Design method of system Gaussian filter under one-step measurement random delay and synchronous noise correlation condition
By introducing Bernoulli random variable sequences and conditional Gaussian distribution lemma into the system, a state model for measuring random delay and noise correlation was constructed, and an extended Kalman filtering algorithm was designed to solve the result of measuring random delay and noise correlation in the system. The target tracking and state estimation problems achieve more accurate state estimation effects.
Patent Information
- Application Number
- CN202411542270.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-31
- Publication Date
- 2025-02-07
AI Technical Summary
In practical engineering applications, due to network delay, random failure of transmission mechanism or unavailability of data, the system's measured values have random delay characteristics, and process noise and measurement noise have related characteristics, resulting in poor target tracking and state estimation effects. good.
Bernoulli random variable sequence is introduced to describe the random delay phenomenon of measurement, to predict measurement noise as state increments, and to use conditional Gaussian distribution lemma to solve noise-related problems, build target state model and measurement model, and design extension Carl Mann filtering algorithm.
It effectively solves the problem of measurement data update delay caused by network delay, and optimizes the state estimation effect, making the estimation result more accurate.
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Figure CN119401982A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a design method for a system Gaussian filter under one-step measurement of random delay and synchronous noise correlation conditions. Background Art
[0002] As a method for realizing system state estimation, filters are widely used in signal processing, integrated navigation, target monitoring and tracking and other fields. The classical Gaussian filtering algorithm has the assumption that measurement information is acquired in real time, and that process noise and measurement noise are independent of each other. However, in practical engineering applications, due to network congestion, random failure of the transmission mechanism, or unavailability of data for a certain period of time, the measurement value of the system has a random delay characteristic; at the same time, since the measurement value is transmitted to the system as output feedback, the process noise and measurement noise of the system have correlation characteristics. Therefore, the present invention adopts Bernoulli random variables to simulate random measurement delays for the measurement delay problem, and at the same time, considering that the conditional probability density contains more information than the original probability density, the conditional Gaussian distribution property is used to solve the noise correlation problem. Summary of the invention
[0003] The purpose of the present invention is to provide a design method for a system Gaussian filter under the conditions of one-step measurement random delay and synchronous noise correlation, so as to solve the target tracking problem that the measurement data cannot be updated in time due to network delay, and at the same time solve the state estimation problem that the system process noise and measurement noise have correlated characteristics.
[0004] The first technical solution adopted by the present invention is: a design method for a system Gaussian filter under one-step measurement random delay and synchronous noise correlation conditions, introducing a Bernoulli random sequence in a nonlinear Gaussian discrete system to describe the measurement one-step random delay phenomenon in the system, using the measurement noise as a state increment to achieve a one-step prediction of the delayed measurement information, and using the conditional Gaussian distribution lemma to solve the noise correlation problem, thereby constructing a target state model and a measurement model with one-step measurement random delay and synchronous correlation noise characteristics, designing an optimal estimation algorithm in the form of a Gaussian filter framework, and using a Taylor series expansion formula to linearize the system, and providing an extended Kalman filter algorithm under one-step measurement random delay and synchronous correlation noise conditions; the specific operation steps are as follows:
[0005] Step 1: Introduce the independent Bernoulli random variable sequence γ into the nonlinear Gaussian discrete system k and the correlation coefficient S k , establish the target state model and measurement model of the nonlinear Gaussian discrete system under the conditions of one-step measurement random delay and synchronous correlated noise, and determine the one-step measurement random delay equation;
[0006] Step 2: Add the measurement noise to the state quantity, use the conditional Gaussian distribution lemma to make a one-step prediction of the augmented state quantity and delayed measurement, and derive the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix
[0007] Step 3: According to the measurement model in step 1 and the one-step measurement random delay equation, the actual measurement y at time k+1 is k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix
[0008] Step 4: One-step prediction using the augmented state vector obtained in steps 2 and 3 One-step prediction of delay measurement The target state is estimated through Bayesian filtering to obtain the posterior estimate of the augmented state at time k+1 and the error covariance matrix
[0009] Step 5, linearize the nonlinear Gaussian weighted integrals in Step 2, Step 3, and Step 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the one-step measurement random delay and synchronous correlated noise conditions proposed above for filtering;
[0010] Step 6: Repeat steps 2-5 until the entire filtering process is completed.
[0011] The present invention is also characterized in that:
[0012] Furthermore, step 1 is as follows:
[0013] Step 1.1, introduce the sequence of independent Bernoulli random variables γ k and the correlation coefficient S k , establish the target state model and measurement model of nonlinear discrete systems under one-step measurement of random delay and synchronous correlated noise conditions:
[0014]
[0015] Among them, x k is the target state, z k is the ideal measurement value, f(·) and h(·) are the system function and the measurement function; the process noise w k and measurement noise v k is the correlated zero-mean Gaussian white noise, and the covariances of process noise and measurement noise are Q k and R k , and satisfy:
[0016]
[0017] Among them, Q k and R k They represent the covariance matrices of process noise and measurement noise at time k respectively; S k represents the cross-covariance matrix between two noises; δ kl represents the Kronecker function;
[0018] Determine the one-step measurement random delay equation y k :
[0019]
[0020] γ k represents a sequence of independent Bernoulli random variables with values of 0 and 1, E([·]) represents the expected value, and p k Represents the probability of delayed measurement at time k:
[0021]
[0022] Furthermore, step 2 is specifically implemented in the following manner:
[0023] Step 2.1, add the measurement noise to the state quantity and construct a new augmented state vector:
[0024]
[0025] Step 2.2, based on the measured noise v k+1 and the measured delay set Y k , target state x k+1 Independent of each other, there are k+1 measurement noises v k+1 One-step prediction and the one-step forecast error covariance matrix
[0026]
[0027] Step 2.3, using the conditional Gaussian distribution lemma, replace the original probability density with the conditional probability density, make a one-step prediction of the target state, and derive the k+1 time x k+1 One-step prediction and the one-step forecast error covariance matrix P k+1|k :
[0028] Conditional Gaussian Distribution Lemma:
[0029] Assume X and Y are random vectors that satisfy Gaussian distribution, and their joint Gaussian distribution is:
[0030]
[0031] Then, given the observation value Y=y, the conditional probability density function of the random vector X is:
[0032]
[0033] Among them, u x and u y Represents the mean of random vector X and random vector Y, P xx and P yy Represents the covariance matrix of random vector X and random vector Y, P xy represents the cross-covariance matrix of X and Y;
[0034] According to the definition:
[0035]
[0036] Due to the process noise w k and the measurement noise v k Synchronous correlation, so E[w k |Y k ]≠0, using the conditional Gaussian distribution lemma, let Then the joint Gaussian distribution of X and Y is as follows:
[0037]
[0038] Noise k At the measured value y k The conditional probability density under the condition is:
[0039]
[0040] therefore:
[0041]
[0042] Further get x k+1 One-step prediction and the one-step forecast error covariance matrix P k+1|k :
[0043]
[0044] in, and P k|k Respectively represent the filter estimate and error covariance matrix of the target state at time k; represents the filtered estimate of the target state at time k-1; represents the process noise w k and delay measurement y k The cross-covariance matrix of ; represents the error covariance matrix of the delay measurement;
[0045] Step 2.4, combining steps 2.2 and 2.3, obtain the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix
[0046]
[0047] Furthermore, step 3 is as follows:
[0048] Step 3.1: Based on the measurement model of step 1.1 and the one-step measurement random delay equation and the one-step prediction of the target state obtained in step 2.3 and the one-step forecast error covariance matrix P k+1|k The actual measurement y at time k+1 k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix
[0049]
[0050] in, and They represent the one-step prediction and one-step prediction error covariance matrices of the k+1 time measurement respectively; and They represent the posterior estimate and error covariance matrix of the measurement at time k respectively.
[0051] Furthermore, step 4 is specifically implemented in the following manner:
[0052] Step 4.1, use the predicted value of the target state obtained in step 2.3 and step 3.1 and the predicted value of the delay measurement to estimate the target state through Bayesian filtering to obtain the estimated value of the target state at time k+1 and the error covariance matrix P k+1|k+1 :
[0053]
[0054] in, is the target state x k+1|k and measure random delay y k The cross-covariance matrix of ; is the target state x k+1|k and the ideal measured value z k The cross-covariance matrix of is the target state x k and the ideal measured value z kThe cross-covariance matrix, S k v k and w k The cross-covariance matrix between k The filter gain representing the target state;
[0055] Step 4.2, using the predicted value of the measurement noise obtained in step 2.2 and step 3.1 and the predicted value of the delay measurement to estimate the measurement noise through Bayesian filtering, and obtain the estimated value of the measurement noise at time k+1 and the error covariance matrix
[0056]
[0057] in, is the measured noise v k+1|k and delay measurement k The one-step forecast error covariance matrix, R k+1 is the measured noise v k+1 The error covariance matrix of
[0058] Step 4.3, combining steps 4.1 and 4.2, we can get the posterior estimate of the augmented state at time k+1 and the error covariance matrix
[0059]
[0060] in, Represents the target state x k+1 and measurement noise v k+1 The cross-covariance matrix of ; Indicates the measurement noise v k+1 and delay measurement y k The one-step forecast error covariance matrix of R k+1 is the measured noise v k+1 The error covariance matrix of Represents the filter gain of the measurement noise.
[0061] Furthermore, step 5 is specifically implemented in the following manner:
[0062] Step 5.1, linearize the nonlinear Gaussian weighted integral in steps 2, 3, and 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the conditions of one-step measurement random delay and synchronous correlated noise proposed above for filtering. This process consists of two parts: time prediction and measurement update, and its content is as follows:
[0063] a) Time prediction:
[0064] 1) Calculate the Jacobian matrix of the target state of the nonlinear system:
[0065]
[0066] 2) Calculate the one-step prediction value of the target state and the error covariance matrix:
[0067]
[0068] b) Measurement update:
[0069] 1) Calculate the Jacobian matrix of the nonlinear system measurement equation:
[0070]
[0071] 2) Approximate calculation formulas (18)~(21), (26)~(27):
[0072]
[0073] 3) Substitute formulas (38) to (43) into the corresponding terms in steps 4.1 and 4.2 to obtain the estimated value of the target state and the error covariance matrix.
[0074] The beneficial effects of the present invention are as follows: the design method of the Gaussian filter under the condition of one-step measurement random delay and synchronous correlated noise proposed by the present invention can solve the target tracking problem that the measurement data cannot be updated in time due to network delay, and can also solve the state estimation problem that the process noise and measurement noise of the system have correlated characteristics. The estimation effect is optimized, making the effect more accurate. BRIEF DESCRIPTION OF THE DRAWINGS
[0075] Figure 1 It is a global flow chart of the design method of the present invention for one-step measurement of Gaussian filter under random delay and synchronous correlated noise conditions;
[0076] Figure 2 The embodiment 1 of the method for designing a Gaussian filter under the condition of random delay and synchronous correlated noise in one step of the present invention is S k =0.6,p k = 0.5 when the target's true trajectory;
[0077] Figure 3 It is a state estimation diagram obtained by respectively using the traditional EKF algorithm and the present algorithm to estimate the target in Example 1 of the design method of the Gaussian filter under the condition of one-step measurement of random delay and synchronous correlated noise of the present invention;
[0078] Figure 4This is a state estimation root mean square error diagram obtained by using the traditional EKF algorithm and the present algorithm to estimate the target in Example 1 of the design method of the Gaussian filter under the conditions of random delay and synchronous correlated noise in one step measurement of the present invention. DETAILED DESCRIPTION
[0079] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments so that the advantages and features of the present invention can be more easily understood by those skilled in the art.
[0080] Example 1
[0081] Step 1: Introduce the independent Bernoulli random variable sequence γ into the nonlinear Gaussian discrete system k and the correlation coefficient S k , establish the target state model and measurement model of the nonlinear Gaussian discrete system under the conditions of one-step measurement random delay and synchronous correlated noise, and determine the one-step measurement random delay equation;
[0082] Step 2: Add the measurement noise to the state quantity, use the conditional Gaussian distribution lemma to make a one-step prediction of the augmented state quantity and delayed measurement, and derive the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix
[0083] Step 3: According to the measurement model in step 1 and the one-step measurement random delay equation, the actual measurement y at time k+1 is k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix
[0084] Step 4: One-step prediction using the augmented state vector obtained in steps 2 and 3 One-step prediction of delay measurement The target state is estimated through Bayesian filtering to obtain the posterior estimate of the augmented state at time k+1 and the error covariance matrix
[0085] Step 5, linearize the nonlinear Gaussian weighted integrals in Step 2, Step 3, and Step 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the one-step measurement random delay and synchronous correlated noise conditions proposed above for filtering;
[0086] Step 6: Repeat steps 2-5 until the entire filtering process is completed.
[0087] Example 2
[0088] Step 1: Introduce the independent Bernoulli random variable sequence γ into the nonlinear Gaussian discrete system k and the correlation coefficient S k , establish the target state model and measurement model of the nonlinear Gaussian discrete system under the conditions of one-step measurement random delay and synchronous correlated noise, and determine the one-step measurement random delay equation;
[0089] Step 1.1, introduce the sequence of independent Bernoulli random variables γ k and the correlation coefficient S k , establish the target state model and measurement model of nonlinear discrete systems under one-step measurement of random delay and synchronous correlated noise conditions:
[0090]
[0091] Among them, x k is the target state, z k is the ideal measurement value, f(·) and h(·) are the system function and the measurement function;
[0092] Process noise w k and measurement noise v k is the correlated zero-mean Gaussian white noise, and the covariances of process noise and measurement noise are Q k and R k , and satisfy:
[0093]
[0094] Among them, Q k and R k They represent the covariance matrices of process noise and measurement noise at time k respectively; S k represents the cross-covariance matrix between two noises; δ kl represents the Kronecker function;
[0095] Determine the one-step measurement random delay equation y k :
[0096]
[0097] γ k represents a sequence of independent Bernoulli random variables with values of 0 and 1, E([·]) represents the expected value, and p k Represents the probability of delayed measurement at time k:
[0098]
[0099] Step 2: Add the measurement noise to the state quantity, use the conditional Gaussian distribution lemma to make a one-step prediction of the augmented state quantity and delayed measurement, and derive the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix
[0100] Step 2.1, add the measurement noise to the state quantity and construct a new augmented state vector:
[0101]
[0102] Step 2.2, based on the measured noise v k+1 and the measured delay set Y k , target state x k+1 Independent of each other, there are k+1 measurement noises v k+1 One-step prediction and the one-step forecast error covariance matrix
[0103]
[0104] Step 2.3, using the conditional Gaussian distribution lemma, replace the original probability density with the conditional probability density, make a one-step prediction of the target state, and derive the k+1 time x k+1 One-step prediction and the one-step forecast error covariance matrix P k+1|k :
[0105] Conditional Gaussian Distribution Lemma:
[0106] Assume X and Y are random vectors that satisfy Gaussian distribution, and their joint Gaussian distribution is:
[0107]
[0108] Then, given the observation value Y=y, the conditional probability density function of the random vector X is:
[0109]
[0110] Among them, u x and u y Represents the mean of random vector X and random vector Y, P xx and P yy Represents the covariance matrix of random vector X and random vector Y, P xy represents the cross-covariance matrix of X and Y;
[0111] According to the definition:
[0112]
[0113] Due to the process noise w k and the measurement noise v k Synchronous correlation, so E[wk |Y k ]≠0, using the conditional Gaussian distribution lemma, let Then the joint Gaussian distribution of X and Y is as follows:
[0114]
[0115] Noise k At the measured value y k The conditional probability density under the condition is:
[0116]
[0117] therefore:
[0118]
[0119] Further get x k+1 One-step prediction and the one-step forecast error covariance matrix P k+1|k :
[0120]
[0121] in, and P k|k Respectively represent the filter estimate and error covariance matrix of the target state at time k; represents the filtered estimate of the target state at time k-1; represents the process noise w k and delay measurement y k The cross-covariance matrix of ; represents the error covariance matrix of the delay measurement;
[0122] Step 2.4, combining steps 2.2 and 2.3, obtain the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix
[0123]
[0124] Step 3: According to the measurement model in step 1 and the one-step measurement random delay equation, the actual measurement y at time k+1 is k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix
[0125] Step 3.1: Based on the measurement model of step 1.1 and the one-step measurement random delay equation and the one-step prediction of the target state obtained in step 2.3 and the one-step forecast error covariance matrix P k+1|k The actual measurement y at time k+1 k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix
[0126]
[0127]
[0128] in, and They represent the one-step prediction and one-step prediction error covariance matrices of the k+1 time measurement respectively; and They represent the posterior estimate and error covariance matrix of the measurement at time k respectively.
[0129] Step 4: One-step prediction using the augmented state vector obtained in steps 2 and 3 One-step prediction of delay measurement The target state is estimated through Bayesian filtering to obtain the posterior estimate of the augmented state at time k+1 and the error covariance matrix
[0130] Step 4.1, use the predicted value of the target state obtained in step 2.3 and step 3.1 and the predicted value of the delay measurement to estimate the target state through Bayesian filtering to obtain the estimated value of the target state at time k+1 and the error covariance matrix P k+1|k+1 :
[0131]
[0132] in, is the target state x k+1|k and measure random delay y k The cross-covariance matrix of ; is the target state x k+1|k and the ideal measured value z k The cross-covariance matrix of is the target state x k and the ideal measured value z k The cross-covariance matrix, S k v k and w k The cross-covariance matrix between k The filter gain representing the target state;
[0133] Step 4.2, using the predicted value of the measurement noise obtained in step 2.2 and step 3.1 and the predicted value of the delay measurement to estimate the measurement noise through Bayesian filtering, and obtain the estimated value of the measurement noise at time k+1 and the error covariance matrix
[0134]
[0135] in, is the measured noise v k+1|k and delay measurement k The one-step forecast error covariance matrix, R k+1 is the measured noise v k+1 The error covariance matrix of
[0136] Step 4.3, combining steps 4.1 and 4.2, we can get the posterior estimate of the augmented state at time k+1 and the error covariance matrix
[0137]
[0138] in, Represents the target state x k+1 and measurement noise v k+1 The cross-covariance matrix of ; Indicates the measurement noise v k+1 and delay measurement y k The one-step forecast error covariance matrix of R k+1 is the measured noise v k+1 The error covariance matrix of Represents the filter gain of the measurement noise.
[0139] Step 5, linearize the nonlinear Gaussian weighted integrals in Step 2, Step 3, and Step 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the one-step measurement random delay and synchronous correlated noise conditions proposed above for filtering;
[0140] Step 5.1, linearize the nonlinear Gaussian weighted integral in steps 2, 3, and 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the conditions of one-step measurement random delay and synchronous correlated noise proposed above for filtering. This process consists of two parts: time prediction and measurement update, and its content is as follows:
[0141] a) Time prediction:
[0142] 1) Calculate the Jacobian matrix of the target state of the nonlinear system:
[0143]
[0144] 2) Calculate the one-step prediction value of the target state and the error covariance matrix:
[0145]
[0146]
[0147] b) Measurement update:
[0148] 1) Calculate the Jacobian matrix of the nonlinear system measurement equation:
[0149]
[0150] 2) Approximate calculation formulas (18)~(21), (26)~(27):
[0151]
[0152] 3) Substitute formulas (38) to (43) into the corresponding terms in steps 4.1 and 4.2 to obtain the estimated value of the target state and the error covariance matrix.
[0153] Step 6: Repeat steps 2-5 until the entire filtering process is completed.
[0154] Embodiment 3:
[0155] On the basis of Example 2, in order to verify the effectiveness of the present invention, the simulation adopts the most commonly used test model in nonlinear filtering - the univariate non-stationary growth model (UNGM). The model contains nonlinear terms such as trigonometric functions and square functions, and has strong nonlinearity. The specific form is as follows:
[0156]
[0157] y k =(1-p k ) k +p k z k-1 (k≥2),y1=z1
[0158] Among them, w k and v k Respectively represent the variance as Q k = 0.2 and R k = 0.5 Gaussian white noise, correlation coefficient S k The value of is 0.6, and the random delay probability p kThe value of is 0.5, and the initial values of the simulation parameters are set to x0 = 5, P0 = 2, and T = 100. In the simulation, the root mean square error (RMSE) of the state estimation result is used as the performance indicator of the evaluation algorithm, which is defined as follows:
[0159]
[0160] Where, N represents the number of Monte Carlo simulations, and N is set to 100;
[0161] Execute step 1 to establish a target state model and a measurement model under one-step measurement random delay and synchronous correlated noise conditions and initialize relevant parameters;
[0162] Execute step 2, and predict the target state and the covariance of the target state at the next moment according to the initial value in step 1 to obtain the predicted value and P k+1|k ;
[0163] Execute step 3, and calculate the actual measurement y at time k+1 according to the measurement model in step 1 and the one-step measurement random delay equation k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix
[0164] Execute step 4, use the predicted value of the target state obtained in step 2 and step 3 and the delayed measurement predicted value to estimate the target state through Bayesian filtering, and obtain the posterior estimated value of the target state at time k+1 and the error covariance matrix
[0165] Go to step 5 and repeat steps 2 to 4 100 times until the whole process is completed.
[0166] Execute step 6, and approximate the nonlinear Gaussian weighted integral in steps 2, 3, and 4 according to the first-order Taylor expansion formula to obtain an improved EKF algorithm under the Gaussian filtering framework.
[0167] Step 7, the final result is as follows Figure 2 to Figure 4 shown.
[0168] Figure 2 The method for designing a Gaussian filter under the condition of random delay and synchronous correlated noise in one step of the present invention is S in Embodiment 3. k =0.6,p k = 0.5 when the target's true trajectory; Figure 3 It is a state estimation diagram obtained by respectively using the traditional EKF algorithm and the method of the present invention to estimate the target in Example 3 of the design method of the Gaussian filter under the condition of one-step measurement of random delay and synchronous correlated noise of the present invention; Figure 4 is a state estimation root mean square error diagram obtained by using the traditional EKF algorithm and the present algorithm to estimate the target in Example 3 of the design method of the Gaussian filter under the condition of one-step measurement of random delay and synchronous correlated noise of the present invention; Figure 3 , Figure 4 It can be seen that the target estimation result of the method of the present invention has a high similarity with the true trajectory, and the accuracy is much improved compared with the existing EKF algorithm.
Claims
1. A design method for a system Gaussian filter under one-step measurement of random delay and synchronous noise correlation conditions, characterized in that: Bernoulli random sequence is introduced into the nonlinear Gaussian discrete system to describe the one-step random delay phenomenon of measurement in the system. The measurement noise is used as the state increment to realize the one-step prediction of the delayed measurement information. At the same time, the conditional Gaussian distribution lemma is used to solve the noise correlation problem, so as to construct the target state model and measurement model with the characteristics of one-step measurement random delay and synchronization correlation noise. An optimal estimation algorithm in the form of Gaussian filtering framework is designed, and the Taylor series expansion formula is used to linearize the system. The extended Kalman filtering algorithm under the conditions of one-step measurement random delay and synchronization correlation noise is given.
2. The design method of the system Gaussian filter under the condition of one-step measurement of random delay and synchronous noise correlation according to claim 1 is characterized in that: Step 1: Introduce the independent Bernoulli random variable sequence γ into the nonlinear Gaussian discrete system k and the correlation coefficient S k , establish the target state model and measurement model of the nonlinear Gaussian discrete system under the conditions of one-step measurement random delay and synchronous correlated noise, and determine the one-step measurement random delay equation; Step 2: Add the measurement noise to the state quantity, use the conditional Gaussian distribution lemma to make a one-step prediction of the augmented state quantity and delayed measurement, and derive the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix Step 3: According to the measurement model in step 1 and the one-step measurement random delay equation, the actual measurement y at time k+1 is k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix Step 4: One-step prediction using the augmented state vector obtained in steps 2 and 3 One-step prediction of delay measurement The target state is estimated through Bayesian filtering to obtain the posterior estimate of the augmented state at time k+1 and the error covariance matrix Step 5, linearize the nonlinear Gaussian weighted integral in step 2, step 3 and step 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the condition of one-step measurement random delay and synchronous correlated noise to perform filtering; Step 6: Repeat steps 2-5 until the entire filtering process is completed.
3. The design method of the system Gaussian filter under the condition of one-step measurement of random delay and synchronous noise correlation according to claim 2 is characterized in that: Step 1 is as follows: Step 1.1, introduce the sequence of independent Bernoulli random variables γ k and the correlation coefficient S k , establish the target state model and measurement model of nonlinear discrete systems under one-step measurement of random delay and synchronous correlated noise conditions: Among them, x k is the target state, z k is the ideal measurement value, f(·) and h(·) are the system function and the measurement function; Process noise w k and measurement noise v k is the correlated zero-mean Gaussian white noise, and the covariances of process noise and measurement noise are Q k and R k , and satisfy: Among them, Q k and R k They represent the covariance matrices of process noise and measurement noise at time k respectively; S k represents the cross-covariance matrix between two noises; δ kl represents the Kronecker function; Determine the one-step measurement random delay equation y k : γ k represents a sequence of independent Bernoulli random variables with values of 0 and 1, E([·]) represents the expected value, and p k Represents the probability of delayed measurement at time k:
4. The design method of the system Gaussian filter under the condition of one-step measurement of random delay and synchronous noise correlation according to claim 2 is characterized in that: Step 2 is specifically implemented as follows: Step 2.1, add the measurement noise to the state quantity and construct a new augmented state vector: Step 2.2, based on the measured noise v k+1 and the measured delay set Y k , target state x k+1 Independent of each other, there are k+1 measurement noises v k+1 One-step prediction and the one-step forecast error covariance matrix Step 2.3, using the conditional Gaussian distribution lemma, replace the original probability density with the conditional probability density, make a one-step prediction of the target state, and derive the k+1 time x k+1 One-step prediction and the one-step forecast error covariance matrix P k+1|k : Conditional Gaussian Distribution Lemma: Assume X and Y are random vectors that satisfy Gaussian distribution, and their joint Gaussian distribution is: Then, given the observation value Y=y, the conditional probability density function of the random vector X is: Among them, u x and u y Represents the mean of random vector X and random vector Y, P xx and P yy Represents the covariance matrix of random vector X and random vector Y, P xy represents the cross-covariance matrix of X and Y; According to the definition: Due to the process noise w k and the measurement noise v k Synchronous correlation, so E[w k |Y k ]≠0, using the conditional Gaussian distribution lemma, let Then the joint Gaussian distribution of X and Y is as follows: Noise k At the measured value y k The conditional probability density under the condition is: therefore: Further get x k+1 One-step prediction and the one-step forecast error covariance matrix P k+1|k : in, and P k|k Respectively represent the filter estimate and error covariance matrix of the target state at time k; represents the filtered estimate of the target state at time k-1; represents the process noise w k and delay measurement y k The cross-covariance matrix of ; represents the error covariance matrix of the delay measurement; Step 2.4, combining steps 2.2 and 2.3, obtain the augmented state quantity at time k+1 One-step prediction and the one-step forecast error covariance matrix 5. The design method of the system Gaussian filter under the condition of one-step measurement of random delay and synchronous noise correlation according to claim 4 is characterized in that: Step 3 is as follows: Step 3.1: Based on the measurement model of step 1.1 and the one-step measurement random delay equation and the one-step prediction of the target state obtained in step 2.3 and the one-step forecast error covariance matrix P k+1|k The actual measurement y at time k+1 k+1 Perform a one-step prediction to obtain a one-step prediction of the delay measurement and the one-step forecast error covariance matrix in, and They represent the one-step prediction and one-step prediction error covariance matrices of the k+1 time measurement respectively; and They represent the posterior estimate and error covariance matrix of the measurement at time k respectively.
6. The design method of the system Gaussian filter under the condition of one-step measurement of random delay and synchronous noise correlation according to claim 5 or 6, characterized in that: Step 4 is specifically implemented as follows: Step 4.1, use the predicted value of the target state obtained in step 2.3 and step 3.1 and the predicted value of the delay measurement to estimate the target state through Bayesian filtering to obtain the estimated value of the target state at time k+1 and the error covariance matrix P k+1|k+1 : in, is the target state x k+1|k and measure random delay y k The cross-covariance matrix of ; is the target state x k+1|k and the ideal measured value z k The cross-covariance matrix of is the target state x k and the ideal measured value z k The cross-covariance matrix, S k v k and w k The cross-covariance matrix between k The filter gain representing the target state; Step 4.2, using the predicted value of the measurement noise obtained in step 2.2 and step 3.1 and the predicted value of the delay measurement to estimate the measurement noise through Bayesian filtering, and obtain the estimated value of the measurement noise at time k+1 and the error covariance matrix in, is the measured noise v k+1|k and delay measurement k The one-step forecast error covariance matrix, R k+1 is the measured noise v k+1 The error covariance matrix of Step 4.3, combining steps 4.1 and 4.2, we can get the posterior estimate of the augmented state at time k+1 and the error covariance matrix in, Represents the target state x k+1 and measurement noise v k+1 The cross-covariance matrix of ; Indicates the measurement noise v k+1 and delay measurement y k The one-step forecast error covariance matrix of R k+1 is the measured noise v k+1 The error covariance matrix of Represents the filter gain of the measurement noise.
7. The design method of the system Gaussian filter under the condition of one-step measurement of random delay and synchronous noise correlation according to claim 5, characterized in that: Step 5 is specifically implemented as follows: Step 5.1, linearize the nonlinear Gaussian weighted integral in steps 2, 3, and 4 using the first-order Taylor expansion formula, and then combine the EKF algorithm with the filtering framework under the conditions of one-step measurement random delay and synchronous correlated noise proposed above for filtering. This process consists of two parts: time prediction and measurement update, and its content is as follows: a) Time prediction: 1) Calculate the Jacobian matrix of the target state of the nonlinear system: 2) Calculate the one-step prediction value of the target state and the error covariance matrix: b) Measurement update: 1) Calculate the Jacobian matrix of the nonlinear system measurement equation: 2) Approximate calculation formulas (18)~(21), (26)~(27): 3) Substitute formulas (38) to (43) into the corresponding terms in steps 4.1 and 4.2 to obtain the estimated value of the target state and the error covariance matrix.