix and observation matrix of KF to match the real dynamic characteristics of the system and the characteristics of the observed data. Its basic principle is to dynamically adjust the state transfer matrix and observation matrix of KF according to the observed data and the estimated covariance matrix to maximize the matching of the real dynamic characteristics of the system and the characteristics of the observed data. By continuously updating the state transfer matrix and the observation matrix, the adaptive Kalman filter based on covariance matching technology can adaptively adjust the filter parameters to better adapt to the dynamic characteristics of the system and the characteristic changes of the observed data, thereby achieving an accurate estimation of the system state.
[0143] In the state estimation task, problems such as model uncertainty and observation noise instability can seriously affect the accuracy and robustness of state estimation. To solve this problem, researchers proposed a strong tracking filter algorithm, which aims to improve the tracking ability of the classic KF algorithm for state changes. The basic steps of the strong tracking filter algorithm are the same as those of the classic KF algorithm. The difference is that the strong tracking filter algorithm introduces a dynamic performance enhancement term, which is the key to the strong tracking filter algorithm to achieve strong tracking ability. Its basic principle is to dynamically adjust the filter parameters to better adapt to the environment and noise conditions. The basis for parameter adjustment can be state variable characteristics, observation data characteristics, etc. The adjusted filter parameters usually include Kalman gain, state covariance adjustment, and process noise adjustment. By properly adjusting the Kalman gain, the adaptability and robustness of the state estimator can be improved. By properly adjusting the variance and covariance of the process noise, the prediction ability of the state estimator can be improved. By properly adjusting the state covariance, the tracking accuracy and stability of the state estimator can be improved.
[0144] The pseudo code of the algorithm steps of the present invention is as follows:
[0145] Input: Initial value of state Initial value of state covariance Error covariance initial value Q0, process noise variance initial value R0, test signal sequence: uts (t0),u ts (t1),...,u ts (t n ), displacement measurement sequence: y1,y2,...,y n , sequence length n.
[0146] Output: state estimation sequence:
[0147] 1: k = 1, Q = Q0, R = R0
[0148] 2: while(k<n+1)
[0149] 3: 4:
[0150] 5:
[0151] 6:
[0152] 7: if (k>g) then
[0153] 8:
[0154] 9:
[0155] 10: if(R k >R0×2)
[0156] 11: R k =R0×2
[0157] 12: end if
[0158] 13: if(R k / R0>α)then
[0159] 14: κ=κ+0.1
[0160] 15: λ k =0.4e -κ +0.0004
[0161] 16:
[0162] 17: else
[0163] 18: κ=0,λ k =0
[0164] 19: end if
[0165] 20: end if
[0166] twenty one:
[0167] twenty two:
[0168] twenty three:
[0169] 24: end while
[0170] 25: return
[0171] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.
Claims
1. A method for estimating the state of a proof mass block based on an adaptive extended Kalman filter, characterized in that: include: Calculate the covariance prediction value of the test mass block at time k according to the classical Kalman filtering method The covariance prediction value of the inspection mass block at time k is given by the following formula: Make adjustments: in, is the covariance prediction value of the inspection mass block at time k after adjustment, λ k is the adjustment function, and: κ k Adjust the parameters for the k moment, when R k / R0≤α,κ k = 0 and λ k =0, when R k / R0>α,κ k =κ k-1 +τ,R k To measure the noise covariance, R0 is the initial value of the process noise covariance, α is the set threshold, and τ is the sampling period; Verify the covariance prediction of the mass block based on the adjusted k moment Calculate the Kalman gain K k ; According to the Kalman gain K k Estimate the state of the proof mass at time k; The measurement noise covariance R k The methods of obtaining include: Use recursion to calculate the mean square error D(ε k ): Among them, ε k , ε k-1 and ε k-g are the innovations at time k, k-1 and kg respectively, g is the number of innovation memories, and D(·) represents the innovation variance function; Using the k-time innovation mean square error D(ε k ) Calculate the measurement noise covariance R k : Among them, H k is the observation matrix at time k; The measurement noise covariance R k The values of are as follows: λ1′ and λ2′ are both set parameters.
2. The method for estimating the state of a proof mass block based on an adaptive extended Kalman filter according to claim 1, characterized in that: The new information ε at time k k The expression is as follows: Among them, x k is the state of the inspection mass block at time k, v k is the observation noise at time k, is the predicted value of the state of the inspection mass block at time k.
3. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 1, characterized in that: The covariance prediction value of the inspection mass block at time k is calculated according to the classical Kalman filtering method include: in, is the covariance estimate at k-1 time, Q k-1 is the k-1 moment process noise covariance, A k-1 is the discrete state transfer matrix at time k-1, B k-1 is the k-1 moment process noise transfer matrix.
4. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 3, characterized in that: The k-1 time discrete state transfer matrix A k-1 and k-1 moment process noise transfer matrix B k-1 The expression is as follows: Where I is the identity matrix, Φ k-1 is the state transfer matrix at time k-1.
5. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 4, characterized in that: The state transition matrix Φ at time k k To use f(x,u ts ) is used to derive the state quantity x of the proof mass, and the expression is: Among them, the expressions of intermediate variables Ψ1 and Ψ2 are: f(·) represents the state transfer function, m is the weight of the test mass block, ω is the electrostatic required stiffness of the suspension drive control system, x1 is the displacement of the test mass block, x2 is the velocity of the test mass block, x3 is the charge of the test mass block, x4 is the rate of change of the charge of the test mass block, and F ts is the resultant force of the four plates around the test mass block on the test mass block, S is the plate area, d0 is the distance between the test mass block and the plates on both sides when it is located at the center of the electrode cage, ε is the vacuum dielectric constant, C tot is the total capacitance between the test mass and the four plates, u ts It is the test voltage signal.
6. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 1, characterized in that: The adjusted k-time covariance prediction value Calculate the Kalman gain K k ,include: The Kalman gain K is calculated according to the following formula: k : Among them, H k is the observation matrix at time k.
7. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 1, characterized in that: According to the Kalman gain K k Estimate the state of the proof mass at time k, including: The estimated state value of the inspection mass block at time k is obtained according to the following formula in, is the predicted value of the state of the inspection mass block at time k, H k is the observation matrix at time k, y k is the state observation value of the inspection mass block at time k.
8. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 1, characterized in that: After obtaining the estimated value of the state of the proof mass block at time k, the state of the proof mass block at time k+1 is predicted by the following formula: in, To verify the predicted state value of the mass block at time k+1, is the estimated value of the state of the inspection mass block at time k. The expressions of the intermediate variables k1, k2, k3, and k4 are as follows: f(·) represents the state transition function, u ts It is the test voltage signal.
9. The method for estimating the state of a proof mass block based on adaptive extended Kalman filtering according to claim 1, characterized in that: Update the k-time covariance estimate according to the following formula Among them, H k is the observation matrix at time k, and I is the unit matrix.