CN106788336B - Linear system filtering estimation method based on output-feedback correction - Google Patents
Linear system filtering estimation method based on output-feedback correction Download PDFInfo
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Abstract
The invention relates to a linear system filtering estimation method based on output-feedback correction, which comprises the following steps: 1) establishing a relationship between the first measurement system and the second measurement system; 2) aiming at system characteristics, a system filtering equation is established; 3) combining the filtering method of the selected filter in the step 2); 4) and performing filtering processing of an output-feedback correction system, performing integration and delay processing on filter output information, compensating the measurement quantity of the first measurement system, performing difference between the compensated measurement quantity and the measurement quantity of the second measurement system, taking the measurement residual as filter input, performing output correction on the output quantity of the first measurement system after the filter output information is integrated, and taking the output quantity as final output of the whole information fusion. The method has applicability to heterogeneous measurement system information fusion, combines output correction and feedback correction, solves the nonlinear problem of output correction, and also considers the independence problem of feedback correction.
Description
Technical Field
The invention relates to the field of automatic control, in particular to a linear system filtering estimation method based on output-feedback correction.
Background
When information of heterogeneous sensors is fused, if measurement parameters directly obtained by the heterogeneous sensors are different and feedback correction cannot be performed through filtering information, the system is difficult to meet linear conditions as time goes on.
The indirect filtering estimation commonly used in engineering is usually based on a small deviation linearization equation, and comprises an output correction mode and a feedback correction mode. When the system adopts the output correction method (as shown in fig. 1), once the system error increases and the linearity condition cannot be satisfied, the filtering accuracy is easily reduced, and even the problem of non-convergence is easily caused. When the system adopts a feedback correction mode (as shown in fig. 2), the independence of each measurement system is weakened, and once one measurement system fails to cause filter pollution, other measurement systems can be polluted.
Disclosure of Invention
Technical problem to be solved
The invention aims to provide a linear system filtering estimation method based on output-feedback correction, which can solve the problem of nonlinearity and independence of feedback correction, wherein the nonlinearity is easy to occur in output correction.
(II) technical scheme
In order to solve the above technical problem, the present invention provides a linear system filtering estimation method based on output-feedback correction, which includes the following steps:
1) establishing a relationship between the first measurement system and the second measurement system;
2) aiming at system characteristics, a system filtering equation is established;
3) combining the filtering method of the selected filter in the step 2);
4) and performing filtering processing of an output-feedback correction system, performing integration and delay processing on filter output information, compensating the measurement quantity of the first measurement system, performing difference between the compensated measurement quantity and the measurement quantity of the second measurement system, taking the measurement residual as filter input, performing output correction on the output quantity of the first measurement system after the filter output information is integrated, and taking the output quantity as final output of the whole information fusion.
In step 2), the system filter equation includes a discretized system state equation and a measurement equation:
in the formula,. DELTA.XkIs the filter state at time k, Δ XK-1Is the filter state at time k-1, phik,k-1Is the state transition matrix from time k-1 to time k, Γk-1For system noise-driven arrays, Wk-1As system noise, Δ ZkTo measure residual, HkTo measure the matrix, vkTo measure noise.
In the step 3), the filter adopts a standard Kalman filtering method, and a filtering equation is established according to a discretized system state equation and a measurement equation:
in the formula,
Pk|k-1one-step prediction matrix, K, of the filtering state and mean square error at time K, respectivelykIn order to filter the gain of the filter,
and PkRespectively, the estimated values of the filtering state at the time k and the mean square error, QkAnd RkIs a covariance matrix of system noise and measurement noise,
for measuring matrix HkThe transpose of (a) is performed,
is an estimate of the filter state at time k-1, PK-1Is an estimated value of the mean square error at the time k-1,
for the state transition matrix phik,k-1The transpose of (a) is performed,
driving an array Γ for system noisek-1I is an identity matrix.
In the step 4), the final output of the whole information fusion is the sum of the output quantity of the first system and the integrated value of the output information of the filter.
(III) advantageous effects
The invention provides a linear system filtering estimation method based on output-feedback correction, which has the following advantages: 1. the method has applicability to heterogeneous measurement system information fusion, combines output correction and feedback correction, solves the nonlinear problem of output correction, and also considers the independence problem of feedback correction. 2. The method of the invention utilizes the superposition principle of a linear system to integrate and delay the filtering estimation state, and is used for measuring and correcting the relevant parameters of a system equation and a measurement equation, thereby ensuring that the system meets the linear condition, avoiding the error caused by nonlinearity during filtering calculation, improving the estimation precision during information fusion of heterogeneous sensors, ensuring the independence of each measurement system and improving the information fusion performance of the heterogeneous sensors.
Drawings
FIG. 1 is a schematic diagram of a conventional output correction filtering system;
FIG. 2 is a schematic diagram of a conventional feedback correction filtering system;
FIG. 3 is a schematic diagram of an output-feedback correction filtering system according to the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
The invention provides a linear system filtering estimation method based on output-feedback correction, which comprises the following steps:
1) establishing a system filter equation
Aiming at system characteristics, a system state equation and a measurement equation are established and discretized:
in the formula, Δ XkIs the filter state at time k, Δ XK-1Is the filter state at time k-1, phik,k-1Is the state transition matrix from time k-1 to time k, Γk-1For system noise-driven arrays, Wk-1As system noise, Δ ZkTo measure residual, HkTo measure the matrix, vkTo measure noise.
The filtering method of the selected filter, such as standard Kalman filtering:
in the formula,Pk|k-1one-step prediction matrix, K, of the filtering state and mean square error at time K, respectivelykIn order to filter the gain of the filter,
and PkRespectively, the estimated values of the filtering state at the time k and the mean square error, QkAnd RkIs a covariance matrix of system noise and measurement noise,for measuring matrix HkThe transpose of (a) is performed,
is an estimate of the filter state at time k-1, PK-1Is an estimated value of the mean square error at the time k-1,
for the state transition matrix phik,k-1The transpose of (a) is performed,
driving an array Γ for system noisek-1I is an identity matrix.
2) Performing output-feedback correction system filtering processing
As shown in fig. 3, integration, delay and compensation stages are added compared to the output feedback. After the filter output information Delta X is integrated and delayed, the measurement quantity M of the measurement system A is measured1Compensated and only after compensation is the output M of the measuring system B2The difference is made and used as the filter input for the estimation calculation. When the filter outputs signalAnd after integrating, carrying out output correction on the output of the measurement system A, and taking the output as the final output of the whole information fusion.
It should be noted that, since the filtering estimation adopts an indirect method, the filter receives the difference of the output values of the same parameter from each measurement system. Because the output-feedback correction and the output correction modes proposed by the scheme are different, the input of the filter is the corrected measurement residual error delta Z which is equal to M2-M3＝M2-M1-C2The final filter correction result needs to consider C2Therefore, in combination with the linear system superposition principle, the filtered estimate is integrated and then corrected. Compared with output correction, the scheme increases integration and delay links. Wherein,
① integral calculation C1To simplify the calculation and to adapt to digital computer processing, the filter states can be directly added up, i.e. by ═ Δ Xdt
② delay calculation C2Using integral value of the filter output during the last calculation period, i.e. C2(k)＝C1(k-1)。
③ compensate for the measurement M of the measurement system A after integration and delay of the filtered output1Make a compensation M3＝M1+C2。
In the above formula, C2Is to M1Is the data of the filter output information DeltaX after integration and delay processing, C1The integrated data of the information Δ X is output for the filter.
4) Output correction
After the filtering estimation and the integration processing are finished, the output M of the measurement system A is output1And carrying out output correction, and taking the output as the output of the whole information fusion system:
Output＝M1+C1＝M1+∫ΔXdt。
the above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (4)
1. A linear system filter estimation method based on output-feedback correction, comprising the steps of:
1) establishing a relationship between the first measurement system and the second measurement system;
2) aiming at system characteristics, a system filtering equation is established;
3) combining the filtering method of the selected filter in the step 2);
4) and performing filtering processing of an output-feedback correction system, performing integration and delay processing on filter output information, compensating the measurement quantity of the first measurement system, performing difference between the compensated measurement quantity and the measurement quantity of the second measurement system, taking the measurement residual as filter input, performing output correction on the output quantity of the first measurement system after the filter output information is integrated, and taking the output quantity as final output of the whole information fusion.
2. The linear system filter estimation method based on output-feedback correction as claimed in claim 1, wherein in step 2), the system filter equations comprise a discretized system state equation and a measurement equation:
in the formula,. DELTA.XkIs the filter state at time k, Δ XK-1Is the filter state at time k-1, phik,k-1Is the state transition matrix from time k-1 to time k, Γk-1For system noise-driven arrays, Wk-1As system noise, Δ ZkTo measure residual, HkTo measure the matrix, vkTo measure noise.
3. The linear system filter estimation method based on output-feedback correction according to claim 2, wherein in the step 3), the filter adopts a standard kalman filter method, and a filter equation is established according to the discretized system state equation and the measurement equation:
wherein,
Pk|k-1one-step prediction matrix, K, of the filtering state and mean square error at time K, respectivelykIn order to filter the gain of the filter,
and PkRespectively, the estimated values of the filtering state at the time k and the mean square error, QkAnd RkIs a covariance matrix of system noise and measurement noise,
for measuring matrix HkThe transpose of (a) is performed,
is an estimate of the filter state at time k-1, PK-1Is an estimated value of the mean square error at the time k-1,
for the state transition matrix phik,k-1The transpose of (a) is performed,
driving an array Γ for system noisek-1I is an identity matrix.
4. The linear system filter estimation method based on output-feedback correction as claimed in claim 1, wherein in step 4), the final output of the whole information fusion is the sum of the output quantity of the first measurement system and the integrated value of the filter output information.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101277103A (en) * | 2007-03-31 | 2008-10-01 | 索尼德国有限责任公司 | Adaptive filter device and method for determining filter coefficients |
| CN103196450A (en) * | 2013-04-02 | 2013-07-10 | 武汉大学 | Kalman filtering method based on analog circuit and analog circuit |
| CN103388471A (en) * | 2013-08-05 | 2013-11-13 | 吴佳平 | Drilling verification instrument and work method thereof |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101277103A (en) * | 2007-03-31 | 2008-10-01 | 索尼德国有限责任公司 | Adaptive filter device and method for determining filter coefficients |
| CN103196450A (en) * | 2013-04-02 | 2013-07-10 | 武汉大学 | Kalman filtering method based on analog circuit and analog circuit |
| CN103388471A (en) * | 2013-08-05 | 2013-11-13 | 吴佳平 | Drilling verification instrument and work method thereof |
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