A multiple decision fusion method based on minimum error rate

Abstract

The present application relates to a kind of multi-element decision fusion methods based on minimum error rate, based on optimization method, realize the multi-element decision fusion in the event multi-classification situation, first classify event and extract the features under each condition, then each source is classified according to the event and combined with the Bayes rule to carry out local decision, secondly, according to the time-varying characteristics of event, select appropriate fusion rule, finally, the decision of each source is fused in the fusion center to obtain the final global decision result.The method solves the limitation of traditional binary decision fusion, which only contains two cases of hypothesis H1 and hypothesis H0 that the event does not exist, at the same time, a variety of fusion rules are used, which further improves the decision accuracy.

Description

Technical Field

[0001] This invention relates to a multiple-hypothesis multi-sensor decision fusion method based on minimizing error rate, belonging to the field of multi-sensor information fusion technology. Background Technology

[0002] Currently, multi-sensor distributed detection systems with data fusion are widely used in civilian and military fields. The optimality of most detection fusion rules implemented in these systems relies on knowledge of the probability distributions of all distributed sensors. Due to the instability of sensor probability density functions, the overall detection performance of the central processing unit (CPU) is often worse than expected. To address the target detection problem in distributed multi-sensor data fusion systems, a novel multi-decision fusion rule is proposed. Summary of the Invention

[0003] To overcome the shortcomings of existing research, this invention provides a multivariate decision fusion method based on minimum error rate, which improves decision accuracy, expands the number of decision categories from two dimensions to multiple dimensions, and broadens the decision space. It also overcomes the limitation of traditional binary decision fusion, which only includes two cases: hypothesis H1 if the event is true and hypothesis H0 if the event is false. Furthermore, by using multiple fusion rules, the decision accuracy is further improved.

[0004] The specific steps of a multivariate decision fusion method based on minimum error rate are as follows:

[0005] Step 1: Classify and model the features of the decision-making objects;

[0006] Step 2: Each observation source extracts the feature quantities of target k at time t;

[0007] Step 3: Each observation source makes local decisions regarding the feature quantities;

[0008] Step 4: Construct a decision information matrix among different sources;

[0009] Step 5: Select either a single-step decision fusion rule or a multi-step decision fusion rule based on the time-varying characteristics of the feature quantities;

[0010] Step 6: The fusion center fuses the local decision results from each observation source to obtain the global decision result.

[0011] Preferably, step three includes the following sub-steps:

[0012] S3.1: Posterior probability, calculated based on prior information of the target category distribution function, the posterior probability value of the target belonging to each category;

[0013] S3.2: Posterior probability ratio, which compares the posterior probability values ​​of the target belonging to different categories to obtain the posterior probability ratio between different categories;

[0014] S3.3: Log-likelihood ratio, which is the log-likelihood ratio of the posterior probabilities obtained by taking the logarithm of the ratio of posterior probabilities between different target categories;

[0015] S3.4: Decision-making: Based on the decision-making rule of maximizing posterior probability, obtain local decision results from different sources;

[0016] Preferably, step four specifically includes:

[0017] For constant feature quantities, such as the physical properties of the target when tracking it, like its contour and natural frequency, to achieve better fusion results, assume that n sensors each make L decisions for the same event.

[0018]

[0019] Where r j Let r be the decision column vector j =[r j1 ,r j2 ,…,r jL ] T Among them, r jL Let l represent the l-th decision made by sensor j.

[0020] For non-constant features where sensors cannot make multiple decisions in a short period, such as velocity features, it is impossible to determine whether a target is a fighter jet before it exhibits its maximum speed. Furthermore, the target's historical decisions may not be suitable for fusion. Therefore, only single-decision fusion rules can be adopted.

[0021] B = [r1, r2, ..., r n ]

[0022] Where, r j (j = 1, 2, ..., n) represents the decision of sensor j.

[0023] Preferably, the specific method of step six is ​​as follows:

[0024] For constant feature quantities, the optimal decision u for the fusion center, according to the optimization method, is as follows:

[0025]

[0026] in,

[0027]

[0028]

[0029] Z is a unit column vector, u i It is a constant column vector.

[0030] For non-constant feature quantities, the constant feature quantity method introduces a fusion weight vector C, which is the fusion rule for multiple decisions. The fusion rule for a single decision is as follows:

[0031] Because of the single decision-making process, the local decision is reduced from a matrix to a vector u = B = [r1, r2, ..., r n ]

[0032] Choose any hypothesis k = 1, 2, ..., m from the m-fold hypotheses and calculate the likelihood ratio:

[0033]

[0034] Define the log-likelihood ratio:

[0035]

[0036] Where, ε j S1 and S2 are the prior anomaly probabilities of sensor j, defined as follows:

[0037]

[0038]

[0039] Therefore, the decision-making rules of the fusion center are as follows:

[0040]

[0041] The main features of this invention are as follows:

[0042] 1. The decision dimension has been expanded from the traditional binary decision to a multi-dimensional decision.

[0043] 2. Provide a model of the events and characteristics of the object to be decided.

[0044] 3. Use multiple fusion center decision rules for decision making.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] 1. By using multiple fusion rules, the accuracy of overall decision-making is improved. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart of the multivariate decision fusion method based on minimum error rate according to the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Reference Figure 1 A multivariate decision fusion method based on minimum error rate includes the following steps:

[0051] Step 1: Classify and model the features of the decision-making objects.

[0052] Before making decisions about an object, it is necessary to classify its events and model its features. This process varies depending on the object's problem and is often determined by empirical or formulaic values. The results are represented using a distribution, where multiple sensors estimate the feature quantities, and each sensor's estimate follows a normal distribution. Let there be m hypotheses H for classifying a certain event. i (i = 1, 2, ..., m), and for any hypothesis i, there exists a hypothesis H that can distinguish it from other hypotheses. k The characteristic μ of (k = 1, 2, ..., m; k ≠ ​​i) i Multiple sensors are currently used to estimate the feature quantities, and the estimation results follow a normal distribution.

[0053]

[0054] Among them, H i P(x) represents the i-th hypothesis of the event being true. j |H i ) represents event H i Under the condition that the sensor j estimates the feature quantity as x j The probability, μ i , These are events H. iGiven that the hypothesis holds true, the mean and variance of the sensor's estimate of the characteristic quantity under a normal distribution, where n is the number of sensors and m is the total number of multiple hypotheses.

[0055] Step 2: Each observation source extracts the feature quantities of target k at time t.

[0056] Step 3: Each observation source makes local decisions regarding the feature quantities.

[0057] The local decision rule for the sensor is as follows: For sensor j, choose any hypothesis k = 1, 2, ..., m from m hypotheses and calculate (m-1) posterior probability ratios:

[0058]

[0059] According to Bayes' theorem, the above equation can be calculated from the following equation:

[0060]

[0061] Among them, P i For event H i The prior probability is unknown in the simulation, so it is set to 1 / m;

[0062] Define the log-likelihood ratio at the local end of the sensor as:

[0063]

[0064] Therefore, the local decision rule for sensor j is as follows:

[0065]

[0066] Step 4: Construct a decision information matrix between different sources.

[0067] For constant feature quantities, such as the physical properties of the target when tracking it, like its contour and natural frequency, to achieve better fusion results, assume that n sensors each make L decisions for the same event.

[0068]

[0069] Where r j Let r be the decision column vector j =[r j1 ,r j2 ,…,r jL ] T Among them, r jL Let l represent the l-th decision made by sensor j.

[0070] For non-constant features where sensors cannot make multiple decisions in a short period, such as velocity features, it is impossible to determine whether a target is a fighter jet before it exhibits its maximum speed. Furthermore, the target's historical decisions may not be suitable for fusion. Therefore, only single-decision fusion rules can be adopted.

[0071] B = [r1, r2, ..., r n ]

[0072] Where, r j (j = 1, 2, ..., n) represents the decision of sensor j.

[0073] Step 5: Select either a single-decision fusion rule or a multi-decision fusion rule based on the time-varying characteristics of the feature quantities.

[0074] Step Six: The fusion center merges the local decision results from each observation source to obtain the global decision result.

[0075] For constant feature quantities, the optimal decision u for the fusion center, according to the optimization method, is as follows:

[0076]

[0077] in,

[0078]

[0079]

[0080] Z is the unit column vector u i It is a constant column vector.

[0081] For non-constant feature quantities, the constant feature quantity method introduces a fusion weight vector C, which is the fusion rule for multiple decisions. The fusion rule for a single decision is as follows:

[0082] Because of the single decision-making process, the local decision is reduced from a matrix to a vector u = B = [r1, r2, ..., r n ]

[0083] Choose any hypothesis k = 1, 2, ..., m from the m-fold hypotheses and calculate the likelihood ratio:

[0084]

[0085] Define the log-likelihood ratio:

[0086]

[0087] Where, ε j S1 and S2 are the prior anomaly probabilities of sensor j, defined as follows:

[0088]

[0089]

[0090] Therefore, the decision-making rules of the fusion center are as follows:

[0091]

[0092] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A minimum error rate based multiple decision fusion method, characterized by: Includes the following steps: Step 1: Classify and model the features of the decision-making objects; Step one specifically includes: Before making decisions about an object, it is necessary to classify its events and model its features. The process varies depending on the object's problem and is often determined by empirical or formulaic values. The results are represented using a distribution, where multiple sensors estimate the feature quantities, and each sensor's estimate follows a normal distribution. Let the classification of a certain event be... Rehypothesis And for any hypothesis Each has a hypothesis that can distinguish it from others. Feature quantity Multiple sensors are used to estimate the feature quantities, and the estimation results follow a normal distribution. : in, Indicates the first The re-assumption holds true. Indicates an event Sensor under established conditions The characteristic quantity is estimated as The probability, These are events Under the condition that the sensor estimates of the feature quantities follow a normal distribution, the mean and variance of the sensor's estimates of the feature quantities are given. It is the number of sensors. It is the total number of multiple hypotheses; Step 2: Each observation source pair Momentary Goal Extract the feature values; Step 3: Each observation source makes local decisions regarding the feature quantities; S3.1: Posterior probability, calculated based on prior information of the target category distribution function, the posterior probability value of the target belonging to each category; S3.2: Posterior probability ratio, which compares the posterior probability values ​​of the target belonging to different categories to obtain the posterior probability ratio between different categories; S3.3: Log-likelihood ratio, which is the log-likelihood ratio of the posterior probabilities obtained by taking the logarithm of the ratio of posterior probabilities between different target categories; S3.4: Decision-making: Based on the decision-making rule of maximizing posterior probability, obtain local decision results from different sources; The sensor local decision rule is: for the sensor ,exist Choose one of the re-assumptions. And calculate The ratio of posterior probabilities: According to Bayes' theorem, the above equation can be calculated from the following equation: in, For the event The prior probability is unknown in the simulation, so let it be set as ; Define the log-likelihood ratio at the local end of the sensor as: Therefore, the sensor The local decision-making rules are as follows: Step 4: Construct a decision information matrix among different sources; Step 5: Select either a single-step decision fusion rule or a multi-step decision fusion rule based on the time-varying characteristics of the feature quantities; Step Six: The fusion center merges the local decision results from each observation source to obtain the global decision result.

2. The multivariate decision fusion method based on minimum error rate according to claim 1, characterized in that: Step four specifically includes: For constant feature quantities, when tracking a target, the contour, intrinsic frequency, and physical properties of the target lead to better fusion results, assuming... The sensors each performed different actions on the same event. This decision in Decision column vector ,in, Indicates sensor The Secondary decision; For non-constant feature quantities and situations where sensors cannot make multiple decisions in a short period of time, a single-decision fusion rule is adopted. in, Indicates sensor The decision.

3. The multivariate decision fusion method based on minimum error rate according to claim 1, characterized in that: Step six specifically includes: For constant feature quantities, the optimal decision of the fusion center is determined according to the optimization method. as follows: in, It is a unit column vector. It is a constant column vector; For non-constant feature quantities, the constant feature quantity method introduces a fusion weight vector. This refers to the fusion rules for multiple decisions. The fusion rules for a single decision are as follows: Because of the single-step decision-making process, the local decision is reduced from a matrix to a vector. exist Choose one of the re-assumptions. And calculate the likelihood ratio: Define the log-likelihood ratio: in, It is a sensor The prior anomaly probability, and The definition is as follows: Therefore, the decision-making rules of the fusion center are as follows: 。

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