A High-Security Ranging Code Design Method Based on Pseudo-Satellite Systems

Abstract

This invention discloses a high-security ranging code design method based on a pseudosatellite system. It utilizes a Legendre polynomial sequence based on quadratic residue theory, incorporating truncation point parameters and phase difference parameters. A Weil code is generated through a shift-and-XOR operation. The generated Weil code sequence is then used to generate the primary ranging code sequence through cyclic truncation and splitting operations. A periodic code-changing scheme is introduced to further enhance the security of this code sequence. This invention improves the security performance of the ranging code without significantly affecting its correlation, making it more suitable for scenarios with high confidentiality and correlation requirements.

Description

Technical Field

[0001] This invention belongs to the field of navigation technology, specifically relating to a high-security ranging code design method based on a pseudo-satellite system. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) are widely used across various industries due to their powerful functions, but as a space-based radio navigation system, they still have many inherent limitations. Because GNSS satellites are approximately 20,000 kilometers above the Earth's surface, the navigation signals are very weak by the time they reach the receiver, and the signals are easily affected by various interferences during propagation. Their service performance is significantly reduced in complex environments such as tunnels, indoor spaces, cities, and canyons. Therefore, various alternative and enhanced auxiliary systems are being developed at an accelerated pace, among which ground-based pseudo-satellite navigation and positioning systems (Pseudolite, PL) have become a key research focus.

[0003] A pseudosatellite is a device used to generate and transmit GNSS-like signals. It can serve as a GNSS augmentation system in complex environments and provide independent navigation and positioning services in GNSS-denied environments. Compared to GNSS satellites, pseudosatellites are much closer to the user receiver, typically within a few hundred meters to several kilometers. Furthermore, the locations of pseudosatellite base stations are fixed and often situated on the ground or in low altitudes, thus eliminating the need to consider ionospheric delay. The principle of a pseudosatellite system is similar to that of a GNSS system, requiring at least four base stations to provide navigation and positioning services. The base stations emit navigation signals, which the user receiver receives to calculate the distance between the user receiver and the base stations. To ensure system effectiveness and reliability, current pseudosatellite systems use ranging codes that are essentially the same as those in existing navigation systems, primarily employing Gold code sequences to form the ranging code.

[0004] Gold codes are generated by modulo-2 summation of two linear feedback shift registers, resulting in a relatively simple generation method and better correlation and security performance compared to m-sequences. Therefore, Gold code sequences are widely used in pseudosatellite systems. However, Gold codes are insufficient for scenarios with higher requirements for confidentiality and correlation. Thus, the use of Weil code sequences to form ranging codes has become a research focus. Weil codes differ from Gold codes in their generation method; they are generated by cyclically shifting two Legendre sequences and then performing a modulo-2 summation. This generation method gives them superior correlation and security performance compared to Gold codes, making them more suitable for navigation systems with high confidentiality and high correlation requirements. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a high-security ranging code design method based on a pseudosatellite system. It utilizes a Legendre polynomial sequence based on quadratic residue theory, incorporating truncation point parameters and phase difference parameters, and generates a Weil code through a shift-and-XOR operation. The generated Weil code sequence is then used to generate the main ranging code sequence through cyclic truncation and splitting operations. A periodic code-changing scheme is introduced to further enhance the security of this code sequence. This invention improves the security performance of the ranging code without significantly affecting its correlation, making it more suitable for scenarios with high confidentiality and correlation requirements.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] Step 1: Generate the Legendre sequence L(k):

[0008]

[0009] Where the value of k ranges from 0 to (N-1), generating a Legendre sequence of length N; the value of x in the formula ranges from 1 to (N-1);

[0010] Step 2: Compare and filter the truncation point parameter p and phase difference parameter w corresponding to different PRN numbers to generate a1 different code sequences; the range of values ​​for the truncation point parameter p and phase difference parameter w is specified during the Weil code generation process.

[0011] Step 3: Calculate and generate the cyclically truncated Weil code sequence;

[0012]

[0013] By replacing the parameter k in the formula with (n+p-1)mod N, the final calculated Weil code sequence with a total length of N after cyclic truncation is obtained.

[0014] Step 4: Take the first m bits of the Weil code sequence obtained in Step 3 to obtain the final ranging code sequence of length m;

[0015] Step 5: Repeat steps 1 to 4 to generate multiple sets of different Weil code sequences.

[0016] Step 6: Apply a periodic code-changing strategy to the generated ranging code sequence, that is, change the intercept point parameter p and the phase difference parameter w of the Weil code at regular intervals, thereby changing the Weil code sequence to improve security; the specific operation is as follows:

[0017] Step 6-1: Determine the code skipping time interval parameter period, using "hours" as the unit of code skipping interval. Set period = h to indicate that the code skipping time interval is h hours once, and record the current time with parameter t;

[0018] Step 6-2: Set the intercept point and phase difference change parameter addnum, initializing it to 1; adjust the addnum value according to the current time information, following the principle: addnum (n) =addnum (n-1) +t (n) The upper right corner superscript represents the serial number information;

[0019] Step 6-3: Define the t-th (n) The phase difference parameter w and the cut-off point parameter p of the code sequence with PRN number s at time s are respectively

[0020] Step 6-4: Limit the range of variation of the phase difference w and the intercept point p using modulo division to ensure that the range of variation of the phase difference parameter w is within the specified range. Between these points, the intercept point parameter p varies within the range [1, N]; when At that time, use the modular division operation to make Complete the setting of the phase difference parameter at this moment; similarly, set the intercept point parameter, when... At that time, use the modular division operation to make Complete the setting of the intercept point parameter p at this moment;

[0021] Step 6-5: Generate a set of distinct Weil code sequences that jump over time.

[0022] Preferably, a1 = 63.

[0023] The beneficial effects of this invention are as follows:

[0024] This invention uses Weil code sequences to form ranging codes because Legendre sequences inherently possess orthogonality and low cross-correlation. Weil codes are generated by shifting and XORing Legendre sequences, which increases the orthogonality and anti-interference performance of the generated Weil code sequences. Therefore, they exhibit better autocorrelation and cross-correlation performance compared to Gold code sequences. Furthermore, based on the values ​​of the phase difference parameter w and the cutoff point parameter p, it can be seen that the Weil code has a total of... The Weil code employs various combinations of code sequences, enhancing its security. Furthermore, a periodic code-changing strategy is used, specifying that the phase difference and cut-off point parameters of the Weil code sequence change over time, thereby generating different sets of Weil code sequences at different times. This strategy further improves the security performance of ranging codes without significantly affecting correlation, making it more suitable for scenarios with high confidentiality and correlation requirements, such as control and navigation systems, including aircraft positioning and navigation systems. Attached Figure Description

[0025] Figure 1 This is a flowchart of the method for generating a high-security ranging code in this invention;

[0026] Figure 2 This is a comparison chart of the correlation between Weil codes and Gold codes between PRN numbers 1 and 2.

[0027] Figure 3 The cross-correlation performance of the Weil codes of PRN numbers 1 and 2 after the 1st and 6th code hopping is shown in the graph. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] Code length and code rate are important parameters of ranging codes. The two are closely related and have a significant impact on the resolution, bandwidth and transmission characteristics of the signal.

[0030] Code length and code rate are usually represented by m and Rc, respectively, and their relationship with code period T can be expressed as:

[0031]

[0032] The code rate determines the time resolution of the signal. A higher code rate corresponds to a shorter chip time, which can provide higher time resolution, thus allowing the receiver to measure the arrival time of the signal more accurately.

[0033] The code length affects the system's anti-interference performance and ranging accuracy. Longer code sequences have better correlation characteristics, which helps to improve the ranging accuracy of the code sequence and the anti-interference performance of the signal.

[0034] Taking into account both the ranging accuracy and anti-interference performance of the ranging code, the code rate R is specified. c It is 10.23 Mcps.

[0035] Since the length of the Legendre sequence must be a prime number, a Legendre sequence of N=10243 is generated here, which generates a Weil code sequence with a code length of 10243. Then, the code sequence with the first m=10230 bits of the original sequence is used to generate the ranging code sequence.

[0036] According to the formula, the corresponding ranging code period is 1ms.

[0037] Finally, the number of base stations p to be selected is determined, and p different ranging codes are selected from the preferred pair sequence. Generally, p is 5 to 8. In this embodiment, 6 code sequences are selected, with PRN numbers 1, 2, 8, 9, 11, and 12, respectively. The specific parameters are shown in Table 1.

[0038] Table 1

[0039]

[0040]

[0041] The phase difference parameter (w) and the intercept point parameter (p) have the following ranges: w∈[1,5121], p∈[1,10243]; at this time, there are a total of w*p=52454403 code family capacities. It is preferable to select 20 groups, i.e., a1=20.

[0042] The specified periodic code skipping parameter is period=3, meaning that a code skipping operation is performed every 3 hours.

[0043] like Figure 1 As shown, the specific steps of the embodiment are as follows:

[0044] Step 1: First, generate the Legendre sequence L(k) according to the formula:

[0045]

[0046] Where k ranges from 0 to 10242, generating a Legendre sequence of length N; x ranges from 1 to 10242 in the formula;

[0047] Step 2: Compare and filter the cut-off point parameter (p) and phase difference parameter (w) of the code sequences corresponding to different PRN numbers to generate 20 different code sequences.

[0048] During the Weil code generation process, the values ​​of these two parameters are specified to be in the range of w∈[1,5121] and p∈[1,10243].

[0049] Step 3: Calculate and generate the initial Weil code sequence after cyclic truncation;

[0050]

[0051] This step replaces the parameter k in the formula with (n+p-1) mod 10243. Finally, the Weil code sequence after cyclic truncation can be calculated.

[0052] Step 4: Take the first m = 10230 bits of each truncated sequence obtained in Step 3, and finally obtain a ranging code sequence with a length of 10230.

[0053] The length of the truncated sequence should be as consistent as possible with the length of the original Weil code sequence to minimize the impact on the correlation of the code sequence.

[0054] Step 5: Repeating steps 1-4 will generate multiple sets of distinct Weil code sequences; to generate 20 sets of sequences, steps 1-4 need to be repeated 20 times.

[0055] Step 6: Apply a periodic code-changing strategy to the generated sequence, that is, change the truncation point parameter (p) and phase difference parameter (w) of the Weil code at regular intervals, thereby changing the Weil code sequence to improve security.

[0056] The specific strategy implementation steps are as follows:

[0057] Step 6-1: Determine the code skipping time interval parameter period, using "hours" as the unit for the code skipping interval. Set period = 3 to indicate that the code skipping time interval is once every 3 hours, and record the current time using parameter t;

[0058] Step 6-2: Set the intercept point and phase difference change parameter `addnum`, initially setting its value to 1. The value of `addnum` will be adjusted based on the current time information (the upper right corner subscript represents the sequence number). The adjustment principle is: `addnum` (n) =addnum (n-1) +t (n) ;

[0059] Step 6-3: Define the t-th (n) The phase difference parameter w and the cut-off point parameter p of the code sequence with PRN number s at time s are respectively

[0060] Step 6-4: Limit the range of variation of the phase difference parameter w and the intercept point parameter p using modulo division. It is necessary to ensure that the range of variation of the phase difference parameter w is between [1, 5121] and the range of variation of the intercept point parameter p is between [1, 10243].

[0061] When w tn When (s)≥5121, use the modulo division operation to make Complete the phase difference parameter settings for this moment. Similarly, set the intercept point parameters as needed. At that time, use the modular division operation to make Complete the setting of the intercept point parameter p at this moment;

[0062] After step 6 is performed, a set of different Weil code sequences that jump over time will be generated.

[0063] In this embodiment, starting from the hour, the value of t is 0, 3, 6, 9, 12, 15, 18, 21, a total of 8 times. The value of the parameter addnum after the end of different times is 1, 4, 10, 19, 31, 46, 64, 85 respectively.

[0064] Figure 2 A comparison of the cross-correlation between Weil and Gold codes between PRN numbers 1 and 2 is shown. The graph reveals that the cross-correlation distribution of the Weil codes is compactly clustered, with a smaller coverage area and lower noise floor.

[0065] Figure 3 The cross-correlation performance of the Weil codes of PRN numbers 1 and 2 after the 1st and 6th code hopping is shown. Calculations show that the maximum correlation sidelobe energies after code hopping are 32.0327 dB and 31.6025 dB, respectively.

Claims

1. A high-security ranging code design method based on a pseudosatellite system, characterized in that, Includes the following steps: Step 1: Generate Legendre sequences L ( k ): in k The value range is 0~( N -1), generate a length of N The Legendre sequence; the value of x in the formula is 1 to (N-1); Step 2: Extract the truncation parameters of the code sequences corresponding to different PRN numbers. p and phase difference parameter w Compare and filter to select the generated a A set of different code sequences; the truncation point parameters are specified during the Weil code generation process. p and phase difference parameter w The range of values ​​is , ; Step 3: Calculate and generate the cyclically truncated Weil code sequence; Parameters in the formula k Replace with (n+p-1) mod N, and finally calculate the Weil code sequence with a total length of N after cyclic truncation; Step 4: Take the first m bits of the Weil code sequence obtained in Step 3 to obtain the final ranging code sequence of length m; Step 5: Repeat steps 1 to 4 to generate multiple sets of distinct Weil code sequences; Step 6: Apply a periodic code-changing strategy to the generated ranging code sequence, that is, change the intercept point parameter of the Weil code at regular intervals. p and phase difference parameter w This achieves the goal of altering the Weil code sequence to improve security; the specific steps are as follows: Step 6-1: Determine the code skipping time interval parameter period, using "hours" as the unit of code skipping interval. Set period=h to indicate that the code skipping time interval is h hours once, and record the current time with parameter t; Step 6-2: Set the intercept point and phase difference change parameters. addnum Set its initial value to 1; adjust according to the current time information. addnum The values ​​are adjusted according to the following principles: The upper right corner superscript represents the serial number information; Step 6-3: Specify the first Phase difference parameter of code sequence at time PRN number s w and intercept point parameters p They are respectively , ; Step 6-4: Phase difference w and intercept point p The range of variation is limited using modulo division to ensure the phase difference parameter w The range of variation is Intercepting point parameters p exist Variations between ranges; when At that time, use the modular division operation to make Complete the setting of the phase difference parameter at this moment; similarly, set the intercept point parameter, when... At that time, use the modular division operation to make Complete the setting of the intercept point parameter p at this moment; Step 6-5: Generate a set of distinct Weil code sequences that jump over time.

2. The high-security ranging code design method based on a pseudosatellite system according to claim 1, characterized in that, a 1=63。

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