Multi-axle hybrid vehicle real-time energy management strategy based on hierarchical control

By adopting a layered energy management strategy combining wavelet filtering and model prediction control in multi-axis hybrid vehicles, the problem of frequent power changes in multi-axis hybrid vehicles is solved, and efficient fuel economy and power battery protection is achieved.

CN119975320APending Publication Date: 2025-05-13JILIN UNIVERSITY

Patent Information

Application Number
CN202510170554.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-17
Publication Date
2025-05-13

AI Technical Summary

Technical Problem

Multi-axle hybrid vehicles have frequent power changes in harsh non-road conditions, and future working conditions are difficult to predict, making it difficult to efficiently control the on-board hybrid system through simple transplanted civilian vehicles.

Method used

A layered energy control strategy is established using a combination of pre-wavelet filtering and post-model prediction control. The load demand power is divided into two parts: high and low through Haar wavelet filtering. The high frequency power is allocated to the supercapacitor. The low frequency power is used as the reference input of the model prediction control layer. The optimal power distribution of the engine-generator set and the power battery pack is solved in real time using the secondary planning method.

Benefits of technology

Through layered control strategies, improve fuel economy, protect engine-generator sets and power battery sets, improve bus voltage quality, and enhance the real-time and adaptability of the hybrid system.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention belongs to the technical field of new energy automobiles, and particularly relates to a multi-axle hybrid vehicle real-time energy management strategy based on hierarchical control, which specifically comprises the following steps of: (1) calculating load power based on a whole vehicle dynamic balance equation, dividing the load demand power into a high part and a low part by adopting Haar wavelet filtering, high-frequency power and low-frequency power are obtained by decomposing and reconstructing an original signal; (2) distributing high-frequency power to a super capacitor, performing secondary optimization distribution on low-frequency power by taking fuel economy, a battery charge state and bus voltage as optimization targets, and solving an optimal power distribution ratio of an engine-generator set and a power battery pack in real time by utilizing a model prediction control method; and (3) establishing a layered energy management strategy by adopting a mode of combining front wavelet filtering and rear model predictive control. On the premise that the dynamic property of the whole vehicle is met, the fuel economy is improved and the multi-power-source characteristic is exerted by reasonably distributing energy flow between the power assemblies.
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Description

Technical Field

[0001] The present invention belongs to the technical field of new energy vehicles, and specifically is a real-time energy management strategy for multi-axle hybrid vehicles based on hierarchical control. Background Art

[0002] With the improvement of motor integration level, battery power density and electronic control real-time performance, the advantages of hybrid technology have become more and more significant and have become the focus of current research. For multi-axle hybrid vehicles, most of them work in harsh off-road conditions, power changes frequently, and future working conditions are difficult to predict. It is difficult to efficiently control the on-board hybrid system by simply transplanting the energy management strategy of civilian vehicles. For this reason, researchers have proposed a real-time energy management strategy for multi-axle hybrid vehicles based on hierarchical control. This strategy uses a combination of pre-wavelet filtering and post-model predictive control to establish a hierarchical energy control strategy. On the premise of meeting the power of the whole vehicle, it improves fuel economy and gives play to the characteristics of multiple power sources by reasonably allocating energy flow between powertrains.

[0003] Some current patents, such as the invention patent with patent number CN202410591225.2, propose an energy management strategy for ammonia-hydrogen zero-carbon internal combustion engine hybrid system based on model predictive control, and the invention patent with patent number CN202210685506.5 proposes a PHEV real-time energy management strategy based on model-free adaptive control. The former predicts the vehicle speed in the future time by the power demand of the whole vehicle at the current moment, obtains the SOC constraint of the whole vehicle in the future time based on the whole vehicle model, and adjusts the volume fraction of ammonia in the mixed fuel gas of the ammonia-hydrogen engine in real time, and uses the model predictive control algorithm to obtain the optimal engine output power sequence. The latter adopts a hierarchical optimization control architecture. The upper layer of the strategy is based on the feedback control principle, and the control variables are output in real time through the feedback of the vehicle target state and the actual state. The lower layer of the strategy completes the optimal allocation of energy between different power sources of the vehicle power system according to the control parameters output by the upper layer of the energy management strategy. Neither of them considers the application of wavelet filtering in real-time energy management strategy. Summary of the invention

[0004] The present invention aims to propose a real-time energy management strategy for a multi-axis hybrid vehicle based on hierarchical control. The strategy adopts a combination of pre-wavelet filtering and post-model predictive control to establish a hierarchical energy control strategy. The load demand power is divided into high and low parts through a Haar wavelet filtering layer, and the high-frequency power is allocated to power-type power sources such as supercapacitors. The low-frequency power is used as a reference input of the model predictive control layer to obtain a linear prediction model. The optimization objective function is established with fuel economy, battery state of charge and bus voltage as optimization targets. Under constraints, the quadratic programming method is used to solve the optimal power allocation of the engine-generator set and the power battery set in real time.

[0005] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0006] A real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control includes the following steps:

[0007] S1: Based on the vehicle dynamics balance equation, the vehicle load power is calculated from the vehicle speed and slope angle. The Haar wavelet filter is used to divide the vehicle load demand power into high and low parts. The high-frequency and low-frequency power components are obtained by decomposing and reconstructing the original signal.

[0008] S2: Allocate high-frequency power to power sources such as supercapacitors, perform secondary optimization of low-frequency power allocation with fuel economy, battery state of charge and bus voltage as optimization targets, and use model predictive control methods to solve the optimal power allocation ratio of the engine-generator set and the power battery set in real time;

[0009] S3: A hierarchical energy management strategy is established by combining pre-wavelet filtering and post-model predictive control. The upper layer is the wavelet filtering layer, the lower layer is the model predictive control layer, and the interactive information between the upper and lower layers is the load demand power.

[0010] In the preferred technical solution, the design process of the wavelet filter layer in step S1 is specifically as follows:

[0011] S11: Determine the wavelet order:

[0012]

[0013] In the formula, f b is the power battery cut-off frequency; N is the wavelet order; t s is the discrete sampling time;

[0014] Considering the smoothness of wavelet and the phase characteristics of wavelet filter, the wavelet coefficient N is taken as the minimum value in the open interval with the minimum positive integer boundary;

[0015] S12: Haar wavelet is selected as the mother function to construct a 2-channel filter bank. The definitions of the high-pass and low-pass decomposition filters in the discrete equation are:

[0016]

[0017] In the formula, H h (z) and H l (z) are high-pass and low-pass analysis filters respectively; z is a variable in the complex frequency domain;

[0018] The original signal is decomposed by wavelet through the decomposition filter to obtain the wavelet coefficients that characterize the fluctuation of the signal. The high-frequency wavelet coefficients of each order and the 4th-order low-frequency wavelet coefficients are grouped independently to extract the high-frequency and low-frequency signals.

[0019] S13: Based on the fact that the wavelet function obtained by wavelet decomposition is usually not equal to the actual power amplitude, a reconstruction filter is constructed to restore the high-frequency and low-frequency wavelet coefficients, which is defined as:

[0020]

[0021] In the formula, G h (z) and G l (z) are high-pass and low-pass reconstruction filters respectively;

[0022] After the high-frequency coefficients of each order are reconstructed, the total high-frequency power component is accumulated; after the highest-order low-frequency coefficients are reconstructed, the required low-frequency power component is directly obtained.

[0023] In the preferred technical solution, the design process of the model prediction control layer in step S2 is specifically as follows:

[0024] S21: Considering that the engine and the generator are not provided with a speed change mechanism, the two are directly connected and maintain the same speed. The engine mechanical torque and the generator electromagnetic torque depend on the efficiency of the generator. The working efficiency of the generator is expressed as:

[0025] α g =f g (α g f Te (P e ),f Te (P e )) (4)

[0026] In the formula, α g is the generator working efficiency; P e Output effective power to the engine;

[0027] The low-voltage side of the bidirectional DC / DC is connected to the power battery, which can autonomously control the switching of the battery's charge and discharge states. Its working efficiency is expressed as:

[0028]

[0029] In the formula, α d is the bidirectional DC / DC working efficiency; P b For power battery efficiency;

[0030] Considering the work efficiency of the two:

[0031] P eg =P e αg

[0032] P bd =P b α d

[0033] Where P eg P is the power output from the engine-generator set to the DC bus; bd The power output from the power battery pack to the DC bus;

[0034] The fuel consumption of the engine is:

[0035]

[0036] In the formula, m f is [t0,t v ] is the fuel consumption in the time period; t0 is the starting time; t v is the end time;

[0037] The battery charge state of the power battery is:

[0038]

[0039] Where SOC is the state of charge of the power battery; Q r is the remaining capacity at the initial moment; Q u Q is the capacity consumed in the time period; a is the rated capacity of the power battery;

[0040] The voltage at the supercapacitor terminal is:

[0041] U out =U s -R s I s (8)

[0042] Where U out is the voltage at the supercapacitor terminal; U s is the open circuit voltage of the supercapacitor; R s is the internal resistance of the supercapacitor; I s is the supercapacitor current;

[0043] Let the variable be

[0044]

[0045] In the formula, x is a 3×1 state vector; y is a 3×1 output vector; u is a 2×1 control vector; v is a measurable disturbance;

[0046] The nonlinear state space equation is obtained:

[0047]

[0048] Formula (10) is expanded by the first order Taylor to obtain the linear prediction model:

[0049]

[0050] Where A is a 3×3 system matrix; B u is a 3×2 control matrix; B v is a 3×1 perturbation matrix; C is a 3×3 output matrix;

[0051] S22: To optimize the engine fuel economy, battery SOC stability, and bus voltage stability, the following optimization objective function is constructed:

[0052]

[0053] Where J is the optimization objective function; α is the fuel economy weight coefficient; β is the battery SOC optimization item weight coefficient; SOC r is the reference value of the power battery SOC; γ is the weight coefficient of the bus voltage optimization term; P is the prediction time domain length; k is an arbitrary assumed starting time; i is a discrete time variable;

[0054] The constraints are

[0055]

[0056] In the formula, the subscript min represents the minimum value of the variable; the subscript max represents the maximum value of the variable;

[0057] Under the premise of satisfying explicit constraints, the optimal control quantity is solved in real time by the quadratic programming method:

[0058]

[0059] In the formula, is the optimal control sequence; arg(·) is the optimal solution reading function.

[0060] S23: To prevent the error accumulation from affecting the prediction accuracy, at the beginning of each calculation cycle, the total error of the previous moment is obtained in real time:

[0061]

[0062] Where δ(k) is the prediction error at time k; y(k) is the measured output at time k; is the corrected prediction output for k-1 at time k;

[0063] Assuming that the error between adjacent moments remains constant, the prediction result at the current moment is corrected:

[0064]

[0065] In the formula, is the corrected prediction output of k at time k+1; y(k+1|k) is the initial prediction output of k at time k+1.

[0066] Compared with the prior art, the advantages of the present invention are:

[0067] 1. The multi-axis hybrid vehicle real-time energy management strategy based on hierarchical control described in the present invention adopts Haar wavelet filtering to separate high-frequency power from load power, giving full play to the advantages of high power density of supercapacitors, avoiding high-frequency charging and discharging of power batteries, which is beneficial to protecting the engine-generator set and power battery pack and improving the bus voltage quality;

[0068] 2. The real-time energy management strategy for multi-axle hybrid vehicles based on hierarchical control described in the present invention takes multi-axle wheel hybrid vehicles as the research object, solves the balance problem between real-time performance, adaptability and optimization effect of traditional energy management strategies, fully optimizes the power distribution between various power sources, improves fuel economy and gives full play to the characteristics of multiple power sources;

[0069] 3. The real-time energy management strategy for a multi-axis hybrid vehicle based on hierarchical control described in the present invention adopts a hierarchical control architecture, which decomposes complex energy management problems into multiple levels for optimization. The upper-level strategy makes optimization decisions based on global information, and the lower-level strategy quickly adjusts the power distribution of each power source according to the real-time working conditions, effectively improving the real-time and adaptability of the hybrid system. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0071] Figure 1 A flowchart of a real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control according to the present invention;

[0072] Figure 2 A schematic diagram of 4th-order wavelet decomposition and reconstruction in a real-time energy management strategy for a multi-axis hybrid vehicle based on hierarchical control according to the present invention;

[0073] Figure 3 A structural diagram of a vehicle-mounted hybrid power system in a real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control according to the present invention; DETAILED DESCRIPTION

[0074] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0075] The present invention will be further described below in conjunction with the accompanying drawings.

[0076] See also Figure 1 The present invention provides a real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control, which specifically includes the following steps:

[0077] S1: Based on the vehicle dynamics balance equation, the vehicle load power is calculated from the vehicle speed and slope angle. The Haar wavelet filter is used to divide the vehicle load demand power into high and low parts. The high-frequency and low-frequency power components are obtained by decomposing and reconstructing the original signal.

[0078] S2: Allocate high-frequency power to power sources such as supercapacitors, perform secondary optimization of low-frequency power allocation with fuel economy, battery state of charge and bus voltage as optimization targets, and use model predictive control methods to solve the optimal power allocation ratio of the engine-generator set and the power battery set in real time;

[0079] S3: A hierarchical energy management strategy is established by combining pre-wavelet filtering and post-model predictive control. The upper layer is the wavelet filtering layer, the lower layer is the model predictive control layer, and the interactive information between the upper and lower layers is the load demand power.

[0080] See also Figure 2 The design process of the wavelet filter layer in step S1 is specifically as follows:

[0081] S11: Determine the wavelet order:

[0082]

[0083] In the formula, f b is the power battery cut-off frequency; N is the wavelet order; t s is the discrete sampling time;

[0084] Considering the smoothness of wavelet and the phase characteristics of wavelet filter, the wavelet coefficient N is taken as the minimum value in the open interval with the minimum positive integer boundary;

[0085] S12: Haar wavelet is selected as the mother function to construct a 2-channel filter bank. The definitions of the high-pass and low-pass decomposition filters in the discrete equation are:

[0086]

[0087] In the formula, H h (z) and H l (z) are high-pass and low-pass analysis filters respectively; z is a variable in the complex frequency domain;

[0088] The original signal is decomposed by wavelet through the decomposition filter to obtain the wavelet coefficients that characterize the fluctuation of the signal. The high-frequency wavelet coefficients of each order and the 4th-order low-frequency wavelet coefficients are grouped independently to extract the high-frequency and low-frequency signals.

[0089] S13: Based on the fact that the wavelet function obtained by wavelet decomposition is usually not equal to the actual power amplitude, a reconstruction filter is constructed to restore the high-frequency and low-frequency wavelet coefficients, which is defined as:

[0090]

[0091] In the formula, G h (z) and G l (z) are high-pass and low-pass reconstruction filters respectively;

[0092] After the high-frequency coefficients of each order are reconstructed, the total high-frequency power component is accumulated; after the highest-order low-frequency coefficients are reconstructed, the required low-frequency power component is directly obtained.

[0093] See also Figure 3 The design process of the model prediction control layer in step S2 is specifically as follows:

[0094] S21: Considering that the engine and the generator are not provided with a speed change mechanism, the two are directly connected and maintain the same speed. The engine mechanical torque and the generator electromagnetic torque depend on the efficiency of the generator. The working efficiency of the generator is expressed as:

[0095] α g =f g (α g f Te (P e ),f Te (P e )) (4)

[0096] In the formula, α g is the generator working efficiency; P e Output effective power to the engine;

[0097] The low-voltage side of the bidirectional DC / DC is connected to the power battery, which can autonomously control the switching of the battery's charge and discharge states. Its working efficiency is expressed as:

[0098]

[0099] In the formula, α d is the bidirectional DC / DC working efficiency; Pb For power battery efficiency;

[0100] Considering the work efficiency of the two:

[0101] P eg =P e α g

[0102] P bd =P b α d

[0103] Where P eg P is the power output from the engine-generator set to the DC bus; bd The power output from the power battery pack to the DC bus;

[0104] The fuel consumption of the engine is:

[0105]

[0106] In the formula, m f is [t0,t v ] is the fuel consumption in the time period; t0 is the starting time; t v is the end time;

[0107] The battery state of charge of the power battery is:

[0108]

[0109] Where SOC is the state of charge of the power battery; Q r is the remaining capacity at the initial moment; Q u Q is the capacity consumed in the time period; a is the rated capacity of the power battery;

[0110] The voltage at the supercapacitor terminal is:

[0111] U out =U s -R s I s (8)

[0112] Where U out is the supercapacitor terminal voltage; U s is the open circuit voltage of the supercapacitor; R s is the internal resistance of the supercapacitor; I s is the supercapacitor current;

[0113] Let the variable be

[0114]

[0115] In the formula, x is a 3×1 state vector; y is a 3×1 output vector; u is a 2×1 control vector; v is a measurable disturbance;

[0116] The nonlinear state space equation is obtained:

[0117]

[0118] Formula (10) is expanded by the first order Taylor to obtain the linear prediction model:

[0119]

[0120] Where A is a 3×3 system matrix; B u is a 3×2 control matrix; B v is a 3×1 perturbation matrix; C is a 3×3 output matrix;

[0121] S22: To optimize the engine fuel economy, battery SOC stability, and bus voltage stability, the following optimization objective function is constructed:

[0122]

[0123] Where J is the optimization objective function; α is the fuel economy weight coefficient; β is the battery SOC optimization item weight coefficient; SOC r is the reference value of the power battery SOC; γ is the weight coefficient of the bus voltage optimization term; P is the prediction time domain length; k is an arbitrary assumed starting time; i is a discrete time variable;

[0124] The constraints are

[0125]

[0126] In the formula, the subscript min represents the minimum value of the variable; the subscript max represents the maximum value of the variable;

[0127] Under the premise of satisfying explicit constraints, the optimal control quantity is solved in real time by the quadratic programming method:

[0128]

[0129] In the formula, is the optimal control sequence; arg(·) is the optimal solution reading function.

[0130] S23: To prevent the error accumulation from affecting the prediction accuracy, at the beginning of each calculation cycle, the total error of the previous moment is obtained in real time:

[0131]

[0132] Where δ(k) is the prediction error at time k; y(k) is the measured output at time k; is the corrected prediction output for k-1 at time k;

[0133] Assuming that the error between adjacent moments remains constant, the prediction result at the current moment is corrected:

[0134]

[0135] In the formula, is the corrected prediction output of k at time k+1; y(k+1|k) is the initial prediction output of k at time k+1.

[0136] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control, characterized in that: The following steps are involved: S1: Haar wavelet filtering is used to divide the vehicle load demand power into high and low parts, and the high-frequency and low-frequency power components are obtained by decomposing and reconstructing the original signal; S2: Allocate high-frequency power to power sources such as supercapacitors, perform secondary optimization of low-frequency power allocation with fuel economy, battery state of charge and bus voltage as optimization targets, and use model predictive control methods to solve the optimal power allocation ratio of the engine-generator set and the power battery set in real time; S3: A hierarchical energy management strategy is established by combining pre-wavelet filtering and post-model predictive control. The upper layer is the wavelet filtering layer, the lower layer is the model predictive control layer, and the interactive information between the upper and lower layers is the load demand power.

2. The real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control according to claim 1 is characterized in that: The design process of the wavelet filter layer in step S1 is specifically as follows: S11: Determine the wavelet order: In the formula, f b is the power battery cut-off frequency; N is the wavelet order; t s is the discrete sampling time; Considering the smoothness of wavelet and the phase characteristics of wavelet filter, the wavelet coefficient N is taken as the minimum value in the open interval with the minimum positive integer boundary; S12: Haar wavelet is selected as the mother function to construct a 2-channel filter bank. The definitions of the high-pass and low-pass decomposition filters in the discrete equation are: In the formula, H h (z) and H l (z) are high-pass and low-pass analysis filters respectively; z is a variable in the complex frequency domain; The original signal is decomposed by wavelet through the decomposition filter to obtain the wavelet coefficients that characterize the fluctuation size of the signal. The high-frequency wavelet coefficients of each order and the 4th-order low-frequency wavelet coefficients are grouped independently to extract the high-frequency and low-frequency signals. S13: Based on the fact that the wavelet function obtained by wavelet decomposition is usually not equal to the actual power amplitude, a reconstruction filter is constructed to restore the high-frequency and low-frequency wavelet coefficients, which is defined as: In the formula, G h (z) and G l (z) are high-pass and low-pass reconstruction filters respectively; After the high-frequency coefficients of each order are reconstructed, the total high-frequency power component is accumulated; after the highest-order low-frequency coefficients are reconstructed, the required low-frequency power component is directly obtained.

3. The real-time energy management strategy for a multi-axle hybrid vehicle based on hierarchical control according to claim 1 is characterized in that: The design process of the model prediction control layer in step S2 is specifically as follows: S21: Considering that the engine and the generator are not provided with a speed change mechanism, the two are directly connected and maintain the same speed. The engine mechanical torque and the generator electromagnetic torque depend on the efficiency of the generator. The working efficiency of the generator is expressed as: a g =f g (α g f Te (P e ),f Te (P e )) (4) In the formula, α g is the generator working efficiency; P e Output effective power to the engine; The low-voltage side of the bidirectional DC / DC is connected to the power battery, which can autonomously control the switching of the battery's charge and discharge states. Its working efficiency is expressed as: In the formula, α d is the bidirectional DC / DC working efficiency; P b For power battery efficiency; Considering the work efficiency of the two: P eg =P e a g P bd =P b a d Where P eg P is the power output from the engine-generator set to the DC bus; bd The power output from the power battery pack to the DC bus; The fuel consumption of the engine is: In the formula, m f is [t0,t v ] is the fuel consumption in the time period; t0 is the starting time; t v is the end time; The battery charge state of the power battery is: Where SOC is the state of charge of the power battery; Q r is the remaining capacity at the initial moment; Q u Q is the capacity consumed in the time period; a is the rated capacity of the power battery; The voltage at the supercapacitor terminal is: U out =U s -R s I s (8) Where U out is the supercapacitor terminal voltage; U s is the open circuit voltage of the supercapacitor; R s is the internal resistance of the supercapacitor; I s is the supercapacitor current; Let the variable be In the formula, x is the 3×1 state vector; y is the 3×1 output vector; u is the 2×1 control vector; v is the measurable disturbance; The nonlinear state space equation is obtained: Formula (10) is expanded by the first order Taylor to obtain the linear prediction model: Where A is a 3×3 system matrix; B u is a 3×2 control matrix; B v is a 3×1 perturbation matrix; C is a 3×3 output matrix; S22: To optimize the engine fuel economy, battery SOC stability, and bus voltage stability, the following optimization objective function is constructed: Where J is the optimization objective function; α is the fuel economy weight coefficient; β is the battery SOC optimization item weight coefficient; SOC r is the reference value of the power battery SOC; γ is the weight coefficient of the bus voltage optimization term; P is the prediction time domain length; k is an arbitrary assumed starting time; i is a discrete time variable; The constraints are In the formula, the subscript min indicates the minimum value of the variable; The subscript max indicates the maximum value of the variable; Under the premise of satisfying explicit constraints, the optimal control quantity is solved in real time by the quadratic programming method: In the formula, is the optimal control sequence; arg(·) is the optimal solution reading function; S23: To prevent the error accumulation from affecting the prediction accuracy, at the beginning of each calculation cycle, the total error of the previous moment is obtained in real time: Where δ(k) is the prediction error at time k; y(k) is the measured output at time k; is the corrected prediction output for k-1 at time k; Assuming that the error between adjacent moments remains constant, the prediction result at the current moment is corrected: In the formula, is the corrected prediction output of k at time k+1; y(k+1|k) is the initial prediction output of k at time k+1.

Citation Information

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