# Over-the-horizon target direct positioning method based on short-wave multi-station angles and satellite time frequency

## An over-the-horizon, short-wave technology, applied in positioning, radio wave measurement systems, measurement devices, etc., can solve the problems of multiple intermediate parameters and limited positioning accuracy, and achieve reliable performance, improved positioning accuracy, and efficient calculations.

Pending Publication Date: 2021-08-20
PLA STRATEGIC SUPPORT FORCE INFORMATION ENG UNIV PLA SSF IEU
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## AI-Extracted Technical Summary

### Problems solved by technology

[0005] Aiming at the problems of limited positioning accuracy and many intermediate parameters that need to be calculated in the existing radio signal positioning methods, the present invention provides a direct positioning method for over-the-horizon targets that coordinates short-wave multi-station angles an...
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### Method used

Compared with existing short-wave multi-station intersection positioning and satellite time-frequency difference positioning, the method provided by the invention can effectively utilize short-wave over-the-horizon positioning and these two positioning systems based on satellite-based radio positioning to achieve compensation The short board of positioning can maintain the effect of positioning advantages, so as to significantly improve the positioning accuracy of the over-the-horizon (long-distance) radiation source on the earth's surface. In addition, the direct positioning method disclosed in the present invention reduces the dimensionality of the multi-parameter joint optimization problem, and realizes positioning through the Newton-type iterative formula, which has a fast convergence speed and does not require grid search. It is a reliable performance and efficient calculation method. Direct location method of over-the-horizon tar...
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## Abstract

The invention provides an over-the-horizon target direct positioning method based on short-wave multi-station angles and satellite time frequency. The method comprises the following steps of: receiving and collecting short-wave signals emitted by a to-be-positioned radiation source by using a plurality of short-wave observation stations, and sequentially establishing algebraic relational expressions between the geographic coordinates of the radiation source and azimuth angles of the short-wave signals emitted by the radiation source to the different short-wave observation stations; using a plurality of satellites to forward the satellite signals emitted by the to-be-positioned radiation source, receiving and collecting the satellite signals, and are sequentially establishing algebraic relational expressions between the geographic coordinates of the radiation source and the propagation time delay and Doppler frequency offset of the satellite signals emitted by the radiation source which are forwarded to a satellite ground station through each satellite, then representing the algebraic relational expressions as an expression related to the geographic coordinates of the to-be-positioned radiation source; and making a ground center station obtain an optimization model for estimating the longitude and latitude of the radiation source based on short wave and satellite signal data, and perform numerical optimization on the optimization model to obtain a longitude and latitude estimated value of the radiation source. The method has high convergence speed and does not need grid search.

Application Domain

Position fixation

Technology Topic

Computational physicsAzimuth +6

## Examples

• Experimental program(1)

### Example Embodiment

[0075] In order to make the objects, technical solutions, and advantages of the present invention, the technical solutions in the embodiments of the present invention will become apparent from the figures of the present invention, which will be described in connection with the drawings of the present invention. Embodiments, not all of the embodiments. Based on the embodiments of the present invention, there are all other embodiments obtained without making creative labor without making creative labor premises.
[0076] Combine figure 1 Sum figure 2 The embodiment of the present invention provides a super-visual target direct positioning method for synergistic short-wave multi-station angles and satellite, including the following steps:
[0077] S101: Using K 1 A short-wave observatory (an array of observatory installation can receive two-dimensional angle information) receives and acquires short-wave signals to be positioned to be positioned, k 1 1;
[0078] S102: Using K 1 The geographic coordinates of a short-wave observatory, sequentially establish the geographic coordinates of the radiation source to reach K 1 Algebraic relationship between the azimuth of the short-wave observatory;
[0079] S103: Sending K 1 Array reception signal for multiple sampling moments of short-wave observations 1A new short-wave receiving signal vector and will k 1 A new short-wave receiving signal vector is represented as an expression associated with geographic coordinates of the radiation source to be positioned;
[0080] S104: Using K 2 The satellite forwards the satellite signal to be positioned to be positioned, and the satellite signal is received and collected through different satellite ground stations;
[0081] S105: Use the geographic coordinates of each satellite and the geographic coordinates of the satellite ground station, and the satellite signal to be positioned to be positioned to the satellite signal to be transferred to the satellite ground station. Algebraic relationship between delay and Doppler frequency offset;
[0082] S106: Sending K 2 Satellite ground station multiple sampling time reception signal composition K 2 A new satellite receives signal vector and will k 2 A new satellite receiving signal vector is expressed as an expression related to geographic coordinates of the radiation source to be positioned;
[0083] S107: Each short-wave observatory and satellite ground station transmits the acquired array signal data to the ground center station (which can be set to a short wave observation station or satellite ground station), and the ground center station is based on the maximum of the received array signal data. Estimation Standard Construction Direct Positioning Optimization Model;
[0084] S108: The ground center station reduces the direct positioning optimization model to obtain a desired optimization model of geographic coordinates and reaching the pitch angle of each short wave observation station to be positioned;
[0085] S109: The ground center station uses the Newton Ieration method to optimize the design of the desired optimization model to obtain an estimate of the geographic coordinates of the radiation source to be positioned.
[0086] It should be noted that the source of the radiation to be positioned in the embodiment of the present invention needs to be able to simultaneously transmit signals of different frequency bands, namely short-wave signals, and satellite signals. In actual scenarios, such as a ship (or aircraft) may simultaneously transmit short-wave signals and satellite signals.
[0087] Compared to existing short-wave multi-station interchange and satellite time frequency difference, the synergistic short-wave multi-station angle and the satellite time-frequency over-band target direct positioning method, which can simultaneously transmit short-wave signals and satellite signals at the same time The source of the radiation to be positioned, which can significantly improve the positioning accuracy of the Earth's surface super-visual (distance) radiation source; and the direct positioning method disclosed in the present invention reduces the combination optimization problem of multi-parameters, and passes the Newton The formula is to achieve positioning, with a faster convergence speed, no grid search, is a direct positioning method of reliable and efficient over-visual target.
[0088] On the basis of the above embodiment, the embodiment of the present invention also provides a synergistic short-wave multi-station angle and a satellite time-frequency over-site-wide target direct positioning method, which includes the following steps:
[0089] As an embodiment, step S101, the kth k 1 The array reception signal model of a short-wave observatory is:
[0090]
[0091] in, Dead k 1 Array reception signal for short wave observation station; Representation 1 Signal Repacking Enterprise of Short Wave Observatory; Dead k 1 The array of short-wave observatory is added to the white noise, the mean of white noise is zero, and the covariance matrix is ( Represents known noise power; Express Main unit matrix; Dead k 1 Number of short-wave observations of the parameter); Indicates the array of arrays of the function in the direction of the signal. and Diamatic signal reaching King 1 The azimuth (clockwise clipping angle of the north direction) and elevation angle.
[0092] As an embodiment, according to the geometric relationship of the short wave signal propagation and the coordinate transition (eg image 3 The shown), in step S102, using K 1 The geographic coordinates of the geographic coordinates (i.e., latitude and longitude) established by the geographic coordinates of the short-wave observatory (i.e., latitude and longitude) to the short-wave signal to which it is transmitted. 1 The algebraic relationship between the azimuth of the short-wave observation station is:
[0093]
[0094] in, Arrive in the short wave signal to King K 1 Azimuth angle of a short wave observation station; and Known k 1 The latitude and longitude, α and gamma of the short-wave observatory are latitude and longitude to position the radiation source, respectively; and Both represent the coordinate system conversion vector, Z (α, γ) represents the position vector of the radiation source to solidly coordinate in the ground, Dead k 1 Short-wave observatory location in the center of solid situats, r a R b The long axis and short axis of the Earth reference ellipsoid are respectively.
[0095] As an embodiment, step S103, the kth k 1 A new short-wave receiving signal vector is represented as an expression associated with geographic coordinates of the source to be positioned.
[0096]
[0097] Among them, T n Indicates the Nth sampling time, n is the number of sampling points; Know 1 A new short-wave receiving signal vector consisting of N sample time of the short wave observation station; Reaching the kth k 1 Vector of the short-wave signal reckoning of the short wave signal of the short-wave observatory; Be the kth 1 Noise vector of the array additive Gaussian noise of short-wave observatory. I N Represents N-dimensional unit matrix, Indicates the Kronecker product of the matrix, Indicates the array of geographic coordinates and pitch angles to position the radiation source to satisfy the arrays of the function. Indicates the array of arrays of the function in the direction of the signal. and Diamatic signal reaching King 1 Azimuth and elevation angle of a short wave observation station.
[0098] As an embodiment, in step S104, the satellite signal to be positioned to be positioned for the radiation source, after k 2 The satellite forwarded the satellite signal, using different satellite ground stations to receive and acquire the forwarding signal, of which 2 Satellite ground station receiving signal model for satellite forwarding is:
[0099]
[0100] in, Indicates a satellite ground station receiving signal replenant with a satellite forwarding; That is in T 0 Time to send and by the kth 2 The satellite forwarded to the satellite ground station delay Signal renewal; Representation 2 The satellite forwarded satellite ground station receiving the additive Gaussia white noise in the channel, the mean of the noise is zero, the power is ( A known); Satellite signal indicating the source of radiation to be positioned by the kth 2 Satellite forwarding the channel propagation coefficient between satellite ground stations (including path loss and antenna reception gain, etc.); Exp (·) represents the natural index operation (or a vector after each vector element to take a natural index operation); and Satellite signals 2 The satellite forwarded to the spread of the satellite ground station and Doppler Frequency.
[0101] As an embodiment, in step S105, the geographic coordinates of the source to be positioned to be positioned and the satellite signals thereof are transmitted. 2 The dissemination of the satellite forward to the satellite ground station, the algebraic relations between Doppler frequency offers are:
[0102]
[0103] Among them, || · || 2 Indicates the Euclidean norm of the vector; c represents the speed of communication; f c Indicates the carrier frequency of the satellite signal; Dead k 2 Satellites in the position of the solid coordinate standard, Dead k 2 Satellite ground standing in the center of solid coordinates, r a R b Earth-reference ellipsoidal long axis, short axis; and Known k 2 Satellite longitude, latitude and height; Know 2 Satellite speeds at the stereotypes of the stealth and Known k 2 The latitude and longitude of the satellite ground station.
[0104] As an embodiment, step S106, the kth k 2 A new satellite reception signal vector is represented as the expression associated with geographic coordinates of the source of the radiation source:
[0105]
[0106] Among them, T n Indicates the Nth Sampling Time, N 'is the number of sampling points; Know 2 A new satellite receiving signal vector consisting of N 'sampling time of satellite ground stations; For DFT transform factors, n = [1, 2, ..., n '] T; S ' 0 = [S ' 1 -t 0 ), s' (t 2 -t 0 ), ..., s' (t N′ -t 0 )]] T Is the source to be positioned in T 0The vector of the satellite signal envelope of the N 'sampling time transmitted at the time; Is the kth of N 'sampling time 2 Noise vector of additive Gaussian white noise in satellite ground station receiving channel; Di k (α, γ) are in relation to the time Doppler Frequency The relevant phase offset matrix, the expression is:
[0107]
[0108] Among them, T s Indicates the sampling cycle; DIAG {·} represents a diagonal matrix composed of vector elements; Exp (·) represents the natural index operation; and Satellite signals 2 The satellite forwarded to the spread of the satellite ground station and Doppler Frequency.
[0109] As an embodiment, in step S107, the direct positioning optimization model constructed by the maximum likelihood estimation criterion is:
[0110]
[0111] Where j represents the target function to be optimized; Dead k 1 Noise power of a short wave observation station; Indicates the noise power of the satellite ground station forwarded by the king satellite; Indicates the Euclidean norm of the vector.
[0112] As an embodiment, step S108 specifically includes the following sub steps:
[0113] S1081: Sequential The best solution
[0114]
[0115] S1082: Sequential The best solution
[0116]
[0117] S1083: will In the direct positioning optimization model in step S107, S 0 'The best solution
[0118]
[0119] in, BLKDIAG {} represents a block-shaped angular matrix made of a matrix or vector as a diagonal element; e max {·} Indicates the feature vector corresponding to the maximum feature value of the matrix;
[0120] S1084: will and Decision optimization model is obtained in the direct positioning optimization model of step S107:
[0121]
[0122] in, Indicates the target function to be optimized; η contains the parameters to be estimated λ max {·} Represents the maximum feature value of the matrix; For the orthogonal projection matrix, its expression is:
[0123]
[0124] in, Express Main unit matrix, Dead k 1 A short wave observation station number number.
[0125] As an embodiment, step S109 specifically includes the following sub steps:
[0126] S1091: Initial estimation of latitude latitude to be positioned radiation sources by using short-wave multi-station intersection or satellite time frequency difference positioning The initial estimate of the pitch angle of each short wave measurement station is obtained by using the MUSIC directional algorithm.
[0127] S1092: Iterations of the desired optimization model using the Newton model method, the iterative formula is:
[0128]
[0129] Among them, i represents the number of iterations, 0 and The gradient vectors of the target function and the HESSIAN matrix are respectively, respectively, and the corresponding calculation formulas are:
[0130]
[0131]
[0132] in
[0133]
[0134] Among them, K 1 = 1, 2, ..., K 1
[0135]
[0136] in,
[0137]
[0138] Hide 1 '(Α, γ), H 2 '(Α, γ), H 3 The nth line of '(α, γ), the expression of the M-column element is:
[0139]
[0140] Among them, RE {·} represents the real part; V n , V m The unit vector of the nth element is 1, and the mth element is 1, respectively; K is a swap matrix to meet VEC [φ T (α, γ)] = kVEC [φ (α, γ)]; and Represent Y H Φ (α, γ) φ H (α, γ) Y characteristic value and the corresponding feature vector.
[0141] The method provided by the present invention can effectively utilize the short-wave supersight positioning and satellite-based radio positioning and satellite-based radio positioning of the present invention to effectively utilize the two positioning systems of the short-wave superstitude positioning and satellite radio positioning. To maintain the effect of positioning advantage, it is possible to significantly improve the positioning accuracy of the global surface super-visual distance (long distance) radiation source. Further, the direct positioning method disclosed herein will reduce the combined optimization problem of multi-parameters, and the positioning is achieved by the Newton type iterative formula, with a faster convergence speed, no mesh search, is a performance reliable, operational efficient Super - distance target direct positioning method.
[0142] In order to verify the effectiveness of the method of the present invention, the present invention also provides the following experiments, as follows:
[0143] There are three short-wave observations and 3 communication satellites to position the radiation source of the Earth surface. The three short-wave observation stations are 60.2 °, 70.5 ° and 72.2 °, respectively, latitude, 34 °, 38.8 ° and 26.5 °, respectively. The length of the three satellites is 50 °, 47 ° and 53 °, the latitude is 20 °, 0 ° and 0 °, the orbit height is 35785.863km; the radiation source is 52.9 °, the latitude is 10.35 °, and the same The transmitted short-wave signal (frequency is 20 MHz) and the satellite signal (200 MHz). Each short wave observation station consists of 9 yuan uniform circulating array with a radius of 40 meters. The positioning method disclosed in the present invention is compared to the conventional short-wave multi-station intersection method and the satellite time frequency difference positioning method.
[0144] Set the signal to noise ratio to 0 dB, and the number of signal sample points is 100, Figure 4 The positioning result of the three methods was given, and a total of 500 Monte Carlo experiment was carried out. As can be seen from the figure, the satellite time frequency difference positioning method is smaller in the radiation source latitude, and the positioning error in the radiation source is large, and the short-wave multi-station interlocation positioning method is opposite, but the present invention The disclosed positioning method is reduced in the positioning error in the radiation source latitude and the longitude direction, which is smaller than the positioning errors in both any directions. The remaining conditions remain unchanged. Figure 5 The positioning root error of three methods is given as the signal-to-noise ratio of the signal-to-noise ratio, since the positioning method disclosed in the present invention is to effectively cooperate with the short-wave multi-station intersection and satellite time frequency difference. The synergy gain is generated, so the positioning method disclosed in the present invention has higher positioning accuracy throughout the signal-to-noise ratio interval compared to the short-wave multi-station intersection method and satellite time frequency difference positioning method.
[0145] It will be noted that the above embodiments are intended to illustrate the technical solutions of the present invention, not to limit the present invention, and will be apparent to those skilled in the art, which will be understood by those skilled in the art. The technical scheme described in the foregoing embodiments is modified, or the equivalent replacement thereof is performed in which these modifications or replacements do not allow the nature of the respective technical solutions to the spirit and scope of the technical solutions of the present invention.

## Description & Claims & Application Information

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