A multi-sensor information fusion method under a Neyman-Pearson decision criterion

Abstract

The application discloses a multisensor information fusion method under a Neyman-Pearson decision criterion, and aims at overcoming the problems of low credibility, low fault tolerance and poor integrity in the prior art, and comprises the following steps: a fusion center acquires a multidimensional data set z, and sets up a test model; observation data in the multidimensional data set z is calculated according to a maximum a posteriori probability criterion, the observation data is substituted into the Neyman-Pearson decision criterion to sequentially make a decision and obtain a single-sensor decision result, and the single-sensor decision result is substituted into a Kalman filtering algorithm to filter and obtain a filtering result; and information fusion is performed on the filtering result to obtain a multisensor information fusion result.

Description

TECHNICAL FIELD

[0001] The present application relates to sensor data detection technology, and in particular to a multi-sensor information fusion method under a Neyman-Pearson decision criterion. BACKGROUND

[0002] With the rapid development of artificial intelligence, big data, 5G, Internet of Things and other technologies, more and more intelligent sensors are changing the way of human life and even social structure with new products, new technologies, new industries and new modes, for example, autonomous vehicles. Any sensor cannot guarantee that its detection accuracy performance reaches 100%, which leads to the problem of poor stability and insufficient precision of a single sensor, which forces the need to extract high-quality data from multiple low-precision sensors.

[0003] In order to extract high-quality data from multiple low-precision sensors, in the prior art, a multi-layer multi-source information fusion rotor unmanned aerial vehicle height measurement algorithm is disclosed, which divides the fusion into two parts, the first part is completed based on historical data using an adaptive space-time algorithm, and the second part uses a traditional complementary filtering method to establish a space-time dual fusion model. The above prior art belongs to a multi-sensor information fusion technology using filtering type.

[0004] However, the prior art is not perfect, although the prior art has good effects on noise and error processing of data, but does not consider the reliable components of the sensor itself, and has the problem of low fault tolerance. On the other hand, with the increase of the number of sensors, the calculation amount of the fusion center will be sharply expanded, and the time lag problem will gradually highlight, resulting in low overall performance of the multi-sensor fusion method. SUMMARY

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

[0006] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0007] A multi-sensor information fusion method under a Neyman-Pearson decision criterion, comprising:

[0008] S1: The fusion center acquires a multi-dimensional data set z, and sets up a test model, wherein 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;

[0009] S2: according to the maximum a posteriori criterion, the observation data in the multi-dimensional data set z are calculated, the observation data are substituted into the Neyman-Pearson decision criterion to obtain a single sensor decision result, and the single sensor decision result is substituted into the Kalman filtering algorithm to obtain a filtering result;

[0010] S3: the filtering result is information fused to obtain a multi-sensor information fusion result.

[0011] As preferred, the step of S1 specifically comprises:

[0012] The fusion center sets the number of sensors as N, the length of the sensor measurement sequence as M, and the Gaussian noise set of the N sensors as The false alarm probability is P F , and the measurement model of the sensor is:

[0013]

[0014] wherein H0 represents that the detection signal is not acceptable, H1 represents that the detection signal is acceptable, x[n] is a measurement sequence of the 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 a Gaussian white noise with zero mean and given variance, the false alarm probability P F is the maximum allowable error of the N sensors under the Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L}, and Δε is the error rate at the factory;

[0015] The false alarm probability P F , wherein L=1 / Δε, the data matrix P F of the N sensors under the false alarm probability P F ∈R N×L , and R is the dimension;

[0016] χ n (m), P D , P F , P A , P S , and J are set, wherein χ n (m) is a vector set of M observations of the nth sensor, m∈{1,2,...,M}, P D is the sensitivity for any sensor, i.e., the detection probability, P A is the probability of the unreliable sensor that needs to be discarded, P S is the probability of the unreliable sensor that retains the data, and J is the overall optimization target;

[0017] χ n (m) satisfies the following formula:

[0018] χ n (m) = {x n (1), x n (2),..., x n (M)} (3);

[0019] P D and P F are just opposite, set up under H1 and H0 P D and P F formula as follows:

[0020]

[0021]

[0022] P A and P S set up due to the presence of unpredictable disturbance when the sensor is working, set up P A and P S meet the following formula:

[0023]

[0024] For the sensor in the error rate of the premise of the factory in line with reasonable decision is, set up limit false alarm probability P F in the allowable value range, so that its error probability P N minimum, meet the following formula:

[0025]

[0026] Where, P F false alarm probability, D1 for the detection probability of the observed data, alpha for the allowable value, P N error probability;

[0027] Set J meet the following formula:

[0028] J = λ z P N + ∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0029] Where, λ z likelihood ratio, λ for the reasonable threshold.

[0030] As preferred, the step of said S2, the Neyman-Pearson criterion meets the false alarm probability P F upper limit under the condition of maximizing the detection probability P D .

[0031] As preferred, the step S2 specifically comprises:

[0032] The observation data in the multi-dimensional data set z of the sensor is calculated according to the maximum a posteriori probability criterion;

[0033] The false alarm probability P F is set to satisfy the condition that the upper limit of the detection probability P D is maximized. The Neyman-Pearson decision criterion is:

[0034]

[0035]

[0036] The observation data of each sensor is substituted into the above formula to obtain the probability value of H1, denoted as P x (m), and P x (m) is the single-sensor decision result.

[0037] P x (m) is substituted into the formula:

[0038]

[0039] The calculation result is: 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 transition matrix of m measurement values, and u(m-1) is the state transition matrix of m measurement values.

[0040] As preferred, the step S3 specifically comprises:

[0041] The sequential decision is performed according to the Neyman-Pearson decision criterion to obtain the multi-sensor decision result.

[0042] The multi-sensor decision result is substituted into the formula:

[0043]

[0044] The calculation result is z(k), wherein z(k) is the multi-sensor information fusion result, k is the number of elements of A k , and A k is a set composed of local decisions with the filtering result being 1.

[0045] On the other hand, the application further discloses a multi-sensor information fusion system under the Neyman-Pearson decision criterion, which is used for executing the multi-sensor information fusion method under the Neyman-Pearson decision criterion, and comprises:

[0046] a plurality of sensors for obtaining a multi-dimensional data set z;

[0047] a fusion center for calculating observation data in the multi-dimensional data set z according to a maximum a posteriori criterion, substituting the observation data into a Neyman-Pearson decision criterion to obtain a single-sensor decision result, substituting the single-sensor decision result into a Kalman filtering algorithm to obtain a filtering result, and performing information fusion on the filtering result to obtain a multi-sensor information fusion result.

[0048] Preferably, the fusion center is further configured to set the number of sensors as N, the length of a sensor measurement sequence as M, a Gaussian noise set of the N sensors as a false alarm probability as P F and a measurement model of the sensor as:

[0049]

[0050] wherein H0 represents that a detection signal is not acceptable, H1 represents that the detection signal is acceptable, x[n] is a measurement sequence of a sensor n at any time, n ∈ {0, 1, …, N-1}, m ∈ {1, 2, …, M}, w[n] is a Gaussian white noise with zero mean and a given variance, a false alarm probability P F is a maximum allowable error of the N sensors under Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L} and Δε is an error rate at factory shipment;

[0051] a false alarm probability P F , wherein L=1 / Δε, a data matrix P F of the N sensors under the false alarm probability P F ∈R N×L , R is a dimension;

[0052] χ n (m), P D , P F , P A , P S and J are set, wherein χ n (m) is a vector set of M observations of the nth sensor, m ∈ {1, 2, …, M}, P D is a sensitivity for any sensor, i.e., a detection probability, P A is a probability of a sensor that needs to be discarded due to unreliability, P S is a probability of a sensor that retains data due to unreliability, and J is an overall optimization target.

[0053] χ n (m) satisfies the following formula:

[0054] χn (m) = {x n (1), x n (2),..., x n (M)} (3) ;

[0055] P D and P F are exactly opposite, P D and P F are as follows:

[0056]

[0057]

[0058] P A and P S are set due to unexpected disturbance when the sensor is working, P A and P S satisfy the following formula:

[0059]

[0060] For the reasonable decision of the sensor under the premise of meeting the error rate at the factory, the false alarm probability P F is set within the allowable value range, so that the error probability P N is minimized, as follows:

[0061]

[0062] where P F is the false alarm probability, D1 is the observation data under the detection probability, a is the allowable value, and P N is the error probability.

[0063] Set J to satisfy the following formula:

[0064] J = λ z P N +∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0065] where λ z is the likelihood ratio, and λ is the reasonable threshold.

[0066] The Neyman-Pearson decision criterion satisfies the condition that the false alarm probability P F is maximized under the upper limit of the detection probability P D .

[0067] As a preferred, 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.

[0068] Let the false alarm probability P be satisfied. F Maximize the detection probability P under the condition of the upper limit. D The Neyman-Pearson ruling criteria are:

[0069]

[0070]

[0071] Substituting the observation data from each sensor into the decision criterion above, we obtain the probability value of H1, denoted as P. x (m), P x (m) represents the decision result of a single sensor.

[0072] P x (m) Substitute into the formula:

[0073]

[0074] Calculated The filtering result is the system matrix of m measurements. Let A(m) be the system matrix with m-1 measurements, A(m) be the state transition matrix with m measurements, and u(m-1) be the state transition matrix with m measurements.

[0075] Preferably, the fusion center is also used to perform sequential decision-making according to the Neyman-Pearson decision criterion to obtain multi-sensor decision results;

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

[0077]

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

[0079] The outstanding and beneficial technical effects of this invention compared to the prior art are:

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

[0081] (2) in the present application, the data of the sensor is firstly subjected to sequential decision by the Neyman-Pearson decision criterion to avoid the cumulative error in subsequent filtering, thereby eliminating the problem of cumulative error of the sensor in the traditional Kalman filtering, and 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 precision of a single sensor, and the design is reasonable and feasible, and compared with the prior art, the anti-interference and fault tolerance are significantly improved.

[0082] (3) from the simulation results, it can be judged that the ROC curve of the filtering result is smoother as the value of M is larger, and the fusion effect is better as the value of N is larger, so that the present application has excellent detection performance in a multi-sensor system with a large number of sensors and a long measurement sequence, and in addition, from the anti-disturbance analysis, it can be concluded that as the value of sigma increases, the multi-sensor information fusion result presents good fault tolerance, and can effectively face the sudden disturbance of the sensor and eliminate the disturbance. 2

[0083] (4) from the actual test, the test results show that the present application can not only complete the intended task in the data processing of the multi-sensor, but also has excellent performance in the following ability of data change, that is, it can not only maintain the sensitivity of the data, but also improve the anti-disturbance ability. BRIEF DESCRIPTION OF DRAWINGS

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

[0085] Figure 2 is a structure schematic diagram of the quadrotor unmanned aerial vehicle of the present application;

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

[0087] Figure 4 (a) to Figure 4 (d) are ROC curve analysis diagrams of the influence of the noise value on the performance of the algorithm of the present application;

[0088] Figure 5 is a part of data table after the acceleration values of four MPU6500 gyroscopes are analyzed and processed by the present application;

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

[0090] Figure 7 (a) to Figure 7 (d) are algorithm qualitative analysis schematic diagrams of the present application; ​

[0091] Figure 8 is a stability comparison chart of the fusion algorithm of the application;

[0092] Figure 9 is a sensor fusion effect comparison chart under various quantities of the application;

[0093] Figure 10 is a step flowchart of the application;

[0094] In the figure: 1-sensor, 2-fusion center. DETAILED DESCRIPTION

[0095] For the convenience of those skilled in the art, the application will be further described below in combination with the drawings and specific embodiments.

[0096] It should be noted that the application needs to make some basic settings: (1) set each sensor to be independently and identically distributed (Independent Identically Distribution, IID); (2) set that the sensor data transmission has synchronicity and there is no offline problem; (3) set that the prior probability of the sensor is the error rate known when the sensor is manufactured, and the error rate when the sensor is manufactured is represented by Δε; (4) set that all the noise affecting the measurement value of the sensor is represented by white Gaussian noise (White Gaussian Noise, WGN).

[0097] As shown in Figure 10 , a multi-sensor information fusion method under the Neyman-Pearson decision criterion mainly solves the problems of poor stability and insufficient precision of a single sensor, and includes the following steps:

[0098] S1: the fusion center acquires a multi-dimensional data set z, and sets up a test model, wherein 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;

[0099] S2: the multi-dimensional data set z is determined by the maximum a posteriori probability criterion to obtain observation data, the observation data is substituted into the Neyman-Pearson decision criterion to obtain a single sensor decision result, and the single sensor decision result is substituted into the Kalman filtering algorithm to obtain a filtering result;

[0100] S3: the filtering result is subjected to information fusion to obtain a multi-sensor information fusion result.

[0101] The step of S1 further specifically includes:

[0102] The fusion center acquires a multi-dimensional data set z, the multi-dimensional data set z is a Gaussian distribution data matrix, and z ∈ R N×M ;

[0103] The fusion center also sets the number of sensors as N, the length of the sensor measurement sequence as M, the Gaussian noise set of the N sensors as The false alarm probability is P F , and the measurement model of the sensor is:

[0104]

[0105] Where H0 represents that the detection signal is not acceptable, H1 represents that the detection signal is acceptable, x[n] is the measurement sequence of the sensor n at any time, n ∈ {0, 1, …, N-1}, w[n] is a Gaussian white noise with zero mean and given variance, the false alarm probability P F is the maximum allowable error of the N sensors under the Gaussian noise, P F ={Δε×0,Δε×1,…,Δε×L}, Δε is the error rate at the factory, A is the amplitude, and the amplitude is a constant;

[0106] The false alarm probability P F , L = 1 / Δε. The data matrix P F of the N sensors under the false alarm probability P F ∈ R N×L , R is the dimension.

[0107] χ n (m), P D , P F , P A , P S and J are set, where χ n (m) is the vector set of the M observations of the nth sensor, m ∈ {1, 2, …, M}, P D is the sensitivity for any sensor, that is, the detection probability, P A is the probability of the unreliable sensor that needs to be discarded, P S is the probability of the unreliable data that is retained, and J is the overall optimization target.

[0108] χ n (m) satisfies the following formula:

[0109] χ n (m) = {x n (1), x n (2), …, x n (M)} (3);

[0110] P D and P FJust opposite, set up P D and P F The formula is as follows:

[0111]

[0112]

[0113] P A and P S The setting is due to the existence of unpredictable disturbance when the sensor is working, set up P A and P S Satisfy the following formula:

[0114]

[0115] For the reasonable decision of the sensor under the premise of meeting the error rate at the factory, set up the limited false alarm probability P F In the allowable value range, so that its error probability P N Minimum, satisfy the following formula:

[0116]

[0117] Where, P F False alarm probability, D1 is the observation data under the detection probability, alpha is the allowable value, P N Error probability;

[0118] Set J satisfy the following formula:

[0119] J = λ z P N + ∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0120] Where, lambda z Is the likelihood ratio, lambda is the reasonable threshold.

[0121] When the multi-sensor information fusion is carried out in the fusion center, the measurement of P(z|H1)-λP(z|H0)<0 can be classified into z0, z0 is the data set classified into H0, and the reasonable threshold λ satisfying optimization needs to be obtained. When the above inequality is established, it is determined as H1, so that the appropriate fusion threshold can be found in multiple sensors or multiple measurement sequences without traversing all sensors or all measurement sequences, preventing the fusion center from producing excessive convergence or expanding the difference.

[0122] The Neyman-Pearson decision criterion satisfies the condition of upper limit of false alarm probability P F Maximize the detection probability P DThe Neyman-Pearson decision criterion can be referred to as an N-P decision criterion.

[0123] In the step S2, the Neyman-Pearson decision criterion satisfies a false alarm probability P F Under the upper limit, the detection probability P D The data of each sensor is mainly processed based on a set statistical principle, and a small error probability P N is exchanged for the maximum detection probability P D .

[0124] The Neyman-Pearson decision criterion adopts the following formula:

[0125]

[0126]

[0127]

[0128] wherein H0 of an unacceptable detection signal is set as an original setting, H1 of an acceptable detection signal is set as an alternative setting, and α and β are constants, η1 and η0 are threshold values, χ n (m) is an n-th sensor M times of observation vector set, m∈{1, 2,..., M}, ∧(χ n (m)) is χ n (m) and the specific value of lamda.

[0129] The Kalman filtering algorithm adopts the following formula:

[0130]

[0131] wherein, is a filtering result, that is, a system matrix of m measurement values, is a system matrix of m-1 measurement values, A(m) is a state transition matrix of m measurement values, and u(m-1) is a state transition matrix of m measurement values. The single sensor decision result P x (m) is substituted into formula (19) to obtain the filtering result

[0132] The step S2 further comprises the following steps.

[0133] First, the observation data in the multi-dimensional data set z of the sensor is calculated according to the maximum a posteriori estimation (MAP), and the observation data is a measurement sequence that cannot be directly observed in the multi-dimensional training data set of the sensor.

[0134] The maximum possible occurrence is selected again (H0 setting of the detection signal is not acceptable as the original setting, and H1 setting of the detection signal is acceptable as the alternative setting), and the basic observation probability characteristic is:

[0135]

[0136]

[0137] The basic likelihood ratio test and decision criterion are constructed:

[0138]

[0139] Based on a small amount of observation data, the false alarm probability P F is usually not small enough or the detection probability P D is large enough, and more measurements need to be continuously obtained, which forms a sequential decision problem, and the Neyman-Pearson decision criterion is established under the condition of satisfying the false alarm probability P F upper limit, and maximizing the detection probability P D .

[0140]

[0141]

[0142] wherein formula (13) is a formula for defining the detection probability P D , is the differential of χ n , χ n is the measurement sequence of the sensor n at any time.

[0143] Based on formula (13) and (14), the formula of the original setting H0 and the alternative setting H1 of the sensor with M observation data is obtained:

[0144]

[0145] wherein ∧(χ n (m)) is the M observation data, χ n (m) is the vector set of the M observation of the nth sensor, m∈{1,2,...,M}, if ∧(χ n (m))≥η1, then it is H1, and if ∧(χ n (m))≤η0, then it is H0.

[0146] The false alarm probability P F (n) = α, the detection probability P M (n) = β, the threshold value η1 and the threshold value η0 are set, and based on formula (15), the following can be obtained:

[0147]

[0148]

[0149] The m measurement sequences of each sensor (i.e., the observation data of each sensor) are substituted into the above formula to obtain the probability value of H1, denoted as P x (m), P x (m) is the single-sensor decision result, and the observation data between the threshold value η1 and the threshold value η0 is selected to perform Kalman filtering. The Kalman filtering algorithm includes a prediction based on a system matrix of a basic state vector, and then an update is provided by a sensor measurement. The discrete time-varying state space model equation is as shown in the following formula:

[0150] x(k)=A(k)x(k-1)+B(k)μ(k-1)+w(k) (18),

[0151] wherein k is a discrete time index, x(k) is a system matrix, A(k) is a state transition matrix, B(k) is an input control matrix, μ(k) is an input signal matrix, and w(k) is a Gaussian white noise.

[0152] Since the Gaussian white noise w(k) has been considered, it is no longer considered when performing Kalman filtering. The formula of the Kalman filtering algorithm is set as:

[0153]

[0154] wherein, is a system matrix of m measurements, is a system matrix of m-1 measurements, A(m) is a state transition matrix of m measurements, and u(m-1) is a state transition matrix of m measurements. The single-sensor decision result P x (m) is substituted into formula (19) to obtain the filtering result

[0155] In the step of S3, specifically comprising:

[0156] When the fusion center fuses the filtering results of the N sensors, a binary decision-based method is used, and the binary decision-based method has two N possible fusion criteria. Let d(μ1, μ2, …, μ n ) be a decision function of the sensor fusion center, and U={μ1, μ2, …, μ n}. A is a set of filtering results. A k is a set composed of local decisions with filtering results of 1. A k is a set composed of local decisions with filtering results of 1. k is the number of elements of A k . U-A k: The set consisting of local decisions whose filtering results are 0. Since the filtering result is binary, then for N sensors, there are 2 N cases, which means that 2 N ratios ∧(z) can be obtained:

[0157]

[0158]

[0159]

[0160] wherein ∧(z) is the specific value of z's lambda.

[0161] Taking logarithm on both sides of formula (22) and simplifying, we obtain:

[0162]

[0163] wherein ln denotes logarithm with base e.

[0164] Since the detection statistic obeys Gaussian distribution with mean value 0 and variance σ 2 / N, after standardization, the following formula is obtained:

[0165]

[0166] wherein Q() is complementary cumulative distribution function, which is a monotone decreasing function, and exists inverse function, so the formula for calculating threshold value γ is:

[0167]

[0168] Since is a constant, α can be calculated to calculate the threshold value γ.

[0169] Let C1 = {∧(z) > λ}, C2 = {z: ∧(z) > λ}, the formulas for calculating P F and P D are as follows:

[0170]

[0171]

[0172] The number of sensors is N, and the original H0 and alternative H1 are as follows:

[0173]

[0174]

[0175] where P (χ n i ) = ∫ (χ n | H1(θ i )) π(θ i ) dθ i , and λ can be obtained when it equals the false alarm probability P F . Referring to equations (16) and (17), the Neyman-Pearson criterion in step S3 is given as follows:

[0176]

[0177] Similarly, when the above inequality can be equal. Let the conditional probability of the joint likelihood ratio of the sensor decision be:

[0178]

[0179] Arrange all the results of ∧(z) in size, denoted as ∧(z(j)), and obtain P∧(z(j)|H1) and P∧(z(j)|H0), and obtain:

[0180]

[0181] where j = 1, 2, …, 2 N According to the order of ∧(z), find the value of j* that satisfies equation (32), and finally substitute j* into the following equation:

[0182]

[0183] Calculate the threshold value λ*.

[0184] Substitute the threshold value λ* into the following equation:

[0185]

[0186] Calculate the detection probability P F that maximizes under the condition that the false alarm probability P is equal to the upper limit.

[0187] Substitute into the following equation:

[0188]

[0189] Calculate z(k), where z(k) is the result of multi-sensor information fusion.

[0190] As Figure 1 ​As shown, a multi-sensor information fusion system under the Neyman-Pearson decision criterion is used to execute the aforementioned multi-sensor information fusion method under the Neyman-Pearson decision criterion, comprising:

[0191] Multiple sensors are used to acquire a multi-dimensional dataset z;

[0192] The fusion center is used to calculate the observation data in the multi-dimensional dataset 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 filtered result, and perform information fusion on the filtered result to obtain the multi-sensor information fusion result.

[0193] The fusion center is also used to establish a system with N sensors, a sensor measurement sequence length of M, and a Gaussian noise set for the N sensors. The false alarm probability is P F The measurement model for the sensor is as follows:

[0194]

[0195] Where H0 represents unacceptable detection signals, H1 represents acceptable detection signals, 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 Let P be the maximum permissible error of N sensors under Gaussian noise. F ={Δε×0,Δε×1,…,Δε×L}, where Δε is the factory error rate;

[0196] False alarm probability P F In the given information, L = 1 / Δε, and N sensors have a false alarm probability P. F The following data matrix P F ∈R N×L R is the dimension;

[0197] Set χ n (m), P D P F P A P S and J, where χ n (m) is the vector set of M observations from the nth sensor, where m∈{1,2,...,M}, P D Let P be the sensitivity of any sensor, which is also the detection probability. A Let P be the probability that an unreliable sensor needs to be discarded. S J represents the probability of retaining sensor data despite unreliable data, and J is the overall optimization objective.

[0198] χ n (m) satisfies the following formula:

[0199] χ n (m) = {x n (1), x n (2), …, x n (M)} (3);

[0200] P D and P F are exactly opposite, set up under H1 and H0 P D and P F The formula is as follows:

[0201]

[0202]

[0203] P A and P S The setting is due to the existence of unpredictable disturbance when the sensor is working, set up P A and P S Satisfy the following formula:

[0204]

[0205] For the reasonable decision of the sensor under the premise of conforming to the error rate when leaving the factory, set up the false alarm probability P F In the allowable value range, so that its error probability P N Minimum, satisfy the following formula:

[0206]

[0207] Where, P F False alarm probability, D1 is the observation data under the detection probability, α is the allowable value, P N Error probability;

[0208] Set J satisfies the following formula:

[0209] J = λ z P N + ∫ z [P(z|H1)-λP(z|H0)]dz (9),

[0210] Where, λ z The likelihood ratio, λ is a reasonable threshold.

[0211] The Neyman-Pearson decision criterion satisfies the condition that the false alarm probability P F Upper limit, maximum detection probability PD .

[0212] The fusion center is further configured to calculate observation data in a multi-dimensional data set z of the sensor according to a maximum a posteriori probability criterion;

[0213] The false alarm probability P F is set to satisfy the upper limit, and the detection probability P D is maximized. The Neyman-Pearson decision criterion is:

[0214]

[0215]

[0216]

[0217] The observation data of each sensor is substituted into the above formula to obtain a probability value of H1, denoted as P x (m), and P x (m) is a single sensor decision result.

[0218] The P x (m) is substituted into the formula:

[0219]

[0220] The calculation result is: is a filtering result, that is, a system matrix of m measurement values, is a system matrix of m-1 measurement values, A(m) is a state transition matrix of m measurement values, and u(m-1) is a state transition matrix of m measurement values.

[0221] The fusion center is further configured to perform sequential decision according to the Neyman-Pearson decision criterion to obtain a multi-sensor decision result.

[0222] The multi-sensor decision result is substituted into the formula:

[0223]

[0224] The calculation result is z(k), wherein z(k) is a multi-sensor information fusion result, k is the number of elements of A k , and A k is a set composed of local decisions with a filtering result of 1.

[0225] In addition, in order to verify the difference between the present application and the prior art, simulation experiments and actual test experiments are respectively performed on the present application and the conventional algorithm, and the simulation experiment of the present application 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 RAM is 128G, and the operating system is Windows 10 Professional; the programming language is Python (version 3.9.7), and the development environment is VS Code.

[0227] In the simulation experiment, in order to verify the rationality of the application, the ROC curve is introduced. The ROC curve is extended from the initial military field to the medical field, and then to the machine learning field, which well evaluates the sensitivity and specificity relationship of the data. As shown in Figure 3 (a) to Figure 3 (d), the ROC curve of the number N and the measured sequence length M is drawn. It can be seen that when the value of M is larger, the ROC curve of the single sensor measurement sequence decision is smoother, which proves that the fusion effect based on the application on the sensor data has a certain effect, but the number of sensors N is small, and the fusion effect is poor. With the increase of N, the fusion effect has changed obviously, and through the ROC curve, the detection performance of different sensors can be compared, and the Figure 3 (a) to Figure 3 (d) can be seen that the detection performance of the multi-sensor fusion is obviously better than that of the single sensor.

[0228] As shown in Figure 4 (a) to Figure 4 (d), in order to check the influence of noise value on the performance of the algorithm, the value of σ 2 is changed. The results show that as the value of σ 2 increases, the application shows good fault tolerance, that is, it can also effectively eliminate the sudden disturbance of the sensor, which proves the superiority of the application.

[0229] As shown in Figure 2 , the actual test experiment uses a quadrotor unmanned aerial vehicle. The sensors used by the quadrotor unmanned aerial vehicle include one high-precision MPU9250 gyroscope and four medium-precision MPU6500 gyroscopes. The high-precision MPU9250 gyroscope is arranged at the center position of the body, and the four MPU6500 gyroscopes are arranged at the ends of the four arms. The high-precision MPU9250 gyroscope is used as the evaluation standard for the four MPU6500 gyroscopes.

[0230] As shown in Figure 5 , part of the data after taking the acceleration values of the four MPU6500 gyroscopes for analysis and processing by the application is shown. As shown in Figure 6 , the multi-sensor information fusion result after the data is fused and processed by the application is shown. From Figure 6As can be seen from the multi-sensor information fusion results of X-axis acceleration, Y-axis acceleration, and Z-axis acceleration, the data variations of a single MPU6500 gyroscope are quite unique, with very low curve overlap. This means that data from just four MPU6500 gyroscopes could yield four different output results, which is undesirable. Figure 6 As shown in the figure, the result of multi-sensor information fusion based on the present invention is well illustrated that the present invention can not only achieve the intended task, but also perform excellently in the ability to follow data changes, maintaining data sensitivity and improving anti-disturbance capability.

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

[0232]

[0233] After calculation, Figure 7 In (b), the maximum absolute value error is only 0.0165, and the averaged absolute value error is only 0.00194. In existing technologies, traditional fusion methods include mean fusion, weighted fusion, and BP neural network-based fusion (BPF). Figure 7 As shown in (c), this is a box plot of the RMSE of the three-axis accelerations for the fusion algorithm of this invention and the traditional fusion method. As can be seen from the plot, 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 prior art overall. From the data distribution, it can be seen that it is closer to a Gaussian distribution model, which provides better assurance of data sensitivity and fault tolerance. Accuracy (the opposite of error) is introduced to describe the qualitative analysis. The cumulative accuracy over a certain period is calculated and plotted, as shown... Figure 7 As shown in (d), the experimental results are quite obvious, and the accuracy of this invention is also superior to that of traditional fusion methods.

[0234] like Figure 8 As shown, a 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 according to this invention. Figure 8It can be seen that the data from the four MPU6500 gyroscopes processed by this invention are better than the data from the MPU9250 gyroscope, which well illustrates the actual performance of this invention.

[0235] like Figure 9 As shown, a comparison of the multi-sensor information fusion results of different numbers of MPU6500 gyroscopes in this 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 accuracy of a single MPU6500 gyroscope, and also improves anti-interference and fault tolerance.

[0236] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape, and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for multi-sensor information fusion under the Neyman-Pearson decision criterion, characterized in that, Comprise: S1: fusion center acquires multi-dimensional data set z, sets up test model, wherein, z={[χ[1],χ[2],…,χ[n]]T},χ[1] It is the observation sequence of sensor 1 at T time,χ[n] It is the observation sequence of sensor n at T time; The step of the S1, specifically includes: The fusion center sets up the number of sensors N, the Gaussian noise set of N sensors , the false alarm probability is P F and the measurement model of the sensor is: ， Wherein, H0 represents that the detection signal is not acceptable, H1 represents that the detection signal is acceptable, x[n] is a measurement sequence of sensor n at any time, n∈{0, 1,…, N-1}, w[n] is a Gaussian white noise with zero mean and given variance, A is a state transition matrix of measurement value, 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. False alarm probability P F In this case, L = 1 / Δε, N sensors in a data matrix P F under false alarm probability P F ∈ R N× L , R is the dimension; Establish χ n (m), P D , P F , P A , P S and J, wherein χ n (m) is the vector set of the nth sensor M observations, m ∈ {1, 2, …, M}, P D is the sensitivity for any sensor, i.e. the detection probability, P A is the probability for unreliable sensors that need to be discarded, P S is the probability for unreliable sensors that are kept instead, and J is the overall optimization objective; Establish χ n (m) satisfies the following equation: χ n (m) = {x n (1), x n (2),..., x n (M)} (3); The P D and P F formula is as follows: ， ； P A and P S satisfies the following equation: ； Set up a false alarm probability P limit F In the allowable value range, so that its error probability P N Minimum, meet the following formula: ， where P F is the false alarm probability, D1 is the observed data at the detection probability, a is the tolerable value, and P N is the error probability. Set up J satisfies the following formula: J = λ z P N +∫ z [P(z|H1)—λP(z|H0)]dz (9), where λ z is the likelihood ratio and λ is a reasonable threshold value. S2: according to maximum posterior probability criterion, the observation data in the multi-dimensional data set z is calculated, the observation data is substituted into the Neyman-Pearson decision criterion to obtain the single sensor decision result, and the single sensor decision result is substituted into the Kalman filtering algorithm to obtain the filtering result; S3: the filtering result is information fused to obtain multi-sensor information fusion result; The step of the S2, specifically includes: According to maximum posterior probability criterion, the observation data in the multi-dimensional data set z of sensor is calculated; The false alarm probability P F The Neyman-Pearson criterion for maximizing the detection probability P D under the condition of satisfying the upper limit of the false alarm probability P ， ， ； Alpha and beta are constants; The observation data of each sensor is substituted into the above formula decision criterion to obtain the probability value of H1, denoted as P x (m), P x (m) is the single-sensor decision result; P x (m) Substitute into the equation: ； The calculation is as follows , is the system matrix of m measurement values, and is the system matrix of m-1 measurement values, A(m) is the state transition matrix of m measurement values, and u(m-1) is the state transition matrix of m measurement values.

2. The method according to claim 1, wherein In the step of S2, the Neyman-Pearson decision criterion satisfies a false alarm probability P F Under the condition of the upper limit, the detection probability P is maximized D .

3. The method for multisensor information fusion under the Neyman-Pearson criterion according to claim 1, characterized in that, The step of the S3, specifically includes: According to the Neyman-Pearson decision criterion, the multi-sensor decision result is obtained by sequential decision; The multi-sensor decision result is substituted into formula: ； The z(k) is calculated, wherein the z(k) is a multi-sensor information fusion result, k is the number of elements of A k The z(k) is calculated, wherein the z(k) is a multi-sensor information fusion result, k is the number of elements of A k The z(k) is calculated, wherein the z(k) is a multi-sensor information fusion result, k is the number of elements of A The z(k) is calculated, wherein the z(k) is a multi-sensor information fusion result, k is the number of elements of A

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