CN112528472A - Multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm - Google Patents

Multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm Download PDF

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CN112528472A
CN112528472A CN202011353685.XA CN202011353685A CN112528472A CN 112528472 A CN112528472 A CN 112528472A CN 202011353685 A CN202011353685 A CN 202011353685A CN 112528472 A CN112528472 A CN 112528472A
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万佑红
张帅帅
达杨阳
徐长城
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses a multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm, which comprises the following steps of 1) establishing a first-order RC circuit model of a lithium battery, writing a state space expression for describing the lithium battery system according to the model, taking current and voltage as input, and identifying parameters by using a recursive least square method; 2) respectively establishing a multi-innovation extended Kalman filter and a multi-innovation filter, defining a mixed filtering performance evaluation index to realize better weight distribution, and establishing a multi-innovation-based mixed Kalman/H-infinity filter; 3) the advantages of high convergence precision and good robustness of a multi-innovation hybrid Kalman/H-infinity filtering algorithm are verified by taking different values for parameters in the weight expression. According to the invention, by establishing a hybrid Kalman/H infinity filter based on multiple innovations, the problem of estimation error increase caused by the fact that the current innovation and historical information are not fully utilized in the existing SOC estimation method is solved, and the SOC estimation precision and the robustness of the filter are improved by reasonably setting the weight.

Description

Multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm
Technical Field
The invention relates to a lithium battery SOC estimation method, in particular to a multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm.
Background
At present, energy storage batteries are developing towards lithium ion batteries using lithium iron phosphate as a positive electrode material, wherein the most important reason is that the lithium batteries have high energy density and long cycle service life, so the energy storage batteries are concerned by experts and researchers in the field. The SOC of the lithium battery is used as a key estimator of a battery management system, and plays an important role in the aspects of the service life, the working efficiency, the protection and the like of the battery. Therefore, accurate estimation of the SOC of the lithium battery is of great significance to efficient use of the lithium battery and the entire energy management system.
In recent years, the common SOC estimation methods for lithium batteries are mainly classified into a conventional SOC estimation method and a novel SOC estimation method. The traditional SOC estimation method mainly comprises a discharge experiment method, an open-circuit voltage method and an ampere-hour integration method. The discharge experiment method performs a discharge experiment on the lithium ion battery with constant current of a certain multiplying power, and the discharge current is multiplied by the discharge time so as to calculate the released electric quantity. Although the method is reliable and accurate, the method is difficult to be widely used due to the harsh experimental conditions. The open circuit voltage method of measuring the SOC of the battery usually requires a shelf for more than 2 hours, and thus takes much time in the work of measuring the open circuit voltage. The ampere-hour integration method is similar to the discharge experiment method, but an exact initial value of the SOC needs to be known, and because the current is subjected to time integration, noise in the measurement process has a large error influence on the calculated capacity value. The novel SOC estimation method mainly comprises a SOC prediction method based on a neural network, a Kalman filtering algorithm and H∞Filtering algorithms and improvements to these methods. The SOC prediction method based on the neural network needs a large amount of sample data and has a large workload. The Kalman filtering algorithm has the advantages of high speed, easiness in operation and the like, but an accurate lithium battery model needs to be obtained by the method, and the noise distribution characteristic in the lithium battery model is unknown, so that the method generates larger errors; the extended Kalman filtering method does not consider the influence of prior data in unknown noise of a system, so that the filtering estimation precision is not high. H∞Although the filtering algorithm has better robustness, the estimation accuracy is not high due to the neglect of historical information.However, the estimation accuracy of the SOC is still affected by uncertain parameters of the battery model. Therefore, how to reasonably process the current data and the historical information is one of the important research problems of future SOC estimation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm, and solves the problem that the estimation error is increased due to the fact that the current innovation and the historical information are not fully utilized in the existing SOC estimation method.
The purpose of the invention is realized as follows: a multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm specifically comprises the following steps:
step 1) establishing a first-order RC circuit model of the lithium battery, writing a state space expression for describing the lithium battery system according to the model, taking current and voltage as input, and performing parameter identification by using a recursive least square method;
step 2) respectively establishing a multi-innovation extended Kalman filter and a multi-innovation H∞The filter discusses the performance of the Kalman filter, defines the evaluation index of the mixed filtering performance to realize better weight distribution, and establishes a mixed Kalman/H based on multiple new information∞A filter;
step 3) finally, verifying the multi-information mixed Kalman/H by taking different values for the parameters in the weight expression∞The filter algorithm has the advantages of high convergence precision and good robustness.
As a further improvement of the present invention, the step 1) specifically comprises:
step 1-1), firstly, establishing a first-order RC circuit model of the lithium battery, and writing a state space expression of the lithium battery according to the model:
Uoc＝U+R1i+Uc (1)
Figure BDA0002802005140000031
in the formulas (1) to (2), U is a terminal voltage of the lithium battery; u shapeocIs the open circuit voltage of the lithium battery; i being a lithium batteryOperating current; r1Ohmic internal resistance of the lithium battery; r2The polarization internal resistance of the lithium battery; c is the polarization capacitance of the lithium battery;
step 1-2), discretizing the state space expression, and identifying model parameters by using a recursive least square method:
Figure BDA0002802005140000032
Figure BDA0002802005140000033
in the formula (3), T is a sampling period; x (k) ═ S (k), Uc(k)]TIs a state variable of the system; u (k) ═ I (k) denotes the control input of the lithium battery system, i.e. the operating current of the battery; y (k) ═ U (k) represents the output of the lithium battery system;
Figure BDA0002802005140000035
is system noise, and the covariance is Q (k); v (k) is the observation noise of the system, the covariance is R (k), and the statistical properties of the system noise and the observation noise are unknown; the system matrix, the input matrix, the output matrix and the direct transfer matrix in the state space model of the lithium battery are respectively as follows:
Figure BDA0002802005140000034
step 1-3) performing parameter identification on the lithium battery model by using a recursive least square method to obtain:
Figure BDA0002802005140000041
in the formula (5), q (k) is a self-defined matrix; phi (k) ═ y (k-1), I (k), I (k-1)]T；θ＝[a1,a2,a3]T,a1,a2,a3Is andparameters related to the lithium battery model can be identified by a recursive least square method; i is an identity matrix; mkIs a gain vector; in the working process of the lithium battery, the physical quantity which can be directly measured comprises the working current I (k) and the working voltage U (k) of the battery; according to the selected recursion relational expression of the lithium battery model, the working current I (k) at the current moment, the working current I (k-1) at the previous moment and the working current I (k-2) at the next previous moment are required to be obtained; the operating voltage U (k) at the present moment, the operating voltage U (k-1) at the previous moment, and the operating voltage U (k-2) at the next previous moment.
As a further improvement of the present invention, the step 2) specifically includes:
step 2-1) defining an index JiThe expression is as follows:
Figure BDA0002802005140000042
ri+1＝y(i+1)-C(i+1)x2(i+1/i)(i+1/i) (7)
by defining the index JiThe weight value of the filter can be flexibly adjusted between 0 and 1 along with the change of the parameters; in the formulae (6) and (7), ri+1For Kalman filter step i +1 innovation, when the system model is accurate, { ri+1Denotes a white noise information sequence, x2(i+1/i)(i +1/i) represents a one-step predicted value of the state of the Kalman filter based on all the quantity measurement before the time i;
step 2-2) further defines an index reflecting Kalman filtering performance in the hybrid filter
Figure BDA0002802005140000043
Figure BDA0002802005140000051
The expression (8) indicates the interval of [ k-M +1, k ] in time steps]Inner pair JiSampling and averaging, wherein M is an empirical value.
Step 2-3) two critical values are defined: j. the design is a square2And J∞If for any time
Figure BDA0002802005140000052
Is provided with
Figure BDA0002802005140000053
When the Kalman filtering performance is good, J is determined2Referred to as the supremum of Kalman filter high-precision operation; if for any time
Figure BDA0002802005140000054
Is provided with
Figure BDA0002802005140000055
At this time, if the Kalman filtering performance is poor and even there is a possibility of divergence, it is called J∞The infimum for the Kalman filter to run at low precision.
Step 2-4) establishing hybrid Kalman/H based on multiple information∞A filter:
Figure BDA0002802005140000056
Figure BDA0002802005140000057
wherein:
Figure BDA0002802005140000058
the parameters a and b in the formula (10) respectively correspond to the weight dk+1The sensitivity to quantization index changes and the stability of the MI-AHKF filter,
Figure BDA0002802005140000059
respectively represent an extended Kalman filter based on multiple information and H based on multiple information∞The estimated value of the filter is used,
Figure BDA00028020051400000510
representing hybrid Kalman/H based on multiple innovations∞An estimate of the filter.
As a further improvement of the present invention, the step 3) specifically includes: carrying out matlab simulation by analyzing the influence of the parameters a and b on the filter; and obtaining the optimal parameter value interval which enables the estimation precision and robustness of the filter through debugging.
By adopting the technical scheme, compared with the prior art, the invention has the beneficial effects that: by establishing a hybrid Kalman/H based on multiple new messages∞The filter fully considers the current information and the historical information, and combines the higher estimation precision of the early stage of the extended Kalman filtering algorithm and the H∞The filtering algorithm has the advantage of good robustness, the problem that the estimation error is increased due to the fact that the existing SOC estimation method cannot fully utilize the current innovation and the historical information is solved, and the SOC estimation precision and the robustness of a filter are improved by reasonably setting the weight.
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FIG. 1 is a flow chart of the present invention.
Fig. 2 is a first-order Thevenin model of a lithium battery of the invention.
FIG. 3 is a SOC-OCV charge/discharge relationship according to the present invention.
Fig. 4 is a state estimation curve for five methods.
Fig. 5 is an estimation error curve for the five methods.
Fig. 6 shows the SOC estimation results of five methods when the parameters a is 2 and b is 0.1.
Detailed Description
As shown in fig. 1, the multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm specifically includes the following steps:
step 1) establishing a first-order RC circuit model of the lithium battery, writing a state space expression for describing the lithium battery system according to the model, taking current and voltage as input, and performing parameter identification by using a recursive least square method;
step 1-1), firstly, establishing a first-order RC circuit model of the lithium battery, namely a first-order Thevenin model of the lithium battery shown in fig. 2, writing a state space expression of the lithium battery according to the model, and obtaining the state space expression by kirchhoff current law and kirchhoff voltage law:
Uoc＝U+R1i+Uc (1)
Figure BDA0002802005140000061
in the formulas (1) to (2), U is a terminal voltage of the lithium battery; u shapeocIs the open circuit voltage of the lithium battery; i is the working current of the lithium battery; r1Ohmic internal resistance of the lithium battery; r2The polarization internal resistance of the lithium battery; c is the polarization capacitance of the lithium battery;
the SOC of the lithium battery can be obtained by an ampere-hour integration method:
Figure BDA0002802005140000071
wherein S istRepresents SOC, Q of lithium battery at time t0Indicating the capacity of the battery.
Step 1-2), discretizing the state space expressions (1) - (3) to obtain a state space model of the lithium battery, wherein the state space model comprises the following steps:
Figure BDA0002802005140000072
Figure BDA0002802005140000073
in the formula (4), T is a sampling period; x (k) ═ S (k), Uc(k)]TIs a state variable of the system; u (k) ═ I (k) denotes the control input of the lithium battery system, i.e. the operating current of the battery; y (k) ═ U (k) represents the output of the lithium battery system;
Figure BDA0002802005140000074
is system noise, and the covariance is Q (k); v (k) is the observation of the systemNoise, with covariance R (k), the statistical properties of both system noise and observed noise are unknown; the system matrix, the input matrix, the output matrix and the direct transfer matrix in the state space model of the lithium battery are respectively as follows:
Figure BDA0002802005140000081
to obtain U in formula (5)ocThe experiment adopts a lithium ion battery with the model number of IFP36103155D-36Ah, the rated voltage is 3.2V, the rated capacity is 36Ah, and the functional relation between the open-circuit voltage and the SOC (SOC-OCV) is obtained by performing a 0.1C multiplying power charge-discharge characteristic experiment on the battery under the experimental environment of 25 ℃. And selecting constant current discharge of 9 equidistant pulses by using SOC-OCV experimental data, and taking the stable battery terminal voltage as an open-circuit voltage. To reduce experimental error, a high order fit can be made to SOC-OCV, and the mean value of the open circuit voltage is selected as the fit data, as shown in fig. 3.
By fitting the experimental data for 5 times, the description lithium battery open-circuit voltage U can be accurately obtainedoc(SOC) as a function of SOC, the fitting results are as follows:
Figure BDA0002802005140000082
and 1-3) because parameters in the lithium battery model are influenced by the self aging and self discharge of the battery and the external environment temperature, performing parameter identification by adopting a recursive least square method. The recursive least square method is an algorithm with infinite memory length, and can be used for carrying out online parameter identification of the system and parameter estimation of the real-time system. The model is carried out by utilizing a recursive least square method to identify parameters of the lithium battery model, and the method can be obtained by:
Figure BDA0002802005140000083
in the formula (5), q (k) is a self-defined matrix;φ(k)＝[y(k-1),I(k),I(k-1)]T；θ＝[a1,a2,a3]T,a1,a2,a3parameters related to the lithium battery model can be identified by a recursive least square method; i is an identity matrix; mkIs a gain vector; in the working process of the lithium battery, the physical quantity which can be directly measured comprises the working current I (k) and the working voltage U (k) of the battery; according to the selected recursion relational expression of the lithium battery model, the working current I (k) at the current moment, the working current I (k-1) at the previous moment and the working current I (k-2) at the next previous moment are required to be obtained; the working voltage U (k) at the current moment, the working voltage U (k-1) at the previous moment and the working voltage U (k-2) at the next previous moment, and then the resistor and the capacitor in the first-order Thevenin model are obtained.
Step 2) respectively establishing a multi-innovation extended Kalman filter and a multi-innovation H∞The filter discusses the performance of the Kalman filter, defines the evaluation index of the mixed filtering performance to realize better weight distribution, and establishes a mixed Kalman/H based on multiple new information∞And a filter.
Step 2-1) in the multi-innovation Kalman filtering algorithm and the multi-innovation H∞Based on a filtering algorithm, a hybrid Kalman/H based on multiple innovations is provided∞And the filtering algorithm can enable the weight value of the filter to flexibly adjust the size of the filter between 0 and 1 along with the change of the parameters. The filter combines the advantages of the two estimators and has high precision and good robustness. In order to realize the weight distribution of the hybrid filtering, an index J is defined according to the theoretical derivationiThe expression is as follows:
Figure BDA0002802005140000091
ri+1＝y(i+1)-C(i+1)x2(i+1/i)(i+1/i) (9)
in the formulae (8) and (9), ri+1For Kalman filter step i +1 innovation, when the system model is accurate, { ri+1Denotes a white noise information sequence, x2(i+1/i)(i +1/i) is based onAll measurements before time i measure the one-step predicted value of the state of the Kalman filter.
Step 2-2) in order to better handle the influence of noise on the estimation result, an index capable of reflecting Kalman filtering performance in the hybrid filter is further defined
Figure BDA0002802005140000092
Figure BDA0002802005140000093
The expression (10) indicates the interval of [ k-M +1, k ] in time steps]Inner pair JiSampling and averaging, wherein M is an empirical value. If the value of M is too large, the evaluation memory is too long, and the aim of evaluating the performance index of the Kalman filter in real time cannot be fulfilled; if the value of M is too small, the purpose of approximating the statistical mean value by time averaging cannot be achieved; in practical application, the range is generally 10,100]And the value of M is internally evaluated, and the influence of the value of M in the interval on the Kalman filtering performance evaluation can be verified through simulation.
Step 2-3) to better design the weight coefficients of the hybrid filter, the following discussion of the Kalman filter performance defines two thresholds: j. the design is a square2And J∞If for any time
Figure BDA0002802005140000101
Is provided with
Figure BDA0002802005140000102
When the Kalman filtering performance is good, J is determined2Referred to as the supremum of Kalman filter high-precision operation; if for any time
Figure BDA0002802005140000103
Is provided with
Figure BDA0002802005140000104
At this time, if the Kalman filtering performance is poor and even there is a possibility of divergence, it is called J∞For Kalman filteringThe infimum of low precision operation of the device.
Step 2-4) establishing a multi-innovation-based hybrid Kalman/H under the premise of fully considering innovation and historical information∞A filter:
Figure BDA0002802005140000105
Figure BDA0002802005140000106
wherein:
Figure BDA0002802005140000107
the parameters a and b in the formula (10) respectively correspond to the weight dk+1The sensitivity to quantization index changes and the stability of the MI-AHKF filter,
Figure BDA0002802005140000108
respectively represent an extended Kalman filter based on multiple information and H based on multiple information∞The estimated value of the filter is used,
Figure BDA0002802005140000109
representing hybrid Kalman/H based on multiple innovations∞Estimated value of the filter, dk+1Representing the weight.
The formula of the extended Kalman filtering algorithm (MIEKF) based on multiple new messages is as follows:
Figure BDA0002802005140000111
in formula (14)
Figure BDA0002802005140000112
The a-posteriori estimates are represented by,
Figure BDA0002802005140000113
representing a priori estimates, definition
Figure BDA0002802005140000114
Then e (k) is called innovation and is used to feedback correct the observed deviation. In the extended Kalman, there is only one innovation e (k), i.e., the prediction of the state at time k uses only the state estimate at time k-1, so the state innovation before time k-1 will be lost. Based on the multiple innovation theory, the single innovation of the extended Kalman filtering algorithm is extended into multiple innovations, and the innovation in the extended form
Figure BDA0002802005140000115
And popularizing the information vector.
E(p,k)＝[e(k)…e(k-p+1)]T∈R2×p (15)
In formula (15), p.gtoreq.1 is the innovation length. In the simulation process, the p value can be selected in the interval [3,8], and the complexity of the algorithm is increased and the operation is difficult due to the overlarge p value.
Multiple innovation based H∞The filter algorithm (MIHIF) is formulated as:
Figure BDA0002802005140000116
in formula (16), is defined
Figure BDA0002802005140000117
Then m (k) is called innovation and used to feedback correct the observed deviation. S (k) is a second order matrix designed according to the degree of importance for each state. H corresponding to formula (16)∞In this case, only one innovation m (k), i.e., the state at time k is predicted only by the state estimate at time k-1, so that state innovation before time k-1 is lost. Forming a new innovation vector M (p, K) and a new gain vector K (p, K) by the innovation M (K) and the filtering gain vector K (K); wherein:
M(p,k)＝[m(k),…,m(k-p+1)]T (17)
K(p,k)＝[K(k),…,K(k-p+1)]∈R2×p (18)
step 3) finally, verifying the multi-information mixed Kalman/H by taking different values for the parameters in the weight expression∞The filtering algorithm has the advantages of high convergence precision and good robustness, and matlab simulation is carried out by analyzing the influence of parameters a and b on the filter; and obtaining the optimal parameter value interval which enables the estimation precision and robustness of the filter through debugging.
Expanding the Kalman Filter Performance indicator of equation (13)
Figure BDA0002802005140000121
Converting into interval [0,1 ] by using nonlinear mapping principle]Weight d of inner valuek+1Wherein the parameters a and b respectively correspond to the weight dk+1Sensitivity to quantization index changes and stability of the MI-AHKF filter. When a, b are small, dk+1Smaller, when the estimation result is more confident in H∞An estimation result of the filter; when a and b are large, dk+1Larger, when the estimation result is more confident in the estimation result of the extended Kalman filter. In order to ensure the stability of the MI-AHKF filter and improve the estimation precision, the values of the parameters a and b need to be properly adjusted. On the other hand, selecting the parameter b too large will degrade the stability of the MI-AHKF filter. As shown in fig. 4 and 5, selecting a to 2 and b to 0.6 may verify that the estimation accuracy of the MI-AHKF filter is significantly higher than that of the other filters. As shown in fig. 6, a is fixed and b is reduced to verify that the MI-AHKF is more robust.
In conclusion, the invention establishes a hybrid Kalman/H based on multiple new messages∞The filter fully considers the current information and the historical information, and combines the higher estimation precision of the early stage of the extended Kalman filtering algorithm and the H∞The filtering algorithm has the advantage of good robustness, the problem that the estimation error is increased due to the fact that the existing SOC estimation method cannot fully utilize the current innovation and the historical information is solved, and the SOC estimation precision and the robustness of a filter are improved by reasonably setting the weight.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.

Claims (4)

1. A multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm is characterized by comprising the following steps:
step 1) establishing a first-order RC circuit model of the lithium battery, writing a state space expression for describing the lithium battery system according to the model, taking current and voltage as input, and performing parameter identification by using a recursive least square method;
step 2) respectively establishing a multi-innovation extended Kalman filter and a multi-innovation H∞The filter discusses the performance of the Kalman filter, defines the evaluation index of the mixed filtering performance to realize better weight distribution, and establishes a mixed Kalman/H based on multiple new information∞A filter;
step 3) finally, verifying the multi-information mixed Kalman/H by taking different values for the parameters in the weight expression∞The filter algorithm has the advantages of high convergence precision and good robustness.
2. The multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm according to claim 1, wherein the step 1) specifically comprises:
step 1-1), firstly, establishing a first-order RC circuit model of the lithium battery, and writing a state space expression of the lithium battery according to the model:
Uoc＝U+R1i+Uc (1)
Figure FDA0002802005130000011
in the formulas (1) to (2), U is a terminal voltage of the lithium battery; u shapeocIs the open circuit voltage of the lithium battery; i is the working current of the lithium battery; r1Ohmic internal resistance of the lithium battery; r2The polarization internal resistance of the lithium battery; c is the polarization capacitance of the lithium battery;
step 1-2), discretizing the state space expression, and identifying model parameters by using a recursive least square method:
Figure FDA0002802005130000021
Figure FDA0002802005130000022
Figure FDA0002802005130000023
in the formula (3), T is a sampling period; x (k) ═ S (k), Uc(k)]TIs a state variable of the system; u (k) ═ I (k) denotes the control input of the lithium battery system, i.e. the operating current of the battery; y (k) ═ U (k) represents the output of the lithium battery system;
Figure FDA0002802005130000024
is system noise, and the covariance is Q (k); v (k) is the observation noise of the system, the covariance is R (k), and the statistical properties of the system noise and the observation noise are unknown; the system matrix, the input matrix, the output matrix and the direct transfer matrix in the state space model of the lithium battery are respectively as follows:
Figure FDA0002802005130000025
step 1-3) performing parameter identification on the lithium battery model by using a recursive least square method to obtain:
Figure FDA0002802005130000026
in the formula (5), q (k) is a self-defined matrix; phi (k) ═ y (k-1), I (k), I (k-1)]T；θ＝[a1,a2,a3]T,a1,a2,a3Parameters related to the lithium battery model can be identified by a recursive least square method; i is an identity matrix; mkIs a gain vector; in the working process of the lithium battery, the physical quantity which can be directly measured comprises the working current I (k) and the working voltage U (k) of the battery; according to the selected recursion relational expression of the lithium battery model, the working current I (k) at the current moment, the working current I (k-1) at the previous moment and the working current I (k-2) at the next previous moment are required to be obtained; the operating voltage U (k) at the present moment, the operating voltage U (k-1) at the previous moment, and the operating voltage U (k-2) at the next previous moment.
3. The multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm according to claim 1, wherein the step 2) specifically comprises:
step 2-1) defining an index JiThe expression is as follows:
Figure FDA0002802005130000031
ri+1＝y(i+1)-C(i+1)x2(i+1/i)(i+1/i) (7)
by defining the index JiThe weight value of the filter can be flexibly adjusted between 0 and 1 along with the change of the parameters; in the formulae (6) and (7), ri+1For Kalman filter step i +1 innovation, when the system model is accurate, { ri+1Denotes a white noise information sequence, x2(i+1/i)(i +1/i) represents a one-step predicted value of the state of the Kalman filter based on all the quantity measurement before the time i;
step 2-2) further defines an index reflecting Kalman filtering performance in the hybrid filter
Figure FDA0002802005130000032
Figure FDA0002802005130000033
The expression (8) indicates the interval of [ k-M +1, k ] in time steps]Inner pair JiSampling and averaging, wherein M is an empirical value.
Step 2-3) two critical values are defined: j. the design is a square2And J∞If for any time
Figure FDA0002802005130000034
Is provided with
Figure FDA0002802005130000035
When the Kalman filtering performance is good, J is determined2Referred to as the supremum of Kalman filter high-precision operation; if for any time
Figure FDA0002802005130000036
Is provided with
Figure FDA0002802005130000037
At this time, if the Kalman filtering performance is poor and even there is a possibility of divergence, it is called J∞The infimum for the Kalman filter to run at low precision.
Step 2-4) establishing hybrid Kalman/H based on multiple information∞A filter:
Figure FDA0002802005130000041
Figure FDA0002802005130000042
wherein:
Figure FDA0002802005130000043
the parameters a and b in the formula (10) respectively correspond to the weight dk+1For quantization index changeHybrid Kalman/H of sensitivity and multi-innovation∞The stability of the filter is such that,
Figure FDA0002802005130000044
respectively represent an extended Kalman filter based on multiple information and H based on multiple information∞The estimated value of the filter is used,
Figure FDA0002802005130000045
representing hybrid Kalman/H based on multiple innovations∞An estimate of the filter.
4. The multi-innovation hybrid Kalman filtering and H-infinity filtering algorithm according to claim 3, wherein the step 3) specifically comprises: carrying out matlab simulation by analyzing the influence of the parameters a and b on the filter; and obtaining the optimal parameter value interval which enables the estimation precision and robustness of the filter through debugging.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113777510A (en) * 2021-09-07 2021-12-10 国网江苏省电力有限公司电力科学研究院 Lithium battery state of charge estimation method and device
CN114184962A (en) * 2021-10-19 2022-03-15 北京理工大学 Multi-algorithm fusion lithium ion battery SOC and SOH joint estimation method
CN114781760A (en) * 2022-06-17 2022-07-22 四川观想科技股份有限公司 Fault prediction method based on big data
CN116400247A (en) * 2023-06-08 2023-07-07 中国华能集团清洁能源技术研究院有限公司 Method and device for determining soft short circuit fault of battery

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113777510A (en) * 2021-09-07 2021-12-10 国网江苏省电力有限公司电力科学研究院 Lithium battery state of charge estimation method and device
CN114184962A (en) * 2021-10-19 2022-03-15 北京理工大学 Multi-algorithm fusion lithium ion battery SOC and SOH joint estimation method
CN114781760A (en) * 2022-06-17 2022-07-22 四川观想科技股份有限公司 Fault prediction method based on big data
CN116400247A (en) * 2023-06-08 2023-07-07 中国华能集团清洁能源技术研究院有限公司 Method and device for determining soft short circuit fault of battery
CN116400247B (en) * 2023-06-08 2023-08-29 中国华能集团清洁能源技术研究院有限公司 Method and device for determining soft short circuit fault of battery

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