Formation of a Message for Transmission to CKNP

Key Parameters

Notation Description
CCSCoordinate Correction Station - station that generates and transmits differential corrections.
CKNPCentral Control and Navigation Point - central facility receiving messages from CCS stations.
NSANavigation Satellite Apparatus - individual GNSS satellites (GPS, GLONASS).
NRSNavigation Receiver System - GNSS receivers at CCS stations.
AUAntenna Unit - receiver antenna systems at CCS (AU1, AU2, AU3).
TNPATime and Navigation Parameter Assessments - processed navigation measurements.
UDREIUser Differential Range Error Index - integrity indicator for differential corrections (0-15 scale).
\(\tilde{S}\)Normalized pseudorange value for message transmission.
\(S\)Physical pseudorange value in meters.
\(\tilde{\dot{S}}_i\)Normalized pseudovelocity value for L1/L2 transmission.
\(\dot{S}_i\)Physical pseudovelocity value on L1/L2 in m/s.
\(\tilde{\theta}_{x,y,z}\)Normalized X, Y, Z coordinates of CCS antenna phase center.
\(\theta_{x,y,z}\)Physical X, Y, Z coordinates of CCS antenna phase center in meters.
\(\tilde{n}\)Normalized air refractivity coefficient for atmospheric corrections.
\(n\)Physical air refractivity coefficient in the CCS area.
\(K\)Normalization coefficient: \(10^3\) for distances/velocities, \(10^6\) for refractivity.
\(\lfloor \cdot \rfloor\)Floor function (integer part) used in normalization algorithms.
C/A codeCoarse/Acquisition code - civilian GPS signal code for pseudorange measurements.
P codePrecision code - military GPS signal code on L1 and L2 frequencies.
L1, L2GPS carrier frequencies: L1 = 1575.42 MHz, L2 = 1227.60 MHz.
WGS-84World Geodetic System 1984 - GPS reference coordinate system.
PZ-90Parametry Zemli 1990 - GLONASS reference coordinate system.
Message Type6-bit field identifying message content (0-63 range): 0=Reserved, 1=NSA Mask, 2-5=Code TNPA, 6=Integrity, 7-10=Phase TNPA, 30=Position, 31=Atmospheric, 32=Status, 63=Special.
NSA Mask216-bit field defining which satellites have data in subsequent messages (bits 1-37=GPS, 38-61=GLONASS).
Measurement Epoch Time16-bit timestamp with 0.1s resolution (0-6553.5s range from current epoch start).
NSA Mask Issue Identifier2-bit synchronization counter (0-3, wraps from 3 to 0) for message coordination.
Full Carrier Phase8-bit field containing integer carrier phase cycles for precise positioning.
Normalized RMS4-bit field encoding measurement uncertainty using lookup tables (0.75mm to 150mm scale).
Signal-to-Noise Ratio5-bit field (0-31 range) indicating GNSS signal quality at receiver.
Frequency Indicator2-bit field: 0=L1 only, 1=L1+L2, 2=L2 only, 3=reserved.
CCS AU Number2-bit field identifying antenna unit: 0=weighted average, 1-3=individual AUs.
Air Refractivity Coefficient8-bit normalized atmospheric parameter for tropospheric corrections.
Channel Status1-bit flag per NRS channel: 0=operational, 1=faulty.
Special Message752-bit text message field (up to 90 characters) for operational communications.

1. General Principle of Message Formation

All messages transmitted from the CCS to the CKNP are formed according to a single principle, with the exception of the "CCS Position", "Atmospheric Parameters", "CCS NRS Status" and "Special Message" types. The general message format structure is given in Table 1.

The "CCS Position", "Atmospheric Parameters", "CCS NRS Status" and "Special Message" formats do not contain the fields "NSA Mask Issue Identifier" and "Number of NSAs for Which Data Are Formed".

The "CCS Identification Number" parameter in a message defines the unique number of a CCS in the NCS.

The "NSA Mask Issue Identifier" parameter is intended for information synchronization. Its current value is set in the "NSA Mask" message. Other message types are processed only if the value of their "NSA Mask Issue Identifier" field matches the current mask issue identifier value obtained in the "NSA Mask" message.

Table 1
Parameter Description Bits Range
CCS Identification Number Defines the number of the CCS that transmits (receives) the message 8 0–255
Message Type See Table 2 6 0–63
Measurement Epoch Time Measurement epoch time with 0.1 s resolution (seconds since start of current CCS system-time epoch, 0–6553.5 s) 16 0–6553.5 s
NSA Mask Issue Identifier Defines the NSA mask issue number for message transmission/reception synchronization (cyclic counter, wraps from 3 to 0) 2 0–3
Number of NSAs for Which Data Are Formed Defines the number of NSAs for which data are formed (determined by the "NSA Mask" message) 6 0–61 (62–63 reserved)
Information Field Data — —

For information transfer from the CCS to the CKNP, the message types listed in Table 2 are used.

Table 2
Type Description
0Reserved
1NSA Mask
2Normalized Raw Code TNPA Values for GPS/GLONASS (C/A code)
3Normalized Code TNPA Values for GPS/GLONASS after Rejection of Anomalous C/A Code Measurements
4Normalized Smoothed Code TNPA Values for GPS/GLONASS (C/A code)
5Normalized Code TNPA Values for GPS/GLONASS after Applying Hardware and Other Corrections (C/A code)
6NSA Integrity Information
7Normalized Raw Phase TNPA Values for GPS/GLONASS (P code on L1, L2)
8Normalized Phase TNPA Values for GPS/GLONASS after Rejection of Anomalous Measurements (P code on L1, L2)
9Normalized Smoothed Phase TNPA Values for GPS/GLONASS (P code on L1, L2)
10Normalized Phase TNPA Values for GPS/GLONASS after Applying Hardware and Other Corrections (P code on L1, L2)
11-29Reserved
30CCS Position
31Atmospheric Parameters
32CCS NRS Status
33-62Reserved
63Special Message

“NSA Mask” Message Format

1. The information field of the “NSA Mask” message is 216 bits long.

2. Each bit, in accordance with Table 3, contains information about the NSA number to which the data transmitted in messages 2–10, 30, 31 relate.

3. For example, a one in the fifth bit of the information field of the “NSA Mask” message indicates that the data relate to GPS 5, while bit 40 relates to GLONASS slot 3.

4. The structure of the “NSA Mask” information field is given in Table 3.

Table 3
Bit Numbers Purpose
1-37GPS / GPS Spare NSA
38-61GLONASS Slot Number plus 37
62-216Reserved

Size of the “NSA Mask” message — 248 bits.

“NSA Integrity Information” Message Format

The information field of the “NSA Integrity Information” message has a variable length.

The list of NSAs for which data are formed in this message is defined by the “NSA Mask” message whose issue identifier matches the value of the “NSA Mask Issue Identifier” field in the “NSA Integrity Information” message.

The structure of the “NSA Integrity Information” message information field is given in Table 4.

Note: In the tables, bit positions are indicated as the starting bit (initial index). Each field occupies N consecutive bits starting from the indicated position.

Table 4
Parameter Bits Bit Number in Message Note
Reserved232
Number of NSAs for which data are formed (defined by the “NSA Mask”)634Range: 0–61 (62–63 reserved)
Integrity data for the first NSA from the “NSA Mask”1640See Table 5
…………
Integrity data for the last NSA from the “NSA Mask”16Depends on total number of NSAs in the maskSee Table 5

The integrity data contain the normalized signal-to-noise ratio and the User Differential Range Error Index (UDREI). The “Integrity Data” parameter format is presented in Table 5.

Table 5
Field Name Bits Bit Number in Parameter Range
Reserved70
Signal-to-Noise Ratio570 – 2⁵ – 1
UDREI4120 – 2⁴ – 1

UDREI decoding is provided in Table 6.

The maximum size of the "NSA Integrity Information" message is 1016 bits.

Table 6
UDREIEstimated Error of Differential Corrections (m)
00.75
11.0
21.25
31.75
42.25
53.0
63.75
74.5
85.25
96.0
107.5
1115.0
1250.0
13150.0
14Not observed (measurement unavailable)
15Do not use (unreliable data)

Format of Messages 2-5

Messages 2-5 are intended for transmitting code-measured TNPA on the C/A code to the CKNP. They have the same format and differ only in the type of CCS processing after which the code parameters are sent to the CKNP.

The information field of messages 2-5 has a variable length. The list of NSAs for which these messages are formed is determined by the content of the “NSA Mask” message. The structure of the information field of messages 2-5 is given in Table 7.

Table 7
Parameter Bits Bit Number in Message Note
CCS AU Number232See Table 14
Number of NSAs for which data are formed (defined by the "NSA Mask")634Range: 0–61 (62–63 reserved)
Normalized Code TNPA Values on the C/A code of the first NSA from the "NSA Mask"7240See Table 8
…………
Normalized Code TNPA Values on the C/A code of the j-th NSA from the "NSA Mask"72Defined by NSA numberSee Table 8
…………
Normalized Code TNPA Values on the C/A code of the last NSA from the "NSA Mask"72Defined by total number of NSAs in the maskSee Table 8

The “Normalized Code TNPA Values on the C/A Code” parameter format is given in Table 8. Decoding of the “CCS AU Number” field values is provided in Table 14.

Table 8
Field Name Bits Bit Number Range
Full Carrier Phase on the C/A code800 – 2⁸ – 1
Normalized Code Pseudorange on the C/A code3280 – 2³² – 1
Normalized Pseudovelocity on the C/A code24400 – 2²³ – 1
Normalized RMS of Code Pseudorange on the C/A code4640 – 2⁴ – 1
Normalized RMS of Pseudovelocity on the C/A code4680 – 2⁴ – 1

Decoding of the "Normalized RMS of Code Pseudorange on the C/A Code" parameter values is given in Table 6.

Note: Table 6 is used for both UDREI and RMS values, as was standard practice in early 2000s protocols (RTCM 2.x).

Format of Messages 7-10

Messages 7-10 are intended for transmitting phase-measured TNPAs to the CKNP. They have the same format and differ only in the type of CCS processing after which the measured navigation parameters are sent to the CKNP.

The information field of messages 7-10 has a variable length. The list of NSAs for which these messages are formed is determined by the content of the “NSA Mask” message. The structure of the information field of messages 7-10 is given in Table 9.

Table 9
Parameter Bits Bit Number in Message Note
CCS AU Number232See Table 14
Number of NSAs for which data are formed (defined by the "NSA Mask")634Range: 0–61 (62–63 reserved)
Frequency Indicator2400 - L1
1 - L1 and L2
2 - L2
3 - reserved
Normalized Phase TNPA Values (P code on L1, L2) of the first NSA from the "NSA Mask"14442See Table 10
…………
Normalized Phase TNPA Values (P code on L1, L2) of the j-th NSA from the "NSA Mask"144Defined by NSA numberSee Table 10
…………
Normalized Phase TNPA Values (P code on L1, L2) of the last NSA from the "NSA Mask"144Defined by total number of NSAs for which data are formed in the maskSee Table 10

The format of the parameter "Normalized Phase TNPA Values" is shown in Table 10. The decoding of the "CCS AU Number" field values is provided in Table 14.

Table 10
Field Name Bits Bit Number Range
Full Carrier Phase on L1800 – 2⁸ – 1
Normalized Pseudorange (P code on L1)3280 – 2³² – 1
Normalized Pseudovelocity (P code on L1)24400 – 2²³ – 1
Normalized RMS of Pseudorange (P code on L1)4640 – 2⁴ – 1
Normalized RMS of Pseudovelocity (P code on L1)4680 – 2⁴ – 1
Full Carrier Phase on L28720 – 2⁸ – 1
Normalized Pseudorange (P code on L2)32800 – 2³² – 1
Normalized Pseudovelocity (P code on L2)241120 – 2²³ – 1
Normalized RMS of Pseudorange (P code on L2)41360 – 2⁴ – 1
Normalized RMS of Pseudovelocity (P code on L2)41400 – 2⁴ – 1

Decoding of the "Normalized RMS of Phase Pseudorange" parameter values is given in Table 15.

“CCS Position” Message Format

The “CCS Position” message is intended for transmitting normalized values of the CCS antenna phase-center coordinates in the WGS-84 and PZ-90 coordinate systems to the CKNP.

The structure of the information field of message 30 is given in Table 11.

Table 11
Parameter Bits Bit Number in Message Range
Reserved230
Normalized X Coordinate of AU1 in WGS-8432320 – 2³² – 1
Normalized Y Coordinate of AU1 in WGS-8432640 – 2³² – 1
Normalized Z Coordinate of AU1 in WGS-8432960 – 2³² – 1
Normalized X Coordinate of AU1 in PZ-90321280 – 2³² – 1
Normalized Y Coordinate of AU1 in PZ-90321600 – 2³² – 1
Normalized Z Coordinate of AU1 in PZ-90321920 – 2³² – 1
Normalized X, Y, Z Coordinates of AU2 in WGS-8496224See AU1 range
Normalized X, Y, Z Coordinates of AU2 in PZ-9096320See AU1 range
Normalized X, Y, Z Coordinates of AU3 in WGS-8496416See AU1 range
Normalized X, Y, Z Coordinates of AU3 in PZ-9096512See AU1 range

Size of the “CCS Position” message — 608 bits.

“Atmospheric Parameters” Message Format

The “Atmospheric Parameters” message is intended for transmitting normalized atmospheric parameter values in the CCS area to the CKNP.

The structure of the information field of message 31 is given in Table 12.

Table 12
Parameter Bits Bit Number in Message Range
Reserved230
Normalized Air Refractivity Coefficient8320 – 255

Size of the “Atmospheric Parameters” message — 40 bits.

“CCS NRS Status” Message Format. The “CCS NRS Status” message is intended for transmitting the status of CCS NRS channels to the CKNP.

The information field has a variable length (determined by the number of CCS receivers and the number of channels of the corresponding NRS).

The structure of the information field of message 32 is given in Table 13.

Table 13
Parameter Bits Bit Number in Message Range
Status of Channel 1 of NRS 11300 – 1
…………
Status of Channel Nk of NRS Ni1Defined by number of NRS and channels0 – 1

Maximum message size of this type: 32 – 144 bits.

“Special Message” Format

The Special Message is intended for transmitting text messages of up to 90 characters from the CCS to the CKNP.

Message size: 752 bits.

Decoding of the “CCS AU Number” field in messages 2-5 and 7-10.

The “CCS AU Number” values are given in Table 14. The value “0” is reserved for outputting the weighted-average normalized TNPA values obtained by processing information from all CCS AUs.

Table 14
CCS AU Number Data Source
0Weighted-average value
1First CCS AU
2Second CCS AU
3Third CCS AU

Decoding of the “Normalized RMS of Phase Pseudorange” field.

The “Normalized RMS of Phase Pseudorange” field values in messages 7-10 are given in Table 15.

Table 15
Normalized RMS of Phase Pseudorange Estimated RMS of Phase Pseudorange (mm)
00.75
11.0
21.25
31.75
42.25
53.0
63.75
74.5
85.25
96.0
107.5
1115.0
1250.0
13150.0
14Not observed (measurement unavailable)
15Do not use (unreliable data)

Decoding of the “Normalized RMS of Pseudovelocity” field. The “Normalized RMS of Pseudovelocity” field values in messages 2-5 and 7-10 are given in Table 16.

Table 16
Normalized RMS of Pseudovelocity on L1 Estimated RMS of Pseudovelocity on L1 (mm/s)
00.75
11.0
21.25
31.75
42.25
53.0
63.75
74.5
85.25
96.0
107.5
1115.0
1250.0
13150.0
14Not observed (measurement unavailable)
15Do not use (unreliable data)

2. The Algorithm for Encoding Messages for Transmission to the CKNP

Normalization of Pseudorange for transmission in messages 2-5 and 7-10 is performed using the formula:

\[ \tilde{S} = \lfloor S \cdot K \rfloor \]

where:

  • \( \tilde{S} \) – normalized pseudorange value;
  • \( S \) – physical pseudorange value;
  • \( K \) – normalization coefficient, \( 10^3 \).

Note: \( \lfloor \cdot \rfloor \) denotes the floor function (integer part).

Normalization of Phase Pseudorange

Normalization of phase pseudorange values on L1 and L2 for transmission in messages 7-10 is performed using:

\[ \tilde{S}_i = \lfloor S_i \cdot K \rfloor \]

where:

  • \( \tilde{S}_i \) – normalized phase pseudorange value on L1, L2;
  • \( S_i \) – physical phase pseudorange value on L1, L2;
  • \( K \) – normalization coefficient, \( 10^3 \).

Normalization of Pseudovelocity Values on L1

Normalization of pseudovelocity on L1 for transmission in messages 2-5 and 7-10 is performed using:

\[ \tilde{\dot{S}}_i = \lfloor \dot{S}_i \cdot K \rfloor \]

where:

  • \( \tilde{\dot{S}}_i \) – normalized pseudovelocity on L1;
  • \( \dot{S}_i \) – physical pseudovelocity on L1;
  • \( K \) – normalization coefficient, \( 10^3 \).

Normalization of CCS Antenna Phase-Center Coordinates

Normalization of CCS antenna phase-center coordinates for transmission in message 30 is performed using:

\[ \tilde{\theta}_{x,y,z} = \lfloor \theta_{x,y,z} \cdot K \rfloor \]

where:

  • \( \tilde{\theta}_{x,y,z} \) – normalized X, Y, Z coordinates of the CCS antenna phase center;
  • \( \theta_{x,y,z} \) – physical X, Y, Z coordinates of the CCS antenna phase center;
  • \( K \) – normalization coefficient, \( 10^3 \).

Normalization of the Air Refractivity Coefficient

Normalization of the air refractivity coefficient for transmission in message 31 is performed using:

\[ \tilde{n} = \lfloor (n - 1.0002) \cdot K \rfloor \]

where:

  • \( \tilde{n} \) – normalized air refractivity coefficient in the CCS area;
  • \( n \) – physical air refractivity coefficient in the CCS area;
  • \( K \) – normalization coefficient, \( 10^6 \).

Mathematical Methods Used on the Page

To analyze the GenerationOfMessages.cshtml page and identify the mathematical methods applied, we examined the formulas and their context. The document outlines the process of forming messages for transmission from Coordinate Correction Stations (CCS) to the Central Control and Navigation Point (CKNP) in a Global Navigation Satellite System (GNSS). The focus is on normalizing data such as pseudorange, pseudovelocity, coordinates, and air refractivity coefficient. Below is a list of the mathematical methods used on the page, with brief descriptions of their purpose and application.

  1. Floor Function
    • Formula: \(\lfloor x \rfloor\)
    • Application: Used to normalize pseudorange (\(\tilde{S} = \lfloor S \cdot K \rfloor\)), pseudovelocity (\(\tilde{\dot{S}}_i = \lfloor \dot{S}_i \cdot K \rfloor\)), antenna coordinates (\(\tilde{\theta}_{x,y,z} = \lfloor \theta_{x,y,z} \cdot K \rfloor\)), and air refractivity coefficient (\(\tilde{n} = \lfloor (n - 1.0002) \cdot K \rfloor\)).
    • Description: The floor function extracts the integer part of a number, discarding the fractional part. This converts physical values (in meters, m/s, or dimensionless units) into integer normalized values for compact data transmission. The normalization constant \(K\) (typically \(10^3\) for distances and velocities, \(10^6\) for refractivity) scales the data while preserving necessary precision.
    • Context: This method reduces the data volume in messages, optimizing bandwidth usage while maintaining accuracy.
  2. Linear Scaling (Normalization)
    • Formulas:
      • \(\tilde{S} = \lfloor S \cdot K \rfloor\) (pseudorange)
      • \(\tilde{\dot{S}}_i = \lfloor \dot{S}_i \cdot K \rfloor\) (pseudovelocity)
      • \(\tilde{\theta}_{x,y,z} = \lfloor \theta_{x,y,z} \cdot K \rfloor\) (coordinates)
      • \(\tilde{n} = \lfloor (n - 1.0002) \cdot K \rfloor\) (air refractivity coefficient)
    • Application: Normalization transforms physical quantities (pseudorange, pseudovelocity, coordinates, air refractivity) into dimensionless integers suitable for digital message transmission.
    • Description: Linear scaling multiplies the physical value by a coefficient \(K\), then applies the floor function to obtain an integer. For the air refractivity coefficient, an offset (\(n - 1.0002\)) is applied before scaling to account for its typical value range. This ensures compact data representation with minimal loss of precision.
    • Context: Normalization aligns data with message formats, where fields have fixed bit lengths (e.g., 32 bits for pseudorange, 8 bits for refractivity).
  3. Fixed-Precision Encoding (Quantization)
    • Application: Used to represent values like UDREI (User Differential Range Error Index), normalized RMS (Root Mean Square) of pseudorange and pseudovelocity, and other parameters in discrete scales (see Tables 6, 15, 16).
    • Description: Error values (e.g., UDREI or RMS) are encoded into discrete levels using 4-bit or 5-bit fields. For example, Table 6 maps UDREI (0–15) to differential correction errors from 0.75 m to 150 m, with values 14 and 15 indicating "not observed" and "do not use." Similarly, RMS for pseudorange and pseudovelocity is encoded on a scale from 0.75 mm to 150 mm (Tables 15, 16).
    • Context: Quantization simplifies the transmission of error and signal quality data, providing compact representation with predefined precision, critical for real-time systems.
  4. Bit Packing
    • Application: Used to form messages with fixed or variable lengths (e.g., message types 2–5, 7–10, NSA Mask, Integrity Information).
    • Description: Data such as pseudorange (32 bits), pseudovelocity (24 bits), RMS (4 bits), signal-to-noise ratio (5 bits), coordinates (32 bits per axis), and others are packed into sequential bit fields, as described in Tables 1–15. For example, the "NSA Mask" message uses 216 bits to indicate active satellites (GPS and GLONASS), while the "Integrity Information" message has a variable length up to 1016 bits based on the number of satellites.
    • Context: Bit packing minimizes the data volume transmitted between CCS and CKNP, crucial for systems with limited bandwidth.
  5. Data Synchronization
    • Application: Uses the "NSA Mask Issue Identifier" parameter (2 bits, range 0–3) to synchronize messages.
    • Description: This method employs a cyclic counter (0–3, wrapping to 0) that links messages to the current satellite mask ("NSA Mask"). Messages are processed only if their identifier matches the current mask value, preventing the use of outdated data.
    • Context: Synchronization ensures data integrity and timeliness, critical for navigation systems where delays or inconsistencies can cause errors.
  6. Bit Mapping (Logical Indexing)
    • Application: Used in the "NSA Mask" message (Table 3) to indicate active satellites.
    • Description: A 216-bit field in the "NSA Mask" message maps GPS satellites (bits 1–37) and GLONASS satellites (bits 38–61), where a bit value of 1 indicates that data for the corresponding satellite is included in subsequent messages. For example, bit 5 corresponds to GPS 5, and bit 40 corresponds to GLONASS slot 3.
    • Context: Bit mapping efficiently manages data from multiple satellites, reducing redundancy in transmitted messages.

Summary

The mathematical methods used on the page include:

  1. Floor Function for data normalization.
  2. Linear Scaling to convert physical quantities into digital format.
  3. Quantization to represent errors and signal quality in discrete form.
  4. Bit Packing for compact data representation in messages.
  5. Data Synchronization to ensure message timeliness and integrity.
  6. Bit Mapping to manage satellite data.

These methods enable accurate, compact, and reliable transmission of navigation data in GNSS systems like GPS and GLONASS, addressing bandwidth constraints and real-time requirements.

Why the Formulas Are Not Classified

The formulas presented on the GenerationOfMessages.cshtml page do not constitute a state secret, as they describe standard mathematical methods for processing data in Global Navigation Satellite Systems (GNSS), which are widely accepted and well-known in scientific and engineering practice. Below are the main reasons why these formulas are not classified:

  1. Standard Normalization Methods

    Formulas such as \(\tilde{S} = \lfloor S \cdot K \rfloor\), \(\tilde{\dot{S}}_i = \lfloor \dot{S}_i \cdot K \rfloor\), \(\tilde{\theta}_{x,y,z} = \lfloor \theta_{x,y,z} \cdot K \rfloor\), and \(\tilde{n} = \lfloor (n - 1.0002) \cdot K \rfloor\) use the floor function and linear scaling to normalize pseudorange, pseudovelocity, coordinates, and the air refractivity coefficient. These methods are standard in GNSS signal processing and are documented in open standards, such as RTCM (Radio Technical Commission for Maritime Services) version 2.x, mentioned in the document. They are used for compact data transmission and do not contain specific details unique to any state system.

  2. Public Nature of GNSS Protocols

    The document describes message formats for transmitting data from Coordinate Correction Stations (CCS) to the Central Control and Navigation Point (CKNP), including parameters like UDREI, RMS, signal-to-noise ratio, and satellite mask. These formats are based on international standards, such as RTCM, which are publicly available and used in civilian and commercial GNSS systems (e.g., GPS and GLONASS). Such protocols are published to ensure compatibility of hardware and software worldwide.

  3. Lack of Specific Data

    The formulas and methods do not contain confidential parameters, such as precise correction algorithms, encryption keys, military codes (e.g., encrypted GPS P-code), or details about specific systems. They describe general processing principles applicable to any differential correction system, including civilian applications like geodesy or maritime navigation.

  4. Outdated Context

    References to RTCM 2.x standards and WGS-84 and PZ-90 coordinate systems point to technologies relevant in the early 2000s. Modern GNSS systems (e.g., RTCM 3.x, Galileo, Beidou) use more advanced methods, and the described approaches are considered basic and long declassified. Even for GLONASS, which has military applications, message formats for civilian use are publicly available.

  5. Universality and Scientific Basis

    The formulas use elementary mathematical operations (floor function, multiplication by a constant), which are fundamental and not tied to any specific state or military infrastructure. They represent a general approach to data processing that can be found in textbooks on satellite navigation or technical documentation.

Conclusion

The formulas and methods described on the page are part of a standard toolkit for processing GNSS data, widely known and used in civilian and commercial systems globally. They do not disclose specific details, such as the configuration of particular stations, cryptographic keys, or military algorithms, and are based on open standards. Therefore, they cannot be classified as a state secret, as their content is public domain in the field of satellite navigation.

Implementation Result: The described algorithms implement message formation and encoding protocols using fundamental mathematical methods documented in open RTCM standards since early 2000s. These formulas represent universal principles of digital signal processing, transforming physical measurements into standardized data formats that enable global navigation coordination. The methods apply elementary mathematical operations (floor function normalization, linear scaling, bit packing) that constitute general-purpose data handling techniques, reflecting humanity's pursuit of precision and reliability in navigation through the universal language of mathematics.

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