Privacy-preserving method and estimator for estimating CO2 concentration in buildings

Abstract

The present invention relates to the field of privacy protection technology, and in particular to a method and an estimator for estimating CO2 concentration in a building with privacy protection, the method comprising: S1, obtaining a sensor measurement value y of the CO2 concentration in the building at time k-1 k‑1 , the initial estimate of CO2 concentration #imgabs0# and the unbiased minimum variance estimate of CO2 concentration #imgabs1#S2, the initial estimate of CO2 concentration in the building at time k is updated based on #imgabs2#, and the initial estimate of CO2 concentration in the building at time k is updated based on #imgabs4# and y k‑1 , update the unbiased minimum variance estimate of the CO2 concentration in the building at time k#imgabs5#S4, add noise α to the #imgabs6# k , and obtain the estimated value #imgabs7# with added noise as the estimated value of CO2 concentration in the building. The present invention can meet the privacy requirements and have the best estimation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of privacy protection technology, and in particular to a privacy-protected method and an estimator for estimating CO2 concentration in a building. Background Art

[0002] With the development and popularization of technologies such as artificial intelligence, the Internet of Things, and big data, more and more sensors and monitoring equipment are being used in building environmental monitoring to achieve real-time monitoring and control of environmental parameters inside buildings. Among them, carbon dioxide concentration is an important environmental parameter, which is of great significance for evaluating the air quality inside buildings, improving indoor comfort, and protecting the health of residents. However, in the process of collecting and using carbon dioxide concentration data, personal privacy protection is often involved.

[0003] Traditional methods for estimating carbon dioxide concentration often require obtaining real-time information about the number of people inside a building in order to more accurately estimate indoor air quality and formulate corresponding control strategies. However, directly obtaining and using information about the number of people may involve the leakage and infringement of personal privacy, raising issues of privacy protection. Therefore, how to estimate the carbon dioxide concentration in a building without exposing the number of people in the building has become an urgent problem to be solved. Summary of the invention

[0004] The present invention provides a privacy-protected method and an estimator for estimating CO2 concentration in a building, to solve the problems existing in the above-mentioned prior art. The technical solution is as follows:

[0005] In one aspect, a method for estimating CO2 concentration in a building with privacy protection is provided, comprising:

[0006] S1. Get the sensor measurement value y of CO2 concentration in the building at time k-1 k-1 , initial estimate of CO2 concentration And the unbiased minimum variance estimate of CO2 concentration

[0007] S2. According to the Update the initial estimate of the CO2 concentration in the building at time k

[0008] S3. According to the and the k-1 , update to obtain the unbiased minimum variance estimate of the CO2 concentration in the building at time k

[0009] S4. Add noise alpha k , and obtain the estimated value with noise added as an estimate of the CO2 concentration in the building.

[0010] Optionally, the S1 specifically includes:

[0011] The sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 The measurement equation is given by the following equation:

[0012] y k-1 =x k-1 +v k-1

[0013] where v k-1 is the measurement noise at time k-1, which is a known quantity and its covariance matrix is ​​R k-1 , x k-1 is the true value of CO2 concentration in the building at time k-1;

[0014] Initial estimate of CO2 concentration in the building at time k-1 Unbiased minimum variance estimation of CO2 concentration is a known quantity.

[0015] Optionally, the S2 specifically includes:

[0016] According to the Use the following formula to update:

[0017]

[0018] Among them, a k is a known update parameter.

[0019] Optionally, the S3 specifically includes:

[0020] use express Relative x k-1 The error covariance matrix of express Relative x k-1 The error covariance matrix of

[0021] The evolution of CO2 concentration in the building is modeled using the following kinetic equation:

[0022] x k =a k x k-1 +b k d k-1 +w k-1

[0023] where x kis the true value of CO2 concentration at time k, which is an unknown quantity; d k-1 is the occupancy rate of the building, which indicates the number of people in the building and is an unknown quantity; w k-1 is the process noise, which is a known quantity and its covariance matrix is ​​Q k-1 ; a k , b k is a known update parameter;

[0024] Then use the following formula to update

[0025]

[0026]

[0027]

[0028]

[0029] And get:

[0030]

[0031] in, express Relative x k The error covariance matrix, R k is the known measurement noise v at time k k The covariance matrix of express Relative x k The error covariance matrix of .

[0032] Optionally, the S4 specifically includes:

[0033] Regarding the Adding Noise get

[0034] And get:

[0035] Among them, ∑ k Represents α k The variance needs to satisfy

[0036] Among them, ∑ k The calculation process is as follows:

[0037] D k =(IK k ) k ,

[0038] k'=k-N+1,

[0039]

[0040] Where block-diag represents a block diagonal matrix, D k , k′, The parameters below are all intermediate variables in the calculation process and have no actual meaning;

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Use k express and The covariance matrix of

[0048]

[0049]

[0050]

[0051] For L 22 Perform singular value decomposition, L 22 =U k (γ k 0) T V k ,

[0052]

[0053] Solve the following semi-deterministic planning problem

[0054]

[0055]

[0056]

[0057] Calculated

[0058] Among them, the rank (bk )=n d , rank (a k )=n x .

[0059] Optionally, the estimation result after adding noise satisfies the requirements of the privacy level Cramér-Rao lower bound CRB, which can be expressed as the following optimization problem:

[0060]

[0061] sttr(CRB(d k-1 ))≥ε,

[0062]

[0063] Among them, tr(∑ k ) represents the trace of the matrix, CRB(d k-1 ) indicates the building k-1 of CRB, ε is a given value used to quantify the privacy level, σ is a small positive real number for numerical stability, and I represents an identity matrix.

[0064] Optionally, the optimization problem has the following two meanings:

[0065] 1) Minimize the error in CO2 concentration estimation;

[0066] 2) Ensure that the privacy level is not lower than the preset value ε;

[0067] The method makes a reasonable trade-off between achieving privacy protection and estimation accuracy: by adding the most appropriate noise, the optimal estimation result is obtained under the constraint of meeting the privacy requirement and ensuring that the number of people in the building is not obtained by malicious adversaries.

[0068] In another aspect, a privacy-preserving estimator for estimating CO2 concentration in a building is provided, the estimator comprising:

[0069] Acquisition module, used to obtain the sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 , initial estimate of CO2 concentration And the unbiased minimum variance estimate of CO2 concentration

[0070] The first updating module is used to update the Update the initial estimate of the CO2 concentration in the building at time k

[0071] The second updating module is used to update the and the k-1, update to obtain the unbiased minimum variance estimate of the CO2 concentration in the building at time k

[0072] Add a module for Add noise alpha k , and obtain the estimated value with noise added as an estimate of the CO2 concentration in the building.

[0073] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the above-mentioned method for estimating the CO2 concentration in a building with privacy protection.

[0074] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the above-mentioned method for estimating the CO2 concentration in a building with privacy protection.

[0075] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0076] By adopting the present invention, privacy requirements can be met while achieving optimal estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0078] Figure 1 is a flow chart of a method for estimating CO2 concentration in a building with privacy protection provided by an embodiment of the present invention;

[0079] Figure 2 It is a schematic diagram of the change trajectory and estimation of CO2 concentration using existing methods;

[0080] Figure 3 It is a schematic diagram of the changing trajectory of the number of people in a building and the inferred estimation of malicious adversaries according to the existing methods;

[0081] Figure 4 It is a schematic diagram of the change trajectory and estimation of CO2 concentration of the method provided in an embodiment of the present invention;

[0082] Figure 5 It is a schematic diagram of the change trajectory of the number of people in a building and the inference estimation of malicious adversaries according to the method provided by an embodiment of the present invention;

[0083] Figure 6 is a structural block diagram of an estimator for estimating CO2 concentration in a building with privacy protection provided by an embodiment of the present invention;

[0084] Figure 7 It is a structural schematic diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0085] In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0086] like Figure 1 As shown, an embodiment of the present invention provides a flowchart of a method for estimating CO2 concentration in a building with privacy protection, and the processing flow of the method may include the following steps:

[0087] S1. Get the sensor measurement value y of CO2 concentration in the building at time k-1 k-1 , initial estimate of CO2 concentration And the unbiased minimum variance estimate of CO2 concentration

[0088] Optionally, the S1 specifically includes:

[0089] The sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 The measurement equation is given by the following equation:

[0090] y k-1 =x k-1 +v k-1

[0091] where v k-1 is the measurement noise at time k-1, which is a known quantity and its covariance matrix is ​​R k-1 , x k-1 is the true value of CO2 concentration in the building at time k-1;

[0092] Initial estimate of CO2 concentration in the building at time k-1 Unbiased minimum variance estimation of CO2 concentration is a known quantity.

[0093] Apart from and is a known quantity. In the embodiment of the present invention, all other quantities at time k-1 are also known quantities. All quantities at time k are unknown. In the embodiment of the present invention, all known quantities at time k-1 are used to update all quantities at time k and obtain an estimated value with added noise. as an estimate of the CO2 concentration in the building.

[0094] S2. According to the Update the initial estimate of the CO2 concentration in the building at time k

[0095] Optionally, the S2 specifically includes:

[0096] According to the Use the following formula to update:

[0097]

[0098] Among them, a k is a known update parameter.

[0099] S3. According to the and the k-1 , update to obtain the unbiased minimum variance estimate of the CO2 concentration in the building at time k

[0100] Optionally, the S3 specifically includes:

[0101] use express Relative x k-1 The error covariance matrix of express Relative x k-1 The error covariance matrix of

[0102] The evolution of CO2 concentration in the building is modeled using the following kinetic equation:

[0103] x k =a k x k-1 +b k d k-1 +w k-1

[0104] where x k is the true value of CO2 concentration at time k, which is an unknown quantity; d k-1 is the occupancy rate of the building, which indicates the number of people in the building and is an unknown quantity; w k-1 is the process noise, which is a known quantity and its covariance matrix is ​​Q k-1 ; a k ,b k is a known update parameter;

[0105] In the embodiment of the present invention, k ,b k It can be time-varying or constant, but it is a known quantity.

[0106] Then use the following formula to update

[0107]

[0108]

[0109]

[0110]

[0111] And get:

[0112]

[0113] in, express Relative x k The error covariance matrix, R k is the known measurement noise v at time k k The covariance matrix of express Relative x k The error covariance matrix of .

[0114] The existing method for estimating CO2 concentration in buildings is to use as an estimate, and the estimator converts Broadcast and share, so that when there is a malicious adversary who wants to obtain the number of people in the building, the number of people in the building is sensitive and highly confidential information. At time k, assume that the malicious adversary has the following two capabilities: 1). It can obtain parameter a k and b k ; 2). It can use N ≥ 2 data broadcast by the estimator, for example To infer the estimated number of people in the building at time k-1 d k-1 ; Assume that a k =0.75,b k =1.75, and w k and v k Modeled as a Gaussian white noise sequence with variances of 0.1 and 0.05, assuming that the number of people in the building changes in the following way d k-1 =round(0.5cos(k)+5), where round() is the rounding function, cos() represents the cosine function, Figure 2 The trajectory of CO2 concentration in buildings and the trajectory of unbiased minimum variance estimation are shown. Figure 3The figure shows the trajectory of the number of people in the building and the trajectory of the malicious adversary's inference of the number of people in the building. It can be seen that the CO2 concentration in the building can be well estimated by the existing method, but the malicious adversary can also accurately infer the number of people in the building, which means that direct sharing The number of people in the building may be obtained by malicious adversaries. Therefore, in order to achieve the goal of privacy protection, the embodiment of the present invention designs a method and an estimator for estimating the CO2 concentration in a building with privacy protection, wherein the Add noise alpha k , and obtain the estimated value with noise added The steps for estimating the CO2 concentration in the building are as follows:

[0115] S4. Add noise alpha k , and obtain the estimated value with noise added as an estimate of the CO2 concentration in the building.

[0116] Optionally, the S4 specifically includes:

[0117] Regarding the Adding Noise get

[0118] And get:

[0119] Among them, ∑ k Represents α k The variance needs to satisfy

[0120] Among them, ∑ k The calculation process is as follows:

[0121] D k =(IK k ) k ,

[0122] k′=k-N+1,

[0123]

[0124] Where block-diag represents a block diagonal matrix, D k , k′, The parameters below are all intermediate variables in the calculation process and have no actual meaning;

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] Use and express and The covariance matrix of

[0132]

[0133]

[0134]

[0135] For L 22 Perform singular value decomposition, L 22 =U k (γ k 0) T V k ,

[0136]

[0137] Solve the following semi-deterministic planning problem

[0138]

[0139]

[0140]

[0141] Calculated

[0142] Among them, the rank (b k )=n d , rank (a k )=n x .

[0143] The embodiment of the present invention is to add noise to the estimated value Broadcast and share, so that malicious adversaries cannot obtain N data, such as Let's infer and estimate the number of people d in the building at time k-1 k-1, meet the privacy requirements. In order to quantify the privacy level of the embodiment of the present invention, the privacy level can be evaluated by CRB (Cramér-Rao lower bound). In estimation theory and statistics, CRB is related to the estimation of deterministic (fixed but unknown) parameters. CRB provides the lowest variance that can be achieved in theory for a given parameter estimation problem. Therefore, it can be used to evaluate the performance of a certain estimation method and measure the quality of the estimation result of the method. In other words, the estimation result after adding noise in the embodiment of the present invention must meet the requirements of CRB.

[0144] Optionally, the estimation result after adding noise satisfies the requirements of the privacy level Cramér-Rao lower bound CRB, which can be expressed as the following optimization problem:

[0145]

[0146] sttr(CRB(d k-1 ))≥ε,

[0147]

[0148] Among them, tr(∑ k ) represents the trace of the matrix, CRB(d k-1 ) indicates the building k-1 of CRB, ε is a given value used to quantify the privacy level, σ is a small positive real number for numerical stability, and I represents an identity matrix.

[0149] Optionally, the optimization problem has the following two meanings:

[0150] 1) Minimize the error in CO2 concentration estimation;

[0151] 2) Ensure that the privacy level is not lower than the preset value ε;

[0152] The method makes a reasonable trade-off between achieving privacy protection and estimation accuracy: by adding the most appropriate noise, the optimal estimation result is obtained under the constraint of meeting the privacy requirement and ensuring that the number of people in the building is not obtained by malicious adversaries.

[0153] After using the method of the embodiment of the present invention, the following conclusions can be obtained:

[0154] Conclusion 1 (accuracy): After using the method designed in the embodiment of the present invention, the estimated value of the CO2 concentration in a building can reach the optimal value, that is, the error between the estimated result and the actual result is very small.

[0155] Conclusion 2 (Privacy): After using the method designed in the embodiment of the present invention, the CO2 concentration in the building can be successfully estimated while avoiding the leakage of important privacy information, that is, malicious adversaries cannot infer the number of people in the building based on the estimation results of the embodiment of the present invention.

[0156] The method designed in the embodiment of the present invention is used to simulate and estimate the CO2 concentration in the building. Assuming that there is a malicious adversary who wants to infer the number of people in the building, the embodiment of the present invention sets σ = 10 -4 , ε=0.5, N=2, the final estimation result is as follows Figure 4 and Figure 5 As shown, it can be seen that the estimation result of the method designed in the embodiment of the present invention is very close to the actual situation and the estimation effect is very good; and it can be seen that the malicious adversary's inferred estimate of the number of people in the building is very different from the actual number of people, indicating that the embodiment of the present invention successfully protects the sensitive information of the number of people in the building from being obtained.

[0157] like Figure 6 As shown, an embodiment of the present invention further provides an estimator for estimating CO2 concentration in a building with privacy protection, the estimator comprising:

[0158] The acquisition module 610 is used to obtain the sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 , initial estimate of CO2 concentration And the unbiased minimum variance estimate of CO2 concentration

[0159] The first updating module 620 is used to update the Update the initial estimate of the CO2 concentration in the building at time k

[0160] The second updating module 630 is used to update the and the k-1 , update to obtain the unbiased minimum variance estimate of the CO2 concentration in the building at time k

[0161] Adding module 640, for Add noise alpha k , and obtain the estimated value with noise added as an estimate of the CO2 concentration in the building.

[0162] An embodiment of the present invention provides an estimator for estimating the CO2 concentration in a building with privacy protection, and its functional structure corresponds to a method for estimating the CO2 concentration in a building with privacy protection provided by an embodiment of the present invention, which will not be repeated here.

[0163] Figure 7 It is a structural diagram of an electronic device 700 provided in an embodiment of the present invention. The electronic device 700 may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) 701 and one or more memories 702, wherein the memory 702 stores at least one instruction, and the at least one instruction is loaded and executed by the processor 701 to implement the steps of the above-mentioned method for estimating the CO2 concentration in a building with privacy protection.

[0164] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions, which can be executed by a processor in a terminal to perform the above-mentioned method for estimating the CO2 concentration in a building with privacy protection. For example, the computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0165] A person skilled in the art will understand that all or part of the steps to implement the above embodiments may be accomplished by hardware or by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc.

[0166] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A privacy-preserving method for estimating CO2 concentration in a building, characterized in that: The method comprises: S1. Get the sensor measurement value y of CO2 concentration in the building at time k-1 k-1 , initial estimate of CO2 concentration And the unbiased minimum variance estimate of CO2 concentration S2. According to the Update the initial estimate of the CO2 concentration in the building at time k S3. According to the and the k-1 , update to obtain the unbiased minimum variance estimate of the CO2 concentration in the building at time k S4. Add noise alpha k , and obtain the estimated value with noise added as an estimate of the CO2 concentration in said building; The S1 specifically includes: The sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 The measurement equation is given by the following equation: and k-1 =x k-1 +v k-1 where v k-1 is the measurement noise at time k-1, which is a known quantity and its covariance matrix is ​​R k-1 , x k-1 is the true value of CO2 concentration in the building at time k-1; Initial estimate of CO2 concentration in the building at time k-1 Unbiased minimum variance estimation of CO2 concentration is a known quantity; The S3 specifically includes: use express Relative x k-1 The error covariance matrix of express Relative x k-1 The error covariance matrix of The evolution of CO2 concentration in the building is modeled using the following kinetic equation: x k =a k x k-1 +b k d k-1 +w k-1 where x k is the true value of CO2 concentration at time k, which is an unknown quantity; d k-1 is the occupancy rate of the building, which indicates the number of people in the building and is an unknown quantity; w k-1 is the process noise, which is a known quantity and its covariance matrix is ​​Q k-1 ; a k , b k is a known update parameter; Then use the following formula to update And get: in, express Relative x k The error covariance matrix, R k is the known measurement noise v at time k k The covariance matrix of express Relative x k The error covariance matrix of The S4 specifically includes: Regarding the Adding Noise get And get: Among them, ∑ k Represents α k The variance needs to satisfy Among them, ∑ k The calculation process is as follows: D k =(I-K k )a k , k′=k-N+1, Where block-diag represents a block diagonal matrix, D k , k′, The parameters below are all intermediate variables in the calculation process and have no actual meaning; Use and express and The covariance matrix of For L 22 Perform singular value decomposition, L 22 =U k (γ k 0) T V k , Solve the following semi-deterministic planning problem Calculated Among them, the rank (b k )=n d , rank (a k )=n x .

2. The method according to claim 1, characterized in that The S2 specifically includes: According to the Use the following formula to update: Among them, a k is a known update parameter.

3. The method according to claim 1, characterized in that The estimated result after adding noise meets the requirements of the privacy level Cramér-Rao lower bound CRB, which can be expressed as the following optimization problem: s.t.tr(CRB(d k-1 ))≥ε, ∑ k ≥σI, Among them, tr(∑ k ) represents the trace of the matrix, CRB(d k-1 ) indicates the building k-1 of CRB, ε is a given value used to quantify the privacy level, σ is a small positive real number for numerical stability, and I represents an identity matrix.

4. The method according to claim 3, characterized in that The optimization problem has the following two implications: 1) Minimize the error in CO2 concentration estimation; 2) Ensure that the privacy level is not lower than the preset value ε; The method makes a reasonable trade-off between achieving privacy protection and estimation accuracy: by adding the most appropriate noise, the optimal estimation result is obtained under the constraint of meeting the privacy requirement and ensuring that the number of people in the building is not obtained by malicious adversaries.

5. A privacy-preserving estimator for estimating CO2 concentration in a building, characterized in that: The estimator includes: Acquisition module, used to obtain the sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 , initial estimate of CO2 concentration And the unbiased minimum variance estimate of CO2 concentration The first updating module is used to update the Update the initial estimate of the CO2 concentration in the building at time k The second updating module is used to update the and the k-1 , update to obtain the unbiased minimum variance estimate of the CO2 concentration in the building at time k Add a module for Add noise alpha k , and obtain the estimated value with noise added as an estimate of the CO2 concentration in said building; The acquisition module is specifically used for: The sensor measurement value y of the CO2 concentration in the building at time k-1 k-1 The measurement equation is given by the following equation: and k-1 =x k-1 +v k-1 where v k-1 is the measurement noise at time k-1, which is a known quantity and its covariance matrix is ​​R k-1 , x k-1 is the true value of CO2 concentration in the building at time k-1; Initial estimate of CO2 concentration in the building at time k-1 Unbiased minimum variance estimation of CO2 concentration is a known quantity; The second updating module is specifically used for: use express Relative x k-1 The error covariance matrix of express Relative x k-1 The error covariance matrix of The evolution of CO2 concentration in the building is modeled using the following kinetic equation: x k =a k x k-1 +b k d k-1 +w k-1 where x k is the true value of CO2 concentration at time k, which is an unknown quantity; d k-1 is the occupancy rate of the building, which indicates the number of people in the building and is an unknown quantity; w k-1 is the process noise, which is a known quantity and its covariance matrix is ​​Q k-1 ; a k , b k is a known update parameter; Then use the following formula to update And get: in, express Relative x k The error covariance matrix, R k is the known measurement noise v at time k k The covariance matrix of express Relative x k The error covariance matrix of The adding module is specifically used for: Regarding the Adding Noise get And get: Among them, ∑ k Represents α k The variance needs to satisfy Among them, ∑ k The calculation process is as follows: D k =(I-K k )a k , k′=k-N+1, Where block-diag represents a block diagonal matrix, D k , k′, The parameters below are all intermediate variables in the calculation process and have no actual meaning; Use and express and The covariance matrix of For L 22 Perform singular value decomposition, L 22 =U k (γ k 0) T V k , Solve the following semi-deterministic planning problem Calculated Among them, the rank (b k )=n d , rank (a k )=n x .

6. An electronic device, comprising a processor and a memory, wherein at least one instruction is stored in the memory, wherein: The at least one instruction is loaded and executed by the processor to implement the method for estimating the CO2 concentration in a building with privacy protection as described in any one of claims 1-4.

7. A computer-readable storage medium, wherein at least one instruction is stored in the storage medium, characterized in that: The at least one instruction is loaded and executed by the processor to implement the method for estimating the CO2 concentration in a building with privacy protection as described in any one of claims 1-4.

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