Distributed sequential estimation method and device for random interference and noise complex correlation

Abstract

The invention discloses a distributed sequential estimation method and device for random interference and noise complex correlation, and belongs to the technical field of multi-sensor system state estimation. The invention aims to solve the related problems of random interference and noise complexity in a multi-sensor system. For a nonlinear multi-sensor system with random interference and complex correlation noise, the method comprises the following steps: firstly, modeling the random interference by adopting Gaussian multiplicative noise and random variables, converting the multiplicative noise of the system into additive noise through equivalent transformation, and establishing a more compact model equivalent to the original system; and then performing state sequential estimation based on sequential fusion estimation and innovation of process noise and measurement noise, and performing calculation by adopting a volume rule in the estimation process to realize sequential fusion estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-sensor system state estimation, and relates to a distributed sequential estimation method and device for a multi-sensor system. Background Art

[0002] In actual scenarios such as radar tracking, environmental monitoring, and power system diagnosis, it is often necessary to estimate the actual state of the system based on the sensor's measurement information to complete specific tasks such as tracking or evaluation. State estimation technology was proposed and continuously improved based on this, bringing more convenience to people's lives and work.

[0003] Actual systems are usually not ideal conditions, and there are often non-ideal situations with complex correlations between random interference and noise. In engineering applications such as navigation systems or tracking systems, when the sensor system is in an interference environment, correlated noise will be generated. In many important physical processes, the uncertainty of model parameters is characterized by additive noise or multiplicative noise, making the established mathematical model more consistent with the actual system. In addition, when the system ages or is damaged, random interference such as measurement attenuation will occur. If these complex non-ideal situations are not handled in a timely manner, they will seriously affect the accuracy of the estimation and the stability of the entire system. At the same time, most actual systems are nonlinear multi-sensor systems, and most current methods can only handle linear systems and cannot be directly extended to nonlinear systems. Summary of the invention

[0004] The present invention aims to solve the problem of random interference and complex noise correlation in a multi-sensor system.

[0005] A distributed sequential estimation method for random interference and complex noise correlation, comprising:

[0006] S100, modeling a nonlinear multi-sensor system with random interference and complex noise correlation as

[0007]

[0008] In the formula, x k ∈R n and denote the state of the system at time k and the observation value of the jth sensor respectively; f(·) and is a nonlinear function in the state equation and the measurement equation, j = 1, 2, ..., L, L is the number of sensors; f (i) (·) is a known nonlinear function representing parameter interference, i = 1,…,τ is used to indicate the type of interference; and is the synchronously correlated system noise and the measurement noise of the jth sensor; Γ k is a matrix of dimension matching the equation of state; is a random variable, is a random variable;

[0009] For systems (1) and (2), the system model is transformed into The process noise and measurement noise in the system model are converted into and The new system is as follows:

[0010] x k+1 =f(x k )+ω k (4)

[0011]

[0012] Based on the new system (4)-(5), the statistical characteristics of system noise and measurement noise at different times are: E[ω k ]=0, and Determine the system noise ω at the same time k , measurement noise Variance and ω k and The covariance S j , and the measurement noise of different sensors and The cross-covariance matrix at the same time

[0013] S200, performing distributed sequential fusion estimation, including the following steps:

[0014] S201, Settings represents the measurement data from the 1st sensor to the jth sensor at time k+1; therefore Represents the measurement data of all sensors from time 1 to time k+1;

[0015] For sensor j, define the filter estimate The measurement noise is estimated as and The superscript s is used to indicate the result of sequential fusion, the superscripts j-1 and j indicate the j-1th and jth sensors, the superscript (j|j-1) indicates the process of fusing the j-1th sensor with the j-1th sensor, the superscript 0 indicates the initial value that needs to be given in advance, and the operator E[a|b] indicates the estimation of a under the condition of b;

[0016] S202, based on the initial value of the sequential fusion filter estimator at time k+1, calculate the sequential filter And the filter error variance matrix And calculate the cross-covariance matrix of state and measurement and an estimate of the measurement noise And measure noise and new information The cross-covariance matrix The estimated error variance matrix of state and measurement noise is calculated simultaneously The estimated error variance matrix between the noise and the measurement noise At time k+1, the L sensors are fused and a one-step prediction is obtained. and the one-step forecast error covariance matrix

[0017] Furthermore, in the nonlinear multi-sensor system and is a correlated white noise, and its statistical characteristics are and

[0018]

[0019] in, and are the submatrices at the corresponding positions and the corresponding covariance matrices respectively; δ k,t is the Dirichlet function. When k = t, δ k,t =1, when k≠t,δ k,t =0.

[0020] Furthermore, the system noise ω at the same time in S100 k , measurement noise Variance and ω k and The covariance S j , and the measurement noise of different sensors and The cross-covariance matrix at the same time as follows:

[0021]

[0022] Further, based on the initial value of the sequential fusion filter estimator at time k+1, the sequential filter is calculated And the filter error variance matrix The process is as follows:

[0023]

[0024] in, is the gain matrix, is the innovation matrix, is the covariance matrix of the new information;

[0025]

[0026]

[0027] Among them, the superscript x(j-1) is used to represent the estimated error covariance matrix of the state, the superscript v(j|j-1) is used to represent the error covariance matrix of the measurement noise after the j-th sensor is fused with the j-1-th sensor, and the superscript x(j-1)v(j|j-1) is used to represent the cross-covariance matrix between the state and measurement noise; the superscript z(j|j-1) is used to represent the estimated error covariance matrix of the measurement after the j-th sensor is fused with the j-1-th sensor, and the superscript x(j-1)z(j|j-1) is used to represent the cross-covariance matrix between the state and measurement.

[0028] Furthermore, the cross-covariance matrix of the state and measurement is calculated and an estimate of the measurement noise The process is as follows:

[0029]

[0030] Wherein, l represents the sensor number to be fused, and its value range is (1, j-1); is the gain matrix of the measurement noise, and the superscript ε(l) is used to represent the noise variance of the innovation of the l-th sensor.

[0031] Furthermore, the measurement noise is calculated and new information The cross-covariance matrix The process is as follows:

[0032]

[0033] Furthermore, the estimated error variance matrix of the state and measurement noise is The estimated error variance matrix between the noise and the measurement noise as follows:

[0034]

[0035] Furthermore, the one-step prediction and the one-step forecast error covariance matrix as follows:

[0036]

[0037] Process noise ω k Sequential fusion filter estimation of as follows:

[0038]

[0039] Among them, the value range of l is (1,L); the gain matrix of the measurement noise as follows:

[0040]

[0041] The superscript w(l-1) is used to represent the error covariance matrix of process noise, and the superscript w(l-1)x(l-1) is used to represent the cross-covariance matrix of state and process noise.

[0042] Furthermore, the process of S200 adopts the volume criterion to solve to realize the distributed sequential estimation, and the specific process includes the following steps:

[0043] Define the volume point as

[0044]

[0045] use express The gth Column elements;

[0046] Then, based on the definition of volume points, measurement noise estimation, state sequential fusion and state sequential fusion prediction are solved;

[0047] The process of solving the measurement noise estimation includes:

[0048] 11) Perform Cholesky decomposition on Δ2 in (22) to obtain

[0049] Δ2=S2(S2) T (38)

[0050] 12) Calculate volume points

[0051]

[0052] Among them, n, p j x k , The vector dimension of Used to indicate The first 2p j row elements, Used to indicate The last 2n rows of elements;

[0053] 13) Volumetric Point Propagation

[0054]

[0055] in,

[0056] 14) Calculate the correlation value

[0057]

[0058] 15) Gain matrix of measurement noise

[0059]

[0060] Then we can get the estimated value of the measurement noise in formula (19):

[0061] The solution process of the state sequential fusion includes:

[0062] 21) Yes The Cholesky decomposition of Δ1 in (16) yields

[0063]

[0064] Δ1=S1(S1) T (45)

[0065] 22) Calculate volume points

[0066]

[0067] in, Used to indicate The first 2n rows of elements, Used to indicate After 2p j row element;

[0068] 23) Propagation volume point

[0069]

[0070] 24) Calculate the one-step prediction value of the measurement information

[0071]

[0072] 25) The expression of the new information is as follows

[0073]

[0074] 26) The cross-covariance matrix of state and measurement information is

[0075]

[0076] 27) The innovation covariance matrix is

[0077]

[0078] Then, we get the filter estimation gain matrix and state estimates The solution process of the state sequential fusion prediction includes:

[0079] 31) Yes The Cholesky decomposition of Δ3 in (28) yields

[0080]

[0081] Δ3=S3(S3) T (55)

[0082] 32) Calculate volume points

[0083]

[0084] Among them, m is The vector dimension of Used to indicate The first 2n rows of elements, Used to indicate The last 2m rows of elements;

[0085] 33) Volumetric Point Propagation

[0086]

[0087] 34) Calculate the final sequential fusion forecast estimate and its error covariance matrix for

[0088]

[0089] Then, we get the one-step forecast state estimate and the one-step forecast state error variance

[0090] A distributed sequential estimation device for random interference and complex correlation of noise, the device comprising a processor and a memory, the memory storing at least one instruction, the at least one instruction being loaded and executed by the processor to implement the distributed sequential estimation method for random interference and complex correlation of noise.

[0091] Beneficial effects:

[0092] For nonlinear multi-sensor systems with random interference and complex correlated noise, the present invention first models the complex system and converts the multiplicative noise into additive noise based on the equivalent conversion principle. Then, based on the method of new information analysis, the system state, measurement noise and process noise are estimated, and a sequential fusion filter estimator is designed to avoid noise decorrelation. Finally, a numerical implementation strategy is given based on the third-order spherical diameter volume rule. The present invention can effectively solve the problem of random interference and complex noise correlation in multi-sensor systems, and provides an effective solution for complex systems with random interference and complex correlated noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 Schematic diagram of the distributed sequential estimation process.

[0094] Figure 2 For tracking and estimating graphs.

[0095] Figure 3 The RMSE curves of the two algorithms are shown in Figure 2.

[0096] Figure 4 ARMSE curves of the two algorithms. DETAILED DESCRIPTION

[0097] In view of the problems pointed out in the background technology, the present invention proposes a distributed sequential estimation method for random interference and complex noise correlation, which is used to solve the estimation problem of random interference and complex noise correlation in a multi-sensor system.

[0098] Specific implementation method 1: Combination Figure 1 To explain this embodiment,

[0099] This implementation is a distributed sequential estimation method for complex correlation of random interference and noise, including:

[0100] Step 1: System modeling and equivalent transformation:

[0101] The nonlinear multi-sensor system with random interference and complex noise correlation is modeled as

[0102]

[0103] In the formula, x k ∈R n and denote the state of the system at time k and the observation value of the jth sensor respectively; f(·) and is a nonlinear function in the state equation and the measurement equation, j = 1, 2, ..., L, L is the number of sensors; f (i)(·) is a known nonlinear function representing parameter interference, i = 1,…,τ is used to indicate the type of interference; and is the synchronously correlated system noise and the measurement noise of the jth sensor; Γ k is a known matrix with appropriate dimensions matching the equation of state.

[0104] The random parameter interference phenomenon in the state equation and the attenuation measurement phenomenon in the measurement equation can be represented by uncorrelated random variables. The first moment of and the second moment (variance matrix) Used to describe the uncertainty of the system model. Random variable is a discrete random variable whose value is between, and The first and second order moments are and Used to describe the phenomenon of measurement attenuation.

[0105] Assumption 1: and is a correlated white noise, and its statistical characteristics are and

[0106]

[0107] in, and are the submatrices at the corresponding positions and the corresponding covariance matrices respectively; δ k,t is the Dirichlet function. When k = t, δ k,t =1, when k≠t,δ k,t =0.

[0108] Assumption 2: The initial value x0 is are uncorrelated, and the mean and variance of the initial value x0 are μ0 and P0 respectively.

[0109] Based on the equivalent transformation principle, the original model is converted into a more compact expression form, which can transform the multiplicative noise into additive noise while avoiding the noise decorrelation operation.

[0110] For systems (1) and (2), the system model is transformed into The process noise and measurement noise in the system model are converted into and The new system can be rewritten as follows:

[0111] x k+1 =f(x k )+ωk (4)

[0112]

[0113] Based on the above assumptions and the new system (4)-(5), the statistical characteristics of the system noise and measurement noise at different times are:

[0114] E[ω k ]=0, and

[0115] Then the system noise ω at the same time k and measurement noise Variance and their covariance S j They are:

[0116]

[0117]

[0118] Measurement noise of different sensors and The cross-covariance matrix at the same time is:

[0119]

[0120] Step 2: Distributed sequential fusion estimation:

[0121] Distributed sequential fusion estimation can use the measurement data of different sensors at the current moment to update the system state.

[0122] set up represents the measurement data from the 1st sensor to the jth sensor at time k+1. Represents the measurement data of all sensors from time 1 to time k+1.

[0123] Assumption 3: State x k+1 In the measurement information Z k The probability density function under Zhang Cheng's linear space condition obeys Gaussian distribution:

[0124]

[0125] in, denote the state prediction estimate and the corresponding error covariance matrix respectively, and the superscript (s) is used to denote the result of sequential fusion.

[0126] Assumption 4: State x k+1 In measuring information The probability density function under Zhang Cheng's linear space condition obeys Gaussian distribution:

[0127]

[0128] Therefore, for sensor j, the filter estimate is defined as The measurement noise is estimated as and The superscript s is used to indicate the result of sequential fusion, the superscripts j-1 and j indicate the j-1th and jth sensors, the superscript (j|j-1) indicates the process of fusing the j-1th sensor with the j-1th sensor, the superscript 0 indicates the initial value that needs to be given in advance, and the operator E[a|b] indicates the estimation of a under the condition of b;

[0129] At time k+1, the initial value of the sequential fusion filter estimator is and

[0130] Sequential Filter And the filter error variance matrix They are:

[0131]

[0132] in, is the gain matrix, which will be given later, and the innovation matrix for:

[0133]

[0134] The covariance matrix of the innovation for:

[0135]

[0136] Among them, the superscript x(j-1) is used to represent the estimated error covariance matrix of the state, the superscript v(j|j-1) is used to represent the error covariance matrix of the measurement noise after the j-th sensor is fused with the j-1-th sensor, and the superscript x(j-1)v(j|j-1) is used to represent the cross-covariance matrix between the state and measurement noise.

[0137] Gain Matrix of Sequential Fusion Filters for:

[0138]

[0139] The superscript z(j|j-1) is used to represent the estimated error covariance matrix of the j-th sensor after fusing the j-1-th sensor, and the superscript x(j-1)z(j|j-1) is used to represent the cross-covariance matrix between the state and the measurement.

[0140] The cross-covariance matrix of states and measurements for:

[0141]

[0142] Estimation of measurement noise The calculation is as follows:

[0143]

[0144] In the above formula (19), l represents the sensor number to be fused, and its value range is (1, j-1). According to the projection theorem, the gain matrix of the measurement noise is The calculation is as follows:

[0145]

[0146] The superscript ε(l) is used to represent the noise variance of the new information of the lth sensor.

[0147] Measuring noise and new information The cross-covariance matrix is:

[0148]

[0149] The estimated error variance matrix of state and measurement noise is The calculation is as follows:

[0150]

[0151] The estimated error variance matrix between the measurement noise The calculation is as follows:

[0152]

[0153] Therefore, the fusion result of the nonlinear multi-sensor sequential fusion filter at time k+1 is:

[0154]

[0155] Then, it is necessary to design a sequential fusion predictor based on the fusion result (filter estimation result) of the last sensor at the current moment, and the initial value is

[0156] At time k+1, the L sensors are fused and one-step prediction is performed. and the one-step forecast error covariance matrix The expression is as follows:

[0157]

[0158] Similar to the estimation expression of measurement noise in equation (19), process noise ω k The expression of the sequential fusion filter estimation is The calculation is as follows:

[0159]

[0160] In the above equation (29), the range of l is (1, L); according to the projection theorem, the gain matrix of the measurement noise is The calculation is as follows:

[0161]

[0162] The superscript w(l-1) is used to represent the error covariance matrix of process noise, and the superscript w(l-1)x(l-1) is used to represent the cross-covariance matrix of state and process noise.

[0163] The cross-covariance matrix of state and process noise is:

[0164]

[0165] The cross-covariance matrix of process noise and measurement noise is:

[0166]

[0167] The cross-covariance matrix of the system noise is:

[0168]

[0169] Step 3: The estimated expressions (12)-(35) obtained in step 2 are numerically realized using the volume criterion:

[0170] Assume that at time k+1, the estimated variables of the first (l-1) sensors are known, such as and The numerical implementation includes the numerical implementation of measurement noise estimation, state sequential fusion and state sequential fusion prediction, as follows:

[0171] First define the volume point

[0172]

[0173] use express The gth Column elements.

[0174] (1) Numerical implementation of measurement noise estimation:

[0175] 11) Perform Cholesky decomposition on Δ2 in (22) to obtain

[0176] Δ2=S2(S2) T (38)

[0177] 12) Calculate volume points

[0178]

[0179] Among them, n, p j x k , The vector dimension of Used to indicate The first 2p j row elements, Used to indicate The last 2n rows of elements.

[0180] 13) Volumetric Point Propagation

[0181]

[0182] in,

[0183] 14) Calculate the correlation value

[0184]

[0185] 15) Gain matrix of measurement noise

[0186]

[0187] Then the estimated value of the measurement noise in formula (19) can be obtained Approximate value of .

[0188] (2) Numerical implementation of state sequential fusion:

[0189] 21) Yes The Cholesky decomposition of Δ1 in (16) yields

[0190]

[0191] Δ1=S1(S1) T (45)

[0192] 22) Calculate volume points

[0193]

[0194] in, Used to indicate The first 2n rows of elements, Used to indicate After 2p j Row element.

[0195] 23) Propagation volume point

[0196]

[0197] 24) Calculate the one-step prediction value of the measurement information

[0198]

[0199] 25) The expression of the new information is as follows

[0200]

[0201] 26) The cross-covariance matrix of state and measurement information is

[0202]

[0203] 27) The innovation covariance matrix is

[0204]

[0205] Then, the filter estimation gain matrix can be obtained and state estimates

[0206] (3) Numerical implementation of state sequential fusion prediction:

[0207] Let k = k + 1. At this time, the L sensors are fused. First, the variance matrix of the sequential fusion is estimated. Decomposition is performed, which is similar to the numerical realization process of the measurement noise estimate. At this moment, the last sensor has completed the sequential fusion estimation, so it is considered that and is known.

[0208] 31) Yes The Cholesky decomposition of Δ3 in (28) yields

[0209]

[0210] Δ3=S3(S3) T (55)

[0211] 32) Calculate volume points

[0212]

[0213] Among them, m is The vector dimension of Used to indicate The first 2n rows of elements, Used to indicate The last 2m rows of elements.

[0214] 33) Volumetric Point Propagation

[0215]

[0216] 34) Calculate the final sequential fusion forecast estimate and its error covariance matrix for

[0217]

[0218] Then, we get the one-step forecast state estimate and the one-step forecast state error variance

[0219] Example

[0220] In order to verify the effectiveness of the present invention, a simulation is performed on a two-dimensional target tracking scenario with multiple radars, and the system is represented as

[0221]

[0222]

[0223] Among them, T = 1 is the sampling period, the state is x k+1 and k+1 Represent the positions in the x and y directions respectively, and represents the speed in the x and y directions, Ω k+1 Represents the turning angle rate. F k =0.001·I 5×5 , Γ k =[10110110 -4 ] T ,Ψ k =[10010 -5 ] T , the actual initial value of the state is x0 = [1000m 300m / s1000m 0m / s 0.052rad] T , the initial value of the filter estimate is and variance and The relationship satisfies the following statistical properties in Q w =10,Q β =0.4, b1=0.1, b2=0.14.

[0224] Consider the random variable The probability density function p1(s) ​​has a value interval of [0.95,1], The value interval of the probability density function p2(s) is [0.85,1].

[0225]

[0226] From (65) and (66), we can get that the random variable The statistical characteristics of describe the attenuation degree of each sensor, expressed as mean and variance:

[0227] The mean square error (RMSE) and cumulative mean square error (ARMSE) are selected as evaluation indicators, expressed as

[0228]

[0229] in and are the true value and estimated value of the state, t and k are the simulation times, N represents the number of Monte Carlo times, and M is the simulation step size.

[0230] A total of 100 Monte Carlo simulations were performed with a simulation step length of 50 steps. The EKF estimation method was selected for comparison. The estimation and tracking curves are shown in Figure 2. Figure 2 As shown in the figure, it can be seen that the present invention has higher tracking ability than the comparison algorithm. The RMSE and ARMSE curves of the two algorithms are shown in Figure 3 and 4 As shown in the figure, it can be seen that the estimation accuracy of the present invention is higher than that of the comparison algorithm, and it is more stable. Therefore, the present invention has better performance when dealing with multi-sensor systems with random interference and complex correlated noise, and provides a more suitable solution for it. Specific implementation method 2:

[0232] This embodiment is a distributed sequential estimation device for random interference and complex correlation of noise, the device includes a processor and a memory. It should be understood that the device includes any device including a processor and a memory described in the present invention, and the device may also include other units and modules that perform display, interaction, processing, control, and other functions through signals or instructions;

[0233] At least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to implement the distributed sequential estimation method for complex correlation of random interference and noise.

[0234] It should be understood that those skilled in the art should understand that at least one instruction stored is a computer program product corresponding to the method or system. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0235] The present application is described with reference to the flowcharts and / or block diagrams of the methods, systems, and computer program products according to the embodiments of the present application, and may also be used for corresponding devices. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0236] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0237] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0238] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0239] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

[0240] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A distributed sequential estimation method for complex correlation of random interference and noise, characterized in that: include: S100, modeling a nonlinear multi-sensor system with random interference and complex noise correlation as In the formula, x k ∈R n and denote the state of the system at time k and the observation value of the jth sensor respectively; f(·) and is a nonlinear function in the state equation and the measurement equation, j = 1, 2, ..., L, L is the number of sensors; f (i) (·) is a known nonlinear function representing parameter interference, i = 1,…,τ is used to indicate the type of interference; and is the synchronously correlated system noise and the measurement noise of the jth sensor; Γ k is a matrix of dimension matching the equation of state; is a random variable, is a random variable; For systems (1) and (2), the system model is transformed into The process noise and measurement noise in the system model are converted into and The new system is as follows: x k+1 =f(x k )+ω k (4) Based on the new system (4)-(5), the statistical characteristics of system noise and measurement noise at different times are: E[ω k ]=0, and Determine the system noise ω at the same time k , measurement noise Variance and ω k and The covariance S j , and the measurement noise of different sensors and The cross-covariance matrix at the same time S200, performing distributed sequential fusion estimation, including the following steps: S201, Settings represents the measurement data from the 1st sensor to the jth sensor at time k+1; therefore Represents the measurement data of all sensors from time 1 to time k+1; For sensor j, define the filter estimate The measurement noise is estimated as and The superscript s is used to indicate the result of sequential fusion, the superscripts j-1 and j indicate the j-1th and jth sensors, the superscript (j|j-1) indicates the process of fusing the j-1th sensor with the j-1th sensor, the superscript 0 indicates the initial value that needs to be given in advance, and the operator E[a|b] indicates the estimation of a under the condition of b; S202, based on the initial value of the sequential fusion filter estimator at time k+1, calculate the sequential filter And the filter error variance matrix And calculate the cross-covariance matrix of state and measurement and an estimate of the measurement noise And measure noise and new information The cross-covariance matrix The estimated error variance matrix of state and measurement noise is calculated simultaneously The estimated error variance matrix between the noise and the measurement noise At time k+1, the L sensors are fused and a one-step prediction is obtained. and the one-step forecast error covariance matrix 2. A distributed sequential estimation method for complex correlation of random interference and noise according to claim 1, characterized in that: The nonlinear multi-sensor system and is a correlated white noise, and its statistical characteristics are and in, and are the submatrices at the corresponding positions and the corresponding covariance matrices respectively; δ k,t is the Dirichlet function. When k = t, δ k,t =1, when k≠t, δ k,t =0.

3. The distributed sequential estimation method for complex correlation of random interference and noise according to claim 2, characterized in that: System noise ω at the same time in S100 k , measurement noise Variance and ω k and The covariance S j , and the measurement noise of different sensors and The cross-covariance matrix at the same time as follows:

4. The distributed sequential estimation method for complex correlation of random interference and noise according to claim 3, characterized in that: Based on the initial value of the sequential fusion filter estimator at time k+1, the sequential filter is calculated And the filter error variance matrix The process is as follows: in, is the gain matrix, is the innovation matrix, is the covariance matrix of the new information; Among them, the superscript x(j-1) is used to represent the estimated error covariance matrix of the state, the superscript v(j|j-1) is used to represent the error covariance matrix of the measurement noise after the j-th sensor is fused with the j-1-th sensor, and the superscript x(j-1)v(j|j-1) is used to represent the cross-covariance matrix between the state and measurement noise; the superscript z(j|j-1) is used to represent the estimated error covariance matrix of the measurement after the j-th sensor is fused with the j-1-th sensor, and the superscript x(j-1)z(j|j-1) is used to represent the cross-covariance matrix between the state and measurement.

5. The distributed sequential estimation method for complex correlation of random interference and noise according to claim 4, characterized in that: Calculate the cross-covariance matrix of states and measurements and an estimate of the measurement noise The process is as follows: Wherein, l represents the sensor number to be fused, and its value range is (1, j-1); is the gain matrix of the measurement noise, and the superscript ε(l) is used to represent the noise variance of the innovation of the l-th sensor.

6. The distributed sequential estimation method for complex correlation of random interference and noise according to claim 5, characterized in that: Calculating measurement noise and new information The cross-covariance matrix The process is as follows:

7. A distributed sequential estimation method for complex correlation of random interference and noise according to claim 6, characterized in that: The estimated error variance matrix of the state and measurement noise is The estimated error variance matrix between the noise and the measurement noise as follows:

8. A distributed sequential estimation method for complex correlation of random interference and noise according to claim 7, characterized in that: The one-step prediction and the one-step forecast error covariance matrix as follows: Process noise ω k Sequential fusion filter estimation of as follows: Among them, the value range of l is (1,L); the gain matrix of the measurement noise as follows: The superscript w(l-1) is used to represent the error covariance matrix of process noise, and the superscript w(l-1)x(l-1) is used to represent the cross-covariance matrix of state and process noise.

9. A distributed sequential estimation method for complex correlation of random interference and noise according to claim 8, characterized in that: The process of S200 adopts the volume criterion to solve to realize the distributed sequential estimation, and the specific process includes the following steps: Define the volume point as use express The gth Column elements; Then, based on the volume point definition, measurement noise estimation, state sequential fusion and state sequential fusion prediction are solved; the measurement noise estimation solution process includes: 11) Perform Cholesky decomposition on Δ2 in (22) to obtain <h2 style=";text-align:left;direction:ltr">Δ2 = S2(S2)<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> (38) 12) Calculate volume points Among them, n, p j x k , The vector dimension of Used to indicate The first 2p j row elements, Used to indicate The last 2n rows of elements; 13) Volumetric Point Propagation in, 14) Calculate the correlation value 15) Gain matrix of measurement noise Then we can get the estimated value of the measurement noise in formula (19): The solution process of the state sequential fusion includes: 21) Yes The Cholesky decomposition of Δ1 in (16) yields Δ1=S1(S1) T (45) 22) Calculate volume points in, Used to indicate The first 2n rows of elements, Used to indicate After 2p j row element; 23) Propagation volume point 24) Calculate the one-step prediction value of the measurement information 25) The expression of the new information is as follows 26) The cross-covariance matrix of state and measurement information is 27) The innovation covariance matrix is Then, we get the filter estimation gain matrix and state estimates The solution process of the state sequential fusion prediction includes: 31) Yes The Cholesky decomposition of Δ3 in (28) yields <h2 style=";text-align:left;direction:ltr">Δ3 = S3(S3)<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> (55) 32) Calculate volume points Among them, m is The vector dimension of Used to indicate The first 2n rows of elements, Used to indicate The last 2m rows of elements; 33) Volumetric Point Propagation 34) Calculate the final sequential fusion forecast estimate and its error covariance matrix for Then, we get the one-step forecast state estimate and the one-step forecast state error variance 10. A distributed sequential estimation device for random interference and complex noise correlation, characterized in that: The device includes 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 a distributed sequential estimation method for complex correlation of random interference and noise as described in any one of claims 1 to 9.

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