Fusion processing method for anti-spoofing interference of GNSS receivers for low-Earth orbit vehicles

Abstract

This invention provides a fusion processing method for resisting deception interference in GNSS receivers of low-Earth orbit (LEO) aircraft. It utilizes the clock bias and orbital data of the LEO aircraft for calculation and compares the results with a set threshold to determine the presence of deception interference signals. Then, it performs corresponding processing calculations using GNSS observations between LEO aircraft to obtain the detection quantity of deception interference signals. Based on the obtained detection quantity, the deception signals are identified and eliminated. This invention effectively solves the problem of deception interference affecting LEO aircraft in scenarios where multiple LEO aircraft simultaneously engage in deception interference, distinguishing and isolating the interfered signals. This ensures that the GNSS receivers on board the LEO aircraft can function normally and complete various navigation enhancement-related tasks.

Description

Technical Field

[0001] This invention relates to the field of anti-spoofing interference technology for GNSS receivers of aircraft, and particularly to a fusion processing method for anti-spoofing interference of GNSS receivers of low-orbit aircraft. Background Technology

[0002] Low Earth Orbit (LEO) vehicles bring new capabilities to navigation and communication enhancement, applicable to various fields such as global integrity monitoring of medium and high Earth orbit (MEO) navigation satellites, and joint orbit determination and communication across high, medium, and low Earth orbits. However, due to their low orbital altitude and the publicly available signal formats of MEO civilian navigation signals, GNSS receivers on LEO vehicles are vulnerable to malicious interference from ground-based equipment. Currently, there are two main methods of interfering with GNSS signals: suppression jamming and deception jamming. Suppression jamming attacks GNSS receivers with high-power signals, causing them to fail in positioning and timing. However, the attacked target can still use backup methods such as inertial navigation for navigation or timing. Deception jamming, on the other hand, transmits signals that are identical or similar to the real signals, causing the receiver to track the deceptive signal and thus obtain incorrect position or time information. Because of the low orbital altitude of LEO vehicles, widespread deception jamming can simultaneously disable multiple LEO GNSS systems, making it difficult for users to realize they are under attack, resulting in the continuous output of incorrect position and time information and potentially serious consequences.

[0003] Among the categories of GNSS interference, deception interference is the most harmful. Given the serious dangers of GNSS deception interference, many scholars both domestically and internationally have conducted in-depth research on GNSS anti-deception interference techniques. For example, Akos DM's paper, "Who's afraid of the spoofer? GPS / GNSS spoofing detection via automatic gain control," identifies deception signals from the perspective of in-band signal power; Swaszek PF's "Analysis of asimple, multi-receiver GPS spoof detector" identifies interference signals by determining the direction of signal arrival through a receiving antenna array. Tang Xiaomei's "GNSS Dual-Receiver Anti-Deception Technology" utilizes two receivers and a single-difference method to achieve anti-interference technology based on pseudorange measurements. All of the above techniques enable the detection of deception signals by ground-based GNSS receivers.

[0004] However, given that the receiver for low-Earth orbit spacecraft needs to take into account factors such as cost, chip resources, and anti-spoofing effectiveness, the existing technology still falls short in terms of anti-interference performance in the face of large-scale spoofing interference. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a fusion processing method for resisting deception interference in GNSS receivers for low-Earth orbit (LEO) vehicles. Targeting scenarios with widespread deception interference, this method utilizes various resources of the onboard GNSS receiver to identify whether the LEO vehicle is experiencing deception interference in such scenarios, and distinguishes and isolates the interfered signals. This solves the problem of LEO vehicles being subject to deception interference in these scenarios and effectively improves the anti-interference performance of the onboard GNSS receiver.

[0006] This invention provides a fusion processing method for resisting deception interference in GNSS receivers of low-Earth orbit vehicles, the specific technical solution of which is as follows:

[0007] S1: Determine whether the GNSS receiver of the low-orbit aircraft is subjected to deception interference based on the clock difference information. If there is a deception interference signal, proceed to step S4; otherwise, proceed to step S2.

[0008] S2: Calculate the geometric distance and laser ranging results between the low-orbit aircraft and nearby low-orbit aircraft, and compare the geometric distance with the laser ranging. If either comparison result is less than the set first threshold, it is determined that there is a deception interference signal, and step S4 is executed; otherwise, step S3 is executed.

[0009] S3: Compare the theoretical coordinates of the low-orbit aircraft with the actual positioning coordinates output by the GNSS receiver of the low-orbit aircraft. If the comparison result exceeds the set first threshold, it is determined that there is a deception interference signal and step S4 is executed. Otherwise, it is determined that no deception interference signal has been received.

[0010] S4: The low-Earth orbit spacecraft acquires the original pseudorange observations through the inter-satellite link, and then combines the low-Earth orbit spacecraft into pairs to obtain the pseudorange set.

[0011] S5: The low-Earth orbit spacecraft calculates the difference between the original pseudorange observations of different low-Earth orbit spacecraft with the same medium-high orbit satellite number based on the pseudorange set, and obtains the pseudorange difference value.

[0012] S6: Sort the obtained pseudorange difference values ​​and calculate the difference between adjacent sorted data to obtain the detection quantity of the deception interference signal;

[0013] S7: Based on the detected amount of the deception interference signal, determine whether there is a deception signal. If there is a deception signal, proceed to step S8. If there is no deception signal, determine that the satellite signal received by the low-orbit spacecraft has not been interfered with.

[0014] S8: Based on the different combinations of satellite signals received by the low-orbit spacecraft, the satellite signals are distinguished, spoofing signals are isolated, and positioning calculations are performed to eliminate spoofing signals.

[0015] Further, step S1 is as follows:

[0016] The low-Earth orbit (LEO) aircraft determines whether its GNSS receiver is being subjected to deception interference based on the clock bias information output by the GNSS receiver. If the clock bias result exceeds the set clock bias threshold, it is determined that there is a deception interference signal; otherwise, it is determined that there is no deception interference signal.

[0017] Further, step S2, the specific process is as follows:

[0018] S201: The low-Earth orbit (LEO) vehicle receives the positioning coordinates and laser ranging results from the GNSS receivers of multiple nearby LEO vehicles via an inter-satellite link.

[0019] S202: Calculate the geometric distance between the low-orbit aircraft based on the positioning coordinates;

[0020] S203: Calculate the difference between the laser range measurement and the geometric distance.

[0021] Furthermore, in step S3, the ground station calculates and obtains the theoretical coordinates of the low-Earth orbit spacecraft based on ephemeris information at a set frequency.

[0022] Furthermore, the first threshold is three times the positioning error of the GNSS receiver.

[0023] Furthermore, in step S4, any of the pseudo-range sets is denoted as S. M S N Specifically, it is expressed as follows:

[0024]

[0025] in, This represents the original observation of the pseudodistance;

[0026] If the low-Earth orbit spacecraft receives a deceptive signal, then the original pseudorange observation is expressed as:

[0027]

[0028] Where, sρ j R represents the pseudorange of high-orbit satellite j in the deception source simulation. si δ represents the physical geometric distance between the deception source and the low-orbit vehicle i. si These are various errors that low-Earth orbit spacecraft receive when receiving deception and jamming signals, including errors in the ionosphere, troposphere, clock bias, and multipath.

[0029] If the low-Earth orbit spacecraft receives signals from medium- or high-Earth orbit satellites, then the pseudorange raw observations are expressed as follows:

[0030]

[0031] Among them, R ji It is the geometric distance from a medium-to-high orbit satellite to a low-orbit spacecraft, δ ji This refers to various errors that low-Earth orbit spacecraft receive from medium- and high-Earth orbit satellites, including ionospheric, tropospheric, clock errors, and multipath errors.

[0032] Furthermore, the pseudorange difference is denoted as ΔP. MN Specifically, it is expressed as follows:

[0033]

[0034] If the low-Earth orbit spacecraft receives a deceptive signal, then To represent a parameter independent of the medium-to-high orbit satellite simulated by the deception source, it is expressed as:

[0035]

[0036] Among them, R SM R represents the geometric distance between the deception source and the low-orbit vehicle M. SN δ represents the geometric distance between the deception source and the low-Earth orbit vehicle N. SM δ represents the various errors in the low-orbit spacecraft M receiving spoofing and jamming signals. SN This represents various errors in the low-orbit spacecraft N receiving deception and interference signals;

[0037] If the low-Earth orbit spacecraft receives signals from medium- or high-Earth orbit satellites, then A parameter related to medium- and high-orbit satellites is expressed as:

[0038]

[0039] Among them, R jM R represents the geometric distance from the medium-to-high orbit satellite j to the low-orbit spacecraft M. jN δ represents the geometric distance from the medium-to-high orbit satellite j to the low-orbit spacecraft N. jM δ represents the various errors in the reception of signals from medium-to-high orbit satellite j by the low-Earth orbit spacecraft M. jN This represents various errors in the reception of signals from medium- and high-orbit satellites by the low-orbit spacecraft N.

[0040] Furthermore, in step S6, the detection quantity of the deception interference signal is expressed as follows:

[0041]

[0042] Where j and k represent adjacent data after sorting;

[0043] If the low-Earth orbit spacecraft receives a deceptive signal, then It follows a receiver noise pattern with a mean of 0 and a variance of σ.2 Gaussian distribution;

[0044] Otherwise, it follows a non-central chi-square distribution related to the distance of the low-Earth orbit vehicle.

[0045] Further, step S7 is as follows:

[0046] The low-Earth orbit spacecraft determines whether a deception signal exists based on the detection quantity of the obtained deception interference signal. If the detection quantity is less than the second threshold for T consecutive seconds, the satellite signal received by the low-Earth orbit spacecraft is determined to be a deception signal.

[0047] Furthermore, the second threshold is three times the receiver noise.

[0048] The beneficial effects of this invention are as follows:

[0049] This invention determines whether a low-Earth orbit (LEO) GNSS receiver is subject to deception interference based on clock bias information. Furthermore, it identifies deception interference signals by comparing the differences in geometric distance and laser ranging between LEO aircraft, as well as the differences between LEO aircraft coordinates and output positioning results. Then, it identifies and extracts deception signals using various raw observation data, thus completing anti-interference processing. This invention integrates and utilizes various existing raw observation data on the aircraft, has lower hardware resource requirements, and is simpler to implement. It effectively solves the problem of LEO aircraft being subject to deception interference in scenarios where multiple LEO aircraft are simultaneously subjected to deception interference, effectively improving the anti-deception interference performance of onboard GNSS receivers. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0051] Figure 2 This is a schematic diagram illustrating the probability of detecting a deception signal in Embodiment 1 of the present invention. Detailed Implementation

[0052] The technical solutions in the embodiments of the present invention are clearly and completely described in the following description. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0053] Example 1

[0054] Embodiment 1 of the present invention discloses a fusion processing method for resisting deception interference in a GNSS receiver of a low-orbit vehicle, such as... Figure 1 As shown, the specific steps are as follows:

[0055] S1: Determine whether the GNSS receiver of the low-orbit aircraft is subjected to deception interference based on the clock difference information. If there is a deception interference signal, proceed to step S4; otherwise, proceed to step S2.

[0056] The clock bias threshold is calculated as follows: The clock bias threshold is related to the Allen variance of the crystal oscillator of the low-Earth orbit spacecraft. Three times the Allen variance can be used as the clock bias threshold. Alternatively, under the condition of no deception interference, the clock bias of the low-Earth orbit spacecraft receiving medium and high orbit satellite signals can be statistically analyzed, and the variance can be calculated to obtain the threshold. The calculation frequency of this step is once per second and can be dynamically adjusted.

[0057] Step S1 is as follows:

[0058] The low-Earth orbit (LEO) aircraft determines whether its GNSS receiver is being subjected to deception interference based on the clock bias information output by the GNSS receiver. If the clock bias result exceeds the set clock bias threshold, it is determined that there is a deception interference signal; otherwise, it is determined that there is no deception interference signal.

[0059] S2: Calculate the geometric distance and laser ranging results between the low-orbit aircraft and nearby low-orbit aircraft, and compare the geometric distance with the laser ranging. If either comparison result is less than the set first threshold, it is determined that there is a deception interference signal, and step S4 is executed; otherwise, step S3 is executed.

[0060] Step S2, the specific process is as follows:

[0061] S201: The low-Earth orbit (LEO) vehicle receives positioning coordinates and laser ranging results from GNSS receivers of multiple nearby LEO vehicles via inter-satellite links. MN ;

[0062] S202: Calculate the geometric distance L between the low-orbit aircraft based on the positioning coordinates. MN The calculation formula is as follows:

[0063]

[0064] Among them, X M and X N Representing the X-axis coordinates and Y-axis coordinates of the two low-Earth orbit spacecraft, respectively. M and Y N These represent the Y-axis coordinates and Z-axis coordinates of the two low-Earth orbit spacecraft, respectively. M and Z N These represent the Z-axis coordinates of the two low-Earth orbit spacecraft.

[0065] S203: Calculate the difference between the laser range measurement and the geometric distance;

[0066] The low-orbit spacecraft calculates the difference between the laser range measurement and the geometric distance obtained from the positioning result, and eliminates the magnification factor. As the detection quantity for this step:

[0067]

[0068] If the value of the detected quantity l is greater than 3 times the positioning error of the receiver, it is considered that there is deception interference, and proceed to step S4; otherwise, proceed to step S3.

[0069] S3: Compare the theoretical coordinates of the low-orbit aircraft with the actual positioning coordinates output by the GNSS receiver of the low-orbit aircraft. If the comparison result exceeds the set first threshold, it is determined that there is a deception interference signal and step S4 is executed. Otherwise, it is determined that no deception interference signal has been received.

[0070] In this embodiment, the theoretical coordinates of the low-orbit spacecraft are obtained by ground stations at a set frequency based on ephemeris information; the first threshold is three times the positioning error of the GNSS receiver.

[0071] S4: The low-Earth orbit spacecraft acquires the original pseudorange observations through the inter-satellite link, and then combines the low-Earth orbit spacecraft into pairs to obtain the pseudorange set.

[0072] In step S4, any of the pseudo-range sets is denoted as S. M S N Specifically, it is expressed as follows:

[0073]

[0074] in, This represents the original observation of the pseudodistance;

[0075] If the low-Earth orbit spacecraft receives a deceptive signal, then the original pseudorange observation is expressed as:

[0076]

[0077] Where, sρ j R represents the pseudorange of high-orbit satellite j in the deception source simulation. si δ represents the physical geometric distance between the deception source and the low-orbit vehicle i. si These are various errors that low-Earth orbit spacecraft receive when receiving deception and jamming signals, including errors in the ionosphere, troposphere, clock bias, and multipath.

[0078] If the low-Earth orbit spacecraft receives signals from medium- or high-Earth orbit satellites, then the pseudorange raw observations are expressed as follows:

[0079]

[0080] Among them, R ji It is the geometric distance from a medium-to-high orbit satellite to a low-orbit spacecraft, δ jiThis refers to various errors that low-Earth orbit spacecraft receive from medium- and high-Earth orbit satellites, including ionospheric, tropospheric, clock errors, and multipath errors.

[0081] S5: The low-Earth orbit spacecraft calculates the difference between the original pseudorange observations of different low-Earth orbit spacecraft with the same medium-high orbit satellite number based on the pseudorange set, and obtains the pseudorange difference value.

[0082] The pseudorange difference is denoted as ΔP. MN Specifically, it is expressed as follows:

[0083]

[0084] If the low-Earth orbit spacecraft receives a deceptive signal, then To represent a parameter independent of the medium-to-high orbit satellite simulated by the deception source, it is expressed as:

[0085]

[0086] Among them, R SM R represents the geometric distance between the deception source and the low-orbit vehicle M. SN δ represents the geometric distance between the deception source and the low-Earth orbit vehicle N. SM δ represents the various errors in the low-orbit spacecraft M receiving spoofing and jamming signals. SN This represents various errors in the low-orbit spacecraft N receiving deception and interference signals;

[0087] If the low-Earth orbit spacecraft receives signals from medium- or high-Earth orbit satellites, then A parameter related to medium- and high-orbit satellites is expressed as:

[0088]

[0089] Among them, R jM R represents the geometric distance from the medium-to-high orbit satellite j to the low-orbit spacecraft M. jN δ represents the geometric distance from the medium-to-high orbit satellite j to the low-orbit spacecraft N. jM δ represents the various errors in the reception of signals from medium-to-high orbit satellite j by the low-Earth orbit spacecraft M. jN This represents various errors in the reception of signals from medium- and high-orbit satellites by the low-orbit spacecraft N.

[0090] S6: Based on the obtained pseudorange difference value, sort the data using the bubble sort method, subtract the adjacent data after sorting, eliminate the method factor β=2, and calculate the detection quantity of the deception interference signal.

[0091] The detection quantity of the deception interference signal is expressed as follows:

[0092]

[0093] Where j and k represent adjacent data after bubble sort;

[0094] If the low-Earth orbit spacecraft receives a deceptive signal, then It follows a receiver noise pattern with a mean of 0 and a variance of σ. 2 Gaussian distribution;

[0095] Otherwise, it follows a non-central chi-square distribution related to the distance of the low-Earth orbit vehicle.

[0096] S7: Based on the detected amount of the deception interference signal, determine whether there is a deception signal. If there is a deception signal, proceed to step S8. If there is no deception signal, determine that the satellite signal received by the low-orbit spacecraft has not been interfered with.

[0097] Since low-Earth orbit vehicles are typically more than a kilometer away from satellites, the isolation between the receiver of the spoofing signal and the medium-to-high-Earth orbit satellite is much greater than three times the receiver noise σ. 2 Therefore, in this embodiment, the second threshold is three times the receiver noise σ. 2 ;

[0098] Step S7 is as follows:

[0099] The low-Earth orbit spacecraft determines the presence of a deception signal based on the detected amount of the deception interference signal. If the detected amount is less than three times the receiver noise σ for T consecutive seconds... 2 If so, the satellite signals j and k received by the low-orbit spacecraft M and N are determined to be spoofing signals; the value of parameter T can be dynamically adjusted according to actual needs.

[0100] S8: Based on the different combinations of satellite signals received by the low-orbit spacecraft, distinguish satellite signals j and k, isolate spoofing signals, perform positioning calculations, and eliminate spoofing signals;

[0101] Specifically, the low-Earth orbit spacecraft selects and combines the received satellites j and k, repeating step 7. If the detection quantity is passed... If the low-Earth orbit spacecraft is not being deceived, then satellite signal j is considered non-deceptive, while satellite signal k is a deceptive signal. Similarly, the received satellite signals can be isolated one by one to determine whether they are deceptive signals. When the low-Earth orbit spacecraft performs positioning calculations, the deceptive signals are eliminated, thus completing the anti-interference processing for deceptive signals.

[0102] Based on the above steps, this embodiment uses SDK and MatLab for simulation, conducting 10,000 repeated experiments, and measuring different receiver noise σ. 2 The probability of successfully detecting a spoofing signal is as follows: Figure 2 As shown, the above steps can effectively identify deception interference in a wide range of scenarios and distinguish and isolate the interfered signals.

[0103] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A fusion processing method for resisting deception interference in a GNSS receiver of a low-orbit aircraft, characterized in that, include: S1: Determine whether the GNSS receiver of the low-orbit aircraft is subjected to deception interference based on the clock difference information. If there is a deception interference signal, proceed to step S4; otherwise, proceed to step S2. S2: Calculate the geometric distance and laser ranging results between the low-orbit aircraft and nearby low-orbit aircraft, and compare the geometric distance with the laser ranging. If either comparison result is less than the set first threshold, it is determined that there is a deception interference signal, and step S4 is executed; otherwise, step S3 is executed. The first threshold is 3 times the positioning error of the GNSS receiver. S3: The ground station calculates the theoretical coordinates of the low-Earth orbit vehicle based on the ephemeris information at a set frequency, and compares the theoretical coordinates of the low-Earth orbit vehicle with the actual positioning coordinates output by the GNSS receiver of the low-Earth orbit vehicle. If the comparison result exceeds the set first threshold, it is determined that there is a deception interference signal and step S4 is executed; otherwise, it is determined that no deception interference signal has been received. S4: The low-Earth orbit spacecraft acquires the original pseudorange observations through the inter-satellite link, and then combines the low-Earth orbit spacecraft into pairs to obtain the pseudorange set. S5: The low-Earth orbit spacecraft calculates the difference between the original pseudorange observations of different low-Earth orbit spacecraft with the same medium-high orbit satellite number based on the pseudorange set, and obtains the pseudorange difference value. S6: Based on the obtained pseudorange difference value, sort the data using the bubble sort method, subtract the adjacent data after sorting, eliminate the method factor β=2, and calculate the detection quantity of the deception interference signal. Calculate the detection quantity of the deception interference signal; The detection quantity of the deception interference signal is expressed as follows: in, and This represents adjacent data after sorting, where M and N represent the low-Earth orbit spacecraft numbers. This indicates that the low-orbit vehicles M and N are related to the vehicle numbered... The difference in pseudorange between medium and high orbit satellites, This indicates that the low-orbit vehicles M and N are related to the numbered... The difference in pseudorange between medium and high orbit satellites, where β represents the method factor; If the low-Earth orbit spacecraft receives a deceptive signal, then It follows a mean of 0 and a variance of receiver noise. Gaussian distribution; Otherwise, it follows a non-central chi-square distribution related to the distance of the low-Earth orbit vehicle; S7: Based on the detected amount of the deception interference signal, determine whether there is a deception signal. If there is a deception signal, proceed to step S8. If there is no deception signal, determine that the satellite signal received by the low-orbit spacecraft has not been interfered with. The low-Earth orbit spacecraft determines whether a deception signal exists based on the detection quantity of the received deception interference signal. If the detection quantity is less than the second threshold for T consecutive seconds, the satellite signal received by the low-Earth orbit spacecraft is determined to be a deception signal. The second threshold is three times the receiver noise. S8: Based on the different combinations of satellite signals received by the low-orbit spacecraft, the satellite signals are distinguished, spoofing signals are isolated, and positioning calculations are performed to eliminate spoofing signals.

2. The fusion processing method according to claim 1, characterized in that, Step S1 is as follows: The low-Earth orbit (LEO) aircraft determines whether its GNSS receiver is being subjected to deception interference based on the clock bias information output by the GNSS receiver. If the clock bias result exceeds the set clock bias threshold, it is determined that there is a deception interference signal; otherwise, it is determined that there is no deception interference signal.

3. The fusion processing method according to claim 1, characterized in that, Step S2, the specific process is as follows: S201: The low-Earth orbit (LEO) vehicle receives the positioning coordinates and laser ranging results from the GNSS receivers of multiple nearby LEO vehicles via an inter-satellite link. S202: Calculate the geometric distance between low-orbit aircraft based on their positioning coordinates; S203: Calculate the difference between the laser range measurement and the geometric distance.

4. The fusion processing method according to claim 1, characterized in that, In step S4, any of the pseudo-range sets is denoted as... Specifically, it is expressed as follows: ={ | and Simultaneously received medium- and high-orbit satellite signals; Low Earth Orbit Vehicle Number in, This represents the original observation of the pseudodistance; If the low-Earth orbit spacecraft receives a deceptive signal, then the original pseudorange observation is expressed as: in, The deception source is simulated by a high-orbit satellite. pseudorange, Indicates the source of deception and low-orbit aircraft The physical geometric distance These are various errors in the low-orbit spacecraft's reception of deceptive interference signals; If the low-Earth orbit spacecraft receives signals from medium- or high-Earth orbit satellites, then the pseudorange raw observations are expressed as follows: in, It is the geometric distance between a medium-to-high orbit satellite and a low-orbit spacecraft. This indicates various errors in the reception of medium and high orbit satellite signals by low-Earth orbit spacecraft.

5. The fusion processing method according to claim 1, characterized in that, The pseudorange difference is denoted as Specifically, it is expressed as follows: ={ ; Low Earth orbit vehicle number, and Simultaneously received medium-to-high orbit satellite signals; If the low-Earth orbit spacecraft receives a deceptive signal, then A parameter independent of the medium-to-high orbit satellite simulated by the deception source is expressed as: in, This represents the geometric distance between the deception source and the low-Earth orbit vehicle M. This represents the geometric distance between the deception source and the low-Earth orbit vehicle N. This represents the various errors in the low-Earth orbit spacecraft M's reception of spoofing and jamming signals. This represents various errors in the low-orbit spacecraft N receiving deception and interference signals; If the low-Earth orbit spacecraft receives signals from medium- or high-Earth orbit satellites, then A parameter related to medium- and high-orbit satellites is expressed as: in, This represents the geometric distance from the medium-to-high orbit satellite j to the low-orbit spacecraft M. This represents the geometric distance from medium-to-high orbit satellite j to low-orbit spacecraft N. This represents the various errors in the reception of signals from medium-to-high orbit satellite j by the low-Earth orbit spacecraft M. This represents various errors in the reception of signals from medium- and high-orbit satellites by the low-orbit spacecraft N.

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