An adaptive kalman noise estimation method and system based on data fusion

Abstract

This invention relates to an adaptive Kalman noise estimation method and system based on data fusion. The method includes using multiple sensors to track a dynamic target and acquiring observations from each sensor; performing a first data fusion based on the observations from the first two sensors to obtain first fused data; performing a second data fusion using the first fused data and the observations from the next sensor to obtain second fused data; and so on, completing the data fusion of observations from multiple sensors to obtain fused observations from multiple sensors; and obtaining estimates of the process noise covariance matrix and measurement noise covariance based on the fused observations from multiple sensors. This invention improves the accuracy of measurement data by fusing measurement sequences obtained from multiple sensors, and solves the filtering problem of unknown second moments in the noise statistical characteristics of the Kalman model.

Description

Technical Field

[0001] This invention belongs to the field of noise estimation technology, specifically relating to an adaptive Kalman noise estimation method and system based on data fusion. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of advanced navigation technologies and the widespread deployment of low-cost sensors, KF (Knowledge Filtering) has become the most important estimation technique in multi-sensor fusion integration, such as robot localization, integrated navigation, and network reversal. Classical or standard KF is optimal when obtaining accurate statistical information on process noise and measurement noise. However, due to factors such as noise dependence on the environment and uncertainties in system dynamics, the constraints of KF are too strong in practical applications and cannot always meet actual needs. Uncertainties in process noise have a significant impact on KF, and can even lead to filter divergence. To reduce the impact of inaccurate statistical information, various extensions of KF have emerged and achieved good results.

[0004] Generally, Kalman Fibonacci (KF) can be viewed as a model-based algorithm for recursively estimating the state mean vector and covariance matrix. The process of obtaining the KF gain matrix is ​​completely unaffected by any information during the measurement update process, indicating that the update of the KF gain matrix is ​​independent of the measurement update process. However, in practical applications, the accuracy of KF is questionable due to the unknown second moments in the noise statistics. To address this issue, existing technology proposes an adaptive KF algorithm (Measurement Sequence Adaptive KF, MSAKF) based on adaptive estimation of the process noise covariance matrix using the measurement sequence and adaptive estimation of the measurement noise covariance matrix using the innovation sequence. This algorithm calculates the estimated values ​​of the process noise covariance matrix and the measurement noise covariance matrix using information from the measurement sequence and the innovation sequence, respectively.

[0005] However, the accuracy of the MSAKF measurement sequence is not well guaranteed when using measurement sequence information to obtain the process noise covariance matrix. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes an adaptive Kalman noise estimation method and system based on data fusion. This invention solves the filtering problem of unknown second moments in the noise statistical characteristics of traditional Kalman models. To obtain satisfactory optimal estimation results, the algorithm obtains estimates of the process noise covariance and measurement noise covariance using both the measurement fusion sequence and the innovation sequence.

[0007] According to some embodiments, the first solution of the present invention provides an adaptive Kalman noise estimation method based on data fusion, which adopts the following technical solution:

[0008] An adaptive Kalman noise estimation method based on data fusion includes:

[0009] Multiple sensors are used to track dynamic targets, and the observation values ​​of each sensor are obtained;

[0010] The first data fusion is performed based on the observations from the first two sensors to obtain the first fused data;

[0011] The second fused data is obtained by fusing the first fused data with the observations from the next sensor.

[0012] By doing so, the observation data from multiple sensors are fused to obtain the fused observation data from multiple sensors;

[0013] A sample sequence is constructed based on the fusion observations of multiple sensors, and the estimated values ​​of the process noise covariance matrix and the measurement noise covariance matrix of the sample sequence are calculated.

[0014] According to some embodiments, the second aspect of the present invention provides an adaptive Kalman noise estimation system based on data fusion, employing the following technical solution:

[0015] An adaptive Kalman noise estimation system based on data fusion includes:

[0016] The data acquisition module is configured to use multiple sensors to track dynamic targets and acquire the observations from each sensor.

[0017] The data fusion module is configured to perform a first data fusion based on the observations of the first two sensors to obtain the first fused data; then perform a second data fusion by combining the first fused data with the observations of the next sensor to obtain the second fused data; and so on, to complete the data fusion of observations from multiple sensors to obtain the fused observations from multiple sensors.

[0018] The noise estimation module is configured to construct a sample sequence based on fused observations from multiple sensors, and to calculate the process noise covariance matrix estimate and measurement noise covariance estimate of the sample sequence.

[0019] According to some embodiments, a third aspect of the present invention provides a computer-readable storage medium.

[0020] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the data fusion-based adaptive Kalman noise estimation method described in the first aspect above.

[0021] According to some embodiments, a fourth aspect of the present invention provides a computer device.

[0022] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the steps of an adaptive Kalman noise estimation method based on data fusion as described in the first aspect above.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0024] This invention improves the accuracy of measurement data by fusing measurement sequences obtained from multiple sensors. It obtains estimates of process noise covariance and measurement noise covariance by using the fused measurement sequence and the innovation sequence, respectively, thus solving the filtering problem of unknown second moments in the noise statistical characteristics of the Kalman model. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 This is a flowchart of the method described in an embodiment of the present invention;

[0027] Figure 2 In this embodiment of the invention, the MSAKF, LKF, and MFSAKF filtering algorithms are used to estimate X respectively. 1,k A schematic diagram;

[0028] Figure 3 yes Figure 2 Enlarged schematic diagram of the horizontal axis [4.1-5];

[0029] Figure 4 yes Figure 2 Enlarged schematic diagram of the horizontal axis [7.3-7.75];

[0030] Figure 5 This is a schematic diagram of the RMSE estimated using the MSAKF, LKF and MSFAKF filtering algorithms in the embodiments of the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0032] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0034] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0035] Example 1

[0036] like Figure 1 As shown, this embodiment provides an adaptive Kalman noise estimation method based on data fusion. This embodiment uses the application of this method to a server as an example for illustration. It is understood that this method can also be applied to terminals, and can also be applied to systems including terminals, servers, and other components, and can be implemented through interaction between the terminal and the server. The server can be an independent physical server, a server cluster composed of multiple physical servers, or a distributed system. It can also be a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network servers, cloud communication, middleware services, domain name services, CDN security services, and big data and artificial intelligence platforms. The terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. The terminal and server can be directly or indirectly connected via wired or wireless communication, which is not limited in this invention. In this embodiment, the method includes the following steps:

[0037] (1) Use multiple sensors to track dynamic targets and obtain the observation values ​​of each sensor. For example, in a vehicle model, the observation values ​​could be lateral acceleration, yaw rate, or front wheel steering angle, etc.

[0038] (2) The first data fusion is performed based on the observations from the first two sensors to obtain the first fused data;

[0039] (3) The first fused data is fused with the observations from the next sensor to obtain the second fused data;

[0040] (4) By analogy, the observation data of multiple sensors are fused to obtain the fused observation values ​​of multiple sensors;

[0041] (5) Construct a sample sequence based on the fusion observations of multiple sensors, and calculate the estimated value of the process noise covariance matrix and the estimated value of the measurement noise covariance matrix of the sample sequence.

[0042] The method of this embodiment will be described in detail below:

[0043] 1. First, the classic Kalman filter will be explained as follows:

[0044] Consider the following model:

[0045]

[0046] Among them, X k ∈R n It is the state matrix; Z k ∈R m It is a measurement matrix; A∈R n×n It is the state transition matrix; H∈R m×n It is the observation matrix; G∈R n×l It is the input matrix. W k It is process noise, V k It is measurement noise, and it is uncorrelated, zero-mean Gaussian white noise with variances satisfying:

[0047]

[0048] Q is the process noise covariance matrix, R is the measurement noise covariance matrix, and δ i,j Let δ be the Kronecker function, and when i = j i,j =1, otherwise 0.

[0049] Assumption 1: The initial state value X0 is independent of the process noise W k and measurement noise V k ,satisfy:

[0050]

[0051]

[0052] in

[0053] Based on equation (1), the classic Kalman filtering process can be divided into two steps.

[0054] Step 1

[0055]

[0056] P k,k-1 =AP k-1 A T +GQG T

[0057] It is a priori state estimation; It is a posterior state estimate; P k-1P is the filter estimation error covariance matrix; k,k-1 This is the covariance matrix of the one-step forecast estimation error.

[0058] Step 2:

[0059] K k =P k,k-1 H T HP k,k-1 H T +R] -1

[0060]

[0061] P k =[IK k H]P k,k-1

[0062] Among them, K k This is the Kalman filter gain matrix; It is a posterior state estimate; Z k ∈R m It is a measurement matrix.

[0063] 2. Data fusion of individual data points

[0064] Suppose a data x k There are k observations (y1, y2, ... y k If we want to use these observational data to obtain an estimate of the true value... The natural thought would be to take the average. Let's assume... but:

[0065]

[0066] As can be seen from equation (2), as the value of k increases, 1 / k decreases, meaning that when there is a large amount of data, the measurement at the current moment is less important. Conversely, when k is relatively small (when there is not much data), it is more dependent on the current measurement. Generalizing (2), we get:

[0067]

[0068] If M = 1 / k, and two sensors are used simultaneously to acquire measurements, with standard deviations σ1 and σ2 respectively, and these measurements conform to a normal distribution, then a data point L is given. The values ​​measured by the two sensors at the same time are L1 and L2. Based on L1 and L2, an estimate of the true value L can be obtained.

[0069]

[0070] if only variance As small as possible The closer the value is to the true value, the better:

[0071]

[0072] Differentiating both sides of equation (5) with respect to M, we get:

[0073]

[0074] Substituting equation (6) into equation (5), we can obtain

[0075]

[0076] The above describes data fusion of data measured by two sensors. From another perspective, it can also be seen as fusing two sensors into a "new sensor," whose standard deviation is... The estimated value is closest to the true value when M takes the value of equation (6).

[0077] 3. Measurement sequence fusion under multiple sensors

[0078] Kalman-based data fusion, including state vector fusion and measurement vector fusion, has been extensively studied in the last decade. This embodiment selects the measurement vector fusion method primarily because it can directly fuse sensor measurements to obtain weighted or combined measurements, and then use a single Kalman filter to obtain the final state estimate based on the fused observations. The measurement vector fusion method generally exhibits good estimation performance and features parallel implementation and fault tolerance mechanisms.

[0079] The multi-sensor measurement model is constructed as follows:

[0080] Z k =HX k +V k

[0081] Suppose there are i sensors, where (1 ≤ s ≤ i):

[0082]

[0083] It is the t-th component measured by the s-th sensor at time k (1≤t≤m).

[0084] As can be seen from the above, each component in matrix (8) can be fused based on the data fusion method of a single data. Therefore, based on equations (4)-(7), we can... Performing i-1 data fusions yields an (r×1) matrix. The detailed process of i-1 data fusions is as follows: the data measured by the first two sensors undergoes the first data fusion; the fused data is then fused with the data measured by the third sensor, and so on, up to the data measured by the i-th sensor, for a total of i-1 fusions. It is not difficult to deduce that:

[0085]

[0086] in:

[0087]

[0088] σ j σ represents the measurement variance of the j-th sensor; (j) Let represent the sensor measurement variance after the (j)th data fusion.

[0089] This represents the difference between the (p+1)th sensor and the sensor after data fusion at time k, specifically the v-th component.

[0090] When p = 1; This represents the p-th component after the v-th data fusion.

[0091] 4. Recursive estimation of multi-sensor sample sequences

[0092] In noise W k and V k When reliable statistical information is limited, the estimation of the process noise covariance matrix and the measurement noise covariance matrix is ​​carried out as follows:

[0093] First, the following assumptions and lemmas are given.

[0094] Lemma 1: Let (x1, x2, ..., x n If is a subsample sequence drawn from the population x, then we have the following statistic.

[0095] Assumption 2: Given a random variable D satisfying D = S + F, where S and F have a mean of 0 and are uncorrelated, and the variance of S is B. Consider an independent and identically distributed sample η of vector D. i (i = 1, 2, ...). From real-time samples η i The exact covariance matrix of F can be obtained from this.

[0096] Theorem 1: Under Assumption 2, the variance of F can be estimated as:

[0097]

[0098] Proof: Based on basic statistical knowledge, we can obtain:

[0099]

[0100] Since E{D}=0, according to the law of large numbers, we get:

[0101]

[0102] Furthermore, S and F are uncorrelated, therefore:

[0103] cov(D)=cov(S)+cov(F) (13)

[0104]

[0105] Therefore, in order to recursively estimate the covariance matrix of F, n takes a large value N, and the following statistical results can be used:

[0106]

[0107] Proof established #

[0108] ① The estimation of the process noise covariance matrix (Q) is as follows:

[0109] To complete the estimation, constructing a noisy sample sequence becomes urgent. From equation (1), based on the measurement sequence from the initial time to time k, a new measurement model is calculated:

[0110]

[0111] Where: X1 represents the initial state value of the system; Represents the sensor measurement sequence; Indicates process noise column; This represents the sensor measurement noise sequence; Represents the extended input matrix; This represents the system's observable matrix.

[0112] in,

[0113] The right-hand side of equation (16) can be divided into two parts: the first part is the initial state value X1 of the system, and the second part is the noise sequence W. k and V k Considering the difficulty of obtaining the precise value of X1 in advance, X1 can be considered to be an unknown constant perturbation to some extent.

[0114] Assumption 3: If there exists a suitable constant matrix β∈R d×km Make:

[0115]

[0116] Then we have:

[0117]

[0118] Thus, equation (18) contains only the noise sequence, since W k and V k It is zero-mean, uncorrelated white noise, therefore

[0119]

[0120] Here, diag() represents a diagonal matrix. In diag(Q...Q) and diag(R...R), the number of Q and R is k, which will not be explained further.

[0121]

[0122] And for For example, its sample sequence is θ i (i = 1, 2, 3, ...), according to (15)-(20):

[0123]

[0124] To describe (21) more clearly, several new symbols Π, μ, ρ will be introduced, let:

[0125]

[0126]

[0127] then,

[0128]

[0129] Furthermore, ρ = μ1 + ... + μ k When the rank of ρ is l, there exists a ρ+ matrix that satisfies the following equation:

[0130] ρ + ρ=I l×l (twenty four)

[0131] Where I l×l Let represent an l-order identity matrix, and ρ+ be the generalized inverse of matrix ρ. Then we have;

[0132] Q = ρ + Π(ρ + ) T (25)

[0133] Based on equation (25), Q can be estimated in real time according to the system measurements. As an estimate of Q, Π k As a real-time calculation of Π, the final result is:

[0134]

[0135]

[0136] ②The estimation process of the process noise covariance matrix (R) is as follows:

[0137] Considering the unknown precise statistical measurement noise covariance matrix R and the innovation sequence There is a certain relationship:

[0138]

[0139] The new information sequence is obtained by a simple transformation of equation (1).

[0140] For linear time-varying systems, we can easily obtain the following C k The estimated value:

[0141]

[0142] In this case, the estimated value C k Substituting into (28), we can finally obtain the estimated value of the covariance matrix R:

[0143]

[0144] Generally, the successful use of KF is severely limited by process noise and measurement noise statistics. While the MSAKF algorithm solves this problem, its accuracy still needs optimization. Based on this, this embodiment proposes a new (MSFAKF) algorithm to address this issue. In this algorithm, when the measurement matrix H is full column rank, a suitable matrix β can be found that satisfies (17). To ensure the stability of the KF algorithm, the system should be controllable and observable. Additionally, the system measures Z... k It should be bounded, which is also satisfied by most physical systems. Based on the above estimation method, the covariance matrices Q and R can be estimated in real time, and thus applied to the KF estimation of the system state in (1). The specific implementation process of the algorithm in this embodiment is as follows:

[0145]

[0146]

[0147] This embodiment addresses the filtering problem of unknown second moments in the statistical characteristics of model noise. The classical Kalman Filter (KF) suffers from estimation errors in the process noise covariance matrix, which in turn corrupts the state estimation, and conversely, the state estimation error corrupts the process noise covariance matrix estimation, thus compromising the stability and optimality of the filter. This embodiment proposes a Measurement Sequence Fusion Adaptive Kalman Filter (MSFAKF) algorithm. To obtain satisfactory optimal estimation results, the algorithm obtains estimates of the process noise covariance and measurement noise covariance using both the measurement fusion sequence and the innovation sequence. Based on the MSFAKF algorithm, the unknown second-moment parameters in the noise statistical characteristics can be adaptively estimated according to the measurement sequence information.

[0148] 5. Simulation Verification

[0149] High-precision positioning and navigation are crucial for autonomous driving systems and advanced vehicle networks. In practical applications, phase-locked loops (PLLs) can be used to track Global Navigation Satellite System (GNSS) signals in environments with degraded signal characteristics. For PLL systems, filtering-based algorithms can be used to estimate the information parameters of the frequency-modulated signal. The signal of a PLL system can be described in the form of a differential equation:

[0150]

[0151] The system can be discretized to obtain:

[0152]

[0153] Where T = t k -t k -1 = kd represents the sampling time interval. Therefore, the phase-locked loop system can be represented as a discrete-time system:

[0154]

[0155] in:

[0156]

[0157] To verify the effectiveness of the MSFAKF algorithm, we used the algorithm in this embodiment to estimate the information parameters of a phase-locked loop frequency modulation signal with unknown noise statistics.

[0158] The simulation parameters are: kd = 0.9, T = 0.001, γ = 10, x 1，0 =0, x 2，0 =0, x 3，0 =0, estimated initial covariance P0 = 10 × I 3×3The input sinusoidal signal is sin(wt+φ), where wt = 2 and φ = 5. Three filtering algorithms—MSAKF, LKF, and MSFAKF—were implemented using Matlab, and the performance of MSFAKF, LKF, and MSAKF algorithms in phase-locked loop signal tracking was analyzed. Simulation results are as follows: Figures 2-5 As shown. From Figures 1-3 It can be seen that MSFAKF and MSAKF outperform LKF in navigation signal tracking. LKF is a filtering algorithm proposed by Rudolf E. Kalman in the 1960s. In LKF, the initial values ​​of the covariance matrices Q and R should be determined based on extensive engineering experience. Although appropriate initial values ​​should be chosen for LKF, its performance is relatively poor in practical applications due to the unknown second moments in the noise statistics. In the MSAKF algorithm, although the exact statistical characteristics of the noise cannot be known, they can be obtained by measuring information in the sequence. Therefore, the MSAKF algorithm can also track navigation signals quickly and accurately. Furthermore, the MSFAKF algorithm in this embodiment can accurately measure the sequence, making the unknown second moments in the obtained statistical characteristics more accurate, thus enabling more precise tracking of navigation signals.

[0159] Figure 5 The results show the root mean square error (RMSE) between the estimated and true values ​​obtained by the three filtering algorithms: MSFAKF, MSAKF, and LKF. Among these, LKF performs the worst. Of the MSAKF and MSFAKF algorithms, MSFAKF has the best accuracy.

[0160] Example 2

[0161] This embodiment provides an adaptive Kalman noise estimation system based on data fusion, including:

[0162] The data acquisition module is configured to use multiple sensors to track dynamic targets and acquire the observations from each sensor.

[0163] The data fusion module is configured to perform the first data fusion based on the observations from the first two sensors to obtain the first fused data;

[0164] The second fused data is obtained by fusing the first fused data with the observations from the next sensor.

[0165] By doing so, the data from multiple sensors are fused to obtain the fused observations from multiple sensors;

[0166] The noise estimation module is configured to obtain process noise covariance matrix estimates and measurement noise covariance estimates based on fused observations from multiple sensors.

[0167] It should be noted that the examples and application scenarios implemented by the above modules and corresponding steps are the same, but are not limited to the content disclosed in Embodiment 1 above. It should also be noted that the above modules, as part of a system, can be executed in a computer system such as a set of computer-executable instructions.

[0168] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0169] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and the division of modules described above is only a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed.

[0170] Example 3

[0171] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the adaptive Kalman noise estimation method based on data fusion as described in Embodiment 1 above.

[0172] Example 4

[0173] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the adaptive Kalman noise estimation method based on data fusion as described in Embodiment 1 above.

[0174] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of hardware embodiments, software embodiments, or embodiments combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computer-usable program code.

[0175] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0176] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0177] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0178] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0179] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An adaptive Kalman noise estimation method based on data fusion, characterized in that, include: Multiple sensors are used to track dynamic targets, and the observation values ​​of each sensor are obtained; In the vehicle model, the observed values ​​are lateral acceleration, yaw rate, or front wheel angle. The first data fusion is performed based on the observations from the first two sensors to obtain the first fused data; The second fused data is obtained by fusing the first fused data with the observations from the next sensor. Similarly, the data fusion of observations from multiple sensors is completed to obtain fused observations from multiple sensors; specifically, obtaining fused observations from multiple sensors involves: ;in, It is the t-th component measured by the s-th sensor at time k; Indicates the first p+1 The sensor and the first p-1 The sensor after data fusion at time k is... v The difference between the components; ; Let represent the measurement variance of the j-th sensor; Let (j) represent the sensor measurement variance after the (j)th data fusion. These are the standard deviations of the measurements obtained from the first two sensors; data fusion is performed on the measurement sequences obtained from multiple sensors to improve the accuracy of the measurement data and solve the filtering problem of unknown second moments in the noise statistical characteristics of the Kalman model; A sample sequence is constructed based on fused observations from multiple sensors. The estimated values ​​of the process noise covariance matrix and measurement noise covariance matrix of the sample sequence are then calculated. Specifically, it includes: ; ;in, , Represents the extended input matrix; ρ+ yes ρ The generalized inverse of a matrix. ρ=µ 1 +···+µ k , Let R be a constant matrix, and let diag() denote a diagonal matrix. In diag(R ... R), the number of R elements is k. θ i for βZ k The sample sequence; for The sample sequence; It is a measurement matrix. It is the measurement noise covariance matrix; Calculate the measurement noise covariance estimate of the sample sequence. Specifically, it includes: ;in, for The estimated value, To estimate the covariance matrix of the one-step forecast error, It is the observation matrix.

2. The adaptive Kalman noise estimation method based on data fusion as described in claim 1, characterized in that, The first data fusion is performed based on the observations from the first two sensors to obtain the first fused data, specifically: in, For data L The estimated value, Data respectively L The values ​​measured by two sensors at the same time; M=1 / k, where k is the number of observations.

3. The adaptive Kalman noise estimation method based on data fusion as described in claim 2, characterized in that, First Fusion Data The variance is: in, for standard deviation These are the standard deviations of the measurements obtained from the first two sensors.

4. The adaptive Kalman noise estimation method based on data fusion as described in claim 1, characterized in that, C k The estimated values ​​are as follows: in, For information sequence, R is the number of observations, and R is the covariance matrix. Let H be the covariance matrix of the one-step forecast estimation error, and H be the observation matrix.

5. An adaptive Kalman noise estimation system based on data fusion, characterized in that, include: The data acquisition module is configured to use multiple sensors to track dynamic targets and acquire the observations from each sensor. In the vehicle model, the observed values ​​are lateral acceleration, yaw rate, or front wheel angle. The data fusion module is configured to perform a first data fusion based on the observations from the first two sensors to obtain first fused data; then perform a second data fusion by combining the first fused data with the observations from the next sensor to obtain second fused data; and so on, to complete the fusion of observations from multiple sensors to obtain fused observations from multiple sensors; specifically, obtaining fused observations from multiple sensors involves: ;in, It is the t-th component measured by the s-th sensor at time k; Indicates the first p+1 The sensor and the first p-1 The sensor after data fusion at time k is... v The difference between the components; ; Let represent the measurement variance of the j-th sensor; Let (j) represent the sensor measurement variance after the (j)th data fusion. These are the standard deviations of the measurements obtained from the first two sensors; data fusion is performed on the measurement sequences obtained from multiple sensors to improve the accuracy of the measurement data and solve the filtering problem of unknown second moments in the noise statistical characteristics of the Kalman model; The noise estimation module is configured to construct a sample sequence based on fused observations from multiple sensors, and calculate the process noise covariance matrix estimate and measurement noise covariance estimate of the sample sequence. Specifically, it includes: ; ;in, , Represents the extended input matrix; ρ+ yes ρ The generalized inverse of a matrix. ρ=µ 1 +···+ µ k , Let R be a constant matrix, and let diag() denote a diagonal matrix. In diag(R ... R), the number of R elements is k. θ i for βZ k The sample sequence; for The sample sequence; It is a measurement matrix. It is the measurement noise covariance matrix; Calculate the measurement noise covariance estimate of the sample sequence. Specifically, it includes: ;in, for The estimated value, To estimate the covariance matrix of the one-step forecast error, It is the observation matrix.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the adaptive Kalman noise estimation method based on data fusion as described in any one of claims 1-4.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the adaptive Kalman noise estimation method based on data fusion as described in any one of claims 1-4.

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