An Optimal Position Estimation Algorithm Based on Differential Evolution and Multivariate Newton Iteration

Abstract

The present invention provides an optimal position estimation algorithm based on differential evolution and multivariate Newton iteration. The algorithm includes a differential evolution algorithm, coordinate transformation, and a multivariate Newton iteration algorithm. The algorithm uses wireless ranging technology and base station positioning technology to obtain the distance data between the target to be located and the base station and the positioning data of the base station required by the algorithm. First, a complete positioning error model mechanism is modeled. Secondly, the differential evolution algorithm is used to initially estimate the initial position value of the target to be located. Furthermore, a relative positioning coordinate system is constructed using the coordinate transformation origin and coordinate transformation is performed. Finally, the multivariate Newton iteration algorithm is used in conjunction with the coordinate transformation result to accurately estimate the position of the target to be located. The optimal position estimation algorithm proposed by the present invention can be used in conjunction with various wireless ranging technologies, can significantly suppress the position estimation error of the target to be located, and greatly improve the relative positioning accuracy based on ranging.

Description

Technical Field

[0001] The present invention belongs to the technical field of ranging and positioning, and particularly relates to an optimal position estimation algorithm based on differential evolution and multivariate Newton iteration. Background Technique

[0002] The ranging and positioning method is the most commonly used position estimation method. When the position information of each base station is available, the distance between each base station and the target to be located can be measured, and the position estimation method can be used to realize the position estimation and calculation of the target to be located. Common ranging and positioning methods are all based on the geometric positioning principle, including TOA ranging and positioning method, TDOA ranging and positioning method, AOA ranging and positioning method, and ranging and positioning methods that are combined with each other.

[0003] Commonly used position estimation methods include the least squares method, Taylor method, Chan's method, etc. However, due to the noise influence in the measurement process and the implementation principle of the position estimation method, the calculation effects of different position estimation methods sometimes vary greatly. Since the positioning results of common position estimation methods are greatly affected by ranging errors and base station position errors, and even if the ranging error and the base station's own position error are only at the centimeter level, it is difficult to easily achieve a high-precision positioning effect at the centimeter level using conventional methods. Therefore, using a more efficient position estimation method is a necessary guarantee for suppressing position estimation errors and achieving high-precision positioning. The present invention designs an optimal position estimation algorithm based on differential evolution and multivariate Newton iteration, which can counteract the adverse effects of base station position errors and ranging errors and effectively suppress the positioning result errors based on ranging. Summary of the Invention

[0004] To solve the above problems, the present invention discloses an optimal position estimation algorithm based on differential evolution and multivariate Newton iteration. The algorithm includes a differential evolution algorithm, coordinate transformation, and a multivariate Newton iteration algorithm. The algorithm uses wireless ranging technology and base station positioning technology to obtain the distance data between the target to be located and the base station and the positioning data of the base station required by the algorithm.

[0005] Among them, the ranging and positioning data includes at least four groups of wireless ranging values between each base station and the target to be located obtained by wireless ranging technology and the position coordinates of each base station.

[0006] Among them, the optimal position estimation algorithm includes a differential evolution algorithm, coordinate transformation, and a multivariate Newton iteration algorithm and requires a complete mechanism modeling of the positioning error model.

[0007] The optimal position estimation algorithm described above: Since the differential evolution algorithm is a global search algorithm, it is not limited by the numerical iteration convergence constraint and can perform rough position estimation over a large range without coordinate transformation. The position estimation effect of the Newton iteration algorithm is affected by the initial iteration value and is limited by the numerical iteration convergence constraint. However, after coordinate transformation, it can meet the numerical iteration convergence condition and perform highly accurate position estimation within a local range, and can well suppress the negative impact of the dynamic measurement deviation of each base station's position on the position estimation of the target to be located. Therefore, the differential evolution algorithm is used to preliminarily estimate the position coordinates of the target to be located, combined with coordinate transformation and using this preliminary estimate as the initial iteration value, and the Newton iteration calculation is used to achieve the accurate position estimation of the target to be located.

[0008] To achieve the above object, the technical solution of the present invention is as follows:

[0009] An optimal position estimation algorithm based on differential evolution and multi - variable Newton iteration, the algorithm includes a differential evolution algorithm, coordinate transformation, and a multi - variable Newton iteration algorithm, and the algorithm uses wireless ranging technology to obtain the ranging and positioning data required by the algorithm.

[0010] Among them, the ranging and positioning data, the ranging and positioning data are at least four groups of wireless ranging values and the position coordinates of each base station with spatial discrimination obtained by using wireless ranging technology between each base station and the target to be located.

[0011] Among them, the optimal position estimation algorithm, the algorithm includes a differential evolution algorithm, coordinate transformation, and a multi - variable Newton iteration algorithm and requires a complete positioning error model mechanism modeling;

[0012] The positioning error model mechanism modeling needs to introduce the ranging error representation between the base station and the target to be located and the position coordinate error representation of the base station, and construct a TOA ranging and positioning model based on this:

[0013]

[0014] Among them, (x i , y i , z i ) are the position coordinates of each base station respectively;

[0015] Among them, α i , β i and γ i are the installation position error of each base station and its error components of autonomous positioning respectively;

[0016] Among them, d i are the true distance values between each base station and the target to be located respectively;

[0017] Among them, δ iThey are respectively the ranging errors between each base station and the target to be located;

[0018] Among them, (x, y, z) is the coordinate position of the target to be located;

[0019] Among them, the optimal position estimation algorithm is jointly implemented based on the differential evolution algorithm, coordinate transformation, and Newton iteration algorithm;

[0020] The differential evolution algorithm is used to preliminarily estimate the position coordinates of the target to be located within a large range, and assign this initial value to the initial value of the Newton iteration algorithm;

[0021] The coordinate transformation is used to ensure that the Newton iteration algorithm can meet the convergence conditions of numerical iteration calculations;

[0022] The optimal position estimation algorithm is jointly implemented based on the differential evolution algorithm, coordinate transformation, and Newton iteration algorithm;

[0023] The specific implementation steps include:

[0024] Step A: Use the differential evolution algorithm to search within a large range and preliminarily estimate the position coordinates (x, y, z) of the target to be located to obtain the estimated initial value X0;

[0025] The implementation steps of the differential evolution algorithm are as follows:

[0026] Step A1: Initialize parameters;

[0027] Step A2: Initialize the population;

[0028] Step A3: Population mutation;

[0029] Step A4: Population crossover;

[0030] Step A5: Select the optimal population;

[0031] Step B: Construct a relative positioning coordinate system through the coordinate transformation origin (x′, y′, z′), and perform coordinate transformation on the position coordinates (x i , y i , z i ) of each base station in the input TOA geometric positioning model;

[0032] Step B1: Randomly translate a small range within dozens of meters according to the coordinate information of any (x i , y i , z i ) to generate the coordinate transformation origin (x′, y′, z′), and construct a relative positioning coordinate system with this origin;

[0033] Step B2: For the (x i , yi , z i ) perform coordinate transformation to transform (x i , y i , z i ) into the relative positioning coordinate system constructed with the coordinate transformation origin (x′, y′, z′), and obtain the representation of (x i , y i , z i ) in this coordinate system: (x i ′, y i ′, z i ′);

[0034] Step C, combined with the coordinate transformation result, adopt the multivariate Newton iteration algorithm, use the estimated initial value X0 as the iteration initial value, and use the following formula to perform optimal estimation on the position coordinates (x, y, z) of the target to be located;

[0035]

[0036] where, with the goal of taking the global minimum value of the objective function f obj , the optimal estimation of the position (x, y, z) of the target to be located can be performed;

[0037] where, (x i ′, y i ′, z i ′) are the transformed position coordinates of each base station after coordinate transformation respectively;

[0038] where, d i ′ = d i + δ i .

[0039] The beneficial effects of the present invention are:

[0040] An optimal position estimation algorithm based on differential evolution and multivariate Newton iteration proposed by the present invention, this algorithm includes a differential evolution algorithm, coordinate transformation and a multivariate Newton iteration algorithm, and this algorithm uses wireless ranging technology and base station positioning technology to obtain the distance data between the target to be located and the base station and the positioning data of the base station required by the algorithm. Since the positioning results of common position estimation methods are greatly affected by ranging errors and base station position errors, and even on the premise of ensuring that the ranging error and the base station's own position error are only at the centimeter level, it is difficult to achieve a high-precision positioning effect at the centimeter level using conventional methods. Therefore, using a more efficient position estimation method is a necessary guarantee for suppressing position estimation errors and achieving high-precision positioning. The present invention designs an optimal position estimation algorithm of differential evolution and multivariate Newton iteration, which can counteract the adverse effects of base station position errors and ranging errors, and effectively suppress the positioning result errors based on ranging. Description of the Drawings

[0041] Figure 1 Schematic diagram of the overall framework of the optimal position estimation algorithm proposed by the present invention.

[0042] Figure 2 Schematic diagram of the overall process of the optimal position estimation algorithm proposed by the present invention. Specific implementation manners

[0043] The present invention will be further clarified below in conjunction with the accompanying drawings and specific implementation manners. It should be understood that the following specific implementation manners are only used to illustrate the present invention and not to limit the scope of the present invention.

[0044] As shown in the figure, an optimal position estimation algorithm based on differential evolution and multivariate Newton iteration according to the present invention includes a differential evolution algorithm, coordinate transformation, and a multivariate Newton iteration algorithm. This algorithm uses wireless ranging technology to obtain the ranging and positioning data required by the algorithm.

[0045] Among them, the ranging and positioning data is characterized in that the ranging and positioning data is at least four sets of wireless ranging values and the position coordinates of each base station with spatial distinguishability between each base station and the target to be located obtained by using wireless ranging technology.

[0046] Among them, the optimal position estimation algorithm is characterized in that this algorithm includes a differential evolution algorithm, coordinate transformation, and a multivariate Newton iteration algorithm and requires a complete mechanism modeling of the positioning error model.

[0047] Among them, the mechanism modeling of the positioning error model needs to introduce the representation of the ranging error between the base station and the target to be located and the representation of the position coordinate error of the base station, and build a TOA ranging and positioning model based on this:

[0048]

[0049] Among them, (x i , y i , z i ) are the position coordinates of each base station respectively;

[0050] Among them, α i , β i and γ i are the installation position error of each base station and its error components of autonomous positioning respectively;

[0051] Among them, d i are the true distance values between each base station and the target to be located respectively;

[0052] Among them, δ i are the ranging errors between each base station and the target to be located respectively;

[0053] Among them, (x, y, z) is the coordinate position of the target to be located;

[0054] Among them, the optimal position estimation algorithm is jointly implemented based on the differential evolution algorithm, coordinate transformation, and Newton iteration algorithm;

[0055] The differential evolution algorithm is used to preliminarily estimate the position coordinates of the target to be located within a large range, and assign this initial value to the initial value of the Newton iteration algorithm;

[0056] The coordinate transformation is used to ensure that the Newton iteration algorithm can meet the convergence conditions of numerical iteration calculations;

[0057] The optimal position estimation algorithm is jointly implemented based on the differential evolution algorithm, coordinate transformation, and Newton iteration algorithm;

[0058] The specific implementation steps include:

[0059] Step A: Use the differential evolution algorithm to search within a large range to preliminarily estimate the position coordinates (x, y, z) of the target to be located, and obtain the initial estimation value X0;

[0060] The implementation steps of the differential evolution algorithm are as follows:

[0061] Step A1: Initialize parameters;

[0062] Step A2: Initialize the population;

[0063] Step A3: Population mutation;

[0064] Step A4: Population crossover;

[0065] Step A5: Optimal population selection;

[0066] Step B: Construct a relative positioning coordinate system through the coordinate transformation origin (x′, y′, z′), and perform coordinate transformation on the position coordinates (x i , y i , z i ) of each base station in the input TOA geometric positioning model;

[0067] Step B1: Perform a small-range random translation within tens of meters according to the coordinate information of any (x i , y i , z i ) to generate the coordinate transformation origin (x′, y′, z′), and construct a relative positioning coordinate system with this origin;

[0068] Step B2: Perform coordinate transformation on the (x i , y i , z i ) in the input TOA ranging positioning model, and transform (xi , y i , z i ) is transformed into a relative positioning coordinate system constructed with the coordinate transformation origin (x′, y′, z′), and (x i , y i , z i ) is obtained in this coordinate system: (x i ′, y i ′, z i ′);

[0069] Step C, combining the coordinate transformation results, using the multi - variable Newton iteration algorithm, taking the estimated initial value X0 as the iteration initial value, and using the following formula to perform an optimal estimation of the position coordinates (x, y, z) of the target to be located;

[0070]

[0071] Among them, taking the global minimum value of the objective function f obj as the goal, the optimal estimation of the position (x, y, z) of the target to be located can be performed;

[0072] Among them, (x i ′, y i ′, z i ′) are the transformed position coordinates of each base station after coordinate transformation respectively;

[0073] Among them, d i ′ = d i +δ i .

[0074] An optimal position estimation algorithm based on differential evolution and multi - variable Newton iteration proposed by the present invention. This algorithm includes a differential evolution algorithm, coordinate transformation, and a multi - variable Newton iteration algorithm. This algorithm uses wireless ranging technology and base station positioning technology to obtain the distance data between the target to be located and the base stations and the positioning data of the base stations required by the algorithm. Since the positioning results of common position estimation methods are greatly affected by ranging errors and base station position errors, and even on the premise that the ranging error and the base station's own position error are only at the centimeter level, it is difficult to achieve a high - precision positioning effect at the centimeter level using conventional methods. Therefore, using a more efficient position estimation method is a necessary guarantee for suppressing position estimation errors and achieving high - precision positioning. The present invention designs an optimal position estimation algorithm of differential evolution and multi - variable Newton iteration, which can counteract the adverse effects of base station position errors and ranging errors, and effectively suppress the positioning result errors based on ranging.

[0075] In summary, an optimal position estimation algorithm based on differential evolution and multivariate Newton iteration proposed by the present invention can significantly improve the ranging-based positioning accuracy, can be used in combination with various wireless ranging technologies, and can significantly suppress the position estimation error of the target to be located. When high-precision distance measurement values at the centimeter level and high-precision base station position coordinates at the centimeter level can be obtained, the optimal position estimation algorithm described in the present invention can counteract the adverse effects of base station position errors and ranging errors, and effectively suppress the ranging-based positioning result errors.

[0076] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. An optimal position estimation algorithm based on differential evolution and multivariate Newton iteration, characterized in that: The algorithm includes a differential evolution algorithm, a coordinate transformation, and a multivariate Newton iteration algorithm. The algorithm uses wireless ranging technology and base station positioning technology to obtain the distance data between the target to be located and the base stations and the positioning data of the base stations required by the algorithm. First, a complete positioning error model mechanism is modeled. Second, the differential evolution algorithm is used to initially estimate the initial position value of the target to be located. Furthermore, a relative positioning coordinate system is constructed using the coordinate transformation origin and coordinate transformation is performed. Finally, the multivariate Newton iteration algorithm is used in conjunction with the coordinate transformation result to accurately estimate the position of the target to be located; Among them, the positioning error model mechanism modeling needs to introduce the ranging error representation between the base station and the target to be located and the position coordinate error representation of the base station, and a TOA ranging positioning model is constructed based on this: Among them, (x i , y i , z i ) are the position coordinates of each base station respectively; where α i , β i and γ i are respectively the installation position error of each base station and the error components of its autonomous positioning; where d i are the true distance values between each base station and the target to be located, respectively; where δ i is the ranging error between each base station and the target to be located, respectively; Among them, (x, y, z) is the coordinate position of the target to be located; Among them, the optimal position estimation algorithm is jointly realized based on the differential evolution algorithm, coordinate transformation, and Newton iteration algorithm; The differential evolution algorithm searches within a large range and initially estimates the position coordinates (x, y, z) of the target to be located to obtain the initial position estimation value X0; The optimal position estimation algorithm is jointly realized based on the differential evolution algorithm, coordinate transformation, and Newton iteration algorithm; The specific implementation steps include: Step A: Use the differential evolution algorithm to search within a large range and initially estimate the position coordinates (x, y, z) of the target to be located to obtain the initial estimation value X0; The implementation steps of the differential evolution algorithm are as follows: Step A1: Initialize the parameters; Step A2: Initialize the population; Step A3: Population mutation; Step A4: Population crossover; Step A5: Optimal population selection; Step B: Construct a relative positioning coordinate system through the coordinate transformation origin (x, y′, z′), and perform coordinate transformation on the position coordinates (x i , y i , z i ) of each base station in the input TOA ranging positioning model; Step B1: Perform a small-range random translation within dozens of meters according to the coordinate information of any (x i , y i , z i ) to generate a coordinate transformation origin (x′, y′, z′), and construct a relative positioning coordinate system with this origin; Step B2: Perform coordinate transformation on (x i , y i , z i ) within the input TOA ranging positioning model, transform (x i , y i , z i ) to the relative positioning coordinate system constructed with the coordinate transformation origin (x′, y′, z′), and obtain the representation of (x i , y i , z i ) in this coordinate system: (x i ′, y i ′, z i ′); Step C: Combine the coordinate transformation result, use the multivariate Newton iteration algorithm, use the initial estimation value X0 as the iteration initial value, and use the following formula to optimally estimate the position coordinates (x, y, z) of the target to be located; Among them, with the objective function f obj taking the global minimum value as the objective, the optimal estimation of the position (x, y, z) of the target to be located can be carried out; Among them, (x i ′, y i ′, z i ′) are the transformed position coordinates of each base station after coordinate transformation respectively; where d i ′ = d i + δ i .

2. The optimal position estimation algorithm based on differential evolution and multivariate Newton iteration according to claim 1, characterized in that: The ranging positioning data are at least four groups of wireless ranging values with spatial discrimination between each base station and the target to be located and the position coordinates of each base station obtained by using wireless ranging technology.

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