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CN-116304508-B - Statistical parameter estimation method, electronic device, medium, and program

CN116304508BCN 116304508 BCN116304508 BCN 116304508BCN-116304508-B

Abstract

The invention discloses a statistical parameter estimation method, electronic equipment, a medium and a program. The method comprises establishing state space model x k+1 ＝Fx k +Gw k ,y k ＝Hx k +v k for local system, and calculating prior estimated value of local system state Obtaining an estimated error e k by subtracting the local system state at time k from its a priori estimate, iterating the estimated error to obtain e k+1 , solving a steady state of an estimated error covariance P k , wherein the estimated error covariance is defined as Calculating an autocovariance matrix B (N) of innovation under a random communication protocol, vector-straightening the autocovariance matrix B (N) to obtain a column vector (B (N)) s , and assuming that a theoretical value column vector (B (N)) s to be solved is equal to the column vector obtained through experiments An estimate of the column vector (B (N)) s is obtained, Column vectors obtained for straightening the auto-covariance matrix of the experimentally obtained innovation under the random communication protocol, and by solving Obtaining To make At the minimum X, the column vectors after Q and R are straightened are obtained by x= [ (Q s ) T ,(R s ) T ] T ), thereby obtaining Q and R.

Inventors

  • ZHANG XIAOGUANG
  • REN XIUXIU

Assignees

  • 华晨宝马汽车有限公司

Dates

Publication Date
20260505
Application Date
20211202

Claims (11)

  1. 1. A statistical parameter estimation method, comprising: establishing a state space model for a local system: , wherein In order to be in the state of the local system, In order to measure the output of the device, In order for the process to be noisy, To measure output noise F, G, H are all known matrices, and where And (3) with The two are uncorrelated and the variance is unknown; By the formula Computing a priori estimates of local system states Wherein In the form of a gain matrix, Is a measurement output under a random communication protocol, wherein the measurement output is obtained by combining the measurement output Diagonal matrix of blocks Multiplying to obtain measurement output under random communication protocol ; Obtaining an estimation error by subtracting the local system state at time k from its a priori estimate And iteratively obtaining the estimation error Wherein A block diagonal matrix having only one block entry as an identity matrix; solving for estimation error covariance Wherein the estimation error covariance is defined as ; Calculating an autocovariance matrix for innovation under a random communication protocol Wherein And The auto-covariances of 0 and j step lags respectively for innovation under a random communication protocol, ; For auto-covariance matrix Vector straightening is carried out to obtain column vectors ; Assuming a theoretical column vector to be solved Equal to the experimentally obtained column vector Thereby obtaining a column vector Wherein Column vectors obtained for straightening an auto-covariance matrix of an experimentally obtained innovation under a random communication protocol, and
  2. 2. The statistical parameter estimation method of claim 1, wherein the estimation error covariance is solved Comprises: 。
  3. 3. The statistical parameter estimation method of claim 2, wherein an autocovariance matrix of the innovation under the random communication protocol is calculated Comprising the following steps:
  4. 4. a statistical parameter estimation method according to claim 3, wherein for auto-covariance
  5. 5. The statistical parameter estimation method of claim 1, wherein the block diagonal matrix Is that 。
  6. 6. A statistical parameter estimation method according to any one of claims 1-3, wherein the innovation under the random communication protocol is Wherein Is an innovation without communication protocol.
  7. 7. The statistical parameter estimation method of claim 6, wherein the statistical parameter can be obtained by real-time analysis
  8. 8. The statistical parameter estimation method according to claim 2, wherein 。
  9. 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 of any of claims 1-8.
  10. 10. A non-transitory computer readable medium having instructions stored thereon for execution by a processor to perform the method of any of claims 1-8.
  11. 11. A computer program product comprising a computer program which, when executed by a processor, performs the steps of the method according to any of claims 1-8.

Description

Statistical parameter estimation method, electronic device, medium, and program Technical Field The present disclosure relates to the field of signal processing and system control, and in particular, to a statistical parameter estimation method, an electronic device, a medium, and a program. Background State space models have been widely used in the field of signal processing and system control to predict system states. The state space model of the system is as follows: xk+1＝Fxk+Gwk, yk＝Hxk+vk。 Where x k is the local system state, y k is the measurement output, w k is the process noise, v k is the measurement noise, and F, G, H is the known matrix. { w k } and { v k } are independent zero-mean Gaussian processes, and covariance is Q and R, respectively. The state of the system is usually predicted by the state space model described above, both with Q and R known. The present application proposes how to estimate Q and R taking into account the scheduling role of the random communication protocol (also called random access protocol RAP: random Access Protocol) and where Q and R are unknown. Disclosure of Invention The application provides a statistical parameter estimation method, electronic equipment, a medium and a program. According to one aspect of the present disclosure, there is provided a statistical parameter estimation method comprising establishing a state space model for a local system, x k+1＝Fxk+Gwk,yk＝Hxk+vk, where x k is the local system state, y k is the measurement output, w k is the process noise, v k is the measurement output noise, F, G, H are both known matrices, and where both w k and v k are uncorrelated and the variance is unknown, by the formulaComputing a priori estimates of local system statesWhere L is the gain matrix and where,The estimation error is obtained by subtracting the state of the local system at the k moment from the prior estimation value of the stateAnd iteratively obtaining the estimation errorWherein Φ ξ(k) is a block diagonal matrix with only one block entry as the identity matrix, solving for the steady state of the estimation error covariance P k, wherein the estimation error covariance is defined asCalculating an autocovariance matrix for innovation under a random communication protocolWherein B 0 and B j are the 0-step and j-step delayed autocovariance of the innovation under the random communication protocol, j E [1, N-1], vector-straightening the autocovariance matrix B (N) to obtain a column vector (B (N)) s, assuming that the theoretical value column vector (B (N)) s to be solved is equal to the experimentally obtained column vectorThereby obtaining an estimate of column vector (B (N)) s, whereColumn vectors obtained for straightening the auto-covariance matrix of the experimentally obtained innovation under the random communication protocol, and by solvingObtainingTo make a match withAt the minimum X, the column vectors after Q and R are straightened are obtained by x= [ (Q s)T,(Rs)T]T) and Q and R are thus obtained, whereIs the generalized inverse of the column full rank matrix a,A=[A1,A2],AndPermutation matrices consisting of 0 and 1. According to another aspect of the present disclosure, there is provided 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 a statistical parameter estimation method according to the present invention. According to yet another aspect of the present disclosure, a non-transitory computer readable medium having instructions stored thereon for execution by a processor to perform a statistical parameter estimation method according to the present invention is provided. According to a further aspect of the present disclosure, there is provided a computer program product comprising a computer program which, when executed by a processor, performs the steps of the statistical parameter estimation method according to the present invention. Other features of the present invention and its advantages will become more apparent from the following detailed description of exemplary embodiments of the invention, which proceeds with reference to the accompanying drawings. Drawings The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the disclosure and together with the description, serve to explain the principles of the disclosure. The disclosure may be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings in which: FIG. 1 illustrates a block diagram of an exemplary computer system/server suitable for use in implementing embodiments of the present invention. Fig. 2 shows a flowchart of a statistical parameter estimation method according to an exemplary embodiment of the present invention. Detailed Description The following description is prese