Fixed single-station passive positioning method and related device based on Gaussian particle filtering

Abstract

The present application discloses a fixed single-station passive positioning method based on Gaussian particle filtering, which can improve the accuracy of determining the motion state information of the target object in Gaussian particle filtering by calculating the weight of particles based on a fuzzy clustering model. The method includes: based on a Gaussian distribution model, determining a first motion state particle set corresponding to the initial motion state information of the target object at the first moment; based on a sensor observation model, converting a second motion state particle set into an observation prediction value set of the target object at the second moment; taking each observation prediction value set as a cluster center, obtaining the membership information of the actual observation value set of the target object at the second moment and the cluster center based on a fuzzy clustering model; based on a state transfer model, taking the first motion state particle set and the membership information as input, obtaining the target motion state information of the target object at the second moment, and the target motion state information includes the target spatial position information and the target speed information.

Description

Technical Field

[0001] The present application relates to the field of radar data processing technology, and in particular to a fixed single-station passive positioning method and related devices based on Gaussian particle filtering. Background Art

[0002] Particle filtering is a method that uses the Monte Carlo method to solve the optimal estimate in Bayesian filtering. Based on particle filtering, the posterior probability distribution of unknown states is approximated by a Gaussian distribution, which is called Gaussian particle filtering. Gaussian particle filtering includes particle sampling, particle prediction, and weight update.

[0003] A method for calculating weights in Gaussian particle filtering is to obtain the predicted values ​​generated by a group of particles, compare them with the actual observed values ​​at that moment, evaluate the predicted values ​​through the observation equation, and obtain the probability of each particle obtaining the actual observed value after entering the observation equation as the output. This probability is the weight of each particle.

[0004] However, when calculating the weight of each particle through the observation equation, the calculation efficiency and accuracy are low, resulting in low accuracy in determining the motion state information of the target object at the current moment using Gaussian particle filtering. Summary of the invention

[0005] The main purpose of the embodiments of the present application is to improve the accuracy of determining the motion state information of the target object at the current moment in Gaussian particle filtering.

[0006] To achieve the above-mentioned purpose, an embodiment of the present application provides a fixed single-station passive positioning method based on Gaussian particle filtering, the method comprising the following steps: based on a Gaussian distribution model, determining a first motion state particle set corresponding to the initial motion state information of the target object at the first moment, the first motion state particle set including at least two motion state particles; based on a state transition model, taking the first motion state particle set as input to obtain a second motion state particle set of the target object at the second moment; based on a sensor observation model, converting the second motion state particle set into an observation prediction value set of the target object at the second moment, each observation prediction value set corresponding to each motion state particle one-to-one; taking each observation prediction value set as a cluster center, obtaining the membership information of the actual observation value set of the target object at the second moment and the cluster center based on a fuzzy clustering model, the membership information indicating the reliability of each motion state particle corresponding to each observation prediction value set; based on the state transition model, taking the first motion state particle set and the membership information as input to obtain the target motion state information of the target object at the second moment, the target motion state information including the target spatial position information and the target speed information.

[0007] To achieve the above-mentioned purpose, an embodiment of the present application also proposes a passive positioning system, which includes a memory, a processor, a program stored in the memory and executable on the processor, and a data bus for realizing connection and communication between the processor and the memory. When the program is executed by the processor, the steps of the aforementioned fixed single-station passive positioning method based on Gaussian particle filtering are implemented.

[0008] To achieve the above-mentioned purpose, the present application provides a storage medium for computer-readable storage, the storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the steps of the aforementioned fixed single-station passive positioning method based on Gaussian particle filtering.

[0009] The fixed single-station passive positioning method and related device based on Gaussian particle filtering proposed in the present application improve the accuracy of determining the motion state information of the target object at the current moment in Gaussian particle filtering by calculating the weight of particles based on a fuzzy clustering model. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0011] Figure 1 A schematic diagram of an architecture for fixed single-station single-target positioning and tracking provided in an embodiment of the present application;

[0012] Figure 2 A flowchart of a fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0013] Figure 3 Another step flow chart of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0014] Figure 4 Another step flow chart of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0015] Figure 5 Another step flow chart of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0016] Figure 6 Another step flow chart of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0017] Figure 7 The positional relationship between the observation station and the radiation source in the two-dimensional space measurement model provided in the embodiment of the present application;

[0018] Figure 8 Another step flow chart of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0019] Fig. 9 The positional relationship between the observation station and the radiation source in the three-dimensional space measurement model provided in the embodiment of the present application;

[0020] Fig.10 A tracking effect diagram in an application scenario of a fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0021] Fig.11 A position error diagram in an application scenario of a fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application;

[0022] Fig.12 A schematic diagram of the structure of a passive positioning system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0023] Radar is an electronic device that uses electromagnetic waves to detect targets. It can detect targets and determine their spatial position and speed.

[0024] The earliest positioning technology for measuring the spatial position and speed of a target was active positioning technology. Active positioning technology means that the observation station actively transmits electromagnetic waves to the target object. The electromagnetic waves are reflected by the target object and received by the observation station. The observation station analyzes the electromagnetic waves obtained after reflection from the target object to determine the spatial position, speed and other status information of the target object.

[0025] Since radars using active positioning technology radiate electromagnetic waves at a relatively fixed frequency, they can be easily detected and tracked by the enemy, and then attacked by the enemy's targeted electronic interference and precision-guided weapons. This will not only reduce the positioning performance of the target, but also endanger the security of the radar positioning system.

[0026] Passive positioning technology means that the observation station no longer actively sends any electromagnetic waves to the target object, but only receives electromagnetic waves generated by the movement of the target object, and determines the state information of the target object by analyzing the electromagnetic waves received by the movement of the target object. Since the radar using passive positioning technology does not radiate electromagnetic waves to the target object, the probability of being discovered by the enemy is reduced, so it is not easy to become a target of anti-radiation missiles.

[0027] Due to the existence of environmental noise and random disturbances, the electromagnetic waves generated by the movement of the target object are disturbed and change, and the electromagnetic waves received by the radar using passive positioning technology are also mixed with a lot of noise. This will cause the actual observation values ​​obtained by directly analyzing the electromagnetic waves received by the radar using passive positioning technology to be often inaccurate. It is necessary to perform data processing on the actual observation values ​​analyzed by the radar using passive positioning technology in order to accurately obtain the motion state of the target object.

[0028] Filtering technology is a technology that extracts useful signals from received signals containing interference. In passive positioning technology, filtering technology is needed to extract electromagnetic wave signals generated by the movement of target objects from electromagnetic wave signals that are disturbed and doped with noise.

[0029] Statistical inference is a statistical method that infers the population through samples. Since the actual observation values ​​obtained by radar analysis using passive positioning technology are inaccurate, it is necessary to predict the motion state of the target object as a whole based on the actual observation values ​​with lower accuracy, and then make corrections based on the actual observation values ​​and the predicted motion state of the target object to improve the accuracy of the predicted motion state.

[0030] Bayesian statistics is a method of statistical inference. Bayesian statistics is to randomly select the unknown model that people want to infer from a class of known models. A random variable is introduced to characterize the unknown model, and then a prior probability distribution of the random variable in the unknown model is constructed. The prior probability refers to the probability obtained based on past experience and analysis. When a known data of the random variable is obtained, the posterior probability distribution of the random variable in the unknown model is derived based on the prior probability distribution and the known data of the random variable. The posterior probability refers to the probability that is revised after obtaining the "result" information.

[0031] Applying Bayesian statistics to filtering technology is called Bayesian filtering. Bayesian filtering is essentially a type of model-driven filtering algorithm that builds corresponding models based on the prior statistical characteristics of the target and sensor system to describe state evolution and observation behavior. Bayesian filtering includes target state transition models and sensor observation models.

[0032] The target state transition model usually contains prior knowledge about the target motion pattern and attribute evolution. This prior knowledge usually includes physical reality constraints and other conditional constraints. It can narrow the scope of the state space that needs to be searched in tracking applications and find targets that meet a certain motion pattern.

[0033] The sensor observation model contains the prior statistical characteristics of the sensor measurement process, that is, the observation model describes the process by which a target with a specific state is mapped into the observation space by the sensor.

[0034] Markov chain usually refers to a random process with Markov property and exists in discrete exponential set and state space. For target positioning and tracking applications, it can be understood that the state of the target at the next moment is only related to the current state, but not to the past state.

[0035] Since target positioning and tracking is a Markov chain, when Bayesian filtering is applied to target positioning and tracking, it is divided into two main steps: prediction step and update step, which correspond to the target state transition model and sensor observation model respectively. The prediction step is the process of predicting the target state at the current moment based on the estimated state of the target at the previous moment (the estimated state at the previous moment is the expectation of the posterior probability distribution of the target state at the previous moment) using the target state transition model (obtaining the expectation of the prior probability distribution of the target state at the current moment); the update step is the process of predicting the measurement state of the target at the current moment using the predicted state at the current moment (the expectation of the prior probability distribution of the target state at the current moment) using the sensor observation model, and correcting the prediction result using the actual measurement result (obtaining the expectation of the posterior probability distribution of the target state at the current moment).

[0036] However, Bayesian filtering is computationally difficult and requires the calculation of multi-dimensional integrals. It is difficult to obtain an analytical solution to the posterior probability through the calculation of the prior probability. As fast computing has gradually become available, a large number of recent research results on Bayesian filtering have focused on how to make Bayesian filtering feasible.

[0037] Particle filtering is a method that uses the Monte Carlo method to solve the optimal estimate in Bayesian filtering, and uses the importance sampling method to obtain a set of continuously updated random samples (called particles) in the state space. This set of particles corresponds to a set of weights. By constantly updating the particles in the system and updating the weights according to the weight size, the system state that needs to be estimated is approximated. The principle of particle filtering is as follows:

[0038] (1) Particle initialization: Since the state of the system is unknown, we assume that the particles are uniformly distributed in the state space of the system and initialize the generated particles. Then all samples are input into the state transfer equation to obtain the predicted particles.

[0039] (2) Particle prediction stage: The particle filter updates the value of each particle through random sampling based on the posterior probability distribution determined at the previous moment, and then inputs the updated particle into the state transfer equation to obtain a set of predicted values. The prediction result at that moment is obtained through the weighted combination of this set of predicted values.

[0040] (3) Weight update phase: After obtaining the predicted values ​​generated by a group of particles, compare them with the actual observed values ​​at that moment and evaluate the predicted values ​​through the observation equation. That is, the probability that the ith particle can obtain the actual observed value after entering the observation equation is taken as the weight of the particle. The more likely the particle is to obtain the actual observed value, the higher the corresponding weight is, which means that the particle is more consistent with the actual probability distribution.

[0041] (4) Particle resampling: In order to avoid particle degradation, particles with lower weights need to be removed and particles with higher weights need to be copied during the algorithm iteration step, so that the distribution of particles is closer to the real solution. In the next filtering process, the resampled particles are used, so that each round of filtering makes the particles more consistent with the probability distribution of the real state, and then the particles are brought into the state transfer equation for prediction, so that the prediction results are more accurate.

[0042] Based on the above particle filter framework, the posterior probability distribution of the unknown state is approximated by a Gaussian distribution, which is called Gaussian Particle Filter (GPF).

[0043] Based on the steps of Bayesian filtering and the principle of Gaussian particle filtering, the steps of Gaussian particle filtering method can be obtained as follows:

[0044] (1) The estimated state at the previous moment is the expectation of the posterior probability distribution of the target state at the previous moment. Assume that the posterior probability distribution of the target state at the previous moment is Gaussian, that is, the estimated state at the previous moment conforms to the Gaussian distribution.

[0045] (2) Based on Gaussian distribution, multiple random samples satisfying Gaussian distribution and the covariance matrix at the previous moment are generated according to the target state at the previous moment and the covariance matrix at the previous moment representing the uncertainty of the system at the previous moment. The random samples are called particles, and each random sample is a possible target motion state at the previous moment.

[0046] (3) Based on the target state transition model, multiple sets of possible target states at the previous moment are used as input to predict multiple possible target motion states;

[0047] (4) Based on the sensor observation model, multiple possible target states are taken as input to obtain multiple sets of predicted observation values ​​corresponding to the multiple possible target states;

[0048] (5) Compare a set of actual observations at the current moment with multiple sets of predicted observations, and evaluate the probability that the particle corresponding to each set of predicted observations can obtain the actual observations as input, that is, the probability that the i-th particle can obtain the true observation after inputting the observation equation. Let this probability be the weight of the particle. The more likely a particle is to obtain the true observation, the higher its corresponding weight will be, which means that the particle is more consistent with the true probability distribution.

[0049] (6) Based on the target state transition model, multiple groups of possible target states at the previous moment and the weights of each group of possible target states are taken as input to obtain the probability distribution of the target state at the current moment. By finding the expectation of the probability distribution of the target state at the current moment, the target state at the current moment can be obtained, and the covariance matrix at the current moment representing the uncertainty of the system at the current moment can be calculated.

[0050] Gaussian particle filter is a non-resampling filtering algorithm, which has better real-time performance than particle filter. However, the calculation of weights in Gaussian particle filter has problems such as low efficiency and particle degradation. Improving the accuracy of weight calculation in Gaussian particle filter has become one of the important research directions.

[0051] The embodiment of the present application provides a fixed single-station passive positioning method and related devices based on Gaussian particle filtering, which can calculate the membership information of each particle as a weight based on a fuzzy clustering model, thereby improving the accuracy of determining the motion state information of the target object at the current moment in the Gaussian particle filtering.

[0052] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0053] The flowcharts shown in the accompanying drawings are only examples and do not necessarily include all the contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may also be decomposed, combined or partially merged, so the actual execution order may change according to actual conditions.

[0054] It should be understood that the terms used in this application specification are only for the purpose of describing specific embodiments and are not intended to limit the application. As used in this application specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0055] See also Figure 1 , Figure 1A schematic diagram of the architecture of fixed single-station single-target positioning and tracking provided in an embodiment of the present application.

[0056] First, the motion model is established using the observation and target state, and the initial state of the target can be directly calculated. After the initial state is determined, the motion trajectory is tracked. First, a maneuver detection is performed on the target to determine whether the target is maneuvering. If the target is detected to be maneuvering, it is necessary to perform maneuvering target tracking processing, otherwise it is processed as uniform linear motion. Finally, the target state prediction is updated using the observation, and the target state at the next moment is estimated based on the fuzzy Gaussian particle filter algorithm. In this way, the positioning and tracking of a single target by a fixed single station can be completed.

[0057] based on Figure 1 The architecture of fixed single-station single-target positioning and tracking is shown, and the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application is introduced below.

[0058] See also Figure 2 , Figure 2 A method flow chart of a fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application.

[0059] 201. Based on a Gaussian distribution model, determine a first motion state particle set corresponding to initial motion state information of a target object at a first moment.

[0060] Sampling from the initial motion state information at the first moment generates multiple random samples, which are called particles. Each random sample represents a possible motion state of the target object at the first moment. Sampling from the initial motion state information at the first moment generates random samples called particles, which need to satisfy Gaussian distribution.

[0061] 202. Based on the state transfer model, the first motion state particle set is used as input to obtain the second motion state particle set of the target object at the second moment.

[0062] The first motion state particle set at the first moment is taken as input, and state prediction is performed based on a state transition model representing state evolution, and the second motion state particle set of the target object at the second moment is obtained as output.

[0063] 203. Based on the sensor observation model, the second motion state particle set is converted into an observation prediction value set of the target object at the second moment.

[0064] Based on the sensor observation model representing the evolution of observations, the set of second motion state particles representing the second moment obtained by state prediction is converted into a set of observation prediction values ​​of the target object at the second moment. The observation prediction value set indicates that when the target object is in a certain motion state, according to the law of the sensor observation model, the observation value that the target object should have when it is in a certain motion state is predicted, and the corresponding observation prediction value set under the motion state is obtained. Each motion state particle corresponds one-to-one to each observation prediction value set.

[0065] 204. Taking each observation prediction value set as a cluster center, obtaining membership information between the actual observation value set of the target object at the second moment and the cluster center based on the fuzzy clustering model.

[0066] Assume that the particle set These particles belong to c classes, Represents the cluster center of each class, and defines the cost function Cost to represent the degree of discreteness of all particles and cluster centers:

[0067]

[0068] Among them, d(X i , V j ) represents the Euclidean distance between the particle and the aggregation center:

[0069] d(X i , V j )=||X i -V j || (2)

[0070] u ij Represents particle X i and cluster center V j Membership, and the membership satisfies the constraints:

[0071]

[0072] Using the Lagrange formula and the maximum entropy principle, the clustering objective function is defined:

[0073]

[0074] Among them, γ i and λ i is the Lagrange multiplier. When the derivative of equation (7) is zero, we can get the particle X i and V j The membership degree of is:

[0075]

[0076] In the Gaussian particle filtering process, the observed predicted value Z at time t ispre As the cluster center V t , at this time, just set the number of cluster centers c to the number of sampled particles N, and then select the appropriate γ i , we can use the membership degree u it Replace the weights of the original Gaussian particle filter

[0077]

[0078] Among them, γ i Possible values ​​are:

[0079]

[0080] in, For example X i The Jacobian matrix of , R is the process noise variance matrix.

[0081] Each observation prediction value set in the multiple observation prediction value sets is taken as a cluster center, and the membership information between the actual observation value set corresponding to the observation prediction value set and the cluster center is calculated according to formula (5).

[0082] 205. Based on the state transfer model, the first motion state particle set and the membership information are used as input to obtain the target motion state information of the target object at the second moment.

[0083] Based on the state transfer model, the first motion state particle set representing multiple groups of possible target states at the previous moment, i.e., the first moment, and the membership information representing the weight of each group of possible target states are taken as input to obtain the probability distribution of the motion state of the target object at the current moment, i.e., the second moment. By calculating the expectation of the probability distribution of the motion state of the target object at the current moment, i.e., the second moment, the target motion state information of the target object at the current moment, i.e., the second moment, can be obtained.

[0084] In the embodiment of the present application, a covariance matrix is ​​required to sample particles from the initial motion state information. The covariance matrix may use the initial covariance matrix or may be further calculated based on the initial covariance matrix.

[0085] See also Figure 3 , Figure 3 A method flow chart of a fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application, based on Figure 2 The embodiment shown, Figure 3 The illustrated embodiment further includes steps 206 to 209 .

[0086] 206. Obtain a first covariance matrix of the target object at a first moment.

[0087] The covariance matrix is ​​used to represent the uncertainty of the system. The passive positioning system obtains a first covariance matrix representing the uncertainty of the passive positioning system with the target object as the core when the target object is at the first moment.

[0088] The initial covariance matrix of traditional target tracking is obtained by the following formula:

[0089]

[0090] 207. Determine Doppler frequency change rate information from the first moment to the second moment according to a first Doppler frequency actual value in an actual observation value set of the target object at the first moment and a second Doppler frequency actual value in an actual observation value set of the target object at the second moment.

[0091] The passive positioning system continuously observes the target object and obtains a set of actual observation values ​​at each moment. The set of actual observation values ​​includes the actual value of Doppler frequency and may also include other types of actual values, such as the actual value of azimuth. The first moment is the moment before the second moment.

[0092] The passive positioning system obtains a first Doppler frequency actual value of the target object in a set of actual observation values ​​at a first moment and a second Doppler frequency actual value of the target object in a set of actual observation values ​​at the first moment.

[0093] The mathematical expression of Doppler frequency is:

[0094]

[0095] From the mathematical expression of Doppler frequency shown in formula (7), it can be seen that the actual value of Doppler frequency is closely related to the speed of the target object. Since the carrier frequency of the target radiation source is generally large and the wavelength of the signal is very short, when the speed of movement changes, the Doppler frequency changes dramatically.

[0096] Assume that the actual value of the Doppler frequency at the second moment is f dk , the Doppler frequency measurement value at the first moment is f dk-1 The passive positioning system calculates the difference between the actual value of the Doppler frequency at the second moment and the actual value of the Doppler frequency at the first moment, and obtains the Doppler frequency change rate information from the first moment to the second moment:

[0097] Δf dk =|f dk -f dk-1 | (8)

[0098] 208. When the Doppler frequency change rate information is greater than or equal to a preset threshold, determine an adaptive adjustment factor corresponding to the Doppler frequency change rate information.

[0099] When the target object does not maneuver, the magnitude and direction of the velocity remain unchanged, even in the presence of noise. dk changes very little; when the target maneuvers, Δf dk The value jumps to ten or even a hundred times when it is not maneuvered.

[0100] Set a large positive number as the threshold. dk >Threshold, the target is considered to have maneuvered, otherwise it is considered that the target has not maneuvered.

[0101] According to Δf dk A λ is selected according to the severity of the value mutation, where λ is an adaptive adjustment factor.

[0102] 209. Calculate the product of the first covariance matrix and the adaptive adjustment factor to obtain a second covariance matrix.

[0103] Assuming the target object maneuvers at time k, Δf dk The value suddenly changes, assuming that the target state covariance matrix is ​​P k-1|k-1 , then adjust P k-1|k-1 The values ​​are:

[0104]

[0105] When the target object maneuvers at the first moment, the Doppler change rate information from the first moment to the second moment changes suddenly, then the product of the first covariance matrix representing the uncertainty of the target object at the first moment and the adaptive adjustment factor is calculated to obtain the second covariance matrix of the target object updated according to the maneuver at the second moment.

[0106] based on Figure 3 The embodiment shown, the specific method of determining the adaptive adjustment factor corresponding to the Doppler frequency change rate information in the embodiment of the present application is introduced below.

[0107] See also Figure 4 , Figure 3 A method flow chart of a fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application, Figure 4 Steps 2081 and 2082 are Figure 3 A specific implementation of step 208 in FIG.

[0108] 2081. When the Doppler frequency change rate information is the first Doppler frequency change rate information, determine that the adaptive adjustment factor is the first adaptive adjustment factor.

[0109] According to the preset correspondence between the Doppler frequency change rate information and the adaptive adjustment factor, when the first Doppler frequency change rate information is greater than a preset threshold, the adaptive adjustment factor is determined to be the first adaptive adjustment factor.

[0110] 2082. When the Doppler frequency change rate information is the second Doppler frequency change rate information, determine that the adaptive adjustment factor is the second adaptive adjustment factor, the second Doppler frequency change rate information is greater than the first Doppler frequency change rate information, and the second adaptive adjustment factor is greater than the first adaptive adjustment factor.

[0111] When the Doppler frequency change rate information shows a second Doppler frequency change rate information that is larger than the first Doppler frequency change rate information, the adaptive adjustment factor is also determined to be a second adaptive adjustment factor that is larger than the first adaptive adjustment factor, that is, the larger the Doppler frequency change rate information, the larger the adaptive adjustment factor.

[0112] In combination with the above introduction, the fixed single-station passive positioning method based on Gaussian particle filtering in the embodiment of the present application is further described in detail below:

[0113] See also Figure 5 , Figure 3 or Figure 4 The illustrated embodiment also includes step 210 .

[0114] 210. Determine a third covariance matrix of the target object at a second moment according to the target motion state information and the second covariance matrix.

[0115] When calculating the motion state information of the target object at the current moment, i.e., the second moment, it is also necessary to calculate the third covariance matrix of the second moment to measure the uncertainty of the passive positioning system at the second moment in order to determine the motion state information of the target object at the next moment, i.e., the third moment.

[0116] A third covariance matrix of the target object at the second moment is calculated according to the target motion state information of the target object at the second moment and the second covariance matrix updated according to the maneuver decision.

[0117] based on Figures 2 to 5 The fixed single-station passive positioning method based on Gaussian particle filtering provided in the illustrated embodiment is further described in detail below:

[0118] See also Figure 6 The fixed single-station passive positioning method based on Gaussian particle filtering provided in the embodiment of the present application also includes step 211 and step 212.

[0119] 211. Based on the two-dimensional space measurement model, the radial velocity and radial distance of the target object at the first moment are determined according to the actual value of the azimuth angle and the actual value of the first Doppler frequency.

[0120] The position relationship between the observation station and the target in a two-dimensional scene is as follows: Figure 7 The observation station is fixed at the origin of the coordinate system, and the measurement information received by the observation station includes the azimuth angle β, Doppler frequency f dk .

[0121] Because the research is about fixed single-station passive positioning in a two-dimensional plane, the Doppler frequency definition can be obtained by f dk and The expression is:

[0122]

[0123]

[0124] When the target radiation source does not have a large maneuver, the effect of acceleration is ignored.

[0125]

[0126] Then the radial distance of the target relative to the observation station is:

[0127]

[0128] The expression of radial velocity is:

[0129]

[0130] 212. Determine the initial motion state information of the target object at the first moment according to the radial velocity and the radial distance.

[0131] According to the geometric relationship, the initial state of the target object is:

[0132]

[0133] based on Figures 2 to 6 The fixed single-station passive positioning method based on Gaussian particle filtering provided in the illustrated embodiment is further described in detail below:

[0134] See also Figure 8 The fixed single-station passive positioning method based on Gaussian particle filtering provided in the embodiment of the present application also includes steps 213 to 215.

[0135] 213. Determine the state equation and observation equation of the target object.

[0136] Assuming that the fixed observation station is located at the origin of the coordinate system, the state equation of the target is as follows:

[0137] X k =f(X k-1 )+e k-1 (18)

[0138] Where f(·) represents the nonlinear state transfer function, Indicates the state of the target. Represents the position x in the x direction respectively k and speed The position yk and velocity in the y direction Position in z direction k and speed e k is a Gaussian process noise with zero mean.

[0139] Since the direction finding information and Doppler frequency information of a single station are used, the observation equation of the system is designed as follows:

[0140] Z k =h(X k )+e k (19)

[0141] Among them, h(X k )∈R n →R m , n represents the dimension of the state, and m represents the dimension of the observation.

[0142] 214. Determine the three-dimensional space measurement model based on the state equation and observation equation.

[0143] In a three-dimensional fixed single-station passive positioning system, we can obtain measurement information including angle information and Doppler, mainly azimuth, elevation, azimuth change rate, elevation change rate and Doppler frequency change rate. The schematic diagram of the spatial relationship of the three-dimensional fixed single-station passive positioning measurement is as follows: Fig. 9 shown.

[0144] Among them, the nonlinear expressions of each measurement are defined as follows:

[0145] The target's azimuth α k and the pitch angle β k It can be defined as:

[0146]

[0147]

[0148] According to the target azimuth and pitch angles defined by equations (20) and (21), the azimuth change rate and the pitch change rate are as follows:

[0149]

[0150]

[0151] in, is the radial distance of the target from the observation station.

[0152] Due to the Doppler effect, if there is a relative radial velocity between the target and the observation station, the radiation source frequency f obtained by the observation station is k The Doppler frequency f dk , assuming the target radiation source frequency is f T Constant, then:

[0153] f k =f T +f dk (twenty four)

[0154] The Doppler frequency rate of change can be defined as follows:

[0155]

[0156] 215. Obtain a two-dimensional space measurement model based on the three-dimensional space measurement model.

[0157] The three-dimensional space measurement model in step 212 is converted into a two-dimensional space measurement model of passive positioning in a two-dimensional plane.

[0158] In combination with the above introduction, an application scenario of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application is introduced below:

[0159] The fixed single-station passive positioning method based on Gaussian particle filtering provided in the embodiment of the present application can be updated in the following manner in practical applications to achieve tracking and positioning of the target.

[0160] (1) Time update

[0161] 1) represents the mean of the posterior probability density, Represents the covariance of the posterior probability density. First, N particles are sampled from the posterior probability density function at time t-1. The particle set is expressed as

[0162] 2) Then calculate the state prediction value of each particle

[0163] 3) Finally, calculate the predicted mean of the target at time t and covariance

[0164]

[0165]

[0166] (2) Measurement update

[0167] 1) Calculate the predicted particle set The Jacobian matrix of each particle in and the observed predicted values ​​of each particle

[0168] 2) Then calculate each predicted particle according to formula (22) The membership degree of is used as the weight of Gaussian particle filter

[0169] 3) Normalize the particle weights.

[0170]

[0171] Finally, calculate the predicted mean of the target at time t and the covariance of the target at time t

[0172]

[0173]

[0174] In combination with the above introduction, another application scenario of the fixed single-station passive positioning method based on Gaussian particle filtering provided in an embodiment of the present application is introduced below:

[0175] In the two-dimensional scenario, the observation station is located at the origin of the coordinate system, the target is 200-300km away from the observation station, and the target radiation source moves at a uniform speed with acceleration disturbance. The total duration of the target movement is 300s. The frequency of the target radiation source is 10GHz, and the target state is: The observed quantities include azimuth angle α, azimuth angle change rate Doppler frequency f, Doppler frequency change rate The standard deviations of the observation noise are: α =1°, σ f =1Hz, The observation period is T=1s. The target changes its heading angle at 150s. 300 Monte Carlo simulations are performed. GPF and FGPF algorithms are used for tracking. The performance of each algorithm is analyzed and compared in the scenario of maneuvering targets with changing heading angles.

[0176] See also Fig.10 and Fig.11 . Fig.10This is the tracking effect diagram of the target. The tracking effect suddenly deteriorates when the target is maneuvering, and then slowly converges again after the maneuver is completed. Fig.11 The position error graph of the target shows that the error at the maneuvering position increases significantly, and then converges slowly. After detecting that the target has maneuvered, the covariance is adaptively adjusted, and then the filtering algorithm is used again for filtering. After the GPF and FGPF algorithms adjust the covariance at the maneuvering position, the position after re-filtering is relatively consistent with the position before the maneuver. The tracking performance of the FGPF algorithm is obviously much better than that of the GPF algorithm, and is more suitable for long-distance, low-precision fixed single-station single-target tracking.

[0177] See also Fig.12 An embodiment of the present application provides a passive positioning system, which includes a processor, a memory, and a network interface connected through a system bus, wherein the memory may include a non-volatile storage medium and an internal memory.

[0178] The non-volatile storage medium can store an operating system and a computer program. The computer program includes program instructions, and when the program instructions are executed, the processor can execute any fixed single-station passive positioning method based on Gaussian particle filtering.

[0179] The processor is used to provide computing and control capabilities and support the operation of the entire computer equipment.

[0180] The internal memory provides an environment for the operation of the computer program in the non-volatile storage medium. When the computer program is executed by the processor, the processor can execute any fixed single-station passive positioning method based on Gaussian particle filtering.

[0181] The network interface is used for network communication, such as sending assigned tasks, etc. Those skilled in the art will appreciate that Figure 8 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0182] It should be understood that the processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among them, the general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0183] A computer-readable storage medium is also provided in an embodiment of the present application, wherein the computer-readable storage medium stores a computer program, wherein the computer program includes program instructions, and the processor executes the program instructions to implement any one of the fixed single-station passive positioning methods for Gaussian particle filtering provided in the embodiments of the present application.

[0184] The computer-readable storage medium may be an internal storage unit of the computer device described in the above embodiment, such as a hard disk or memory of the computer device. The computer-readable storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, a smart memory card (SmartMedia Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the computer device.

[0185] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present application, and these modifications or replacements should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A fixed single-station passive positioning method based on Gaussian particle filtering, characterized in that: include: Acquire a first covariance matrix of the target object at a first moment, wherein the first covariance matrix represents the uncertainty of the passive positioning system at the first moment; Determine Doppler frequency change rate information from the first moment to the second moment according to a first Doppler frequency actual value in the actual observation value set of the target object at the first moment and a second Doppler frequency actual value in the actual observation value set of the target object at the second moment; When the Doppler frequency change rate information is greater than or equal to a preset threshold, determining an adaptive adjustment factor corresponding to the Doppler frequency change rate information; Calculating the product of the first covariance matrix and the adaptive adjustment factor to obtain a second covariance matrix, wherein the second covariance matrix represents the uncertainty of the passive positioning system between the first moment and the second moment, and the second covariance matrix is ​​used to determine a first motion state particle set; Based on the Gaussian distribution model, determining the first motion state particle set corresponding to the initial motion state information of the target object at the first moment, wherein the first motion state particle set includes at least two motion state particles; Based on the state transfer model, taking the first motion state particle set as input, a second motion state particle set of the target object at the second moment is obtained; Based on the sensor observation model, converting the second motion state particle set into an observation prediction value set of the target object at the second moment, each of the observation prediction value sets corresponding to each of the motion state particles one by one; Taking each of the observation prediction value sets as a cluster center, obtaining membership information of the actual observation value set of the target object at the second moment and the cluster center based on a fuzzy clustering model, wherein the membership information indicates the reliability of each of the motion state particles corresponding to each of the observation prediction value sets; Based on the state transfer model, the first motion state particle set and the membership information are used as input to obtain target motion state information of the target object at the second moment, wherein the target motion state information includes target spatial position information and target speed information.

2. The fixed single-station passive positioning method based on Gaussian particle filtering according to claim 1 is characterized in that: The determining of the adaptive adjustment factor corresponding to the Doppler frequency change rate information includes: When the Doppler frequency change rate information is the first Doppler frequency change rate information, determining the adaptive adjustment factor to be the first adaptive adjustment factor; When the Doppler frequency change rate information is the second Doppler frequency change rate information, the adaptive adjustment factor is determined to be the second adaptive adjustment factor, the second Doppler frequency change rate information is greater than the first Doppler frequency change rate information, and the second adaptive adjustment factor is greater than the first adaptive adjustment factor.

3. The fixed single-station passive positioning method based on Gaussian particle filtering according to claim 1 or 2, characterized in that: After taking the first motion state particle set and the membership information as input to obtain the target motion state information of the target object at the second moment, the method further includes: A third covariance matrix of the target object at a second moment is determined according to the target motion state information and the second covariance matrix, wherein the third covariance matrix represents the uncertainty of the passive positioning system at the second moment, and the third covariance matrix is ​​used to obtain the target motion state information of the target object at a third moment.

4. The fixed single-station passive positioning method based on Gaussian particle filtering according to claim 3 is characterized in that: The actual observation value set of the target object at the first moment includes an actual value of the azimuth angle; the method further includes: Based on the two-dimensional space measurement model, determining the radial velocity and radial distance of the target object at the first moment according to the actual value of the azimuth angle and the actual value of the first Doppler frequency; The initial motion state information of the target object at the first moment is determined according to the radial velocity and the radial distance.

5. The fixed single-station passive positioning method based on Gaussian particle filtering according to claim 4 is characterized in that: Before determining the radial velocity and radial distance of the target object at the first moment according to the actual value of the azimuth angle and the actual value of the first Doppler frequency based on the two-dimensional space measurement model, the method further includes: Determining a state equation and an observation equation of the target object; Determine a three-dimensional space measurement model according to the state equation and the observation equation; The two-dimensional space measurement model is acquired according to the three-dimensional space measurement model.

6. A passive positioning system, characterized in that: The passive positioning system includes a memory, a processor, a program stored in the memory and executable on the processor, and a data bus for realizing connection and communication between the processor and the memory. When the program is executed by the processor, the steps of the fixed single-station passive positioning method based on Gaussian particle filtering as described in any one of claims 1 to 5 are realized.

7. A storage medium for computer-readable storage, characterized in that: The storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the steps of the fixed single-station passive positioning method based on Gaussian particle filtering as described in any one of claims 1 to 5.

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