Shortwave Time Difference Location Method with Joint Optimization of Ionospheric Height and Target Location

Abstract

The present invention belongs to the field of signal parameter measurement and estimation, and discloses a short-wave time difference of arrival (TDOA) positioning method for joint optimization of ionospheric height and target position. First, a short-wave over-the-horizon TDOA positioning model is established; then, a two-dimensional cross-ambiguity correlation algorithm is used for the received signals to obtain the time delay difference between any two receiving stations; next, in the line-of-sight scenario, that is, assuming the ionospheric height is zero, the Chan algorithm is used to obtain the rough positioning result; finally, on the basis of the rough positioning result, a genetic algorithm is used to jointly optimize the ionospheric height and the target position to obtain the accurate positioning result. Compared with the existing technologies, the solution provided by the present invention can achieve high-precision and effective positioning without prior information about ionospheric parameters, has a wide application range of the algorithm, strong robustness, and is simple to implement.

Description

Technical Field

[0001] The present invention belongs to the field of signal parameter measurement and estimation, and particularly relates to a short-wave over-the-horizon time difference positioning method based on the joint optimization of ionospheric height and target position. Background Art

[0002] Short-wave communication is the only long-distance communication means that is not restricted by network hubs and active relays. Through the transmission mode of ionospheric reflection, its propagation distance can reach thousands of kilometers. Scholars at home and abroad have conducted some research on short-wave over-the-horizon positioning. Currently, the commonly used positioning methods mainly include two categories: double-station / multi-station direction-finding intersection positioning technology and single-station direction-finding positioning technology. The traditional double-station / multi-station direction-finding intersection positioning technology is based on the arrival angle positioning method, and the radiation source position is determined by the intersection of two or more angular directions; while the single-station direction-finding positioning technology measures the azimuth angle, elevation angle of the short-wave signal and the ionospheric reflection height to achieve single-receiving-station positioning. Both of these methods require direction-finding of the incoming wave signal, and direction-finding necessarily requires the use of an antenna array. Compared with the microwave band, the short-wave array has a large footprint. To achieve high direction-finding accuracy, the array aperture can reach several hundred meters; at the same time, the equipment is complex, and the production and maintenance costs are high. Therefore, it is considered to adopt the time difference positioning method. Compared with the traditional direction-finding positioning technology, it has simple equipment, short processing time, low cost and strong mobility. A few scholars at home and abroad have established a time difference positioning model based on the known ionospheric height or the ionospheric height deduced through some empirical information to calculate the position of the target radiation source. This time difference positioning method requires an in-depth understanding of the ionospheric characteristics and a large amount of data accumulation of the ionospheric historical parameter information in each region. Obviously, it is sometimes not possible; at the same time, there is a problem that the deduced ionospheric height is inaccurate, resulting in a sharp decline in positioning accuracy. Summary of the Invention

[0003] The purpose of the present invention is to provide a short-wave over-the-horizon time difference positioning method based on the joint optimization of ionospheric height and target position, and solve the problems that the ionospheric reflection height is not easy to solve in the existing methods and the positioning accuracy is limited due to inaccurate calculation results.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A short-wave time difference positioning method for the joint optimization of ionospheric height and target position specifically includes the following steps:

[0006] Step 1, construct a short-wave over-the-horizon time difference positioning model, specifically as follows:

[0007] In the short-wave signal over-the-horizon transmission model, the signal transmission distance from the target radiation source to each receiving station is expressed as:

[0008]

[0009]

[0010] Wherein, N r represents the number of receiving stations, N r ≥4, h i represents the ionospheric reflection height in the i-th path, d i (·) represents the great circle distance between two points on the ground, obtained by the spherical cosine formula (2), and respectively represent the longitude and latitude coordinates of the target radiation source and the i-th receiving station;

[0011] Assume that the target radiation source emits a signal at time t0, the time when the i-th receiving station receives the signal is t i , the time when the j-th receiving station receives the signal is t j , j≠i, then there is

[0012]

[0013] Wherein, τ i and τ j respectively correspond to the time delays corresponding to the i-th path and the j-th path, V c is the electromagnetic wave propagation speed. Let the time delay difference Δτ ij =τ i -τ j , then the time difference positioning equation is expressed as:

[0014]

[0015] Plus the earth surface equation:

[0016]

[0017] From equations (1), (4) and (5), a system of multivariate nonlinear equations about is formed;

[0018] Step 2: Use the two-dimensional cross ambiguity function algorithm to find the time delay difference between any two receiving stations, specifically as follows:

[0019] Use the two-dimensional cross ambiguity function formula

[0020]

[0021] Wherein, g i (t) and g j (t) respectively correspond to the narrowband signals received by the i-th receiving station and the j-th receiving station, Δτ ij is the time delay difference between the two signals, Doppler frequency difference of two signals. By searching for the maximum value in the two-dimensional ambiguity plane jointly formed by the time delay axis and the Doppler frequency axis, the time delay difference Δτ between the two signals can be obtained. ij and Doppler frequency shift difference

[0022] Step 3: Substitute the time delay difference Δτ obtained in Step 2 ij into Equation (3), and at the same time, without considering the ionospheric reflection height h i That is, let h i = 0, then a binary equation system only about is formed by Equations (1), (3) and (4), and the rough positioning result of the target radiation source is calculated by using the Chan algorithm in traditional LOS time difference positioning.

[0023] Step 4: According to the rough positioning result obtained in Step 3, randomly generate sample individuals to form an initial population, and use the genetic algorithm to jointly optimize the target position and the ionospheric virtual height of each path to obtain the accurate position of the target radiation source.

[0024] Among them, the specific steps of the above-mentioned Step 4 are as follows:

[0025] 1) Select the coding strategy: According to the rough positioning result obtained in Step 3, determine the value ranges of the parameters l and h i to be optimized, and select the binary coding method to code each parameter to be estimated;

[0026] 2) Define the fitness function:

[0027]

[0028] 3) Randomly generate K sample individuals to form an initial population, and the kth sample is expressed as

[0029] 4) Calculate the fitness function value f(x k ) corresponding to each sample individual, where k = 1, 2,..., K;

[0030] 5) Judge whether the performance of the population meets the maximum genetic iteration times. If it meets, output the optimal parameters; otherwise, according to the genetic strategy, use the selection operator, crossover operator and mutation operator to act on the population to generate the next generation population, and then go to Step 4).

[0031] The beneficial effects of the present invention are as follows:

[0032] 1. The present invention adopts the short-wave time difference positioning method. Compared with the traditional direction finding and positioning technology, the equipment is simple, the processing time is short, the cost is low, and the mobility is strong.

[0033] 2. The present invention adopts a short-wave over-the-horizon time difference positioning method based on the joint optimization of ionospheric height and target position, which does not require prior estimation of the ionospheric height, has a wide application range, and the algorithm is simple and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic diagram of short-wave signal propagation;

[0035] Figure 2 is a short-wave signal over-the-horizon transmission model;

[0036] Figure 3 is a flowchart for jointly optimizing the target position and ionospheric height using the GA algorithm;

[0037] Figure 4 is a graph showing the variation of the fitness function with the number of genetic generations and the variation of the average distance between adjacent generations with the number of genetic generations during the process of jointly estimating the target position and ionospheric height using the GA algorithm.

[0038] Figure 5 is a graph showing the variation of the positioning accuracy of the algorithm proposed by the present invention with the number of Monte Carlo simulations. DETAILED DESCRIPTION OF THE INVENTION

[0039] The present invention will be further described below in conjunction with the drawings and the detailed implementation manners.

[0040] The technical solution adopted by the short-wave time difference positioning method for jointly optimizing the ionospheric height and target position of the present invention is as follows: First, a short-wave over-the-horizon time difference positioning model is established; then, the two-dimensional cross-ambiguity correlation algorithm is used to obtain the time delay difference between any two receiving stations; then, in the line-of-sight scenario, that is, assuming the ionospheric height is zero, the rough positioning result is obtained using the Chan algorithm; finally, on the basis of the rough positioning result, the genetic algorithm is used to jointly optimize the ionospheric height and target position to obtain the precise positioning result. Specifically as follows:

[0041] Step 1: Construct a short-wave over-the-horizon time difference positioning model

[0042] As Figure 1 shown in the schematic diagram of short-wave signal propagation, the short-wave signal is transmitted through ionospheric reflection. Obviously, in the time difference positioning method, in addition to the longitude and latitude of the radiation source, the virtual height of the ionosphere for each path is also an important unknown parameter. As Figure 2 shown in the short-wave signal over-the-horizon propagation model, the signal transmission distance from the target radiation source to each receiving station can be approximately expressed as

[0043]

[0044]

[0045] In the formula, Nr Indicates the number of receiving stations, N r ≥4, h i Is the ionospheric reflection height in the i-th path, d i (·) represents the great circle distance between two points on the ground, which can be obtained from the spherical cosine formula (2). and Respectively represent the longitude and latitude coordinates of the target radiation source and the i-th receiving station.

[0046] Assume that the target radiation source emits a signal at time t0, and the time when the i-th receiving station receives the signal is t i , and the time when the j-th receiving station (j≠i) receives the signal is t j , there is

[0047]

[0048] In the formula, τ i 、τ j Respectively represent the time delays corresponding to the i-th path and the j-th path, V c Is the electromagnetic wave propagation speed. Let Δτ ij =τ i -τ j Obviously, Δτ ij Is the time delay difference corresponding to the i-th path and the j-th path, and the time difference positioning equation can be expressed as

[0049]

[0050] Plus the earth's surface equation,

[0051]

[0052] From equations (1), (4), and (5), a multivariate non-linear equation system about Multivariate non-linear equation system.

[0053] Step 2: Use the two-dimensional cross ambiguity function algorithm to find the time delay difference between any two receiving stations

[0054] The reason for using the two-dimensional cross ambiguity function algorithm is that when the short-wave channel propagates signals, there are not only fluctuations in the signal amplitude caused by fading, but also frequency drift of the transmitted signal caused by the Doppler effect; the reason for the Doppler frequency shift is the frequent rapid movement of the ionosphere and the rapid change in the height of the reflection layer, which causes the propagation path length to change continuously and the signal phase to change accordingly. This phase change can be regarded as the Doppler frequency shift of the high-frequency carrier caused by the irregular movement of the ionosphere.

[0055] Use the two-dimensional cross ambiguity function formula

[0056]

[0057] Among them, g i (t), g j (t) are the narrowband signals received by the i-th receiving station and the j-th receiving station, and Δτ ij is the time delay difference between the two signals. is the Doppler frequency difference between the two signals. By searching for the maximum value in the two-dimensional ambiguity plane jointly formed by the time delay axis and the Doppler frequency axis, the time delay difference Δτ ij and the Doppler frequency shift difference

[0058] Step 3: Obtain the rough positioning result using the Chan algorithm in the line-of-sight scenario

[0059] Substitute the time delay difference Δτ ij obtained in Step 2 into Equation (3), and at the same time, without considering the ionospheric reflection height h i that is, let h i = 0. In this way, a binary equation system only about is formed by Equations (1), (3), and (4), and the rough positioning result of the target radiation source is calculated using the Chan algorithm in traditional line-of-sight time difference positioning.

[0060] Step 4: Use the genetic algorithm to jointly optimize the ionospheric height and the target position to achieve precise positioning

[0061] According to the rough positioning result obtained in Step 3, randomly generate sample individuals to form an initial population, and use the Genetic Algorithm (GA) to jointly optimize the target position and the virtual ionospheric height of each path to obtain the precise position of the target radiation source. The specific process is as Figure 3 shown:

[0062] 1) Select the coding strategy: According to the rough positioning result obtained in Step 3, determine the value range of the parameters l, h i to be optimized, and select the binary coding method to code each parameter to be estimated.

[0063] 2) Define the fitness function:

[0064]

[0065] 3) Randomly generate K sample individuals to form an initial population. The k-th sample can be expressed as

[0066] 4) Calculate the fitness function value f(x k ), k = 1, 2,..., K.

[0067] 5) Determine whether the population performance meets the optimization criterion: Here, the maximum number of genetic iterations Iter_max is selected as the optimization criterion. If it is met, the optimal parameters are output; otherwise, according to the genetic strategy, the selection operator, crossover operator, and mutation operator are used to generate the next generation population, and a new generation of genetics begins.

[0068] 6) Go to step 4), and calculate the fitness function values of each sample individual in the new population.

[0069] The following is a more specific embodiment:

[0070] In the experiment of the present invention, 4 short-wave receiving stations are respectively located in Harbin, Shunyi, Shanghai, and Fujian, and the radiation source is set in Xi'an. The great circle distances between each receiving station and the radiation source are 1900km, 953km, 1240km, and 1385km respectively. In addition, the ionospheric reflection heights corresponding to the four paths are h1 = 180km, h2 = 320km, h3 = 265km, and h4 = 230km. According to formula (1), the actual distances between the receiving stations and the target after ionospheric reflection can be calculated as 1934km, 1148km, 1349km, and 1459km. The distances are converted into corresponding time delay values, and N r = 4 short-wave receiving signals with time delay information are simulated. The signal modulation type is BPSK, the signal carrier frequency is 13.2MHz, the signal bandwidth is 10KHz, the intermediate frequency sampling rate is 100KHz, the signal noise is Gaussian white noise, and the signal-to-noise ratio is 13 = 12dB. At the same time, Doppler frequency shift is added to each short-wave signal First, the two-dimensional cross-correlation algorithm is used to estimate the time difference of the received signals, and then the traditional line-of-sight time difference positioning Chan algorithm is used to obtain the rough positioning result of the target radiation source Next, the GA algorithm is used to jointly estimate the target position and the ionospheric height to achieve precise positioning, where the parameters l, h i The value range of h i ∈[100km, 350km]. The binary coding method is selected. The coding length of l is 10, The coding length of i is 10, and the coding length of h c is 12. The maximum number of iterations Iter_max = 600, the number of samples in the population is K = 100, the selection operator uses non-replacement remainder random sampling, the crossover operator uses the crossover probability P e = 0.5, and the mutation operator uses the mutation probability P Figure 4The figure shows the variation of the fitness function with the number of genetic generations and the variation of the average distance between adjacent generations with the number of genetic generations during the process of jointly estimating the target position and the ionospheric height using the GA algorithm, as Figure 5 The figure shows the variation of the positioning accuracy of the algorithm proposed by the present invention with the number of Monte Carlo simulations, proving that the algorithm provided by the present invention can still achieve high-precision positioning without prior information about ionospheric parameters, and has a fast convergence speed, a wide application range of the algorithm, and is simple and effective.

[0071] The above is only a preferred embodiment of the present invention, and does not impose any other form of limitation on the present invention. Any modification or equivalent change made based on the technical essence of the present invention still belongs to the scope claimed by the present invention.

Claims

1. A short-wave time difference positioning method for joint optimization of ionospheric height and target position, characterized in that, Specifically, it includes the following steps: Step 1: Construct a short-wave over-the-horizon time difference of arrival (TDOA) positioning model, specifically as follows: In the short-wave signal over-the-horizon transmission model, the signal transmission distances from the target radiation source to each receiving station are expressed as: Where, N r represents the number of receiving stations, N r ≥4, h i represents the ionospheric reflection height in the i-th path, d i (·) represents the great circle distance between two points on the ground, which is obtained by the spherical cosine formula (2), and respectively represent the longitude and latitude coordinates of the target radiation source and the i-th receiving station; Assume that the target radiation source emits a signal at time t0, and the time when the i-th receiving station receives the signal is t i , and the time when the j-th receiving station receives the signal is t j , j≠i, then there is where τ i and τ j correspond to the time delays corresponding to the i-th path and the j-th path respectively, V c is the electromagnetic wave propagation speed. Let the time delay difference Δτ ij = τ i - τ j , then the time difference positioning equation is expressed as: Plus the equation of the Earth's surface: Equations (1), (4) and (5) form a system of multivariate non-linear equations regarding ; Step 2: Use the two-dimensional cross-ambiguity correlation algorithm to find the time delay difference between any two receiving stations, specifically as follows: Use the two-dimensional cross-ambiguity formula Among them, g i (t) and g j (t) respectively correspond to the narrowband signals received by the i-th receiving station and the j-th receiving station. Δτ ij is the time delay difference between the two signals, is the Doppler frequency difference between the two signals. By searching for the maximum value in the two-dimensional ambiguity plane jointly formed by the time delay axis and the Doppler frequency axis, the time delay difference Δτ ij between the two signals and the Doppler frequency shift difference Step 3: Substitute the time delay difference Δτ obtained in Step 2 ij into Equation (3), and at the same time, do not consider the ionospheric reflection height h i That is, let h i = 0, then a binary equation system only about is formed by Equations (1), (3) and (4), and the rough positioning result of the target radiation source is calculated by using the Chan algorithm in traditional LOS time difference positioning Step 4: According to the rough positioning result obtained in Step 3, randomly generate sample individuals to form an initial population, and use the genetic algorithm to jointly optimize the target position and the virtual height of the ionosphere for each path to obtain the accurate position of the target radiation source.

2. The short-wave TDOA positioning method for jointly optimizing the ionospheric height and the target position according to claim 1, wherein The specific steps of Step 4 are as follows: 1) Select the coding strategy: Based on the rough positioning result obtained in step 3, determine the value range of the parameters l and h i to be optimized, and select the binary coding method to code each parameter to be estimated; 2) Define the fitness function: 3) Randomly generate K sample individuals to form an initial population, and the k-th sample is denoted as 4) Calculate the fitness function value f(x k ), where k = 1, 2, …, K; 5) Judge whether the population performance meets the maximum number of genetic iterations. If it meets, output the optimal parameters; otherwise, according to the genetic strategy, apply the selection operator, crossover operator, and mutation operator to the population to generate the next generation population, and go back to Step 4).

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