Statistical parameter estimation methods, electronic devices, media and programs

Abstract

This invention discloses a statistical parameter estimation method, electronic device, medium, and program. The method includes: establishing a state-space model for a local system: x k+1 =Fx k +Gw k y k =Hx k +v k The prior estimate of the local system state is calculated by subtracting the local system state at time k from its prior estimate, thus obtaining the estimation error e. k The estimation error is obtained by iteratively calculating e. k+1 Solve for the estimated error covariance P. k The steady state is given by the estimation error covariance, which is defined as the autocovariance matrix B(N) of the innovation under the random communication protocol; the autocovariance matrix B(N) is vectorized to obtain the column vector (B(N)). s Assume we need to find the theoretical value column vector (B(N)). s This is equivalent to obtaining a column vector (B(N)) from a column vector obtained through experiments. s The estimated value is the column vector obtained by straightening the autocovariance matrix of the innovation under the random communication protocol obtained through experiments; and X is obtained by solving for the value that minimizes the value, through X = [(Q s ) T , (R s ) T ] T Obtain the straightened column vectors of Q and R, and thus obtain Q and R.

Description

Technical Field

[0001] This disclosure relates to the fields of signal processing and system control, and more specifically, to methods, electronic devices, media, and programs for estimating statistical parameters. Background Technology

[0002] In the fields of signal processing and system control, state-space models are widely used to predict system states. The state-space model of the system is as follows:

[0003] x k+1 =Fx k +Gw k ,

[0004] y k =Hx k +v k .

[0005] Where x k For the local system status, y k For measuring output, w k For process noise, v k For noise measurement, F, G, and H are known matrices. k} and {v k Let be independent zero-mean Gaussian processes with covariances Q and R, respectively. Typically, the system state is predicted using the state-space model described above, given that Q and R are known.

[0006] This application proposes a method for estimating Q and R when considering the scheduling role of a random communication protocol (also called a random access protocol RAP) and when Q and R are unknown. Summary of the Invention

[0007] This application proposes a statistical parameter estimation method, electronic device, medium, and program.

[0008] According to one aspect of this disclosure, a statistical parameter estimation method is provided, comprising: establishing a state-space model for a local system: x k+1 =Fx k +Gw k y k =Hx k +v k , where x k For the local system status, y k For measuring output, w k For process noise, v k To measure the output noise, F, G, and H are all known matrices, and w is a given matrix. k With v kThe two are uncorrelated and their variances are unknown; through the formula Calculate the prior estimate of the local system state Where L is the gain matrix. This is the measurement output under a random communication protocol; the estimation error is obtained by subtracting the local system state at time k from its prior estimate. And the estimation error is obtained through iteration. Where Φ ξ(k) Given a block diagonal matrix with only one block entry being the identity matrix; solve for the estimation error covariance P. k The steady state, where the estimation error covariance is defined as Calculate the autocovariance matrix of the innovation under a random communication protocol. Among them, B0 and B j Let B(N) be the autocovariances of the information at 0-step and j-step lags under the random communication protocol, respectively, where j∈[1,N-1]. The column vector (B(N)) is obtained by vector straightening the autocovariance matrix B(N). s Assume we need to find the theoretical value column vector (B(N)). s Equal to the column vector obtained through experiments Thus, the column vector (B(N)) is obtained. s The estimated value, of which This refers to the column vector obtained by straightening the autocovariance matrix of the innovation under a random communication protocol that can be obtained experimentally; and by solving... get In order to make The smallest X is obtained through X = [(Q s ) T , (R s ) T ] T Obtain the straightened column vectors of Q and R, and from these, obtain Q and R, where Let A be the generalized inverse of a full-rank matrix. A = [A1, A2], and It is a permutation matrix composed of 0s and 1s.

[0009] According to another aspect of this disclosure, an electronic device is provided, comprising: one or more processors; and a memory coupled to the one or more processors, the memory storing computer-readable program instructions that, when executed by the one or more processors, perform a statistical parameter estimation method according to the present invention.

[0010] According to another aspect of this disclosure, a non-transitory computer-readable medium is provided having instructions stored thereon for execution by a processor to perform a statistical parameter estimation method according to the invention.

[0011] According to another aspect of this disclosure, a computer program product is provided, comprising a computer program that, when executed by a processor, performs the steps of the statistical parameter estimation method according to the present invention.

[0012] Other features and advantages of the invention will become clearer from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings. Attached Figure Description

[0013] The accompanying drawings, which form part of this specification, illustrate embodiments of this disclosure and, together with the specification, serve to explain the principles of this disclosure.

[0014] This disclosure will become clearer with reference to the accompanying drawings and the following detailed description, wherein:

[0015] Figure 1 A block diagram is shown that is suitable for implementing an exemplary computer system / server according to an embodiment of the present invention.

[0016] Figure 2 A flowchart of a statistical parameter estimation method according to an exemplary embodiment of the present invention is shown. Detailed Implementation

[0017] The following description is provided to enable those skilled in the art to implement and use the embodiments, and is provided in the context of a particular system and its requirements. Various modifications will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and systems without departing from the spirit and scope of the embodiments. Therefore, the embodiments are not limited to those shown, but are to be given the widest scope consistent with the principles and features disclosed herein.

[0018] Figure 1 A block diagram is shown that is suitable for implementing an exemplary computer system / server 12 according to an embodiment of the present invention. Figure 1The computer system / server 12 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0019] like Figure 1 As shown, the computer system / server 12 is represented in the form of a general-purpose computing device. The components of the computer system / server 12 may include, but are not limited to: one or more processors or processing units 16, system memory 28, and a bus 18 connecting different system components (including system memory 28 and processing units 16).

[0020] System memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Computer system / server 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be used to read and write non-removable, non-volatile magnetic media. Although... Figure 1 Not shown, a disk drive and an optical disk drive may also be provided. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of the present invention.

[0021] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 42 typically perform the functions and / or methods described in the embodiments of the present invention.

[0022] The computer system / server 12 can also communicate with one or more external devices 14 (e.g., keyboard, pointing device, etc.) and a display 24, as well as with one or more devices that enable a user to interact with the computer system / server 12, and / or with any device that enables the computer system / server 12 to communicate with one or more other computing devices (e.g., network interface card, modem, etc.). This communication can be performed via input / output (I / O) interface 22. Furthermore, the computer system / server 12 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 20. As shown, network adapter 20 communicates with other modules of the computer system / server 12 via bus 18. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with the computer system / server 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0023] Considering the Random Communication Protocol (RAP), a local system might perform measurements using a set of sensors divided into N nodes, each node potentially containing one or more sensors. To prevent data collisions, only one node is allowed to transmit data through a shared communication channel at each time step.

[0024] Let N nodes be labeled Ω = {1, 2, ..., M}, and define a random variable ξ(k) (ξ(k) ∈ Ω) to represent the node selected at time step k. For example, ξ(k) = i indicates that the i-th node is selected to send the measurement result at time step k. Therefore, {ξ(k)}, which describes the scheduling effect of the random communication protocol, can be treated as a sequence of independent and identically distributed random variables. Here, Prob{ξ(k) = i} = pi represents the probability that the i-th node is selected at the time constant k, where pi ∈ (0, 1), and

[0025] To represent the remotely received measurement results in a compact form, a block diagonal matrix Φ is used, in which only one block entry is the identity matrix. ξ(k) =diag{δ(ξ(k)-1)I, δ(ξ(k)-2)I,..., δ(ξ(k)-N)I} to represent the introduction of RAP.

[0026] The measurement output after considering the random communication protocol RAP is: in

[0027] As a concrete example, suppose y k For six dimensions And take M = 3 groups. And further assume y 1，k With y 2，k For the first group ξ(k)=1, y 3，k For the second group ξ(k)=2, y 4，k y 5，k and y 6，k The third group has ξ(k) = 3.

[0028] Then when ξ(k)=1, Φ ξ(k) =Φ1,

[0029] When ξ(k) = 2, Φ ξ(k) =Φ2, and

[0030] When ξ(k) = 3, Φ ξ(k) =Φ3,

[0031] The prior estimate of the local system state under the random communication protocol RAP is Where L is the gain matrix.

[0032] The estimation error is By iterating over the estimation error, we can obtain

[0033] News under random communication protocols is in For information that is not introduced by a random communication protocol (also known as under no communication protocol), it is an intermediate variable that can be obtained by measurement.

[0034] definition Then there is

[0035]

[0036] Define the estimation error covariance Let its steady state be P, then we have

[0037] in

[0038] In w k With v k In the case of no relation, in

[0039] Define the autocovariances of the innovation at 0 and j-step lags without introducing a random communication protocol as follows:

[0040]

[0041] in The autocovariance of the information at 0 and j-step lags under the random communication protocol and They are respectively

[0042]

[0043] Define the autocovariance matrix of the innovation under a random communication protocol.

[0044] Calculations yield the following results.

[0045]

[0046] in

[0047] By flattening B(N) into a column vector, we can obtain

[0048]

[0049] Where Qs and Rs represent the column vectors obtained by straightening Q and R, respectively, and and It is a permutation matrix composed of 0s and 1s.

[0050] The autocovariance of the innovation under random communication protocols can be obtained experimentally. In other words, it can be obtained experimentally. and This allows us to obtain experimental values.

[0051] Let the theoretical value It is possible to obtain the straightened estimate of the autocovariance matrix of the innovation under a random communication protocol.

[0052] Specifically, let X = [(Q s ) T , (R s ) T ] T , A = [A1, A2], where

[0053] By solving It indicates a request Let X be the smallest value equal to 1. The solution can be found as follows: in Let A be the generalized inverse of a column full-rank matrix A. The generalized inverse of A may not exist, but if A is column full-rank, its generalized inverse is guaranteed to exist.

[0054] In other words, by obtaining We can obtain X, since X = [(Q s ) T , (R s ) T ] T Therefore, we can obtain the straightened column vectors of Q and R, and thus obtain Q and R.

[0055] Figure 2 A flowchart of a statistical parameter estimation method 200 according to an exemplary embodiment of the present invention is shown. This method can, for example, be derived from... Figure 1 The computer system / server 12 performs the operation.

[0056] like Figure 2 As shown, in step 201, a state-space model is established for the local system: x k+1 =Fx k +Gw k y k =Hx k +v k Here, the local system can be, for example, an industrial system, such as a permanent magnet synchronous motor system, but is not limited to this.

[0057] In step 202, a measurement output that takes into account the scheduling effect of random communication protocols is obtained by multiplying the measurement output with a block diagonal matrix containing only one block entry as an identity matrix. According to an exemplary embodiment of the invention, this block diagonal matrix is ​​Φ. ξ(k) =diag{δ(ξ(k)-1)I,δ(ξ(k)-2)I,...,δ(ξ(k)-N)I}, then the output under the random communication protocol

[0058] In step 203, a priori estimates of the local system state are calculated. According to an example embodiment of the present invention, this is achieved using the formula... Calculate the prior estimate of the local system state Where L is the gain matrix, which can be obtained experimentally.

[0059] In step 204, the system state at time k is subtracted from its prior estimate to obtain the estimation error, and the estimation error is iterated. According to an example embodiment of the present invention, the obtained estimation error is: Iteratively obtain the estimation error

[0060] In step 205, the steady-state solution for the estimation error covariance is obtained. The estimation error covariance is defined as... According to an exemplary embodiment of the present invention, by formula Solve for the estimation error covariance P k The steady state. And among them,

[0061] In step 206, the autocovariance matrix of the innovation under the random communication protocol is calculated. According to an example embodiment of the present invention, this is achieved using the formula... Calculate the autocovariance matrix of the innovation under a random communication protocol.

[0062] in

[0063] In step 207, column vectors are obtained by vector straightening the autocovariance matrix of the information under the random communication protocol.

[0064] According to an exemplary embodiment of the present invention, the column vector obtained by vector straightening the autocovariance matrix B(N) of the innovation under the random communication protocol is:

[0065]

[0066] Q s and R s These represent the column vectors obtained by straightening Q and R, respectively.

[0067] In step 208, it is assumed that the theoretical value column vector to be solved is (i.e., the column vector (B(N)) obtained by vector straightening the autocovariance matrix B(N) of the innovation under the random communication protocol). s ) is equal to the column vector that can be obtained experimentally (i.e., the autocovariance matrix of the innovation under a random communication protocol that can be obtained experimentally). The column vector obtained by straightening This allows us to obtain an estimate of the theoretical column vector. Let be the autocovariance matrix of the information that can be obtained experimentally under a random communication protocol. and Let be the autocovariances of the 0-step and j-step lags of the information under the random communication protocol, which can be obtained experimentally, j∈[1,N-1].

[0068] In step 209, by solving get Where X = [(Q s ) T , (R s ) T ] T Therefore, we can obtain the straightened column vectors of Q and R, and from this, we can obtain Q and R. A = [A1, A2],

[0069] By employing the statistical parameter estimation method according to the present invention, and introducing RAP to make the measured output y k Even with incomplete data, it is possible to estimate the state of a dynamic system from a series of uncorrelated process and measurement noises with unknown variances, and to estimate the covariance of the process and measurement noises.

[0070] This invention can be implemented by electronic devices, methods, and / or computer program products. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of the invention.

[0071] According to one embodiment of the present invention, an electronic device is provided, including one or more processors and a memory coupled to the one or more processors, the memory storing computer-readable program instructions that, when executed by the one or more processors, perform a statistical parameter estimation method according to the present invention.

[0072] According to another embodiment of the present invention, a non-transitory computer-readable medium is provided having instructions stored thereon for execution by a processor to perform a statistical parameter estimation method according to the present invention.

[0073] According to another embodiment of the present invention, a computer program product is provided, comprising a computer program that, when executed by a processor, performs the steps of the statistical parameter estimation method according to the present invention.

[0074] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0075] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0076] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0077] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0078] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0079] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0080] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0081] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical applications, or technical improvements to the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A statistical parameter estimation method, comprising: Establish a state-space model for the local system: , ,in This refers to the local system status. For measurement output, For process noise, To measure the output noise, F, G, and H are all known matrices, and where... and The two are unrelated and their variances are unknown; Through formula Calculate the prior estimate of the local system state ,in Here is the gain matrix. For measurement output under a random communication protocol, wherein the measurement output is... Block diagonal matrix Multiplication yields measurement output under a random communication protocol. ; The estimation error is obtained by subtracting the local system state at time k from its prior estimate. And obtain the estimation error through iteration. ,in A block diagonal matrix with only one block entry being the identity matrix; Solving for the covariance of the estimation error The steady-state P, where the estimation error covariance is defined as ； Calculate the autocovariance matrix of the innovation under a random communication protocol. ,in and Let be the autocovariances of the information at 0-step and j-step lags, respectively, under a random communication protocol. ; For the autocovariance matrix Straighten the vectors to obtain column vectors ; Suppose we want to find the theoretical value column vector. Equal to the column vector obtained through experiments Thus, column vectors are obtained. The estimated value, of which The column vector is obtained by straightening the autocovariance matrix of the innovation under a random communication protocol that can be obtained experimentally; and 2. The statistical parameter estimation method according to claim 1, wherein the estimation error covariance is solved. The steady-state P includes: 。 3. The statistical parameter estimation method according to claim 2, wherein the autocovariance matrix of the innovation under the random communication protocol is calculated. include:

4. The statistical parameter estimation method according to claim 3, wherein the autocovariance...

5. The statistical parameter estimation method according to claim 1, wherein the block diagonal matrix for .

6. The statistical parameter estimation method according to any one of claims 1-3, wherein the innovation under the random communication protocol is ,in This refers to information without a communication protocol.

7. The statistical parameter estimation method according to claim 6, wherein it can be achieved through actual...

8. The statistical parameter estimation method according to claim 2, wherein... .

9. An electronic device, comprising: One or more processors; and A memory coupled to the one or more processors, the memory storing computer-readable program instructions that, when executed by the one or more processors, perform the method as described in any one of claims 1-8.

10. A non-transitory computer-readable medium having instructions stored thereon for execution by a processor to perform the method according to any one of claims 1-8.

11. A computer program product comprising a computer program that, when executed by a processor, performs the steps of the method as described in any one of claims 1-8.

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