CN114114038A - Lithium battery SOC and available capacity joint estimation method under full-life and full-temperature conditions - Google Patents

Abstract

The invention relates to a lithium battery SOC and available capacity joint estimation method under full-life and full-temperature conditions, which comprises the following steps: step 1: collecting charge and discharge data of a lithium ion battery at a preset temperature; step 2: constructing a second-order RC equivalent circuit model with wide dynamic temperature compensation; and step 3: performing self-adaptive identification on the model parameters of the second-order RC equivalent circuit model in the step 2 by utilizing a particle swarm optimization algorithm integrated data and dynamic updating technology; and 4, step 4: carrying out high-precision estimation on the battery capacity by using the long-short term memory neural network to obtain the available capacity of the battery; and 5: and (4) taking the model parameters dynamically updated in the step (3) and the available capacity of the battery obtained in the step (4) as input values to carry out SOC estimation. The method fully considers the influence of battery aging and environmental temperature on SOC estimation, adds a periodic updating strategy in a parameter identification link, and can effectively realize the accurate estimation of SOC and available capacity of the lithium ion battery under the full-life and full-temperature conditions by combining the built model and the available capacity estimation result.

Description

Lithium battery SOC and available capacity joint estimation method under full-life and full-temperature conditions

Technical Field

The invention belongs to the technical field of lithium ion batteries, and particularly relates to a lithium battery SOC and available capacity joint estimation method under full-life and full-temperature conditions.

Background

Lithium ion batteries are a major energy source for electric vehicles due to their high electrical energy potential, high energy density, preferred safety characteristics, and long life. The battery management system is the core and key of the power battery technology, and a fully functional battery management system is crucial to battery state detection, battery internal state estimation, battery energy control management and battery safety protection. The accurate SOC value can more accurately control the charging and discharging current and the cut-off time, avoid overcharge, overdischarge and overload work, effectively protect the battery and prolong the service life of the battery. Meanwhile, accurate available capacity information can improve SOC estimation and promote high-quality management of the battery. Therefore, efficient and accurate SOC and available capacity estimation is critical.

At present, various methods have been developed to estimate the SOC value, and model-based estimation methods have been widely studied and applied because they have better online application capability, higher accuracy and initial error correction capability, but such methods depend on the accuracy of the model to a large extent, and the parameters and capacity of the battery model will change continuously with the aging of the battery and affect the estimation result of the battery SOC, and meanwhile, the change of the working environment temperature of the lithium ion battery also has a coupling effect on the internal parameters of the battery, resulting in further reduction of the estimation accuracy of the lithium ion battery SOC, so in order to ensure the SOC estimation accuracy of the lithium ion battery over the full-life and full-temperature range, it is necessary to study the combined estimation of the lithium ion battery SOC and the available capacity with wide dynamic temperature variation.

Disclosure of Invention

The invention aims to solve the technical problem of providing a lithium battery SOC and available capacity joint estimation method under the full-life and full-temperature conditions to solve the problem that parameters and available capacity of a battery model can change along with the temperature and aging of a battery, so that the estimation result of the battery SOC is influenced in the prior art.

In order to solve the technical problems, the technical scheme of the invention is as follows: the method for jointly estimating the SOC and the available capacity of the lithium battery at the full temperature in the whole service life is characterized by comprising the following steps of:

step 1: collecting charge and discharge data of a lithium ion battery at a preset temperature;

step 2: constructing a second-order RC equivalent circuit model with wide dynamic temperature compensation;

and step 3: performing self-adaptive identification on the model parameters of the second-order RC equivalent circuit model in the step 2 by utilizing a particle swarm optimization algorithm integrated data and dynamic updating technology;

and 4, step 4: selecting the duration of a voltage increase interval of the battery in the constant current charging process as a battery health characteristic quantity, and performing high-precision estimation on the battery capacity by using a long-short term memory neural network to obtain the available capacity of the battery;

and 5: and (4) taking the model parameters dynamically updated in the step (3) and the available capacity of the battery obtained in the step (4) as input values, and performing SOC estimation by using a square root cubature Kalman filter.

Further, the charge and discharge data of the lithium ion battery collected in the step 1 at the preset temperature specifically includes: the battery charging method comprises the steps of charging the battery by adopting a constant-current constant-voltage charging mode, discharging the lithium ion battery by adopting a vehicle working condition in the discharging process, wherein the vehicle working condition is HPPC (high power programmable controller) or UDDS (universal digital data broadcasting) or other working conditions which can be used for discharging the lithium ion battery.

Further, a second-order RC equivalent circuit model with wide dynamic temperature compensation is constructed in the step 2, and the derivation of a model parameter equation is as follows:

because the temperature change has a great influence on the model parameters, the model parameters should be updated along with the temperature change, and the update formula is as follows:

in the formula Q_aIs the available capacity of the battery, f is the relation between SOC and model parameter, T is the temperature of the battery, U_ocIs an open circuitVoltage OCV, R₀Is ohmic resistance, C₁、C₂Is R₁、R₂Polarization capacitance at both ends, R₁、R₂Is C₁、C₂The polarization resistance across the terminals, SOH is the state of health of the cell, which is defined as

C_nThe rated capacity of the battery;

the second order equivalent circuit model parametric equation with wide dynamic temperature compensation is expressed as:

in the formula of U_t(t) terminal voltage of model at time t, U₀(t) is ohmic resistance R₀Voltage across, U₁(t)、U₂(t) is a polarization resistance R₁、R₂And a polarization capacitor C₁、C₂The voltage across the two terminals is such that,

the SOC at time t is defined as:

where η is coulombic efficiency, i is current value, SOC (t)₀) Is the SOC value at the initial time.

Further, in step 3, a particle swarm optimization algorithm is used for integrating data and a dynamic updating technology, model parameters of the second-order RC equivalent circuit model with wide dynamic temperature compensation in step 2 are adaptively identified, and the method specifically comprises the following steps:

(31) identifying model parameters by utilizing a particle swarm optimization algorithm;

(32) setting the accumulated data length required by starting the particle swarm optimization algorithm, recording battery discharge data, activating the particle swarm optimization algorithm when the measured data length is greater than the set accumulated data length, identifying model parameters according to the accumulated current and voltage data, automatically updating the model parameter result identified in the previous period by using an automatic updating technology, and continuing to use the model parameters identified in the previous cycle without triggering the particle swarm optimization algorithm and updating the model parameters when the measured data length is less than the set accumulated data length.

Further, the accumulated data length setting principle is as follows: after a specific model of battery is selected, different data lengths are set to respectively identify and update battery model parameters, the SOC of the battery is estimated based on the same filtering algorithm and is compared with a real SOC value, and the data length selected when the SOC estimation precision is higher is selected as a set standard.

Further, the long-short term memory neural network regression function in step 4 is:

in which i, g, O, c and Op_kRespectively representing an input gate, a forgetting gate, an output gate, a state unit and an output unit, b represents the deviation of the forgetting gate, IW and OW represent the final input and output weights, sigma represents an activation function, and the limiting output value is [0,1 ]]Tanh is a hyperbolic function, c_k-1Representing a unit arranged by elements.

Further, in step 5, the SOC estimation is performed by using a square root cubature kalman filter with the model parameters dynamically updated in step 3 and the available capacity of the battery obtained in step 4 as input values, which specifically includes the following steps:

(51) the discrete formula of the state space function of the square root cubature Kalman filtering algorithm is as follows:

wherein x is_kAnd y_kRespectively representing state and system values, u_kRepresenting input values, f (-) and h (-) respectively representing a state equation and a measurement equation, according to the established second-order RC equivalent circuit model with wide dynamic temperature compensation, f (-) and h (·) is expressed as:

based on the established second-order RC equivalent circuit model with wide dynamic temperature compensation, the state variable of the system is x_k＝[U_1,k U_1,k SOC_k]^TInput variable is u_k＝i_kThe output variable is y_k＝U_t,kAt the same time

In the formula, delta t is sampling time, and eta is coulombic efficiency;

(52) square root volumetric Kalman filtering algorithm initialization

In the formula X₀Is an initial value of a state variable, P₀Representing the error covariance matrix, S₀Represents the square root, chol represents the Cholesky decomposition, and E (. cndot.) represents expectation.

(53) Time update of square root volumetric kalman filter algorithm

The sampling points at time k-1 are expressed as:

xi in the formula_iA set of sample points is represented that is,

i is 1,2, …, m, m is 2n, n represents the number of states;

the state of each sample point is expressed as:

after the trade-off points, the predicted state is determined:

error covariance of prior estimates of system state variables

Where Tria (. cndot.) represents QR decomposition,

and Q_k-1Expressed as:

(54) measurement update of square root volumetric kalman filter algorithm

Calculating input sampling points of a measurement equation:

estimate the measured output of each sample point: y is_g,k∣k-1＝h(u_k,x_g,k∣k-1)

Calculating a predicted value of the observation output:

observation error covariance mean prediction: s_yy,k∣k-1＝Tria[ζ_k∣k-1,S_R,k]

Wherein S_R,kIs measuring the noise R_kSquare root of

ζ_k∣k-1Is defined as

Covariance matrix square root calculation:

wherein

The kalman gain calculation, the state variable estimation value update calculation, and the error covariance square root update calculation are as follows:

kalman gain calculation:

updating the state variable estimation value:

wherein e_kIs composed of

Updating the square root of the covariance of the system error: s_k∣k＝Tria[χ_k∣k-1-K_kζ_k∣k-1,K_kS_R,k]

The SOC is a state variable of a square root cubature Kalman filtering algorithm, the estimation value of the state variable is updated and calculated to finish estimation operation of the SOC, and error covariance square root update calculation is to update system noise of the square root cubature Kalman filtering algorithm to improve accurate estimation of the SOC value by the algorithm.

Compared with the prior art, the invention has the beneficial effects that:

(1) the invention discloses a combined estimation method of lithium ion battery SOC and capacity considering temperature change, which realizes self-adaptive identification of model parameters by establishing a second-order equivalent circuit model considering wide dynamic temperature compensation and combining a particle swarm optimization algorithm with data accumulation and updating, then estimates the battery SOC by utilizing the regenerated model parameters and the regenerated available capacity based on a volume square root Kalman filter algorithm, and effectively ensures the SOC estimation precision of the battery in the whole life cycle at different temperatures.

(2) The invention considers that the temperature change has obvious influence on the model parameters, establishes a second-order equivalent circuit model with wide dynamic temperature compensation, is used for simulating the electrical characteristics of the battery and adapts to the rapid change of the internal and external temperatures.

(3) The method fully considers the influence of aging on the battery model parameters, and adds a periodic updating strategy in the parameter identification link, so that the adaptability of the model parameters to the battery aging and the accuracy of the model in the whole life cycle can be effectively improved.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.

Fig. 1 is a flow chart of a framework for jointly estimating the SOC and the available capacity of a lithium battery at full temperature and full life according to the present invention.

FIG. 2 is a schematic diagram of a second-order equivalent circuit model with wide dynamic temperature compensation for use in the present invention.

FIG. 3 is a diagram of a long short term memory neural network used in the present invention.

FIG. 4 is a flow chart of a square root cubature Kalman filter algorithm used in the present invention.

Detailed Description

In order that those skilled in the art will better understand the disclosure, the invention will be further described with reference to the accompanying drawings.

The invention provides a lithium battery SOC and available capacity joint estimation method under the whole service life and the whole temperature, and an estimation framework flow of the method is shown in figure 1. Firstly, acquiring charge and discharge data of a lithium ion battery at a preset temperature; meanwhile, the provided capacity prediction algorithm identifies the available capacity of the battery according to the health quantity generated by the constant-current constant-voltage charging voltage curve; in addition, the charging and discharging data are accumulated until the length of the measured data is greater than the set accumulated data length, and model parameter identification is carried out by adopting a particle swarm optimization algorithm; after the battery capacity and the model parameters are obtained, the SOC is estimated by using an SOC estimation algorithm based on square root volumetric Kalman filtering. On the other hand, when the length of the measured data is smaller than the set accumulated data length, the particle swarm algorithm is not called to update the model parameters. In this case, the SOC estimation algorithm uses the previously determined capacity results to predict SOC, with specific detailed steps described below:

step 1: collecting charge and discharge data of a lithium ion battery at a preset temperature; the collected charging and discharging data of the lithium ion battery at the preset temperature specifically comprises the following steps: the charging process of the battery adopts a constant-current constant-voltage charging mode, the discharging process adopts a vehicle working condition to discharge the lithium ion battery, and the vehicle working condition is HPPC or UDDS or other working conditions which can be used for discharging the lithium ion battery.

Step 2: constructing a second-order RC equivalent circuit model with wide dynamic temperature compensation, wherein the model structure is shown in figure 2, and U in the figure_ocIs open circuit voltage OCV, R₀Is ohmic resistance, C₁、C₂Is R₁、R₂Polarization capacitance at both ends, R₁、R₂Is C₁、C₂Polarization resistances at both ends; the model parameter equation is derived as follows:

because the temperature change has a great influence on the model parameters, the model parameters should be updated along with the temperature change, and the update formula is as follows:

in the formula Q_aFor the available capacity of the battery, f (.) is a relation between SOC and model parameters, T is the temperature of the battery, SOH is the state of health of the battery, and is defined as

C_nThe rated capacity of the battery;

further, the second order equivalent circuit model parametric equation with wide dynamic temperature compensation is expressed as:

in the formula of U_t(t) terminal voltage of model at time t, U₀(t) is ohmic resistance R₀Voltage across, U₁(t)、U₂(t) is a polarization resistance R₁、R₂And a polarization capacitor C₁、C₂The voltage across the two terminals is such that,

the SOC at time t is defined as:

where η is coulombic efficiency, i is current value, SOC (t)₀) Is the SOC value at the initial time.

And step 3: performing adaptive identification on the model parameters of the second-order RC equivalent circuit model with wide dynamic temperature compensation in the step 2 by utilizing a particle swarm optimization algorithm integrated data and dynamic updating technology; the method specifically comprises the following steps:

(31) identifying model parameters by utilizing a particle swarm optimization algorithm;

(32) setting the accumulated data length required by starting the particle swarm optimization algorithm, recording battery discharge data, activating the particle swarm optimization algorithm when the measured data length is greater than the set accumulated data length, identifying model parameters according to the accumulated current and voltage data, automatically updating the model parameter result identified in the previous period by using an automatic updating technology, and continuing to use the model parameters identified in the previous cycle without triggering the particle swarm optimization algorithm and updating the model parameters when the measured data length is less than the set accumulated data length.

Preferably, the accumulated data length setting principle of the present invention is: after a specific model of battery is selected, different data lengths are set to respectively identify and update battery model parameters, the SOC of the battery is estimated based on the same filtering algorithm and is compared with a real SOC value, and the data length selected when the SOC estimation precision is higher is selected as a set standard.

And 4, step 4: selecting the duration of a voltage increase interval of the battery in the constant-current charging process as a battery health characteristic, and performing high-precision prediction on the battery capacity by using a long-short term memory neural network to obtain the available capacity of the battery; FIG. 3 is a common configuration of a long-short term memory neural network. It can be seen that there are three gates, an input gate, a forgetting gate, and an output gate to read or modify current or historical information. Further, a tanh function and a sigmoid function are generally performed to select information.

The primary job in implementing a long-short term memory neural network is to determine which messages will be ignored by the forgetting gate. It will enter IP_kAnd OP_k-1Compression of 0 to 1, where IP_kInput representing the current step, OP_k-1Represents the output of the k-1 step, and the upper limit value 1 represents the value which should be completely reserved; conversely, the lower limit value of 0 indicates information that should be completely discarded. The forgetting gate can be expressed as:

f_k＝σ(b_f+Ip_kW_i+Op_k-1OW_i)

wherein f, i, O and c respectively represent a forgetting gate, an input gate, an output gate and a storage unit, b represents the deviation of the forgetting gate, and OW and IW respectively represent the weights of the last output and input. Then, it is necessary to determine which information should be stored, and this step is divided into two parts, one part is called an "input gate" and determines which values are to be updated; the other part creates a new candidate vector, called "input node", which can be expressed as:

accordingly, the current cell state is:

c_k＝c_k-1f_k+g_ki_k

finally, the output gate determines the final output information from the updated cell state, input gate and input node information, expressed as:

wherein p is_kIs an internal variable of the long-short term memory neural network. Battery capacity prediction may be achieved by the above formula based on the selected battery health characteristics.

And 5: using the dynamically updated model parameters in step 3 and the available battery capacity obtained in step 4 as input values, and performing SOC estimation by using a square root cubature kalman filter, where the flow of the square root cubature kalman filter is shown in fig. 4. The method specifically comprises the following steps:

(51) general discrete formula for establishing state space function of square root cubature Kalman filter

The discrete formula of the square root volumetric kalman filter state space function is as follows:

wherein x is_kAnd y_kRespectively representing state and system values, u_kRepresenting the input values, f (-) and h (-) respectively representing a state equation and a measurement equation, wherein f (-) and h (-) are expressed as follows according to the second-order RC equivalent circuit model with wide dynamic temperature compensation established in the step 2:

based on the established second-order RC equivalent circuit model with wide dynamic temperature compensation, the state variable of the system is x_k＝[U_1,k U_1,k SOC_k]^TInput variable is u_k＝i_kThe output variable is y_k＝U_t,kAt the same time

In the formula, delta t is sampling time, and eta is coulombic efficiency;

(52) square root volumetric Kalman filtering algorithm initialization

In the formula X₀Is an initial value of a state variable, P₀Representing the error covariance matrix, S₀Represents the square root, chol represents the Cholesky decomposition, and E (. cndot.) represents expectation.

(53) Time update of square root volumetric kalman filter algorithm

The sampling points at time k-1 are expressed as:

xi in the formula_iA set of sample points is represented that is,

i is 1,2, …, m, m is 2n, n represents the number of states;

the state of each sample point is expressed as:

after the trade-off points, the predicted state is determined:

error covariance of prior estimates of system state variables

Where Tria (. cndot.) represents QR decomposition,

and Q_k-1Expressed as:

(54) measurement update of square root volumetric kalman filter algorithm

Calculating input sampling points of a measurement equation:

estimate the measured output of each sample point: y is_g,k∣k-1＝h(u_k,x_g,k∣k-1)

Calculating a predicted value of the observation output:

observation error covariance mean prediction: s_yy,k∣k-1＝Tria[ζ_k∣k-1,S_R,k]

Wherein S_R,kIs measuring the noise R_kSquare root of

ζ_k∣k-1Is defined as

Covariance matrix square root calculation:

wherein

The kalman gain calculation, the state variable estimation value update calculation, and the error covariance square root update calculation are as follows:

kalman gain calculation:

updating the state variable estimation value:

wherein e_kIs composed of

Updating the square root of the covariance of the system error: s_k∣k＝Tria[χ_k∣k-1-K_kζ_k∣k-1,K_kS_R,k]

The SOC is a state variable of a square root cubature Kalman filtering algorithm, the estimation value of the state variable is updated and calculated to finish estimation operation of the SOC, and error covariance square root update calculation is to update system noise of the square root cubature Kalman filtering algorithm to improve accurate estimation of the SOC value by the algorithm.

Claims (7)

1. A lithium battery SOC and available capacity joint estimation method under the whole service life and the whole temperature is characterized by comprising the following steps:

step 1: collecting charge and discharge data of a lithium ion battery at a preset temperature;

step 2: constructing a second-order RC equivalent circuit model with wide dynamic temperature compensation;

and step 3: performing self-adaptive identification on the model parameters of the second-order RC equivalent circuit model in the step 2 by utilizing a particle swarm optimization algorithm integrated data and dynamic updating technology;

and 4, step 4: selecting the duration of a voltage increase interval of the battery in the constant current charging process as a battery health characteristic quantity, and performing high-precision estimation on the battery capacity by using a long-short term memory neural network to obtain the available capacity of the battery;

and 5: and (4) taking the model parameters dynamically updated in the step (3) and the available capacity of the battery obtained in the step (4) as input values, and performing SOC estimation by using a square root cubature Kalman filter.

2. The method of claim 1, wherein the step 1 of collecting the charge and discharge data of the lithium ion battery at a preset temperature specifically comprises: the battery charging method comprises the steps of charging the battery by adopting a constant-current constant-voltage charging mode, discharging the lithium ion battery by adopting a vehicle working condition in the discharging process, wherein the vehicle working condition is HPPC (high power programmable controller) or UDDS (universal digital data broadcasting) or other working conditions which can be used for discharging the lithium ion battery.

3. The method of claim 1, wherein the method comprises the following steps: in the step 2, a second-order RC equivalent circuit model with wide dynamic temperature compensation is constructed, and the derivation of a model parameter equation is as follows:

because the temperature change has a great influence on the model parameters, the model parameters should be updated along with the temperature change, and the update formula is as follows:

in the formula Q_aIs the available capacity of the battery, f is the relation between SOC and model parameter, T is the temperature of the battery, U_ocIs open circuit voltage OCV, R₀Is ohmic resistance, C₁、C₂Is R₁、R₂Polarization capacitance at both ends, R₁、R₂Is C₁、C₂The polarization resistance across the terminals, SOH is the state of health of the cell, which is defined as

C_nThe rated capacity of the battery;

the second order equivalent circuit model parametric equation with wide dynamic temperature compensation is expressed as:

in the formula of U_t(t) terminal voltage of model at time t, U₀(t) is ohmic resistance R₀Voltage across, U₁(t)、U₂(t) is a polarization resistance R₁、R₂And a polarization capacitor C₁、C₂The voltage across the two terminals is such that,

the SOC at time t is defined as:

where η is coulombic efficiency, i is current value, SOC (t)₀) Is the SOC value at the initial time.

4. The method of claim 1, wherein in the step 3, the particle swarm optimization algorithm is used to integrate data and a dynamic update technology, so as to adaptively identify the model parameters of the second-order RC equivalent circuit model with wide dynamic temperature compensation in the step 2, and the method specifically comprises the following steps:

(31) identifying model parameters by utilizing a particle swarm optimization algorithm;

(32) setting the accumulated data length required by starting the particle swarm optimization algorithm, recording battery discharge data, activating the particle swarm optimization algorithm when the measured data length is greater than the set accumulated data length, identifying model parameters according to the accumulated current and voltage data, automatically updating the model parameter result identified in the previous period by using an automatic updating technology, and continuing to use the model parameters identified in the previous cycle without triggering the particle swarm optimization algorithm and updating the model parameters when the measured data length is less than the set accumulated data length.

5. The method of claim 4, wherein the SOC and the available capacity of the lithium battery at the full temperature are jointly estimated at the full temperature and the full life, and the method comprises the following steps: the setting principle of the accumulated data length is as follows: after a specific model of battery is selected, different data lengths are set to respectively identify and update battery model parameters, the SOC of the battery is estimated based on the same filtering algorithm and is compared with a real SOC value, and the data length selected when the SOC estimation precision is higher is selected as a set standard.

6. The method of claim 1, wherein the method comprises the following steps: the long-short term memory neural network regression function in the step 4 is as follows:

in which i, g, O, c and Op_kRespectively representing an input gate, a forgetting gate, an output gate, a state unit and an output unit, b represents the deviation of the forgetting gate, IW and OW represent the final input and output weights, sigma represents an activation function, and the limiting output value is [0,1 ]]Tanh is a hyperbolic function, c_k-1Representing a unit arranged by elements.

7. The method of claim 1, wherein the method comprises the following steps: in the step 5, the model parameters dynamically updated in the step 3 and the available capacity of the battery obtained in the step 4 are used as input values, and a square root cubature kalman filter is used for SOC estimation, specifically comprising the following steps:

(51) the discrete formula of the state space function of the square root cubature Kalman filtering algorithm is as follows:

wherein x is_kAnd y_kRespectively representing state and system values, u_kRepresenting input values, f (-) and h (-) respectively represent a state equation and a measurement equation, and according to the established second-order RC equivalent circuit model with wide dynamic temperature compensation, f (-) and h (-) are expressed as:

based on the established second-order RC equivalent circuit model with wide dynamic temperature compensation, the state variable of the system is x_k＝[U_1,k U_1,k SOC_k]^TInput variable is u_k＝i_kThe output variable is y_k＝U_t,kAt the same time

In the formula, delta t is sampling time, and eta is coulombic efficiency;

(52) square root volumetric Kalman filtering algorithm initialization

In the formula X₀Is an initial value of a state variable, P₀Representing the error covariance matrix, S₀Represents the square root, chol represents the Cholesky decomposition, and E (. cndot.) represents expectation.

(53) Time update of square root volumetric kalman filter algorithm

The sampling points at time k-1 are expressed as:

xi in the formula_iA set of sample points is represented that is,

represents the number of states;

the state of each sample point is expressed as:

after the trade-off points, the predicted state is determined:

error covariance of prior estimates of system state variables

Where Tria (. cndot.) represents QR decomposition,

and Q_k-1Expressed as:

(54) measurement update of square root volumetric kalman filter algorithm

Calculating input sampling points of a measurement equation:

estimate the measured output of each sample point: y is_g,k∣k-1＝h(u_k,x_g,k∣k-1)

Calculating a predicted value of the observation output:

observation error covariance mean prediction: s_yy,k∣k-1＝Tria[ζ_k∣k-1,S_R,k]

Wherein S_R,kIs measuring the noise R_kSquare root of

ζ_k∣k-1Is defined as

Covariance matrix averageAnd (3) square root calculation:

wherein

The kalman gain calculation, the state variable estimation value update calculation, and the error covariance square root update calculation are as follows:

kalman gain calculation:

updating the state variable estimation value:

wherein e_kIs composed of

Updating the square root of the covariance of the system error: s_k∣k＝Tria[χ_k∣k-1-K_kζ_k∣k-1,K_kS_R,k]

The SOC is a state variable of a square root cubature Kalman filtering algorithm, the estimation value of the state variable is updated and calculated to finish estimation operation of the SOC, and error covariance square root update calculation is to update system noise of the square root cubature Kalman filtering algorithm to improve accurate estimation of the SOC value by the algorithm.

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