Online source positioning and navigation method based on measurement of time difference of arrival with noise

Abstract

The invention relates to the technical field of source positioning and adaptive control, in particular to an online source positioning and navigation method based on noisy time difference of arrival measurement, which comprises the following steps: a base station and an unmanned aerial vehicle respectively receive signals sent by a target source to obtain time difference of arrival measurement; performing estimation based on the time difference of arrival measurement to obtain a target source position estimation value; comprises: establishing a linear regression model; determining a compensation item; based on the compensation item, adopting a modified stochastic gradient algorithm to identify a linear regression model, and obtaining a target source position estimation value; acquiring control input of the unmanned aerial vehicle based on the target source position estimation value, including determining expected control input according to the target source position estimation value; adding attenuation excitation into the expected control input to obtain the control input; controlling the unmanned aerial vehicle to navigate by the control input to reach a target source position; according to the invention, the adaptability, precision and robustness of source positioning and navigation can be improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of source positioning and adaptive control, and particularly relates to an online source positioning and navigation method based on noisy time difference of arrival measurement. BACKGROUND

[0002] Unmanned aerial vehicles (UAVs) are widely used in disaster rescue, environmental monitoring, military reconnaissance and other fields. Their flexibility and adaptability make them important tools for performing search and positioning tasks in hidden or difficult-to-reach targets. However, achieving efficient and accurate source positioning and navigation control in complex environments is still a technical problem that needs to be solved. Traditional navigation control methods rely on external positioning systems such as the Global Positioning System (GPS) to provide accurate position information. However, in complex environments such as urban areas with high-rise buildings, underground, indoor or disaster sites, GPS signals often suffer severe attenuation or even complete failure. In addition, the target source in many application scenarios is often non-cooperative and cannot actively provide range measurement information, further increasing the difficulty of source positioning. To ensure that UAVs can efficiently perform tasks in these complex dynamic environments, it is urgent to develop online source positioning methods and adaptive navigation control techniques based on passive sensing technologies such as Time Difference of Arrival (TDOA) measurement. The core problem is how to use TDOA measurement information to accurately estimate the position of the target source in real time, and on this basis, design a closed-loop control system to ensure that the UAV can stably reach the target source location.

[0003] Existing traditional solutions mainly rely on multi-base station configuration, high signal-to-noise ratio measurement environment or separate design of positioning and control modules. In the problem of source positioning based on TDOA measurement, existing technologies mostly use multi-base station configuration and rely on batch offline processing methods to achieve positioning. Typically, the nonlinear TDOA measurement model is linearized using inverse function methods, and classical estimation algorithms such as least squares and least mean square error are used to design positioning algorithms. However, in practical applications, sensor measurements are often disturbed by random noise, making it difficult for traditional positioning algorithms to guarantee the convergence of estimation errors, and even more difficult to provide efficient and stable navigation control performance. Therefore, in the presence of noise interference, how to design an online source positioning algorithm based on TDOA measurement, and further design an adaptive controller based on the positioning result to achieve autonomous navigation control of the UAV, is an important research topic with significant engineering application value.

[0004] Due to the strong nonlinear coupling between TDOA measurements and the relative positions of the unmanned aerial vehicle (UAV), base station, and target source, and the mutual constraints between source localization and navigation control tasks, the integrated algorithm design for online source localization and adaptive navigation control faces severe challenges. Therefore, overcoming the insufficient adaptability of existing algorithms in complex dynamic environments, ensuring positioning accuracy and control performance, and constructing efficient and accurate online source localization and adaptive navigation control algorithms have become key technical problems urgently needing to be solved in this field. Summary of the Invention

[0005] In view of the above problems, the present invention provides an online source localization and navigation method based on noisy time difference of arrival measurement, which solves the technical problems of poor adaptability, poor accuracy and robustness of UAV localization and navigation in the prior art.

[0006] This invention provides an online source localization and navigation method based on noisy time difference of arrival measurement, comprising the following steps: Step S1: The drone and the base station respectively receive the signal emitted by the target source and record their respective signal arrival times; based on the signal arrival times of the drone and the base station, the arrival time difference measurement is calculated. Step S2: Based on the time difference of arrival measurement, estimate the location of the target source; including: establishing a linear regression model; determining a compensation term; and using a modified stochastic gradient algorithm to identify the linear regression model based on the compensation term to obtain the estimated location of the target source. Step S3: Obtain the control input of the UAV based on the target source position estimate, including: determining the desired control input from the target source position estimate; adding a decay excitation to the desired control input to obtain the control input; Step S4: The control input controls the drone to navigate to the target source location.

[0007] Preferably, in step S1, the step of obtaining the time difference of arrival measurement based on the time when the UAV and the base station receive the signal emitted by the target source specifically includes: The base station and the drone each receive signals emitted by the target source. The time difference of arrival (TDOA) is measured by subtracting the arrival time of the signal received by the drone from the target source from the arrival time of the signal received by the base station. The expression is as follows:

[0008]

[0009] in, Indicates the first Measurement of the time difference of arrival of the step This represents the distance difference between the drone and the base station to the target source. Indicates the speed of signal propagation. Indicates measurement noise; Indicates that the drone is in The position of the step, Indicates the location of the target source. This represents the Euclidean norm.

[0010] Preferably, step S2 specifically includes: Step S2-1: Establish a linear regression model, which is used to represent the linear relationship between the system output and the regression operator; the system output and the regression operator are obtained based on the position and time difference of arrival of the UAV, and the undetermined coefficients of the linear relationship are system parameters related to the position of the target source. Step S2-2: Determine the compensation item based on the time difference of arrival measurement and the estimated system parameters; Step S2-3: Based on the compensation term, the modified stochastic gradient algorithm is used to identify the linear regression model and obtain the target source location estimate.

[0011] Preferably, in step S2-1, the expression of the linear regression model is:

[0012]

[0013]

[0014] in, Indicates system output, Indicates the speed of signal propagation Represents the regression operator. Indicates system parameters, Indicates system noise. Indicates measurement noise The variance.

[0015] Preferably, in step S2-2, the expression for the compensation term is:

[0016] in, express transpose, Indicates the first Estimates of system parameters for the step. Indicates except the first Each component is The remaining components are of 3D column vector; In steps S2-3, the step of identifying the linear regression model using the modified stochastic gradient algorithm specifically includes: A modified stochastic gradient update model was established based on the aforementioned compensation term, and its expression is:

[0017] in, Indicates the first Estimates of system parameters for the step. Indicates the step size. , express Transpose of; The target source location estimate is obtained using the modified stochastic gradient update model, expressed as:

[0018] in, Indicates the first The target source location estimate for the step. Represents the dimension of a vector. .

[0019] Preferably, step S3 specifically includes: Step S3-1: Project the estimated target source position onto the constraint set, and calculate the difference between the projected point and the current UAV position as the desired control input; Step S3-2: Add a damping excitation to the desired control input to obtain the control input; the damping excitation is obtained from random noise.

[0020] Preferably, in step S3-1, the expression for the desired control input is:

[0021] in, Indicates the first The expected control input for the step, Represents the projection operator. Represents a set of constraints. It is a convex compact set that satisfies .

[0022] Preferably, in step S3-2, the expression for the control input is:

[0023] in, Indicates the first Step control input, Indicates the first The excitation signal of the step, Indicates the attenuation factor; with measurement noise are mutually independent; The probability density distribution of is symmetric and continuous, and satisfies the following conditions:

[0024] wherein, represents the calculation of expectation, is the transpose of , a first given normal number, represents represents is a unit matrix of dimension represents the square of the Euclidean norm, represents a second given normal number.

[0025] Compared with the prior art, the present application has at least the following beneficial effects: (1) The present application realizes effective fusion of information by cooperative collection of target source signal arrival time difference measurement by base stations and unmanned aerial vehicles, can avoid the problem of ignoring dynamic coupling in the traditional "positioning first, control later" separation framework, enhances the adaptability of the system to complex dynamic environment, and improves the collaboration and real-time response performance of positioning and navigation.

[0026] (2) The present application performs online identification on a linear regression model with random noise based on a stochastic gradient algorithm, and introduces a compensation term, which can effectively handle the random noise interference of sensor measurement in the real environment, and improve the accuracy and stability of target source position estimation.

[0027] (3) The present application converts the target source position estimation value into an expected control input, and introduces a decay excitation to realize adaptive control, which not only ensures the high precision and robustness of unmanned aerial vehicle navigation, but also reduces the dependence on complex configuration of multiple base stations, so that the system not only has the advantage of low cost, but also can cope with dynamic and uncertain actual application scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0028] The accompanying drawings are for the purpose of illustrating the specific embodiments only and are not to be construed as limiting the present application.

[0029] Figure 1 The flow chart of the online source positioning and navigation method based on noisy arrival time difference measurement provided by the present application.

[0030] Figure 2 The schematic diagram of the unmanned aerial vehicle navigation problem to an unknown signal source provided by the present application.

[0031] Figure 3 The schematic diagram of the change trajectory of the source positioning error with time provided by the present application.

[0032] Figure 4 A schematic diagram of the trajectory of the unmanned aerial vehicle and the target source position changing with time is provided in the present application. DETAILED DESCRIPTION

[0033] In order to more clearly understand the above-mentioned purposes, features and advantages of the present application, the present application will be further described in detail below in combination with the drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict. In addition, the present application can also be implemented in other ways different from those described herein, and therefore, the protection scope of the present application is not limited by the specific embodiments disclosed below.

[0034] The present application proposes an online source positioning and unmanned aerial vehicle adaptive navigation method capable of processing random noise interference, and can realize theoretical guarantee of closed-loop performance for discrete-time systems with uncertain dynamics and random noise measurements. The method provided by the present application breaks through the traditional separation framework of "positioning first and then controlling", realizes cooperative design and online coupling of positioning and control, and has strong adaptability, high precision and strong robustness.

[0035] In order to illustrate the effectiveness of the method proposed in the present application, the above technical solutions of the present application will be described in detail below through a specific embodiment. As shown in Figure 1 An online source positioning and navigation method based on noisy time difference of arrival measurement is disclosed, and the specific implementation steps are as follows: Step S1, the unmanned aerial vehicle and the base station respectively receive the signal emitted by the target source, and record the respective signal arrival time; based on the signal arrival time of the unmanned aerial vehicle and the base station, the time difference of arrival measurement is calculated; As shown in Figure 2 The positioning system of the present application includes a base station, an unmanned aerial vehicle and a target source, and the present application is used to solve the navigation problem of the unmanned aerial vehicle reaching the target source. Among them, the base station and the unmanned aerial vehicle can receive the signal emitted by the target source, and the unmanned aerial vehicle and the base station respectively obtain the arrival time of the signal emitted by the target source.

[0036] The signal receiving sensors of the base station and the unmanned aerial vehicle are limited by hardware precision and environmental factors, and the time measurement generally exists random noise interference. In the actual environment, adaptive processing needs to be performed for noise interference, and finally the precise navigation of the unmanned aerial vehicle reaching the target source is realized.

[0037] The present application first completes the unmanned aerial vehicle motion model and the measurement model, which describes the online source positioning and adaptive navigation control problem.

[0038] The unmanned aerial vehicle follows the following first-order discrete-time dynamic model, and the expression is:

[0039] wherein, respectively represent the position of the UAV in the step, is the control input in the step, represents the dimension of the vector.

[0040] The control input is used to drive the UAV, and change the position of the UAV in the next step.

[0041] When the target source sends signals for the kth time, the base station and the UAV respectively receive the signals sent by the target source, and the arrival time difference measurement is obtained by subtracting the arrival time of the signals received by the UAV from the arrival time of the signals received by the base station.

[0042] wherein, represents the arrival time difference measurement in the step, represents the propagation speed of the signals, represents the measurement noise.

[0043] The distance difference between the UAV and the base station to the target source is defined as:

[0044] wherein, represents the distance difference between the UAV and the base station to the target source, represents the position of the target source, represents the Euclidean norm.

[0045] Unlike the prior art, the present application fully considers the interference of random measurement noise , which is assumed to be a zero-mean Gaussian white noise with a variance of . Through the establishment of the above model, the target of the online source positioning and adaptive navigation control problem is clarified, that is, under the condition of only using a series of arrival time difference measurements with noise, a controller is designed for the UAV, so that it can finally reach the unknown signal source position .

[0046] In this step, the base station and the UAV respectively receive the signals sent by the target source, and the arrival time difference measurement is obtained by subtracting the arrival time of the signals received by the UAV from the arrival time of the signals received by the base station.

[0047] Step S2, estimating based on the time difference measurement, obtaining the target source position estimate; comprising: establishing a linear regression model; determining a compensation term; identifying the linear regression model based on the compensation term using a modified stochastic gradient algorithm to obtain the target source position estimate; This step includes establishing a linear regression model, determining a compensation term, and identifying the linear regression model based on the compensation term using a modified stochastic gradient algorithm, which is described in detail as follows.

[0048] (1) Establishing a linear regression model In order to convert the nonlinear source positioning problem into a linear regression problem, the auxiliary variables required by the linear regression model are first established, which are defined as:

[0049]

[0050]

[0051] Wherein, represents the system output, represents the propagation speed of the signal, represents the regression operator, represents the system parameter, represents the system noise, represents the measurement noise variance.

[0052] Through mathematical transformation, the following linear regression equation can be obtained:

[0053] Wherein, represents the transpose of .

[0054] Since the position of the unmanned aerial vehicle is known, the time difference measurement can be obtained in real time, so the system output and the regression operator can be calculated online. Thus, the problem of estimating the target source position is converted into the problem of identifying the system parameter according to the available information sequence .

[0055] (2) Determining the compensation term The present application provides a non-decreasing - algebraic sequence , Algebra can be understood as a set system containing all "measurable events," defining which events in a probability space can be probabilistically calculated. "Non-decreasing" refers to the current... - The information contained in algebra must include the past. - The information contained in algebra, that is, the information obtained in each step contains at least all the information of the previous step.

[0056] Indicates up to the The available information for the step is expressed as:

[0057] in, Indicates the k-th step -Algebra, Let represent the minimal σ-algebra generated by the random variables or sets enclosed in curly braces, ensuring that this σ-algebra is the minimal family of events containing all information about these variables. Indicates that the drone is in The position of the step, Indicates the first Step measurement noise, Representing the initial time -Algebra, The empty set is represented by the non-decreasing σ-algebraic sequence, which is used to define the information set upon which each step of the decision depends.

[0058] according to and Definition, It is not a martingale difference sequence. Therefore, the classic stochastic gradient descent algorithm is directly used to identify the parameters of a fixed-length system. This may result in a biased estimate.

[0059] To correct the above deviation, this invention provides a compensation term, expressed as:

[0060] in, express transpose, Indicates the first Estimates of system parameters for the step. Indicates except the first Each component is The remaining components are of Dimensional column vector.

[0061] (3) Identify the linear regression model using a modified stochastic gradient algorithm based on the compensation term. The present application establishes a revised stochastic gradient update model based on the compensation term, and the expression is:

[0062] wherein, represents the estimated value of the system parameter of the step, represents a step length, represents the transpose of. The value of can be . .

[0063] Finally, according to the definition of , the target source position estimation value of the step can be obtained. , represents the dimension of the vector.

[0064] Step S3, obtaining the control input of the unmanned aerial vehicle based on the target source position estimation value, comprising: determining the expected control input from the target source position estimation value; adding a decay incentive to the expected control input to obtain the control input. In this step, the present application processes the target source position estimation value, including two parts of determining the expected control input and adding a decay incentive.

[0065] (1) Determining the expected control input Based on the "certain equivalence" principle and the source position estimation value , the following expected adaptive control law is set:

[0066]

[0067] wherein, represents the expected control input of the step, represents a projection operator, is a convex compact set, satisfying , represents the input quantity of the projection operator, represents a real number field of dimension, represents an element in the convex compact set .

[0068] Through the above expected control law, the present application projects the target source position estimation value into the constraint set, and then calculates the difference between the projection point and the current unmanned aerial vehicle position as the expected control input, driving the unmanned aerial vehicle to move towards the estimated target source position.

[0069] (2) Adding a decay incentive​​ In practical application, as the UAV position gradually approaches the target source position, the expected controller amplitude tends to 0, resulting in insufficient excitation of the UAV movement, which will lead to difficulty in providing excitation conditions required to meet the estimator error convergence, ultimately affecting the convergence and accuracy of the source position estimation.

[0070] Therefore, in this step, the present application adds a decaying excitation signal to the expected control input, expressed as:

[0071] wherein, represents the control input of the step, represents the excitation signal of the step, which is an independent and identically distributed random vector sequence, represents a decay factor, .

[0072] The probability density distribution of is symmetric and continuous, and satisfies the following conditions:

[0073] wherein, represents the calculation expectation, is the transpose of , represents a first given normal number, represents a dimension unit matrix, represents the square of the Euclidean norm, represents a second given normal number. In addition, the decaying excitation signal

[0074] is independent of the measurement noise sequence .

[0075] Through the above steps, the present application provides a decaying excitation, providing a larger excitation signal at the initial stage of navigation to promote parameter estimation convergence, and as time increases, the disturbance decays at a logarithmic rate, gradually reducing the impact on navigation accuracy, and ultimately achieving accurate arrival at the target source position.

[0076] Step S4, controlling the UAV to navigate to the target source position by the control input.

[0077] In this step, the UAV is controlled to navigate based on the control input obtained in the previous step, the UAV position is updated in real time, and finally the target source position is reached.

[0078] The whole navigation process is adaptive, and the source positioning and navigation task can be completed by relying on the online acquisition of noisy TDOA measurement values, and is suitable for complex practical application environments.

[0079] In order to verify the effectiveness of the online source positioning algorithm based on noisy TDOA measurement and the adaptive navigation control method proposed in the application, the online source positioning algorithm proposed in the application is used by the MATLAB unmanned aerial vehicle, and the performance of the adaptive navigation control method proposed in the application is verified. It is verified that the method proposed in the application can make the unmanned aerial vehicle reach the unknown signal source position based on TDOA measurement in the environment with noise interference. The main simulation process is as follows: (1) Simulation setting: the simulation experiment is carried out in a two-dimensional scene. The position of the static unknown signal source is set to . The TDOA measurement data collected is added with zero-mean Gaussian noise, and the noise standard deviation is . The excitation signal obeys the uniform distribution of , and the attenuation factor is .

[0080] (2) Result analysis: in order to evaluate the effectiveness of the proposed online source positioning algorithm, the application first observes the change of the estimation error . The results obtained by simulation show that the source position estimation error gradually decreases and tends to as time increases, as shown in Figure 2 . In order to further verify the performance of the application in practical application, the application calculates the mean navigation error (i.e. the distance of the unmanned aerial vehicle to the target source) under 3000 times of Monte Carlo simulation. Figure 3 , Figure 4 The simulation results are shown in , which show that the distance between the unmanned aerial vehicle and the target source gradually decreases and tends to zero over time when the method of the application is used.

[0081] These simulation results prove the effectiveness and accuracy of the application in source positioning and adaptive navigation control.

[0082] The detailed description of the application describes and illustrates with reference to certain specific embodiments. However, the description and illustrations are intended to be merely illustrative and not restrictive of the application. While the application has been described and illustrated with reference to specific embodiments, it will be recognized that variations and modifications can be made by persons skilled in the art depending upon the overall teachings of the present application. In particular, those skilled in the art will recognize that elements of the present application can readily be combined to provide further embodiments of the present application. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments described herein. It is, therefore, to be understood that the application is not to be limited to the specific embodiments disclosed and that modifications and / or substitutions are intended to be included within the scope of the present application. Such equivalents are considered within the scope of the present application.

[0083] The detailed description of the application describes and illustrates with reference to certain specific embodiments. However, the description and illustrations are intended to be merely illustrative and not restrictive of the application. While the application has been described and illustrated with reference to specific embodiments, it will be recognized that variations and modifications can be made by persons skilled in the art depending upon the overall teachings of the present application. In particular, those skilled in the art will recognize that elements of the present application can readily be combined to provide further embodiments of the present application. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments described herein. It is, therefore, to be understood that the application is not to be limited to the specific embodiments disclosed and that modifications and / or substitutions are intended to be included within the scope of the present application. Such equivalents are considered within the scope of the present application.

Claims

1. An online source localization and navigation method based on noisy time difference of arrival measurements, characterized by, The method comprises the following steps: Step S1, receiving signals emitted by a target source by a UAV and a base station respectively, and recording respective signal arrival times; based on the signal arrival times of the UAV and the base station, calculating a time difference measurement; Step S2, estimating based on the time difference measurement to obtain a target source position estimate, comprising: establishing a linear regression model; determining a compensation term; based on the compensation term, identifying the linear regression model using a modified stochastic gradient algorithm to obtain the target source position estimate; Step S3, obtaining a control input of the UAV based on the target source position estimate, comprising: determining an expected control input from the target source position estimate; adding a decay incentive to the expected control input to obtain the control input; Step S4, controlling the UAV to navigate to the target source position based on the control input.

2. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 1, wherein, In step S1, the step of obtaining the time difference measurement based on the times at which the base station and the UAV receive the signals emitted by the target source comprises: The base station and the UAV respectively receive the signals emitted by the target source, and the time difference measurement is obtained by subtracting the arrival time of the signal received by the UAV from the arrival time of the signal received by the base station, expressed as: wherein, denotes the distance difference between the UAV and the base station to the target source at step denotes the time difference of arrival measurement at step denotes the distance difference between the UAV and the base station to the target source, denotes the propagation speed of the signal, denotes the measurement noise; denotes the position of the UAV at step denotes the position of the target source, denotes the position of the target source, denotes the Euclidean norm.

3. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 2, wherein, Step S2 specifically comprises: Step S2-1, establishing a linear regression model, wherein the linear regression model is used to represent the linear relationship between the system output and the regression operator; the system output and the regression operator are obtained based on the position of the UAV and the time difference measurement; the undetermined coefficient of the linear relationship is a system parameter related to the position of the target source; Step S2-2, determining a compensation term based on the time difference measurement and the system parameter estimate; Step S2-3, based on the compensation term, identifying the linear regression model using a modified stochastic gradient algorithm to obtain the target source position estimate.

4. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 3, wherein, In step S2-1, the expression of the linear regression model is: where denotes the system output, denotes the propagation speed of the signal denotes the regression operator, denotes the system parameter, denotes the system noise, denotes the measurement noise of the variance.

5. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 4, wherein, In step S2-2, the expression of the compensation term is: wherein denotes the transpose of , denotes the estimate of the system parameter in the th step, denotes the th component of , and the remaining components are -dimensional column vector. In step S2-3, the step of identifying the linear regression model using the modified stochastic gradient algorithm specifically comprises: A modified stochastic gradient update model is established based on the compensation term, expressed as: wherein denotes the step an estimate of the system parameter at step denotes the step size, , denotes the transpose of The target source position estimate is obtained using the modified stochastic gradient update model, expressed as: wherein, represents the target source position estimate value of the step represents the target source position estimate value of the step represents the vector dimension, .

6. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 5, wherein, Step S3 specifically comprises: Step S3-1, projecting the target source position estimate into a constraint set, and calculating the difference between the projection point and the current UAV position as the expected control input; Step S3-2, adding a decay incentive to the expected control input to obtain the control input; the decay incentive is obtained from random noise.

7. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 6, wherein, In step S3-1, the expression of the expected control input is: in, Indicates the first The expected control input for the step, Represents the projection operator. Represents a set of constraints. It is a convex compact set that satisfies .

8. The online source localization and navigation method based on noisy time difference of arrival measurements of claim 7, wherein, In step S3-2, the expression of the control input is: wherein represents the control input of the step, represents the excitation signal of the step, represents a decay factor; is mutually independent from the measurement noise . The probability density distribution of is symmetric and continuous and satisfies the following conditions: wherein denotes the calculation of the expectation, is the transpose of denotes a first given normal number, denotes denotes the identity matrix of dimension denotes the square of the Euclidean norm, denotes a second given normal number.

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