A method for correcting positioning error of a single station single channel frequency-only motion

Abstract

This invention relates to a method for correcting positioning errors using a single station and single channel with only frequency measurement, belonging to the field of radio radiation source positioning. It solves the problem of increased target positioning errors caused by measurement errors in the position and velocity of the observation station in existing technologies. The method includes: deploying a reference radiation source that transmits a reference signal to an observation station; the observation station measuring its own position and velocity at N observation positions, receiving the reference signal, and estimating its frequency value; calculating the position error and velocity error matrix of the observation station based on the position of the reference radiation source, the position and velocity of the observation station measured at the N observation positions, and the estimated frequency value of the reference signal; and correcting the position error and velocity error of the observation station based on the position error and velocity error matrix. By using the corrected position and velocity data of the observation station to locate the target, this method can effectively improve the accuracy of target radiation source positioning using only frequency measurement.

Description

Technical Field

[0001] This invention relates to the field of radio radiation source localization, and in particular to a method for correcting positioning errors of a single station and single channel using only frequency measurement. Background Technology

[0002] Radio source localization refers to calculating the location information of a target radiation source by receiving radio signals emitted by that source. Based on different parameter measurement methods, radio source localization can be categorized into different technical systems, mainly including: direction-finding localization, time difference-of-flight (TDF) localization, frequency-finding localization, frequency difference-of-flight (FTF) localization, time-frequency difference-of-flight (TFEF) localization, and combinations of these methods. Direction-finding localization requires each observation station to be equipped with multi-channel receiving equipment; while TDF, FTF, and FTF localization only require observation stations to be equipped with single-channel receiving equipment, multiple observation stations must work together to achieve localization; other combined localization methods either require multiple observation stations to work together or require each station to be equipped with multi-channel receiving equipment. All these localization technical systems place high demands on the localization system's hardware.

[0003] The relative motion between the target radiation source and the observation station will generate a Doppler frequency shift in the radio signal. The magnitude of this value is related to factors such as the target's direction of motion and speed relative to the observation station. Frequency measurement and positioning only requires one observation station equipped with a single-channel receiving device. By moving to different positions to measure and calculate the frequency shift of the stationary target radiation source multiple times, the target can be located. This method is also known as moving single-station single-channel frequency measurement and positioning only.

[0004] Frequency measurement and positioning methods require the observation station to measure its own position and velocity information during movement. When there are errors in the position and velocity of the observation station, it will lead to an increase in the positioning error of the target radiation source. Summary of the Invention

[0005] Based on the above analysis, the present invention aims to provide a method for correcting positioning errors of a single station and single channel using only frequency measurement, in order to solve the problem of increased target positioning errors caused by errors in the measurement of station position and velocity.

[0006] The objective of this invention is mainly achieved through the following technical solutions:

[0007] This invention provides a method for correcting positioning errors of a single station and single channel using only frequency measurement, comprising the following steps:

[0008] Deploy a reference radiation source, which will transmit a reference signal to the observation station;

[0009] The observation station measures its own position and velocity at N observation locations, receives the reference signal and estimates its frequency value;

[0010] Calculate the position error and velocity error matrix of the observation station based on the location of the reference radiation source, the position and velocity of the observation station measured at N observation locations, and the estimated reference signal frequency value;

[0011] The position and velocity errors of the observation station are corrected based on the position and velocity error matrices of the observation station.

[0012] Further, the step of calculating the position error and velocity error matrix of the observation station based on the location of the reference radiation source, the positions and velocities of the observation stations measured at N observation locations, and the estimated reference signal frequency value includes:

[0013] Calculate the position and velocity error diagonal matrix Q B Signal frequency error diagonal matrix Q C And the difference h between the estimated reference signal frequency value and the theoretical reference signal frequency. C ;

[0014] The Jacobian matrix G is calculated based on the location of the reference radiation source, the locations and velocities of the observation stations measured at N observation locations, and the frequency of the reference signal. C ;

[0015] According to the position velocity error diagonal matrix Q B Signal frequency error diagonal matrix Q C Estimate the difference h between the reference signal frequency and the theoretical reference signal frequency. C and Jacobian matrix G C Calculate the position error and velocity error matrix ψ.

[0016] Furthermore, the calculated position-velocity error diagonal matrix Q B Its formula is:

[0017] Q B =diag(Q σ )

[0018] Q σ =[x err y err v x_err v y_err … x err y err v x_err v y_err ] 1×4N

[0019] Where, x err Let y be the variance of the x-axis position error of the observation station. err v is the variance of the y-axis position error of the observation station. x_err Let v be the variance of the velocity error of the observation station in the x-axis direction. y_errLet represent the variance of the velocity error of the observation station in the y-axis direction; diag(·) indicates that the vector (·) is a diagonal matrix constructed with the diagonal line as the diagonal.

[0020] Furthermore, the calculated signal frequency error diagonal matrix Q C Its formula is:

[0021] Q C =diag(Q f )

[0022] Q f =]f err f err … f err ] 1×N

[0023] Among them, f err This represents the variance of the measurement error of the signal frequency by the observation station.

[0024] Furthermore, the calculated difference h between the estimated reference signal frequency and the theoretical reference signal frequency... C Its formula is:

[0025]

[0026] in f is the frequency of the reference signal estimated at N observation points during the movement of the observation station; r_0 =[f r_0,1 f r_0,2 … f r_0,N [ ] represents the theoretical frequency of the reference signal at N observation points during the movement of the observation station.

[0027] Furthermore, the Jacobian matrix G is calculated based on the location of the reference radiation source, the locations and velocities of the observation stations measured at N observation points, and the frequency of the reference signal. C Its formula is:

[0028]

[0029] Among them, f r The reference signal continuously emitted by the reference radiation source to the observation station is denoted by c, where c is the speed of light. The reference radiation source position u c To the observation position u of the observation station i distance, The observation station moves to the observation position u i The radial velocity between the time and the reference radiation source, v i The observation station moves to the observation position u i The velocity is given by time, where i is the i-th observation position of the observation station, and 1 ≤ i ≤ N.

[0030] Furthermore, the formula for calculating the position error and velocity error matrix ψ is as follows:

[0031]

[0032] in(·) -1 To perform the inverse operation, (·) T This is a matrix transpose operation, where ψ is a 4N×1 dimensional matrix.

[0033] Furthermore, the observation station moves to the observation position u i Time-estimated reference signal frequency The calculation method is as follows:

[0034] The position u of the observation station is obtained using the following formula. i Time to receive reference signal data y r,i (t):

[0035]

[0036] Where A r,i f is the amplitude of the signal received at the i-th observation position; r,i It is the frequency of the received signal; w r,i (t) has zero mean and variance σ. 2 Gaussian white noise; t m =mΔ, f sr The sampling frequency is m = 1, ..., M, where M is the number of samples of the reference signal data;

[0037] Based on the observation position u i Received reference signal data y r,i (t), estimate the reference signal frequency

[0038]

[0039] Furthermore, the observation station measures its own position and velocity at N observation locations, including:

[0040] The observation station moves to the observation position u i At that time, measure and record the location u of the observation station. i =[x i ,y i ] T and the speed of the observation station

[0041] Further, the step of correcting the position error and velocity error of the observation station based on the position error and velocity error matrix of the observation station includes:

[0042] The position error and velocity error matrices ψ are transformed into ψ1 in column order.

[0043] ψ1 = reshape(ψ,2,2N)

[0044] Transpose the matrix ψ1 to obtain the matrix ψ2;

[0045] The odd-numbered rows of data are extracted from the matrix ψ2 to form an N×2 dimensional observation station location error estimation matrix Φ. xy ;

[0046] The even-numbered rows of data are extracted from the matrix ψ2 to form an N×2 dimensional observation station velocity error estimation matrix Φ. v ;

[0047] The following formula is used to correct for errors in the measured observation station position U and velocity V:

[0048] U = [u1 u2 … u] N ] T

[0049] V = [v1 v2 … v] N ] T

[0050] U1=U-Φ xy

[0051] V1=V-Φ v

[0052] The corrected station position matrix U1 and the corrected station velocity matrix V1 are obtained.

[0053] The technical solution of this invention can achieve at least one of the following beneficial effects:

[0054] 1. This invention uses a single-station, single-channel frequency measurement method, which has lower hardware requirements compared to other positioning methods;

[0055] 2. This invention improves the accuracy of target positioning by deploying a reference radiation source, having the observation station receive its signals at N observation positions and measure its own position and velocity, and calculating and correcting the position and velocity errors of the observation station itself.

[0056] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0057] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0058] Figure 1 A schematic diagram illustrating the positioning error caused by self-positioning position and velocity errors;

[0059] Figure 2 This is a flowchart illustrating a frequency-only positioning error correction method according to an embodiment of the present invention;

[0060] Figure 3 This is a schematic diagram of the target localization results before and after correction;

[0061] Figure 4 This is a histogram comparing the positioning error before and after correction. Detailed Implementation

[0062] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0063] Errors in the self-positioning location and velocity of the observation station will lead to errors in the location of the radiation source. For example... Figure 1 As shown, the actual locations of the observation stations are: u1 = [0,0] T (m), u2=[50000,0] T (m), velocity v1=v2=[500,0] T (m / s), radiation source location x T =u T =[20000,70000] T (m). In the absence of self-positioning error of the observation station, the location of the radiation source can be obtained by intersecting the equal frequency shift curves of the observation station at position 1 and position 2.

[0064] Introducing the self-positioning error of the observation station, the self-positioning positions of the observation station are as follows: The corresponding isofrequency shift curves are used to estimate the location of the radiation source obtained by their intersection, as follows: Figure 1 As shown in (a).

[0065] Introducing a station velocity error of -50 m / s, the estimated location of the radiation source obtained by intersecting the isofrequency shift curves is as follows: Figure 1 As shown in (b), it can be seen that the self-positioning error of the observation station can lead to the positioning error of the radiation source.

[0066] To address the problem of increased target positioning errors caused by errors in observation station position and velocity measurement, a specific embodiment of the present invention provides a method for correcting positioning errors of a single-station, single-channel, frequency-only positioning method, the flowchart of which is shown below. Figure 2 As shown, it includes the following steps:

[0067] Step 1. Deploy a reference radiation source at a known location and transmit a reference signal of a known frequency to the observation station;

[0068] Specifically, deploy a reference radiation source u C Reference radiation source u C The position is known, denoted as u. C =[x C ,y C ] T (km), such as Figure 3 As shown in the diagram; the reference radiation source continuously emits a reference signal, exemplarily, the reference signal having a frequency of f. r The known monotone signal;

[0069] Step 2. The observation station moves to N locations, measures and records its own position and velocity at each location, and receives a reference signal at each location and estimates its frequency value. The specific steps are as follows:

[0070] In the localization scenario, the initial position of the observation station is x1 = [300, -20]. T (km), observations were conducted at 10 locations, such as Figure 3 As shown in the middle*.

[0071] Specifically, when the observation station moves to the i-th position (1≤i≤10), it measures and records its own position u. i and velocity v i , where its own position u i =[x i ,y i ] T Speed ​​of movement

[0072] Record and calculate the reference signal data y received by the observation station. r,i (t), based on the signal amplitude and frequency value received at the i-th position, with zero mean and variance σ. 2 Gaussian white noise, the formula for calculating the reference signal data is as follows: Where A r,i f is the amplitude of the signal received at position i; r,i w is the frequency of the signal received at position i; r,i (t) has zero mean and variance σ. 2 Gaussian white noise; t m=mΔ, f sr Let m be the sampling frequency, m = 1, ..., M, and M be the number of samples of the reference signal data.

[0073] Furthermore, the observation station moves to position u i The reference signal frequency value obtained by time estimation as follows:

[0074]

[0075] Repeat step 2 until you obtain position data, velocity data, and estimated reference signal frequency values ​​for 10 observation locations.

[0076] Step 3. Based on the numerical results obtained in Step 2, calculate the position error and velocity error matrix of the observation station;

[0077] Specifically, calculate the position error and velocity error matrix ψ:

[0078]

[0079] in(·) -1 To perform the inverse operation, (·) T This is a matrix transpose operation, where ψ is a 4N×1 dimensional matrix.

[0080] The variables in the formula are as follows:

[0081] Optionally, the variance x of the x-axis position error of the observation station relative to the observation location, obtained statistically, can be used. err The variance of the position error of the y-axis. err The variance of the x-axis velocity error, v x_err The variance of the velocity error along the y-axis, v y_err Their values ​​are independent; construct matrix Q σ :

[0082] Q σ =[x err y err v x_err v y_err … x err y err v x_err v y_err ] 1×4N

[0083] Furthermore, with vector Q σ Construct a diagonal matrix Q for position and velocity errors along the diagonal. B Q B =diag(Q σ );

[0084] Optionally, the variance f of the signal frequency measurement error received by the observation station relative to the observation location, obtained statistically, can be used. err Construct matrix Q f =[f err f err … f err ] 1×N .

[0085] Furthermore, with vector Q f Construct a diagonal matrix Q for the signal frequency error. C ,

[0086] Q C =diag(Q f );

[0087] Optionally, construct the Jacobian matrix G. C Its formula is:

[0088]

[0089] In the formula, f r The reference signal frequency is known from step 1, and c is the speed of light. Reference radiation source to observation station u i Distance of location For the observation station to move to u i The radial velocity between the position and the reference radiation source; i ranges from 1 to N.

[0090] Optionally, calculate the difference between the estimated reference signal frequency and the theoretical reference signal frequency.

[0091] In the formula, It is the estimated reference signal frequency during the movement of the observation station; according to the formula The theoretical frequency f of the reference signal during the observation station's movement was calculated. r_0 =[f r_0,1 f r_0,2 … f r_0,N ].

[0092] Step 4. Use the calculated position error and velocity error matrix ψ to correct the position error and velocity error of the observation station.

[0093] Specifically, the position error and velocity error matrix ψ obtained in step 3 is transformed into ψ1 = reshape(ψ,2,2N) in column order, where ψ1 is a 2×2N dimensional matrix.

[0094] Furthermore, transposing matrix ψ1 yields ψ2 = (ψ1). T .

[0095] Furthermore, odd-numbered rows are extracted from matrix ψ2 to form an N×2 dimensional observation station position error estimation matrix Φ. xy =ψ2(1:2:(2N-1),:).

[0096] Furthermore, an even number of rows are extracted from matrix ψ2 to form an N×2 dimensional observation station position error estimation matrix Φ. v =ψ2(2:2:2N,:).

[0097] Furthermore, the measured observation station position U and velocity V are corrected for errors using the following formula:

[0098] U = [u1 u2 … u] N ] T

[0099] V = [v1 v2 … v] N ] T

[0100] U1=U-Φ xy

[0101] V1=V-Φ v

[0102] U1 is the corrected N×2-dimensional station position matrix, which is N×2-dimensional; V1 is the corrected N×2-dimensional station position and velocity matrix.

[0103] For example, the target location is x = [120, 150]. T (km), such as Figure 3 As shown in the diagram; according to step 3, increase the frequency measurement error, which follows a zero mean and a variance of 5Hz; increase the observation station position error and velocity error, where the observation station position error follows a zero mean and a variance of 1000m, and the velocity error follows a zero mean and a variance of 10m / s. Use the same frequency measurement and positioning algorithm to locate the target. Figure 3 The image displays the location result for a specific location:

[0104] 1) In the case of no observation station position and velocity error, the target positioning result is as follows: Figure 3 The position of the triangle in the middle;

[0105] 2) There are errors in the position and velocity of the observation station, and no correction has been made. The target positioning result is as follows: Figure 3 The position of the plus sign;

[0106] 3) Errors exist in the position and velocity of the observation station, and error corrections have been performed. The target positioning result is as follows: Figure 3 The position of the square in the middle.

[0107] This shows that the observation station error leads to a large target positioning error; after the observation station error is corrected, the target positioning error is significantly reduced.

[0108] For example, under the same conditions described above, 200 test samples were analyzed to obtain the positioning error histograms before and after correction, as shown below. Figure 4 As shown, the average positioning error of the observation station is 1964m when the position and velocity errors are included but not corrected, and the average positioning error is 890m when the position and velocity errors are included and corrected.

[0109] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting the positioning error of a mono-static mono-channel frequency-only tracking radar, characterized in that, The method comprises the following steps: deploying a reference radiation source, which emits a reference signal to the observation station; the observation station measures its own position and speed at N observation positions, receives the reference signal and estimates the frequency value of the reference signal; calculating the position error and speed error matrix of the observation station according to the position of the reference radiation source, the position and speed of the observation station measured at the N observation positions and the estimated frequency value of the reference signal, comprising: Computing a position velocity error diagonal matrix Q B , a signal frequency error diagonal matrix Q C and a difference h between the estimated reference signal frequency value and a reference signal theoretical frequency C ; calculating a Jacobian matrix G from the reference radiation source position, the observer position and velocity measured at N observation positions, and the reference signal frequency C ; a position velocity error diagonal matrix Q B , a signal frequency error diagonal matrix Q C , an estimated reference signal frequency difference h C and a Jacobian matrix G C , a position error and velocity error matrix ψ; correcting the position error and speed error of the observation station according to the position error and speed error matrix of the observation station.

2. The method of claim 1, wherein, The calculated position velocity error diagonal matrix Q B The formula is: Q B = diag(Q σ ) Q σ = [x err y err v x_err v y_err … x err y err v x_err v y_err ] 1×4N where x err is the variance of the position error of the observer in the x-axis, y err is the variance of the position error of the observer in the y-axis, v x_err is the variance of the velocity error of the observer in the x-axis, v y_err is the variance of the velocity error of the observer in the y-axis; diag() indicates that the vector () is constructed into a diagonal matrix.

3. The method of claim 2, wherein, the computed signal frequency error diagonal matrix Q C which is given by Q C = diag(Q f ) Q f = [f err f err …f err ] 1×N where f err is the variance of the signal frequency measurement error for the observation station.

4. The method of claim 3, wherein, The calculation estimates a reference signal frequency difference h from the reference signal theoretical frequency C The formula is: wherein frefis the reference signal frequency estimated at the N observation points during the motion of the observation station; r_0 = [f r_0,1 f r_0,2 … f r_0,N ] is the theoretical reference signal frequency at the N observation points during the motion of the observation station.

5. The method of claim 1, wherein, calculating a Jacobian matrix G from the reference radiation source position, the observer position and velocity measured at N observation points, and the reference signal frequency C which is given by wherein f r is the reference signal continuously emitted by the reference radiation source to the observation station, c is the value of the speed of light, is the position of the reference radiation source u c to the observation station observation position u i , is the radial velocity between the observation station and the reference radiation source when the observation station moves to the observation position u i , i is the velocity of the observation station when it moves to the observation position u i , i is the i-th observation position of the observation station, and 1≤i≤N.

6. The method according to any one of claims 1 to 5, characterized in that, The calculation of the position error and speed error matrix ψ is as follows: where (·) -1 for the inverse operation, (·) T is the matrix transpose operation, and ψ is a 4N x 1 matrix.

7. The method of claim 4 wherein, The observation station moves to the observation position u i The estimated reference signal frequency at time t The calculation method is as follows: The station motion to observation position u is obtained by the following equation i The reference signal data y is received at time t r,i (t) where A r,i is the amplitude of the received signal at the i-th observation location; f r,i is the frequency of the received signal; w r,i (t) is a zero-mean, variance σ 2 2 Gaussian white noise; t m = mΔ, f sr is the sampling frequency, m = 1,..., M, and M is the number of samples of the reference signal data; According to the observation position u i Receiving reference signal data y r,i (t), estimate the reference signal frequency 8. The method of claim 1 or 5, wherein, the observation station measures its own position and speed at N observation positions, comprising: The observation station measures and records the position u i of the observation station at the moment of movement to the observation position u i = [x i , y i ] T and the movement speed of the observation station 9. The method of claim 1, wherein, correcting the position error and speed error of the observation station according to the position error and speed error matrix of the observation station, comprising: performing matrix transformation on the position error and speed error matrix ψ in column order to obtain ψ1 ψ1 = reshape (ψ, 2, 2N) performing a transpose operation on the matrix ψ1 to obtain a matrix ψ2; extracting from the matrix ψ2 the odd rows to form an N x 2 dimensional observation station position error estimation matrix Φ xy ; extracting even row data from the matrix ψ2 to form an N x 2 dimensional observation station velocity error estimation matrix Φ v ; performing error correction on the measured observation station position U and motion speed V by using the following formula: U = [u1 u2... un]T N ] T V = [v1 v2... vn]T N ] T U1 = U - Φ xy V1 = V - Φ v obtaining the corrected observation station position matrix U1 and the corrected observation station speed matrix V1.

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