Multi-station time difference positioning method based on space-time correlation

Abstract

The invention discloses a multi-station time difference positioning method based on space-time correlation, and belongs to the technical field of radio positioning. The method comprises the following specific steps: step 1, constructing an aerial radiation source antenna emission model; 2, constructing a ground receiving unit signal model; 3, constructing a ground multi-station space-time correlation matching model; and 4, establishing a multi-station time difference positioning equation. According to the method, the time delay between the radiation source and the multiple stations can be determined in an extremely short time, so that a multi-station positioning equation is constructed, and the position of the radiation source is solved. The core of the method is that after the detection of the arrival time of the radiation source is completed, the pulses of the radiation source with the same label are aligned, then correlation matching is carried out as shown in figure 2, errors caused by time synchronization are removed, and the receiving delay among multiple stations is refined. And then a multi-station passive positioning equation is established, and the position of a radiation source is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of radio positioning, and in particular relates to a time difference positioning method based on time-space correlation. Background Art

[0002] With the rapid development of the modern low-altitude economy, the rapid positioning of aerial targets is of great significance. Compared with active detection, passive positioning has the characteristics of low cost, small scale, and long range, which is suitable for large-scale application and meets the needs of the development of the low-altitude economy. At the same time, the positioning accuracy of the traditional GPS system and Beidou system is low (meter level), which is difficult to meet the demand for precise positioning of low-altitude targets. Therefore, it is of great significance to develop a high-precision positioning method to assist in the confirmation of the flight coordinates of low-altitude targets, realize the precise positioning of aerial targets and even the detailed planning of air routes, and promote the rapid development of the low-altitude economy.

[0003] Traditional time-of-day positioning primarily uses the time-of-arrival delay difference to calculate the distance difference between the target emitter and the receiving station, and then constructs a time-of-day positioning equation to solve for the emitter's position. This positioning method is primarily limited by the accuracy of the time-of-arrival calculation. The poor precision of the synchronized clocks at traditional receiving stations leads to high uncertainty in the distance difference calculation, which in turn introduces positioning errors. Due to the current limitations of transmission rates and the accuracy of the clocks themselves, it is difficult to significantly improve clock accuracy. Although the use of high-precision clocks such as rubidium clocks for absolute time base synchronization has been proposed, the cost and application limitations of rubidium clocks currently make large-scale application difficult and difficult to meet the current needs of low-altitude economic development. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-station time difference positioning method based on time-space correlation. This method introduces time-space correlation matching of radiation source signals before time difference positioning solution, which can effectively improve the delay accuracy and thus improve the positioning solution accuracy.

[0005] The technical solution of the present invention:

[0006] A multi-station time difference positioning method based on time-space correlation, the specific steps are:

[0007] Step 1: Build an aerial radiation source antenna transmission model

[0008]

[0009] Where: s(t) is the pulse signal of the radiation source; t is the time hand; T p is the pulse width (seconds); f0 is the radar carrier frequency (Hz); μ is the frequency modulation slope (Hz / s), B is the frequency modulation bandwidth; rect(·) is the rectangular function; j is the imaginary unit;

[0010] Step 2: Build a ground receiving unit signal model

[0011] Assume that there are n+1 ground receiving units A0, A1, A2, A3, ..., A k ,…,A n , where A0 is the main station and the other n are auxiliary stations, k = 1~n, and the distances between the main station and the auxiliary station and the radar radiation source are D0, D1, D2, D3, ..., D k ,…,D n , then the signal receiving model of the ground receiving unit is:

[0012] 1) The signal received by the master station A0 is:

[0013]

[0014] Where: r 0i (t) is the i-th pulse signal received by station A0; Amp 0i is the pulse amplitude of the i-th pulse signal received by station A0; c is the speed of light;

[0015] Since it is used for low-altitude and low-speed target positioning, the influence of Doppler frequency shift is ignored.

[0016] 2) Slave stations A1 to A n The received signal is:

[0017]

[0018] Where: r 1i (t) is the i-th pulse signal received by station A1; Amp 1i is the pulse amplitude of the i-th pulse signal received by station A1; r 2i (t) is the i-th pulse signal received by station A2; Amp 2i is the pulse amplitude of the i-th pulse signal received by station A2; r 3i (t) is the i-th pulse signal received by station A3; Amp 3i is the pulse amplitude of the i-th pulse signal received by station A3; r ni (t) is A n The i-th pulse signal received by the station; Amp ni A n The pulse amplitude of the i-th pulse signal received by the station;

[0019] Step 3: Constructing a ground multi-station spatiotemporal correlation matching model

[0020] Assume: h(t) = r 0i * (-t)(6)

[0021] Among them, h(t) is the received pulse signal r of the master station A0 0i (t) Matched filter impulse response;

[0022] The ground multi-station spatiotemporal correlation matching model can be established as:

[0023]

[0024] Among them When y i (t) maximum value. Therefore, the distance difference between the radar radiation source and n receiving units can be obtained from the peak point delay;

[0025] Step 4: Establish multi-station time difference positioning equation

[0026] The time difference positioning equation is constructed based on the position of the receiving station and the arrival time difference of the receiving station.

[0027] First, the coordinate system is constructed with the master station A0, and the positions of the n ground receiving stations are A0(x a0 ,y a0 ,z a0 ), A1(x a1 ,y a1 ,z a1 ), A2(x a2 ,y a2 ,z a2 ), A3(x a3 ,y a3 ,z a3 ),…,A q (x ak ,y ak ,z ak ),…,A n (x an ,y an ,z an ). The target position of the radiation source is P(x p ,y p ,z p );like Figure 3 As shown;

[0028] The arrival time delay between the current n slave stations and the master station can be expressed as:

[0029] τ k0 =τ e +τ f ±τ t +δ (8)

[0030] Where: τ k0 is the arrival time delay difference between the kth slave station and the master station; τ eis the time delay difference representing the time-space matching correlation (peak point); τ f represents the sampling error caused by the sampling rate in the process of spatiotemporal matching; τ t represents the clock error between multiple stations; δ represents the transmission delay error (fixed error) between multiple stations;

[0031] Among them, τ f It cannot be avoided or estimated, δ is a fixed value and can be eliminated by system solution, so τ is not considered here. f and δ, so the above formula is rearranged to:

[0032] τ k0 ≈τ e ±τ t

[0033] Based on the above model, the time difference positioning equation can be constructed as follows:

[0034]

[0035] Then we can get:

[0036]

[0037] Where: x ak is the X-axis coordinate of each slave station; y ak is the Y-axis coordinate of each slave station; z ak is the Z-axis coordinate of each slave station; (x a0 -x ak ) is the X-direction projection distance from each slave station to the master station, set as L x0k ;(y a0 -y ak ) is the Y-direction projection distance from each slave station to the master station, set as L y0k ;(z a0 -z ak ) is the Z-direction projection distance from each slave station to the master station, set as L z0k ;

[0038] The above formula can be changed to:

[0039]

[0040] Solving the above equations we can get the radiation source P(x p ,y p ,z p ).

[0041] The beneficial effects of the present invention are as follows: an innovative multi-station time difference positioning method based on time-space correlation is proposed. This method can complete the time delay determination between the radiation source and multiple stations in a very short time, and then construct a multi-station positioning equation to solve the radiation source position. The core of this method is to align the radiation source pulses with the same tag after completing the radiation source arrival time detection, and then perform correlation matching. Figure 2 As shown in the figure, the error caused by time synchronization is removed and the reception delay between multiple stations is refined. Then, a multi-station passive positioning equation is established to solve the radiation source position. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a schematic diagram of the positioning process.

[0043] Figure 2 Schematic diagram of multi-station space-time matching.

[0044] Figure 3 Schematic diagram of the spatial relationship of receiving stations.

[0045] Figure 4 It is the radiation source signal diagram.

[0046] Figure 5 Receive signal diagram for the receiving site.

[0047] Figure 6 This is a comparison chart of clock error and theoretical value.

[0048] Figure 7 To match the delay difference graph.

[0049] Figure 8 This is the GDOP simulation diagram. DETAILED DESCRIPTION

[0050] The specific implementation method is described below. The process is as follows: Figure 1 shown.

[0051] Step 1: Construct an aerial radiation source antenna transmission model and generate a signal such as Figure 4 shown.

[0052] Step 2: Construct the ground receiving unit signal model, and receive the signal as Figure 5 shown.

[0053] Step 3: Simulate the random clock error between the slave and master stations, such as Figure 6 As shown, the master station cannot know the clock error at this time, so the arrival time delay difference obtained by the master station is Figure 5 consistent.

[0054] Step 4: Construct a ground multi-station spatiotemporal correlation matching model and calculate the delay difference of the matching peak point

[0055]

[0056] Then we can get τ 10 ,τ 20 ,τ 30 ,like Figure 7 As shown, we have:

[0057] [ΔD1, ΔD2, ΔD3] = [τ 10 ,τ 20 ,τ 30 ]·c (12)

[0058] Depend on Figure 7 It can be seen that the signal matching result expresses the result of the wave arrival time delay and the accumulation of clock error. Figure 5 The comparison of the arrival time can estimate the clock error, which allows the master station to obtain Figure 5 clock error.

[0059] Step 5: Construct the time difference positioning equation. Based on Formula 9, we can get:

[0060] LX=Z (13)

[0061] in:

[0062] L=[L x0k ,L y0k ,L z0k ]

[0063] X=[x p ,y p ,z p ]

[0064]

[0065] Then we can get:

[0066]

[0067] According to the station location, enter A0(x a0 ,y a0 ,z a0 ), A1(x a1 ,y a1 ,z a1 ), A2(x a2 ,y a2 ,z a2 ), A3(x a3 ,y a3 ,z a3 ) Position coordinates and relative distance [L x0k ,L y0k ,L z0k ], the target position can be calculated.

[0068] Simulation analysis, geometric positioning accuracy simulation for different time delay errors and absolute position errors:

[0069] The simulation parameters are as follows:

[0070] Site Main Station Slave 1 Slave 2 Slave 3 Radiation source X 0 2600 -2600 0 2000 Y 0 1500 1500 -3000 3000 Z 100 90 90 90 2500

[0071] The simulation results are as follows Figure 8 As shown in the figure, it can be seen that when the relative error is 1m, the delay error is within 10ns and the positioning accuracy is within 10m. The delay error of this method can be improved to the order of 1ns according to the increase in the number of matching points.

Claims

1. A multi-station time difference positioning method based on time-space correlation, characterized in that: The specific steps are: Step 1: Construct an aerial radiation source antenna emission model; Step 2: Construct a ground receiving unit signal model; Step 3: Construct a ground multi-station spatiotemporal correlation matching model; Step 4: Establish the multi-station time difference positioning equation.

2. The multi-station time difference positioning method based on time-space correlation according to claim 1, characterized in that: Step 1: Constructing the aerial radiation source antenna emission model is as follows: Where: s(t) is the pulse signal of the radiation source; t is the time hand; T p is the pulse width (seconds); f0 is the radar carrier frequency (Hz); μ is the frequency modulation slope (Hz / s), B is the frequency modulation bandwidth; rect(·) is the rectangular function; j is the imaginary unit.

3. The multi-station time difference positioning method based on time-space correlation according to claim 1, characterized in that: Step 2: Constructing the ground receiving unit signal model is as follows: Assume that there are n+1 ground receiving units A0, A1, A2, A3, ..., A k ,…,A n , where A0 is the main station and the other n are auxiliary stations, k = 1~n, and the distances between the main station and the auxiliary station and the radar radiation source are D0, D1, D2, D3, ..., D k ,…,D n , then the signal receiving model of the ground receiving unit is: 1) The signal received by the master station A0 is: Where: r 0i (t) is the i-th pulse signal received by station A0; Amp 0i is the pulse amplitude of the i-th pulse signal received by station A0; c is the speed of light; Since it is used for low-altitude and low-speed target positioning, the influence of Doppler shift is ignored; 2) Slave stations A1 to A n The received signal is: Where: r 1i (t) is the i-th pulse signal received by station A1; Amp 1i is the pulse amplitude of the i-th pulse signal received by station A1; r 2i (t) is the i-th pulse signal received by station A2; Amp 2i is the pulse amplitude of the i-th pulse signal received by station A2; r 3i (t) is the i-th pulse signal received by station A3; Amp 3i is the pulse amplitude of the i-th pulse signal received by station A3; r ni (t) is A n The i-th pulse signal received by the station; Amp ni A n The pulse amplitude of the i-th pulse signal received by the station.

4. The multi-station time difference positioning method based on time-space correlation according to claim 1, characterized in that: Step 3: Constructing a ground multi-station spatiotemporal correlation matching model is as follows: Assume: h(t) = r 0i * (-t)(6) Among them, h(t) is the received pulse signal r of the master station A0 0i (t) Matched filter impulse response; The ground multi-station spatiotemporal correlation matching model can be established as: Among them When y i (t) maximum value; therefore, the distance difference from the radar radiation source to the n receiving units can be obtained from the peak point delay.

5. The multi-station time difference positioning method based on time-space correlation according to claim 1, characterized in that: Step 4: The multi-station time difference positioning equation is established as follows: The time difference positioning equation is constructed based on the receiving station position and the arrival time difference of the receiving station; First, the coordinate system is constructed with the master station A0, and the positions of the n ground receiving stations are A0(x a0 ,y a0 ,z a0 ), A1(x a1 ,y a1 ,z a1 ), A2(x a2 ,y a2 ,z a2 ), A3(x a3 ,y a3 ,z a3 ),…,A q (x ak ,y ak ,z ak ),…,A n (x an ,y an ,z an ); the target position of the radiation source is P(x p ,y p ,z p ); The arrival time delay between the current n slave stations and the master station can be expressed as: t k0 =t e +t f ±τ t +d(8) Where: τ k0 is the arrival time delay difference between the kth slave station and the master station; τ e is the time delay difference representing the time-space matching correlation (peak point); τ f represents the sampling error caused by the sampling rate during the spatiotemporal matching process; τ t represents the clock error between multiple stations; δ represents the transmission delay error (fixed error) between multiple stations; Among them, τ f It cannot be avoided or estimated, δ is a fixed value and can be eliminated by system solution, so τ is not considered here. f and δ, so the above formula is rearranged to: t k0 ≈t e ±τ t Based on the above model, the time difference positioning equation can be constructed as follows: Then we can get: Where: x ak is the X-axis coordinate of each slave station; y ak is the Y-axis coordinate of each slave station; z ak is the Z-axis coordinate of each slave station; (x a0 -x ak ) is the X-direction projection distance from each slave station to the master station, set as L x0k ;(y a0 -y ak ) is the Y-direction projection distance from each slave station to the master station, set as L y0k ;(z a0 -z ak ) is the Z-direction projection distance from each slave station to the master station, set as L z0k ; The above formula can be changed to: Solving the above equations we can get the radiation source P(x p ,y p ,z p ).

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