Robust fusion estimation method for coping with two-step random time lag and loss observation uncertainty

Abstract

The invention relates to the technical field of information engineering, in particular to a robust fusion estimation method for coping with two-step random time lag and loss observation uncertainty, which comprises the following steps: firstly, assuming a multi-sensor networked system model meeting conditions, and then applying an augmentation method, a de-randomization method and a virtual noise technology to obtain a multi-sensor networked system model; a considered system is converted into a multi-model multi-sensor system only containing uncertain noise variance, then a robust local time-varying Kalman filter and a smoother are designed based on a robust local time-varying Kalman predictor, and three robust weighted state fusion time-varying Kalman estimators are provided under a unified framework. And the robustness of the robust weighted state fusion time-varying Kalman estimator is proved by combining actual and conservative weighted fusion Kalman estimation error variances with a unified form. A multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties is introduced for a simulation experiment, and the accuracy of the method is further proved.

Description

Technical Field

[0001] The present invention relates to the technical field of information engineering, and in particular to a robust fusion estimation method for coping with two-step random time delay and lost observation uncertainty. Background Art

[0002] The field of networked system estimation and control has been widely used in many fields, including state monitoring, space development, deep space exploration, mobile communications, satellite navigation and positioning, unmanned aerial vehicle systems, robots, radar tracking, remote sensing image processing, etc. However, since the data communication of networked systems is limited by bandwidth and energy, there are inevitably random uncertainties caused by networking, such as lost observations, attenuated observations, packet loss, and random observation lags. This brings new difficulties and challenges to the design of robust fusion filters.

[0003] Insufficiency and deficiencies of existing technologies: For linear discrete time-varying multi-sensor stochastic systems with uncertain noise variance, a robust local and weighted fusion Kalman filter is proposed based on the principle of minimax robust estimation and the worst-case conservative system with a conservative upper limit of the noise variance. However, only the uncertainty of the noise variance is considered, while multiplicative noise, measurement loss and random sensor delay are not considered, and systems with correlated noise cannot be processed. For multi-sensor networked systems with multiplicative noise in the system state and observation matrix, packet loss and uncertain noise variance, a robust weighted state fusion Kalman estimator is proposed, but it does not consider the uncertainty of random observation time delay. For multi-sensor networked systems with multiplicative noise in the system state and observation matrix, one-step random observation lag and uncertain noise variance, a comprehensive covariance cross-fusion robust Kalman estimator is proposed; for multi-sensor networked systems with multiplicative noise, two-step random observation lag, observation value loss and uncertain noise variance, the literature proposes robust centralized fusion and weighted observation fusion steady-state Kalman estimators, but the above results do not consider noise-dependent multiplicative noise. Summary of the invention

[0004] The purpose of the present invention is to provide a robust fusion estimation method for coping with two-step random time lag and lost observation uncertainty, comprehensively considering multiplicative noise, two-step random time lag, lost observation value and uncertain noise variance in different situations, and improving the reliability of a robust weighted time-varying Kalman estimator.

[0005] To achieve the above object, the present invention provides a robust fusion estimation method for coping with two-step random time delay and lost observation uncertainty, comprising the following steps:

[0006] Step 1: Build a multi-sensor networked system model as the original system;

[0007] Step 2: applying augmentation method, de-randomization method and virtual noise technology, transforming the multi-sensor network system model into a multi-model multi-sensor system containing only uncertain noise variance;

[0008] Step 3: Based on the minimax robust estimation principle, obtain the local optimal time-varying Kalman predictor, and then further design the robust local time-varying Kalman filter and smoother respectively;

[0009] Step 4: Three robust weighted state fusion time-varying Kalman estimators are proposed in a unified framework, and it is proved that the three robust weighted state fusion time-varying Kalman estimators are robust under the defined assumptions;

[0010] Step 5: A simulation example is demonstrated using a multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties.

[0011] Optionally, the multi-sensor networked system model is expressed as follows:

[0012]

[0013] v i (t) = D i w(t)+η i (t)

[0014]

[0015] And meet the following assumptions:

[0016] ξ i (t)∈R 1 , i (t)∈R 1 , and γ i (t)∈R 1 , i = 1, ..., L is an uncorrelated Bernoulli white noise with a value of 0 or 1 and with a known probability Prob(ξ i (t) = 1) = π i ,Prob(ξ i (t) = 0) = 1 - π i , Prob(γ i (t) = 1) = λ i ,Prob(γ i (t) = 0) = 1 - λ i , where π i , and λ i is known, and 0≤π i ≤1, and 0≤λ i≤1. In addition, ξ i (t),ζ i (t) and γ i (t) uncorrelated with other random signals;

[0017] w(t),η i (t),α k (t) and β k (t) are mutually uncorrelated zero-mean white noise sequences, and their covariance is

[0018]

[0019] in, and They are white noise w(t),η i (t),α k (t) and β k The unknown uncertain actual / true variance of (t), δ kj represents the Kronecker function, δ kk =1,δ kj =0(k≠j);

[0020] The initial state x(0) and the random signal w(t),η i (t),α k (t),β k (t),ξ i (t),ζ i (t) and γ i (t) is not relevant, and where μ 0 is the known mean of x(0), P 0 is its unknown uncertain actual variance;

[0021] Q, and P 0 They are and A known conservative upper bound of .

[0022] Optionally, during the execution of step 2, the state augmentation method is used to perform model transformation in the robust Kalman filter, and the behavior of the system in the face of uncertainty and external disturbances is evaluated by calculating the actual and conservative second-order non-center distances, and augmented noise is further introduced to improve the robustness of the filter.

[0023] Optionally, in step 3, the expression of the local optimal time-varying Kalman predictor is as follows:

[0024]

[0025] The robust local time-varying Kalman filter and smoother are as follows:

[0026]

[0027] Optionally, the execution process of step 4 is specifically to adopt the optimal weighted fusion rule to uniformly give three robust weighted fusion time-varying Kalman estimators of the original system model, and obtain their corresponding conservative fusion error variances based on the three weighted weights, and further obtain the corresponding actual and conservative weighted fusion Kalman estimation error variances with a unified form based on the robust time-varying Kalman estimator under the unified model, and finally combine the assumptions and corresponding theorems to prove that the three robust weighted fusion time-varying Kalman estimators are robust under the conditions defined by the assumptions.

[0028] Optionally, the three matrix weights in the optimal weighted fusion rule are as follows:

[0029] The optimal matrix weight is

[0030]

[0031] The optimal diagonal matrix weights are

[0032] [ω 1j (t|t+N),…,ω Lj (t|t+N)]=[e T (P jj (t|t+N)) -1 e] -1 e T (P jj (t|t+N)) -1 ,j=1,…,n

[0033]

[0034] The optimal scalar weight is

[0035]

[0036] Where θ=m,d,s represents matrix weighting, diagonal matrix and scalar weighted fusion, e is the identity matrix with matrix elements equal to 1, and P is the corresponding augmented conservative covariance matrix.

[0037] Optionally, the execution process of step 5 is specifically to consider a multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties, and design its corresponding robust local and fused time-varying Kalman estimator based on this signal, and convert it into a special case of the original system model, and obtain the error variance of the signal s(t) is also robust. Finally, the tracking diagram of the ARMA signal simulation instance and the error variance curve are analyzed to verify the success of the technical solution.

[0038] The present invention provides a robust fusion estimation method for dealing with two-step random time lag and lost observation uncertainty. First, a qualified multi-sensor networked system model is assumed, and then the augmentation method, derandomization method and virtual noise technology are applied to transform the considered system into a multi-model multi-sensor system containing only uncertain noise variance. Then, based on the robust local fusion time-varying Kalman predictor, robust local fusion time-varying Kalman filters and smoothers are designed respectively. Three robust weighted state fusion time-varying Kalman estimators are proposed under a unified framework. Combined with the actual and conservative weighted fusion Kalman estimation error variances with a unified form, the robustness of the robust weighted state fusion time-varying Kalman estimator is proved. In addition, a multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties is introduced for simulation experiments to further prove the accuracy of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 It is a schematic flow chart of the steps of a robust fusion estimation method for coping with two-step random time delay and lost observation uncertainty of the present invention.

[0041] Figure 2 It is a schematic diagram of the formation and robustness proof process of the unified three weighted fusion time-varying Kalamn estimators in the present invention.

[0042] Figure 3 It is a schematic diagram of the multi-sensor single-channel ARMA signal application process in the present invention.

[0043] Figure 4 It is a schematic diagram of the trace comparison of conservative and practical local and fused time-varying Kalman prediction error variances in a specific embodiment of the present invention.

[0044] Figure 5Schematic diagram of the signal s(t) and its actual local and fusion predictors in an embodiment of the present invention.

[0045] Figure 6 Schematic diagram of the first component of the state x(t) and its local and fusion filters in a specific embodiment of the present invention.

[0046] Figure 7 is the actual fusion one-step smoothing error curve and and Schematic diagram of the boundary.

[0047] Figure 8 is the random parameter perturbation β in the specific embodiment of the present invention k (t) Impact on the robust accuracy of the robust scalar weighted fusion time-varying Kalman signal predictor. DETAILED DESCRIPTION

[0048] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0049] See also Figure 1 The present invention provides a robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty, comprising the following steps:

[0050] S1: The architecture of the multi-sensor networked system model is the original system;

[0051] S2: applying augmentation method, derandomization method and virtual noise technology, transforming the multi-sensor network system model into a multi-model multi-sensor system containing only uncertain noise variance;

[0052] S3: Based on the minimax robust estimation principle, the local optimal time-varying Kalman predictor is obtained, and then the robust local fusion time-varying Kalman filter and smoother are further designed;

[0053] S4: Three robust weighted state fusion time-varying Kalman estimators are proposed in a unified framework, and it is proved that the three robust weighted state fusion time-varying Kalman estimators are robust under the defined assumptions;

[0054] S5: A simulation example is demonstrated using a multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties.

[0055] The following is a further explanation based on the specific execution steps:

[0056] In step S1, a reasonable system model is designed for the qualified multi-sensor networked system, and appropriate assumptions and definitions are made for the variables therein.

[0057] Specifically, the qualified multi-sensor networked system model is:

[0058]

[0059]

[0060] v i (t)=D i w(t)+η i (t)

[0061]

[0062] And it satisfies the following assumptions:

[0063] ξ i (t)∈R 1 , ζ i (t)∈R 1 , and γ i (t)∈R 1 , i = 1, …, L are uncorrelated Bernoulli white noises taking values of 0 or 1, and have known probabilities Prob(ξ i (t)=1)=π i , Prob(ξ i (t)=0)=1 - π i , Prob(γ i (t)=1)=λ i , Prob(γ i (t)=0)=1 - λ i , where π i , and λ i are known, and 0 ≤ π i ≤ 1, and 0 ≤ λ i ≤ 1. In addition, ξ i (t), ζ i (t) and γ i (t) are uncorrelated with other random signals;

[0064] w(t), η i (t), α k (t) and β k (t) are uncorrelated zero-mean white noise sequences, and their covariance is

[0065]

[0066] in, and They are white noise w(t),η i (t),α k (t) and β k The unknown uncertain actual / true variance of (t), δ kj represents the Kronecker function, δ kk =1,δ kj =0(k≠j);

[0067] Initial state x(0) and random signal w(t),η i (t),α k (t),β k (t),ξ i (t),ζ i (t) and γ i (t) is not relevant, and where μ 0 is the known mean of x(0), P 0 is its unknown uncertain actual variance;

[0068] Q, and P 0 They are and A known conservative upper bound of .

[0069] Based on the above assumptions, the problem solved in the present invention is to design a robust local and fusion time-varying Kalman estimator (predictor, filter, smoother) for the assumed state in an uncertain multi-sensor networked system. So that for all allowed uncertainties, their actual steady-state estimate error variance With the corresponding minimum upper bound P θ (t|t+N), that is

[0070]

[0071] Among them, θ=i,m,s,d represents the i-th local robust estimator, the matrix-weighted fusion estimator, the diagonal matrix-weighted fusion estimator, and the scalar-weighted fusion estimator, respectively.

[0072] The purpose of step S2 is to transform the system model into a multi-model multi-sensor system containing only uncertain noise variance, firstly into the following multi-model augmented system:

[0073] x ai (t+1)=Φ ai (t)x ai (t)+Γ ai (t)w ai(t)

[0074] y i (t) = H ai (t)x ai (t)+G ai (t)v i (t)

[0075] To better describe the system model, define

[0076] x ai (t) = [x(t) z i (t-1) z i (t-2)] T ,w ai (t) = [w T (t) v i T (t)] T

[0077]

[0078] Definition iz (t),ζ iz (t),γ iz (t), and is uncorrelated white noise. Then we get Φ ai (t),Γ ai (t), Η ai (t) and G ai (t) The respective random deviation terms and From the calculation, we know that and Contains α k (t),β k (t),ξ iz (t),ζ iz (t),γ iz (t), and And from the above description, we can know that they are all uncorrelated white noise. Therefore, the original system with multiplicative noise, multi-step random delay, missing measurement value and uncertain noise variance will be transformed into the following system with multiplicative noise and uncertain actual noise variance and Augmented multi-model multi-sensor system.

[0079]

[0080] in

[0081]

[0082] The augmentation method used in step S2 is state augmentation. By adding the system's delay measurement or other uncertainties that need to be considered as additional state variables to the state vector, the original Kalman filtering problem is converted into an augmented state space problem. The augmentation method can fuse data from multiple sensors or information sources to improve the accuracy and reliability of the measurement. It is suitable for dynamically changing systems and can update state estimates in real time to adapt to system changes. This method retains the state space representation and simplifies the extension of delay processing methods to other methods, such as moving horizon estimation (MHE), nonlinear dynamic data coordination (NDDR), unscented Kalman filter (UKF), particle filter, etc.

[0083] Furthermore, augmented noise and augmented state vector x are introduced g (t), augmented noise δ fi (t) is

[0084]

[0085] in

[0086]

[0087] According to w fi (t) and v fi The calculation of the actual and conservative cross-covariance of (t) gives the augmented noise δ fi (t) and δ fj The actual and conservative cross-covariances of (t) are

[0088]

[0089] in

[0090]

[0091] Define the augmented noise δ fi The actual variance and conservative variance of (t) are and Λ fi (t) = Λ fii (t).

[0092] For all allowed uncertain actual variances and have

[0093] By augmenting the state vector, the system state variable estimation that needs to be performed simultaneously during the identification process can be reduced, thereby reducing the computational workload and improving computational efficiency.g (t) is expressed as follows

[0094]

[0095] Its actual and conservative second-order non-central distance and X g (t) are

[0096]

[0097] The second-order noncentral distance is a characteristic number that describes the characteristics of a random variable. It provides information about the shape of the distribution of the random variable, especially the distribution characteristics beyond the mean and variance. Calculating the actual and conservative second-order noncentral distances can help us understand the statistical properties of random variables more comprehensively. The actual second-order noncentral distance of the augmented state vector can be used to analyze the stability of the system. By considering the noncentral distance, the behavior of the system in the face of uncertainty and external disturbances can be more accurately evaluated, thereby improving the robustness of the system.

[0098] For all allowed uncertain actual variances and have

[0099] The formation and proof process of the weighted fusion time-varying Kalamn estimator during the execution of step S3 and step S4 is as follows: Figure 2 shown.

[0100] First, the robust local time-varying Kalman estimator is formulated, where the predictor is

[0101]

[0102]

[0103] Filters and smoothers are of the following form:

[0104]

[0105] For a known conservative noise variance Q,R ηi , and P 0 The worst-case original multi-sensor system is given by using the optimal weighted fusion rule to unify the three robust weighted fusion time-varying Kalman estimators of the original system as follows:

[0106]

[0107] The weighted fusion rule in step S4 is as follows:

[0108] First of all, the optimal weighted fusion rule is a method used in multi-sensor data fusion. Its core idea is to obtain more accurate fusion results by assigning different weights to the data of different sensors. It improves the overall prediction accuracy by combining the prediction results of multiple models, and the weight of each model can be determined during the training process through cross-validation. In a multi-sensor system, the distribution of weights has a significant impact on the fusion effect. If the weights are properly distributed, the fusion effect is good; if the distribution is unreasonable, the system accuracy and reliability will not be improved much.

[0109] In the sense of linear minimum variance, there are three weighting methods for weighted fusion: 1. Matrix weighting; 2. Scalar weighting; 3. Diagonal weighting. The advantages and disadvantages of these three weighting methods are mainly analyzed from the perspective of computational complexity and error. Computational complexity: matrix weighting > diagonal weighting > scalar weighting; error: scalar weighting > diagonal weighting > matrix weighting.

[0110] In matrix weighted fusion, the weight is a matrix, which means that more factors are taken into account when calculating the weight matrix. The fused state value is also composed of multiple state values, so the estimated value calculated by this method has a smaller estimation error. This method is suitable for situations where the state space model is more complex and there is correlation between the states. Since it involves matrix operations, the amount of calculation is relatively large, but it can provide more accurate fusion results.

[0111] Diagonal matrix weighting is actually a special case of scalar weighting, in which the weights appear in the form of a diagonal matrix, which means that each state value has a corresponding weight, but the weights between different states are independent. This method is more sophisticated than simple scalar weighting because it allows different weights to be given to each state dimension, which may result in better estimation accuracy than scalar weighting. The amount of computation is between scalar weighting and matrix weighting.

[0112] Scalar weighted fusion is the simplest information fusion method, in which all sensor observations are multiplied by a common scalar weight. This method takes fewer factors into account, so the estimation error is relatively large. It is suitable for simple systems or when the information provided by sensors is similar in all dimensions. Since it only involves scalar calculations, it has the least amount of computation, but may sacrifice some fusion accuracy.

[0113] The 3 matrix weights include:

[0114] The optimal matrix weight is

[0115]

[0116] The optimal diagonal matrix weights are

[0117] [ω1j (t|t+N),…,ω Lj (t|t+N)]=[e T (P jj (t|t+N)) -1 e] -1 e T (P jj (t|t+N)) -1 ,j=1,…,n

[0118]

[0119] The optimal scalar weight is

[0120]

[0121] Where θ=m,d,s represents matrix weighting, diagonal matrix and scalar weighted fusion, e is the identity matrix with matrix elements equal to 1, and P is the corresponding augmented conservative covariance matrix.

[0122] The multi-sensor single-channel ARMA signal in step S5 means that in a multi-sensor system, the signal observed by each sensor can be modeled as an autoregressive moving average (ARMA) process. The ARMA model is one of the commonly used models in time series analysis. It combines the characteristics of the autoregressive (AR) model and the moving average (MA) model, and can describe the dynamic characteristics of time series data and the influence of random disturbances. In a multi-sensor system, the ARMA model can be used for information fusion. By weighting by matrix, diagonal matrix and scalar, the estimation accuracy can be improved, and information fusion, filtering and smoothing problems can be uniformly handled. The specific design is mainly divided into the following steps:

[0123] First, the order of the ARMA model needs to be determined (i.e., the order p of the AR part and the order q of the MA part). This can be done by analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) plots of the time series. An ACF plot showing tailing (i.e., the autocorrelation values ​​slowly decrease to zero) may indicate the suitability of an AR model, while a PACF plot that is truncated after a certain order may indicate the suitability of an MA model.

[0124] Secondly, after determining the order of the ARMA model, the next step is to estimate the model parameters. This can be done by methods such as maximum likelihood estimation (MLE) or least squares (OLS). The purpose of parameter estimation is to find the best (autoregressive coefficients) and (moving average coefficients).

[0125] Finally, after the model is fitted, it needs to be tested to ensure its suitability. Once the model passes the test, it can be used to predict future values. ARMA models generally perform well in short-term time series forecasting, especially when the data has significant autocorrelation and random fluctuations.

[0126] Specifically consider the following multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties

[0127] A t (q -1 )s(t)=u(t)

[0128] z i (t) = s(t) + r(t) + η i (t)

[0129] B t (q -1 )r(t)=e(t)

[0130] The ARMA signal model with random parameters can be transformed into an equivalent state space model as follows

[0131] x s (t+1)=Φ s (t)x s (t)+Γ s (t)u(t)

[0132] s(t)=H s x s (t)+u(t)

[0133] The colored observation noise has an equivalent state space model:

[0134] x r (t+1)=Φ r (t)x r (t)+Γ r e(t)

[0135] r(t)=H r (t)x r (t)+e(t)

[0136] Specifically, by combining the process of converting the signal model into the original system model that meets the conditions, we can obtain s(t) = H s x s (t)+u(t)=[H s (0) 1×n ]x(t)+u(t), therefore, the robust signal estimation problem can be solved by the corresponding robust local state estimation. The estimation error of the signal s(t) is

[0137] The cross covariance of the actual and conservative local estimation errors of the signal s(t) is expressed as

[0138] N=-1,N≥0

[0139] Through the proof in the above steps, it is easy to conclude that the error variance of the signal s(t) is also robust. And there is the following relationship:

[0140]

[0141] tP m (t|t+N)≤trP d (t|t+N)≤trP s (t|t+N)≤trP i (t|t+N),i=1,…,L

[0142] The entire ARMA signal application process is as follows Figure 3 shown.

[0143] Furthermore, the present invention is also illustrated by a simulation example:

[0144] In this example, we assume n=2, L=3, and define

[0145]

[0146] λ 1 =0.8,λ 2 =0.85,λ 3 =0.8,a 1 =-0.85,a 2 =-0.045,b 1 =-0.6, Figure 4 The traces of the conservative and actual local and fused time-varying Kalman prediction error variances are given. Since the traces of the error variances of the three weighted fusion time-varying predictors are the same, the three lines are displayed as a green line in the figure. The trajectory shown in the figure verifies the time-varying accuracy relationship.

[0147] Since matrix weighting, scalar weighting, and diagonal weighting have the same effect, Figure 5 In the figure, only the effect curve of matrix weighted fusion is given. Compared with the robust local time-varying predictor, the robust matrix weighted fusion time-varying predictor s m (t|t+1) has better tracking performance.

[0148] In order to better verify the proposed technology, in addition to the simulation application of the signal s(t), the inventors also provide relevant simulation results of the system state, the specific situation is as follows:

[0149] Consider the following system model:

[0150]

[0151] Assuming that the system is observed by three sensors, i.e. L=3, and considering the time delay and packet loss in the data transmission process, the problem is to design a robust weighted fusion time-varying Kalman estimator for the above three-sensor networked uncertain system.

[0152] Table 1 Comparison of time-varying robust accuracy and actual accuracy when t = 100

[0153]

[0154] In the simulation experiment,

[0155]

[0156] H 3 =[0 0 1; 1 0 0],H 11 =H 21 =H 31 =[1 0 0; 0 0 0],H 12 =H 22 =H 32 =[0 0 0; 0 01],π 1 =0.8,π 2 =0.88,π 3 =0.85, λ 1 =0.8,λ 2 =0.9,λ 3 =0.9, Q=8.5,

[0157] D 1 =[0.10.2] T ,D 2 =[0.10.1] T ,D 3 =[0.10] T ,The simulation results are as follows:

[0158] Table 1 gives the comparison between the time-varying robust accuracy and the actual accuracy at t=100, which verifies the accuracy relationship given by equation (5.24). The robust accuracy of the smoother is higher than that of the filter, while the robust accuracy of the filter is higher than that of the predictor.

[0159] Figure 6 The first component of the robust local and weighted fusion time-varying filter is given The tracking effect of the three robust weighted fusion time-varying predictors can be clearly seen. Compared with the robust local time-varying filter, the three robust weighted fusion time-varying predictors have better tracking performance. The tracking performance is the best.

[0160] To illustrate The robustness of the noise is arbitrarily determined by taking three different actual noise variances

[0161]

[0162] It is easy to obtain the corresponding three robust scalar weighted fusion time-varying one-step smoothers and the corresponding actual and conservative robust scalar weighted fusion time-varying one-step smoothing error variances and P d (t|t). The actual error curves of the first components of the corresponding three fused smoothers and their 3 times standard deviation bounds are Figure 7 The actual fusion smoothing error curve is shown in , where the solid line represents the actual fusion smoothing error curve. Figure 7 It can be seen that for each error curve, more than 99% of the fusion smoothing error values ​​are located at and between and also between and This verifies the robustness of the first component of the robust scalar weighted fusion step smoothing and the actual standard deviation correctness.

[0163] In summary, the following conclusions are drawn: For a multi-sensor networked system with the same state-dependent multiplicative noise in the system state transfer matrix and the observation matrix, as well as noise-dependent multiplicative noise, uncertain noise variance, two-step random observation lag and packet loss, the augmentation method, derandomization method and virtual noise technology are applied to transform it into a multi-model multi-sensor system with only uncertain noise variance. According to the minimax robust estimation principle, a robust local Kalman estimator is proposed. According to the three fusion methods of matrix weighted fusion, scalar weighted fusion and diagonal weighted, a robust weighted fusion time-varying Kalman estimator is proposed. The relationship between the robustness of the estimator and the accuracy of the estimator is proved, and the accuracy of the proposed method is verified through simulation examples.

[0164] Compared with the prior art, the present invention has the following beneficial effects:

[0165] 1. The system model simultaneously considers multiplicative noise, two-step random time lag, measurement loss and uncertain noise variance in different situations, which better reflects the actual situation.

[0166] 2. Aiming at the multi-sensor networked system with mixed uncertainty, a robust local fusion time-varying Kalman estimator is proposed. The principle is to design robust local time-varying Kalman filter and smoother based on the robust local fusion time-varying Kalman predictor respectively. Three robust weighted state fusion time-varying Kalman estimators are proposed under a unified framework.

[0167] 3. Time-varying weighting can adapt to the dynamic changes of the system and environment, so that the estimator can update the state estimation in real time and adapt to the dynamically changing system. According to different weighting schemes, the fusion strategy can be flexibly adjusted to adapt to different application scenarios and sensor configurations.

[0168] 4. An example of ARMA signal processing is given, which shows that the robust weighted state fusion estimation problem of the signal can be solved by the state estimation problem. The reliability of the proposed technical solution can be better seen by recording the tracking diagram and the error variance table.

[0169] What is disclosed above is only a preferred embodiment of the present invention, and it certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A robust fusion estimation method for dealing with two-step random time delay and missing observation uncertainty, characterized in that: The following steps are involved: Step 1: Build a multi-sensor networked system model as the original system; Step 2: applying augmentation method, de-randomization method and virtual noise technology, transforming the multi-sensor network system model into a multi-model multi-sensor system containing only uncertain noise variance; Step 3: Based on the minimax robust estimation principle, obtain the local optimal time-varying Kalman predictor, and then further design the robust local time-varying Kalman filter and smoother respectively; Step 4: Three robust weighted state fusion time-varying Kalman estimators are proposed in a unified framework, and it is proved that the three robust weighted state fusion time-varying Kalman estimators are robust under the defined assumptions; Step 5: A simulation example is demonstrated using a multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties.

2. The robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty as claimed in claim 1, characterized in that: The expression of the multi-sensor networked system model is as follows: v i (t)=D i w(t)+η i (t) And meet the following assumptions: ξ i (t)∈R 1 , i (t)∈R 1 , and γ i (t)∈R 1 , i = 1, ..., L is an uncorrelated Bernoulli white noise with a value of 0 or 1 and a known probability Prob(ξ i (t) = 1) = π i ,Prob(ξ i (t) = 0) = 1 - π i , Prob(γ i (t) = 1) = λ i ,Prob(γ i (t) = 0) = 1 - λ i , where π i , and λ i is known, and and 0≤λ i ≤1; In addition, ξ i (t),ζ i (t) and γ i (t) uncorrelated with other random signals; w(t),η i (t),α k (t) and β k (t) are mutually uncorrelated zero-mean white noise sequences, and their covariance is in, and They are white noise w(t),η i (t),α k (t) and β k The unknown uncertain actual / true variance of (t), δ kj represents the Kronecker function, δ kk =1,δ kj =0(k≠j); The initial state x(0) and the random signal w(t),η i (t),α k (t),β k (t),ξ i (t),ζ i (t) and γ i (t) is not relevant, and Where μ0 is the known mean of x(0), and P0 is its unknown uncertain actual variance; Q,R ηi , and P0 are and A known conservative upper bound of .

3. The robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty as claimed in claim 2, characterized in that: During the execution of step 2, the state augmentation method is used to transform the model in the robust Kalman filter. At the same time, the behavior of the system in the face of uncertainty and external disturbances is evaluated by calculating the actual and conservative second-order non-center distances, and augmented noise is further introduced to improve the robustness of the filter.

4. The robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty as claimed in claim 3, characterized in that: In step 3, the expression of the local optimal time-varying Kalman predictor is as follows: The robust local time-varying Kalman filter and smoother are as follows:

5. The robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty as claimed in claim 4, characterized in that: The execution process of step 4 is to adopt the optimal weighted fusion rule to uniformly give three robust weighted fusion time-varying Kalman estimators of the original system model, and obtain their corresponding conservative fusion error variances based on the three weighted weights. Further, based on the robust time-varying Kalman estimator under the unified model, the corresponding actual and conservative weighted fusion Kalman estimation error variances with a unified form are obtained. Finally, combining the assumptions and corresponding theorems, it is proved that the three robust weighted fusion time-varying Kalman estimators are robust under the conditions defined by the assumptions.

6. The robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty as claimed in claim 5, characterized in that: The three matrix weights in the optimal weighted fusion rule are as follows: The optimal matrix weight is The optimal diagonal matrix weights are The optimal scalar weight is Where θ=m,d,s represents matrix weighting, diagonal matrix and scalar weighted fusion, e is the identity matrix with matrix elements equal to 1, and P is the corresponding augmented conservative covariance matrix.

7. The robust fusion estimation method for coping with two-step random time delay and missing observation uncertainty as claimed in claim 6, characterized in that: The execution process of step 5 specifically considers the multi-sensor single-channel ARMA signal with colored noise and multiple uncertainties, and designs the corresponding robust local and fusion Kalman estimators based on this signal, and converts it into the form of a special case of the original system model, and it is concluded that the error variance of the signal s(t) is also robust. Finally, the tracking diagram of the ARMA signal simulation instance and the error variance curve are analyzed to verify the feasibility of the technical solution.

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