A multi-sensor information fusion system based on Neyman-Pearson decision criterion

Abstract

The present invention discloses a multi-sensor information fusion system under the Neyman-Pearson decision criterion, aiming to overcome the problems of low credibility, low fault tolerance and poor integrity in the prior art. The system comprises multiple sensors and a fusion center, wherein the multiple sensors are used to obtain a multi-dimensional data set z, the fusion center is used to calculate observation data in the multi-dimensional data set z according to a maximum a posteriori probability criterion, the observation data is substituted into the Neyman-Pearson decision criterion for sequential judgment to obtain a single-sensor judgment result, the single-sensor judgment result is substituted into a Kalman filtering algorithm for filtering to obtain a filtered result, and information fusion is performed on the filtered result to obtain a multi-sensor information fusion result.

Description

Technical Field

[0001] The present invention relates to sensor data detection technology, and in particular to a multi-sensor information fusion system under the Neyman-Pearson decision criterion. Background Art

[0002] With the rapid development of technologies such as artificial intelligence, big data, 5G, and the Internet of Things, a growing number of smart sensors are transforming human lifestyles and even social structures through new products, technologies, industries, and models. Self-driving cars are one example of this. However, no single sensor can guarantee 100% detection accuracy. This leads to poor stability and insufficient precision in a single sensor, necessitating the need to extract and fuse high-quality data from multiple low-precision sensors.

[0003] To extract high-quality data from multiple low-precision sensors, existing technologies have disclosed a multi-layer, multi-source information fusion algorithm for rotorcraft UAV altitude measurement. This fusion is divided into two parts: the first part uses an adaptive spatiotemporal algorithm based on historical data, and the second part uses a traditional complementary filtering method to establish a dual spatiotemporal fusion model. This prior art belongs to the category of multi-sensor information fusion using filtering.

[0004] However, existing technologies are not perfect. While they effectively handle noise and errors in data, they do not consider the trustworthiness of the sensors themselves, resulting in low fault tolerance. Furthermore, as the number of sensors increases, the computational workload of the fusion center increases dramatically, and time lag issues become increasingly prominent, resulting in lower overall performance of multi-sensor fusion systems. Summary of the Invention

[0005] In order to overcome the deficiencies and problems of the prior art, the present invention provides a multi-sensor information fusion method and system under the Neyman-Pearson decision criterion, which is based on statistical decision and the Neyman-Pearson (NP) criterion.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a multi-sensor information fusion system under the Neyman-Pearson decision criterion, comprising:

[0008] A plurality of sensors for acquiring a multi-dimensional dataset z;

[0009] The fusion center is used to calculate the observation data in the multidimensional data set z according to the maximum a posteriori probability criterion, substitute the observation data into the Neyman-Pearson decision criterion for sequential decision to obtain the single-sensor decision result, substitute the single-sensor decision result into the Kalman filter algorithm for filtering to obtain the filtering result, and perform information fusion on the filtering result to obtain the multi-sensor information fusion result.

[0010] Preferably, the fusion center is further configured to establish a number of sensors N, a length of a sensor measurement sequence M, and a Gaussian noise set of N sensors. The false alarm probability is P F The measurement model of the sensor is:

[0011]

[0012] Where H0 indicates that the detection signal is unacceptable, H1 indicates that the detection signal is acceptable, x[n] is the measurement sequence of sensor n at any time, n∈{0,1,…,N-1}, m∈{1,2,…,M}, w[n] is Gaussian white noise with zero mean and given variance, and the false alarm probability P F is the maximum allowable error of N sensors under Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L}, Δε is the error rate at the factory;

[0013] False alarm probability P F In the equation, L = 1 / Δε, N sensors have a false alarm probability P F The data matrix P under F ∈R N×L , R is the dimension;

[0014] Establishment n (m), P D 、P F 、P A 、P S and J, where χ n (m) is the vector set of the M observations of the n-th sensor, m∈{1,2,...,M}, P D is the sensitivity of any sensor, that is, the detection probability, P A is the probability of discarding unreliable sensors, P S is the probability of retaining the sensor for unreliable data, and J is the overall optimization goal;

[0015] Establishment n (m) satisfies the following formula:

[0016] χ n (m) = {x n(1),x n (2),…,x n (M)} (3);

[0017] P D and P F Just opposite, under H1 and H0, P D and P F The formula is as follows:

[0018]

[0019]

[0020] P A and P S The setting of P is due to the unpredictable disturbances that occur when the sensor is working. A and P S Satisfies the following formula:

[0021]

[0022] A reasonable decision for the sensor under the premise of meeting the error rate at the factory is to set a limit on the false alarm probability P F Within the allowable value range, the error probability P N Minimum, as follows:

[0023]

[0024] Among them, P F is the false alarm probability, D1 is the observed data under the detection probability, α is the allowable value, P N is the error probability;

[0025] Set J to satisfy the following formula:

[0026] J=λ z P N +∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0027] Among them, λ z is the likelihood ratio, and λ is a reasonable threshold.

[0028] The Neyman-Pearson decision criterion satisfies the false alarm probability P F Under the upper limit condition, maximize the detection probability P D .

[0029] Preferably, the fusion center is further configured to calculate the observation data in the multi-dimensional data set z of the sensor according to the maximum a posteriori probability criterion;

[0030] Set up to meet the false alarm probability P F Under the upper limit condition, maximize the detection probability P D The Neyman-Pearson decision criterion is:

[0031]

[0032]

[0033] Substituting the observation data of each sensor into the above decision criterion, the probability value of H1 is recorded as P x (m), P x (m) is the judgment result of a single sensor;

[0034] P x Substitute (m) into the formula:

[0035]

[0036] Calculated is the filtering result, that is, the system matrix of m measurement values, is the system matrix of m-1 measurement values, A(m) is the state transfer matrix of m measurement values, and u(m-1) is the state transfer matrix of m measurement values.

[0037] Preferably, the fusion center is further configured to perform sequential decision making according to the Neyman-Pearson decision criterion to obtain a multi-sensor decision result;

[0038] Substitute the multi-sensor judgment results into the formula:

[0039]

[0040] Calculate z(k), where z(k) is the multi-sensor information fusion result, and k is A k The number of elements of A k A set consisting of local decisions whose filtering result is 1.

[0041] On the other hand, a multi-sensor information fusion method under the Neyman-Pearson decision criterion is implemented using the multi-sensor information fusion system under the Neyman-Pearson decision criterion, comprising:

[0042] S1: The fusion center obtains a multidimensional data set z and establishes a test model, where z={[χ[1],χ[2],…,χ[n]] T}, χ[1] is the observation sequence of sensor 1 at time T, and χ[n] is the observation sequence of sensor n at time T;

[0043] S2: Observation data in the multidimensional data set z is calculated according to the maximum a posteriori probability criterion, the observation data is substituted into the Neyman-Pearson decision criterion for sequential decision to obtain a single sensor decision result, and the single sensor decision result is substituted into the Kalman filter algorithm for filtering to obtain a filtering result;

[0044] S3: Perform information fusion on the filtering results to obtain the multi-sensor information fusion result.

[0045] Preferably, the step S1 specifically includes:

[0046] The number of sensors set up in the fusion center is N, the length of the sensor measurement sequence is M, and the Gaussian noise set of N sensors is The false alarm probability is P F The measurement model of the sensor is:

[0047]

[0048] Where H0 indicates that the detection signal is unacceptable, H1 indicates that the detection signal is acceptable, x[n] is the measurement sequence of sensor n at any time, n∈{0,1,…,N-1}, m is the mth measurement value in the measurement sequence, m∈{1,2,…,M}, w[n] is Gaussian white noise with zero mean and given variance, and the false alarm probability P F is the maximum allowable error of N sensors under Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L}, Δε is the error rate at the factory;

[0049] False alarm probability P F In the equation, L = 1 / Δε, N sensors have a false alarm probability P F The data matrix P under F ∈R N×L , R is the dimension;

[0050] Establishment n (m), P D 、P F 、P A 、P S and J, where χ n (m) is the vector set of the M observations of the n-th sensor, m∈{1,2,...,M}, P D is the sensitivity of any sensor, that is, the detection probability, P A is the probability of discarding unreliable sensors, P S is the probability of retaining the sensor for unreliable data, and J is the overall optimization goal;

[0051] Establishment n(m) satisfies the following formula:

[0052] χ n (m) = {x n (1),x n (2),…,x n (M)} (3);

[0053] P D and P F Just opposite, set up P under H1 and H0 D and P F The formula is as follows:

[0054]

[0055]

[0056] P A and P S The setting of P is due to the unpredictable disturbances that occur when the sensor is working. A and P S Satisfies the following formula:

[0057]

[0058] A reasonable decision for the sensor under the premise of meeting the error rate at the factory is to set a limit on the false alarm probability P F Within the allowable value range, the error probability P N Minimum, satisfying the following formula:

[0059]

[0060] Among them, P F is the false alarm probability, D1 is the observed data under the detection probability, α is the allowable value, P N is the error probability;

[0061] Set J to satisfy the following formula:

[0062] J=λ z P N +∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0063] Among them, λ z is the likelihood ratio, and λ is a reasonable threshold.

[0064] As a preference, in the step S2, the Neyman-Pearson decision criterion satisfies the false alarm probability P F Under the upper limit condition, maximize the detection probability P D .

[0065] Preferably, the step S2 specifically includes:

[0066] The observation data in the multi-dimensional data set z of the sensor is calculated according to the maximum a posteriori probability criterion;

[0067] Set up to meet the false alarm probability P F Under the upper limit condition, maximize the detection probability P D The Neyman-Pearson decision criterion is:

[0068]

[0069]

[0070] Substituting the observation data of each sensor into the above decision criterion, the probability value of H1 is recorded as P x (m), P x (m) is the judgment result of a single sensor;

[0071] P x Substitute (m) into the formula:

[0072]

[0073] Calculated is the filtering result, that is, the system matrix of m measurement values, is the system matrix of m-1 measurement values, A(m) is the state transfer matrix of m measurement values, and u(m-1) is the state transfer matrix of m measurement values.

[0074] Preferably, the step S3 specifically includes:

[0075] The multi-sensor decision result is obtained by sequential decision making according to the Neyman-Pearson decision criterion;

[0076] Substitute the multi-sensor judgment results into the formula:

[0077]

[0078] Calculate z(k), where z(k) is the multi-sensor information fusion result, and k is A k The number of elements of A k A set consisting of local decisions whose filtering result is 1.

[0079] Compared with the prior art, the present invention has the following outstanding and beneficial technical effects:

[0080] (1) In the present invention, by fusing the data of multiple sensors, the problems of insufficient accuracy of a single sensor and easy error of sensor data are compensated, and better detection effect and accuracy can be achieved.

[0081] (2) In the present invention, the sensor data is first sequentially judged by the Neyman-Pearson decision criterion to avoid cumulative errors during subsequent filtering, eliminating the problem of cumulative errors in traditional Kalman filter sensors. In addition, in the information fusion process, the Neyman-Pearson decision criterion is introduced to complete the multi-dimensional evaluation of multi-sensor information fusion, effectively solving the problems of poor stability and insufficient accuracy of a single sensor. The design is reasonable and feasible, and has significantly improved the anti-interference and fault tolerance compared to the existing technology.

[0082] (3) Judging from the simulation results, as the value of M increases, the ROC curve of the filtering result becomes smoother, and as N increases, the fusion effect becomes better. Therefore, the present invention has excellent detection performance in a multi-sensor system with a large number of sensors and a long measurement sequence. In addition, from the anti-disturbance analysis, it is concluded that as σ increases, 2 The multi-sensor information fusion results show good fault tolerance and can effectively deal with sudden disturbances of the sensor and eliminate the disturbances.

[0083] (4) From the actual test, the test results show that the present invention can not only complete the given tasks in multi-sensor data processing, but also excel in the ability to follow data changes, which can maintain the sensitivity of the data and improve the anti-disturbance ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a schematic diagram of the system framework structure of the present invention;

[0085] Figure 2 It is a schematic structural diagram of the quadrotor drone of the present invention;

[0086] Figure 3 (a) to Figure 3 (d) is an ROC curve analysis diagram of the influence of the number N and the measurement sequence length M on the algorithm performance of the present invention;

[0087] Figure 4 (a) to Figure 4 (d) is an ROC curve analysis diagram of the effect of noise value on the performance of the algorithm of the present invention;

[0088] Figure 5 This is a partial data table obtained by analyzing the acceleration values ​​of four MPU6500 gyroscopes and processing them according to the present invention;

[0089] Figure 6is a schematic diagram of a multi-sensor information fusion result output by a sensor of the present invention;

[0090] Figure 7 (a) to Figure 7 (d) is a schematic diagram of the qualitative analysis of the algorithm of the present invention;

[0091] Figure 8 is a stability comparison diagram of the fusion algorithm of the present invention;

[0092] Figure 9 This is a comparison diagram of sensor fusion effects under various quantities of the present invention;

[0093] Figure 10 It is a schematic diagram of the steps of the present invention;

[0094] In the figure: 1-Sensor, 2-Fusion Center. DETAILED DESCRIPTION

[0095] To facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings and specific embodiments.

[0096] It should be noted that the present invention requires some basic settings: (1) All sensors are assumed to be independent and identically distributed (IID); (2) Sensor data transmission is assumed to be synchronous and there is no offline problem; (3) The prior probability of the sensor is assumed to be the error rate of the sensor when it leaves the factory, which is represented by Δε; (4) All noise that affects the measurement value of the sensor is assumed to be represented by white Gaussian noise (WGN).

[0097] like Figure 1 As shown in Figure 1, a multi-sensor information fusion system based on the Neyman-Pearson decision criterion mainly solves the problems of poor stability and insufficient accuracy of a single sensor, including:

[0098] A plurality of sensors for acquiring a multi-dimensional dataset z;

[0099] The fusion center is used to calculate the observation data in the multidimensional data set z according to the maximum a posteriori probability criterion, substitute the observation data into the Neyman-Pearson decision criterion for sequential decision to obtain the single-sensor decision result, substitute the single-sensor decision result into the Kalman filter algorithm for filtering to obtain the filtering result, and perform information fusion on the filtering result to obtain the multi-sensor information fusion result.

[0100] The fusion center is also used to set the number of sensors as N, the length of the sensor measurement sequence as M, and the Gaussian noise set of N sensors as The false alarm probability is P F The measurement model of the sensor is:

[0101]

[0102] Where H0 is the detection signal that is unacceptable, H1 is the detection signal that is acceptable, x[n] is the measurement sequence of sensor n at any time, n∈{0,1,…,N-1}, m∈{1,2,…,M}, w[n] is Gaussian white noise with zero mean and given variance, and the false alarm probability P F is the maximum allowable error of N sensors under Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L}, Δε is the error rate at the factory;

[0103] False alarm probability P F In the equation, L = 1 / Δε, N sensors have a false alarm probability P F The data matrix P under F ∈R N×L , R is the dimension;

[0104] Establishment n (m), P D 、P F 、P A 、P S and J, where χ n (m) is the vector set of the M observations of the n-th sensor, m∈{1,2,...,M}, P D is the sensitivity of any sensor, that is, the detection probability, P A is the probability of discarding unreliable sensors, P S is the probability of retaining the sensor for unreliable data, and J is the overall optimization goal;

[0105] Establishment n (m) satisfies the following formula:

[0106] χ n (m) = {x n (1),x n (2),…,x n (M)} (3);

[0107] P D and P F Just opposite, set up P under H1 and H0 D and P F The formula is as follows:

[0108]

[0109]

[0110] P A and P S The setting of P is due to the unpredictable disturbances that occur when the sensor is working. A and P S Satisfies the following formula:

[0111]

[0112] A reasonable decision for the sensor under the premise of meeting the error rate at the factory is to set a limit on the false alarm probability P F Within the allowable value range, the error probability P N Minimum, satisfying the following formula:

[0113]

[0114] Among them, P F is the false alarm probability, D1 is the observed data under the detection probability, α is the allowable value, P N is the error probability;

[0115] Set J to satisfy the following formula:

[0116] J=λ z P N +∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0117] Among them, λ z is the likelihood ratio, and λ is a reasonable threshold.

[0118] The Neyman-Pearson decision criterion satisfies the false alarm probability P F Under the upper limit condition, maximize the detection probability P D .

[0119] The fusion center is also used to calculate the observation data in the multi-dimensional data set z of the sensor according to the maximum a posteriori probability criterion;

[0120] Set up to meet the false alarm probability P F Under the upper limit condition, maximize the detection probability P D The Neyman-Pearson decision criterion is:

[0121]

[0122]

[0123]

[0124] Substituting the observation data of each sensor into the above decision criterion, the probability value of H1 is recorded as P x (m), P x (m) is the judgment result of a single sensor;

[0125] P x Substitute (m) into the formula:

[0126]

[0127] Calculated is the filtering result, that is, the system matrix of m measurement values, is the system matrix of m-1 measurement values, A(m) is the state transfer matrix of m measurement values, and u(m-1) is the state transfer matrix of m measurement values.

[0128] The fusion center is further configured to perform sequential judgment according to the Neyman-Pearson judgment criterion to obtain a multi-sensor judgment result;

[0129] Substitute the multi-sensor judgment results into the formula:

[0130]

[0131] Calculate z(k), where z(k) is the multi-sensor information fusion result, and k is A k The number of elements of A k A set consisting of local decisions whose filtering result is 1.

[0132] like Figure 10 As shown, a multi-sensor information fusion method under the Neyman-Pearson decision criterion is implemented using the multi-sensor information fusion system under the Neyman-Pearson decision criterion, including the following steps:

[0133] S1: The fusion center obtains a multidimensional data set z and establishes a test model, where z={[χ[1],χ[2],…,χ[n]] T}, χ[1] is the observation sequence of sensor 1 at time T, and χ[n] is the observation sequence of sensor n at time T;

[0134] S2: The multidimensional data set z is judged by the maximum a posteriori probability criterion to obtain the observation data, the observation data is substituted into the Neyman-Pearson decision criterion for sequential judgment to obtain the single sensor judgment result, and the single sensor judgment result is substituted into the Kalman filter algorithm for filtering to obtain the filtering result;

[0135] S3: Perform information fusion on the filtering results to obtain multi-sensor information fusion results.

[0136] The step S1 further specifically includes:

[0137] The fusion center obtains a multidimensional dataset z, which is a Gaussian distribution data matrix, and z∈R N×M ;

[0138] The fusion center also sets the number of sensors as N, the length of the sensor measurement sequence as M, and the Gaussian noise set of N sensors as The false alarm probability is P F The measurement model of the sensor is:

[0139]

[0140] Among them, H0 means that the detection signal is unacceptable, H1 means that the detection signal is acceptable, x[n] is the measurement sequence of sensor n at any time, n∈{0,1,…,N-1}, w[n] is Gaussian white noise with zero mean and given variance, and the false alarm probability P F is the maximum allowable error of N sensors under Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L}, where Δε is the error rate at the factory.

[0141] False alarm probability P F In the equation, L = 1 / Δε. N sensors have a false alarm probability P F The data matrix P under F ∈R N×L , R is the dimension.

[0142] Establishment n (m), P D 、P F 、P A 、P S and J, where χ n (m) is the vector set of the M observations of the n-th sensor, m∈{1,2,...,M}, P D is the sensitivity of any sensor, that is, the detection probability, P A is the probability of discarding unreliable sensors, P S is the probability of retaining the sensor for unreliable data, and J is the overall optimization goal.

[0143] Establishment n (m) satisfies the following formula:

[0144] χ n (m) = {x n (1),x n (2),…,x n (M)} (3);

[0145] PD and P F Just opposite, set up P under H1 and H0 D and P F The formula is as follows:

[0146]

[0147]

[0148] P A and P S The setting of P is due to the unpredictable disturbances that occur when the sensor is working. A and P S Satisfies the following formula:

[0149]

[0150] A reasonable decision for the sensor under the premise of meeting the error rate at the factory is to set a limit on the false alarm probability P F Within the allowable value range, the error probability P N Minimum, satisfying the following formula:

[0151]

[0152] Among them, P F is the false alarm probability, D1 is the observed data under the detection probability, α is the allowable value, P N is the error probability;

[0153] Set J to satisfy the following formula:

[0154] J=λ z P N +∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0155] Among them, λ z is the likelihood ratio, and λ is a reasonable threshold.

[0156] When performing multi-sensor information fusion at the fusion center, measurements with P(z|H1)-λP(z|H0)<0 can be assigned to z0. z0 is the data set assigned to H0, and a reasonable threshold λ that satisfies the optimization needs to be obtained. When the above inequality holds, it is determined to be H1. In this way, a suitable fusion threshold can be found among multiple sensors or multiple measurement sequences without traversing all sensors or all measurement sequences, preventing the fusion center from over-converging or widening the range.

[0157] The Neyman-Pearson decision criterion satisfies the false alarm probability P FUnder the upper limit condition, maximize the detection probability P D , the Neyman-Pearson decision criterion can also be called the NP decision criterion.

[0158] In the step S2, the Neyman-Pearson decision criterion satisfies the false alarm probability P F Under the upper limit condition, maximize the detection probability P D , mainly processes the data of each sensor based on the principle of set statistics, through a small error probability P N In exchange for the maximum detection probability P D .

[0159] The Neyman-Pearson decision criterion adopts the following formula:

[0160]

[0161]

[0162]

[0163] Among them, H0, which is an unacceptable detection signal, is set as the original setting, H1, which is an acceptable detection signal, is set as the alternative setting, α and β are constants, η1 and η0 are threshold values, and χ n (m) is the vector set of the M observations of the n-th sensor, m∈{1,2,...,M}, ∧(χ n (m)) is χ n (m) The specific value of lamda.

[0164] The Kalman filter algorithm uses the following formula:

[0165]

[0166] in, is the filtering result, that is, the system matrix of m measurement values, is the system matrix of m-1 measurement values, A(m) is the state transfer matrix of m measurement values, and u(m-1) is the state transfer matrix of m measurement values. x Substitute (m) into formula (19) to obtain the filtering result

[0167] The step S2 further specifically includes:

[0168] First, the observation data in the multidimensional data set z of the sensor is calculated according to the Maximum A Posteriori-estimation (MAP) criterion. The observation data is a measurement sequence that cannot be directly observed in the multidimensional training data set of the sensor.

[0169] Then select the most likely setting (H0, where the detection signal is unacceptable, is set as the original setting, and H1, where the detection signal is acceptable, is set as the alternative setting). The basic observation probability characteristics are:

[0170]

[0171]

[0172] Construct the basic likelihood ratio test and decision criterion:

[0173]

[0174] Based on a small amount of observation data, the false alarm probability P is usually not satisfied. F Small enough or detection probability P D Large enough, it is necessary to continuously obtain more measurements, which forms a sequential decision problem, established under the condition that the false alarm probability P F Under the upper limit condition, maximize the detection probability P D The Neyman-Pearson decision criterion is:

[0175]

[0176]

[0177] Among them, formula (13) defines the detection probability P D The formula, is χ n The differential of n is the measurement sequence of sensor n at any time.

[0178] Since the sensor has M observation data, the formulas for the original setting H0 and the alternative setting H1 are obtained based on formulas (13) and (14):

[0179]

[0180] Among them, ∧(χ n (m)) is the M observation data, χ n (m) is the vector set of the n-th sensor M observations, m∈{1,2,...,M}, if ∧(χ n (m))≥η1, then H1, if ∧(χ n When (m))≤η0, then it is H0.

[0181] Establish P F (n) = α, P M (n) = β, threshold value η1 and threshold value η0, based on formula (15), we can get:

[0182]

[0183]

[0184] Substitute the m measurement sequences of each sensor (i.e., the observation data of each sensor) into the above formula to determine the probability value of H1, which is recorded as P x (m), P x (m) is the single sensor decision result. The observation data between the thresholds η1 and η0 are selected for Kalman filtering. The Kalman filter algorithm involves a prediction of the system matrix based on the basic state vector, which is then updated by sensor measurements. Its discrete time-varying state space model equation is shown below:

[0185] x(k)=A(k)x(k-1)+B(k)μ(k-1)+w(k) (18),

[0186] Where k is the discrete time index, x(k) is the system matrix, A(k) is the state transition matrix, B(k) is the input control matrix, μ(k) is the input signal matrix, and w(k) is the Gaussian white noise.

[0187] Since Gaussian white noise w(k) has been considered, it is no longer considered when performing Kalman filtering. The formula for setting the Kalman filtering algorithm is:

[0188]

[0189] in, is the system matrix of m measurement values, is the system matrix of m-1 measurement values, A(m) is the state transfer matrix of m measurement values, and u(m-1) is the state transfer matrix of m measurement values. x Substitute (m) into formula (19) to obtain the filtering result

[0190] The step S3 specifically includes:

[0191] When the fusion center fuses the filtering results of N sensors, it uses the binary decision method. The binary decision method has two N There are possible fusion criteria. Set d(μ1,μ2,…,μ n ) is the decision function of the sensor fusion center, U={μ1,μ2,…,μ n}. A is the set of filtering results. A k A set consisting of local decisions whose filtering result is 1. kA set consisting of local decisions whose filtering results are 1. k is A k The number of elements of UA k : A set of local decisions whose filtering results are 0. Since the filtering results are binary, there are 2 for N sensors. N In this case, it means that we can get 2 N Ratio ∧(z):

[0192]

[0193]

[0194]

[0195] Among them, ∧(z) is the specific value of lamda of z.

[0196] Taking the logarithm of both sides of formula (22) and simplifying it, we can obtain:

[0197]

[0198] Here, ln refers to the logarithm to the base e.

[0199] Since the test statistic It is subject to mean 0 and variance σ 2 The Gaussian distribution of / N is standardized to obtain the following formula:

[0200]

[0201] Where Q(·) is the complementary cumulative distribution function, which is a monotonically decreasing function and has an inverse function. The formula for calculating the threshold value γ is:

[0202]

[0203] because is a constant, so we can use α to calculate the threshold value γ.

[0204] Set C1 = {∧(z) > λ}, C2 = {z:∧(z) > λ}, calculate P F and P D The formula is as follows:

[0205]

[0206]

[0207] The number of sensors is N, and the original setting H0 and the alternative setting H1 are as follows:

[0208]

[0209]

[0210] Among them, P(χ n |H i )=∫(χ n |H1(θ i ))π(θ i )dθ i , when equal to the false alarm probability P F The upper limit can be obtained. Referring to formulas (16) and (17), the Neyman-Pearson decision criterion in step S3 adopts the following formula:

[0211]

[0212] Same reason At this time, the above inequality can be equalized. The conditional probability of the joint likelihood ratio of the sensor decision is set as:

[0213]

[0214] Arrange all the results of ∧(z) by size, record them as ∧(z(j)), and calculate P∧(z(j)|H1) and P∧(z(j)|H0), and we get:

[0215]

[0216] Where j = 1, 2, ..., 2 N We find the value of j* that satisfies formula (32) according to the order of ∧(z), and finally substitute j* into the following formula:

[0217]

[0218] The threshold value λ* is calculated.

[0219] Substitute the threshold value λ* into the following formula:

[0220]

[0221] The calculated false alarm probability P F Maximize the detection probability under the upper limit That is the result of multi-sensor judgment;

[0222] Will Substitute the following formula:

[0223]

[0224] Calculate z(k), where z(k) is the multi-sensor information fusion result.

[0225] In addition, in order to verify the difference between the present invention and the prior art, simulation experiments and actual test experiments are carried out on the present invention and the traditional algorithm respectively. The simulation experiment of the present invention on a computer is introduced below.

[0226] The basic configuration of the computer used in the simulation experiment is as follows: the CPU is Intel(R) Xeon CPU E5-2680 v2 @2.80GHz; the machine has 128G of RAM, the operating system is Windows 10 Professional Edition; the programming language is Python (version 3.9.7), and the development environment is VS Code.

[0227] In the simulation experiment, in order to test the rationality of the present invention, the ROC curve is introduced. The ROC curve has been extended from the military field to the medical field and now to the field of machine learning, and it is a good way to evaluate the relationship between the sensitivity and specificity of the data. Figure 3 (a) to Figure 3 As shown in (d), the ROC curves of the number N and the measurement sequence length M are plotted. It can be seen that when the value of M is larger, the ROC curve of the single sensor measurement sequence judgment is smoother, proving that the present invention has a certain effect on the fusion effect of sensor data. However, when the number of sensors N is small, the fusion effect is poor. As N increases, the fusion effect changes significantly. The detection performance of different sensors can be compared through the ROC curve, which can be seen from the Figure 3 (a) to Figure 3 (d) It can be seen that the detection performance of multi-sensor fusion is significantly better than that of a single sensor.

[0228] like Figure 4 (a) to Figure 4 (d) In order to check the effect of noise value on the performance of the algorithm, σ 2 The results show that as σ 2 As the value increases, the present invention exhibits better fault tolerance, that is, it can effectively eliminate sudden disturbances of the sensor, which proves the superiority of the present invention.

[0229] like Figure 2 As shown in the figure, the actual test experiment used a quadrotor drone. The sensors used in the quadrotor drone include one high-precision MPU9250 gyroscope and four medium-precision MPU6500 gyroscopes. The high-precision MPU9250 gyroscope is located at the center of the drone, while the four MPU6500 gyroscopes are placed at the ends of the four arms. The high-precision MPU9250 gyroscope served as the evaluation standard for the four MPU6500 gyroscopes.

[0230] like Figure 5As shown in FIG, the acceleration values ​​of four MPU6500 gyroscopes are analyzed and processed by the present invention. Figure 6 The figure shows the multi-sensor information fusion result after the data is fused by the present invention. Figure 6 It can be seen from the multi-sensor information fusion results of X-axis acceleration, Y-axis acceleration, and Z-axis acceleration that the data changes of a single MPU6500 gyroscope are quite unique, and the curve overlap is very low. This means that if the data of four MPU6500 gyroscopes are combined, four different output results may be obtained, which is undesirable. Figure 6 As shown in the figure, the multi-sensor information fusion result based on the present invention is shown. The multi-sensor information fusion result well illustrates that the present invention can not only achieve the established tasks, but also excel in the ability to follow data changes, and can maintain the sensitivity of the data while improving the anti-disturbance ability.

[0231] Based on the above analysis, if Figure 7 As shown in (a), in order to qualitatively analyze the error value, the absolute value error and root mean square error (RMSE) are introduced, and their mathematical expressions are as follows:

[0232]

[0233] After calculation, in Figure 7 The maximum absolute error in (b) is only 0.0165, and the average absolute error is 0.00194. In the prior art, traditional fusion methods include mean fusion, weighted fusion, and fusion based on BP neural network (BPF). Figure 7 (c) shows a box plot of the RMSE of the three-axis acceleration of the present invention and the traditional fusion algorithm. As can be seen from the figure, the mean and median of the present invention are lower than those of the traditional fusion method. In other words, the present invention is superior to the existing technology as a whole. From the data distribution, it can be seen that it is closer to the Gaussian distribution model, which has a good guarantee for data sensitivity and fault tolerance. Accuracy (the opposite of error) is introduced to describe the qualitative analysis. The cumulative accuracy over a certain period of time is calculated and plotted, as shown in the figure. Figure 7 As shown in (d), the experimental effect is more obvious, and the accuracy of the invention is also better than the traditional fusion method.

[0234] like Figure 8As shown in the figure, the stability comparison of the actual test experiment is plotted. In the figure, the red line represents the z-axis acceleration curve of the MPU9250 gyroscope, and the green line represents the curve of the multi-sensor information fusion result obtained by processing the z-axis acceleration curves of four MPU6500 gyroscopes in the present invention. Figure 8 It can be seen that the data of the four MPU6500 gyroscopes processed by the present invention are better than the data of the MPU9250 gyroscope, which well illustrates the actual performance of the present invention.

[0235] like Figure 9 As shown in the figure, a comparison of the multi-sensor information fusion results of different numbers of MPU6500 gyroscopes in the present invention is plotted. In the figure, the blue line represents the z-axis acceleration curve of a single MPU6500 gyroscope, the magenta line represents the curve of the z-axis acceleration fusion structure of three MPU6500 gyroscopes, and the green line represents the curve of the z-axis acceleration fusion structure of four MPU6500 gyroscopes. Figure 9 It can be seen that the present invention effectively solves the problems of poor stability and insufficient precision of a single MPU6500 gyroscope, and also improves aspects such as anti-interference and fault tolerance.

[0236] The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, any equivalent changes made based on the structure, shape, and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-sensor information fusion system under the Neyman-Pearson decision criterion, characterized in that: include: A plurality of sensors for acquiring a multi-dimensional dataset z; A fusion center is used to calculate the observation data in the multidimensional data set z according to the maximum a posteriori probability criterion, substitute the observation data into the Neyman-Pearson decision criterion for sequential decision to obtain a single-sensor decision result, substitute the single-sensor decision result into the Kalman filter algorithm for filtering to obtain a filtered result, and perform information fusion on the filtered result to obtain a multi-sensor information fusion result; The fusion center is also used to set the number of sensors as N, the length of the sensor measurement sequence as M, and the Gaussian noise set of N sensors as , the false alarm probability is P F The measurement model of the sensor is: ， Where H0 indicates that the detection signal is unacceptable, H1 indicates that the detection signal is acceptable, x[n] is the measurement sequence of sensor n at any time, n∈{0, 1,…, N-1}, m∈{1, 2,…, M}, w[n] is Gaussian white noise with zero mean and given variance, and the false alarm probability PF is the maximum allowable error of N sensors under Gaussian noise, P F ={Δε× 0 ,Δε× 1 ,…,Δε× L}, Δε is the error rate at the factory; False alarm probability P F In the equation, L = 1 / Δε, N sensors have a false alarm probability P F The data matrix P under F ∈R N× L , R is the dimension; set χ n (m), P D 、P F 、P A 、P S and J, where χ n (m) is the vector set of the M observations of the n-th sensor, m∈{1, 2, ..., M}, P D is the sensitivity of any sensor, that is, the detection probability, P A is the probability of discarding unreliable sensors, P S is the probability of retaining the sensor for unreliable data, J is the overall optimization goal; set χ n (m) satisfies the following formula: χ n (m)={x n (1) ,x n (2) ,… ,x n (M)} (3); P D and P F Just opposite, under H1 and H0, P D and P F The formula is as follows: ， ； P A and P S The setting of P is due to the unpredictable disturbances that occur when the sensor is working. A and P S Satisfies the following formula: ， A reasonable decision for the sensor under the premise of meeting the error rate at the factory is to set a limit on the false alarm probability P F Within the allowable value range, the error probability P N Minimum, as follows: ， Among them, P F is the false alarm probability, D1 is the observed data under the detection probability, α is the allowable value, P N is the error probability; Set J to satisfy the following formula: J=λ z P N +∫ z [P(z|H1)-λP(z|H0)]dz(9), Among them, λz is the likelihood ratio, λ is the reasonable threshold; The Neyman-Pearson decision criterion satisfies the false alarm probability P F Under the upper limit condition, maximize the detection probability P D ; The fusion center is also used to calculate the observation data in the multi-dimensional data set of the sensor according to the maximum a posteriori probability criterion; F Under the upper limit condition, maximize the detection probability P D The Neyman-Pearson decision criterion is: , , Substituting the observation data of each sensor into the above decision criterion, the probability value of H1 is recorded as P x (m), P x (m) is the judgment result of a single sensor; P x Substitute (m) into the formula: ； Calculated is the filtering result, that is, the system matrix of m measurement values, is the system matrix of m-1 measurement values, A(m) is the state transfer matrix of m measurement values, and u(m-1) is the state transfer matrix of m measurement values.

2. The multi-sensor information fusion system under the Neyman-Pearson decision criterion according to claim 1, characterized in that: The fusion center is further configured to perform sequential judgment according to the Neyman-Pearson judgment criterion to obtain a multi-sensor judgment result; Substitute the multi-sensor judgment results into the formula: ； Calculate z(k), where z(k) is the multi-sensor information fusion result, and k is A k The number of elements of A k The set of local decisions whose filtering result is 1, is the multi-sensor decision result, N is the number of sensors, and x(k) is the system matrix.

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