RU2558699C1 - Complex method of aircraft navigation - Google Patents

Abstract

FIELD: aircraft engineering.

SUBSTANCE: generated is extra data base including antenna patterns of satellite receiver antenna and onboard antenna of long-range signal transceiver. navigation satellite signals received and navigation parameters defined by satellite navigation procedure (SNP), working constellation composition and angular coordinates of navigation satellites are isolated. Satellite receiver SNR is isolated to generate SNP error correlation matrix. Navigation satellite (NS) direction vectors are shaped to define NS weight factors in working constellation by aircraft orientation, refined aircraft position, NS angular coordinates and satellite receiver antenna pattern. Composition of satellite constellation is corrected by NS weight factors to correct navigation parameters by corrected composition of NS working constellation. Then, oriented correlation SNP error matrix is shaped with due allowance for aircraft orientation on the basis of corrected composition of said constellation and NS weight factors. Simultaneously, long-range navigation process (LRN) is used to shape correlation matrix of LRN error matrix. Direction vectors and shaped to define ground radio beacon (GRB) weight factors by aircraft orientation, refined aircraft position, GRB coordinates and said transceiver onboard antenna pattern. GRB working composition is corrected by their weight factors. LGN error correlation matrix is generated with allowance for aircraft orientation. Corrected working composition of HRM and their weight factors allowed for are used to generate oriented parameters for LGN and SNP to be used in onboard computer for generation of complex navigation parameters. Note here that output results are presented as a refined position of aircraft corrected with allowance for aircraft orientation. Invention discloses the process version exploiting for definition of data on aircraft orientation of orientation operator computed in inertial navigation process. Besides, it discloses the process version that defines the LGS transceiver one onboard antenna pattern selection. Besides, in compliance with another version, aircraft multi-beam pattern is taken to depend on aircraft orientation to correct its position depending on the level of multipathing.

EFFECT: higher reliability and precision, lower risks of disasters.

4 cl, 5 dwg, 3 app

Description

The invention relates to the field of navigation of aircraft (LA) using an integrated navigation method that functionally combines the inertial navigation method, satellite navigation method and rangefinding navigation method. The invention can be used in the navigation of highly dynamic aircraft in difficult navigation conditions during intensive maneuvers, characterized by an increased level of variability in the composition of the working constellation (SRS) of navigation satellites (NS) and the working composition of ground-based radio beacons (NRM).

Each of the mentioned navigation methods has its advantages and disadvantages.

In the inertial navigation method (INS), the location (hereinafter referred to as the position) of an aircraft is determined by integrating the navigation parameters from the readings of inertial sensors, for example, values of angular velocity and acceleration [1, 2]. The main advantage of this method is the high noise immunity, and the disadvantage is the accumulation of errors over time. Therefore, the ISN requires periodic correction of the position of the aircraft using radio-technical navigation methods - satellite and rangefinder. In the satellite navigation method (SSN), the calculation of the navigation parameters of the aircraft is carried out using the signals of N navigation satellites forming the working constellation [3, 4]. The advantage of CCH is global and high measurement accuracy. The disadvantage is low noise immunity and high, in terms of flight safety, the probability of failure. In addition, maneuverable aircraft are characterized by the variability of CPC satellites due to the large roll angles and pitch of the aircraft (see Fig. 1). In this case, the accuracy of satellite navigation definitions of the position of the aircraft significantly decreases. Satellite positioning also becomes impossible if an insufficient number of NS falls into the radio visibility zone of the satellite antenna of the aircraft. When restoring a horizontal flight of an aircraft (with a decrease in the roll and pitch angles) in satellite equipment, a second search for working satellites occurs, tracking them, extracting information and measuring navigation parameters, which determine pseudorange (PD) and pseudo-speed (PS) with respect to each radio-visible NS.

In the rangefinder navigation method (SDS), the calculation of the navigation parameters of the aircraft is carried out using the signals L of terrestrial beacons (NRM), forming a working group. In this case, the determination of the aircraft ranges to L NRM is performed by emitting interrogated rangefinder signals from the aircraft, receiving these signals on the NRM, generating and emitting response rangefinder signals, measuring onboard the aircraft the delay time of the response rangefinder signals relative to the interrogating rangefinder signals and determining using this measurement aircraft navigation parameters [5]. This navigation method is inferior to the CCH in accuracy, but has the advantage of reliability and noise immunity. However, SDS, like SSN, depends on the maneuvering of the aircraft and, at large angles of roll and pitch of the aircraft, communication with some NRMs is possible due to the lack of radio visibility (see Figure 1). When organizing the rangefinder mode, one set of on-board equipment is used in the sequential frequency-code scanning mode, and the selection of the receiver is performed without taking into account the orientation of the on-board antenna [6]. Maneuvering an aircraft leads to a loss of communication with some NRMs, a decrease in accuracy, and interruptions in determining the position of the SDS.

One of the ways to improve the accuracy of navigation definitions when maneuvering an aircraft is the integrated use of ISN, SSN and SDS. Such a combination is considered in a number of analogues of the invention.

A useful model of an on-board radio-technical complex for navigation and landing of a sea-based aircraft [7] is designed to provide navigation and control of aircraft, using the following navigation systems: inertial navigation system (ANN), satellite radio navigation system (SRNS), short-range radio navigation system (RSBN) , respectively, implementing the above navigation methods (ISN, CCH, SDS). The peculiarity of this complex is that the RSBN beacon can be installed on a movable object, and a computing device is additionally included in the navigation system of the aircraft, generating output signals according to an algorithm that is tunable depending on the operating conditions. However, the analogue does not consider any methods for optimally integrating navigation data and generating output signals; navigation data are not corrected when the aircraft orientation changes.

The patent [8] proposes a navigation system for aircraft containing sources of navigation data - SRNS, ANN, DME rangefinder system or VOR / DME azimuth-rangefinder system. This system is designed for safe flight in difficult weather conditions. The composition of the equipment is similar [7], since the RSBN equipment is equivalent to VOR / DME. However, this patent also does not discuss methods for optimally integrating navigation data and their correction when changing the orientation of the aircraft.

The application [9] discusses the use of two navigation methods - ISN and CCH, taking into account the orientation of the aircraft. In this case, a comprehensive optimal processing of navigation data is performed. However, the integrity of the system based on these two navigation methods is insufficient due to the lack of the above-mentioned positive characteristics provided by the rangefinding navigation method. In addition, in [9] does not provide for the adjustment of the data composition taking into account the orientation of the aircraft, which does not allow to achieve the required effectiveness of the proposed method, even in terms of the use of ISN and CCH.

The prototype method [10] consists in the fact that a comprehensive method for navigation of aircraft (LA) is proposed, which provides for the use of inertial, satellite and rangefinding navigation methods to determine the position of the aircraft, while the navigation parameters and position of the aircraft are determined in the inertial navigation method (ISN) according to the readings of inertial sensors, in the satellite navigation method (SSN) on N navigation satellites (NS), NS signals are received on the aircraft, navigation parameters are determined by the SSN with data on the position of the aircraft in the form of pseudo-ranges and pseudo-velocities, and in the rangefinding navigation method (SDS), the formation and emission of interrogation rangefinder signals are performed on the aircraft, the reception of the interrogation signals on terrestrial beacons (NRM) with known coordinates, the formation and emission of the response rangefinder signals, the reception of the response signals to Aircraft and determine the navigation parameters in the form of ranges to L NRM, and then in the on-board computer form complex navigation parameters of the aircraft from the navigation parameters defined by about SSN and SDS, and form a comprehensive matrix of errors SSN and SDS, with which the errors of the position of the aircraft determined by the ISS are estimated, and by correcting the position of the aircraft determined by the ISS, the specified position of the aircraft is determined, in addition, the operating staff is selected in the on-board computer NRM according to the updated position of the aircraft and the coordinates of the NRM from the database, paired with the on-board computer, while the working composition of the NRM carry out the corresponding generation and emission of interrogated rangefinder signals, and the output results are set in the form of an updated position of the aircraft.

The flowchart for the prototype method [10] is given in Appendix 1.

The disadvantage of the prototype method [10], as well as the above counterparts using three navigation methods [7, 8], is the lack of consideration of the influence of the angular orientation of the aircraft during its maneuvering to change navigation data (composition of the working constellation of the SNA and the working composition of the NRM) and, accordingly, to the operation of the algorithm for complex data processing of inertial and radio engineering navigation methods, leading to a decrease in the accuracy of coordinate estimation in difficult navigation conditions. In the prototype [10] and analogues [7, 8], the choice of the working constellation is based on the almanac of satellites and the position of the aircraft, and the selection of the working composition of the NRM is based on information about the coordinates of the NRM from the database and, also, the position of the aircraft. A change in the angular orientation of the aircraft (for example, with a roll) leads to a violation of the reception of signals of some NS and NRM.

The objective of the proposed method is to increase the accuracy of estimating the coordinates of aircraft in difficult navigation conditions by taking into account the orientation of the aircraft in the formation of navigation data ISN, SSN and SDS and their complex processing.

The problem is solved as follows. A complex method of navigation of aircraft (LA) is proposed, which provides for the use of inertial, satellite and rangefinding navigation methods to determine the position of the aircraft, while the inertial navigation method (INS) determines the navigation parameters and the position of the aircraft according to the readings of inertial sensors, in the satellite navigation method (SSN) ) using N navigation satellites (NS), receive NS signals on an aircraft, determine navigation parameters with data on the position of the aircraft in the form of pseudorange and pseudo-speeds and in the rangefinder navigation method (SDS), the formation and emission of interrogation rangefinder signals on the aircraft, the receipt of the aforementioned interrogation signals on ground radio beacons (NRM) with known coordinates, the formation and emission of the response rangefinder signals, the reception of the response signals on the aircraft and determine the navigation parameters in the form of ranges to L NRM, and then in the on-board computer form the integrated navigation parameters of the aircraft, from the navigation parameters determined by SSN and SDS, and form a complex matrix the error index of the SSN and SDS, with the help of which the errors of the position of the aircraft determined by the ISS are estimated, and by correcting the position of the aircraft determined by the ISS, the specified position of the aircraft is determined, in addition, the on-board computer selects the working composition of the NRM according to the updated position of the LA and the coordinates of the NRM from database associated with the on-board computer, while the working composition of the NRM conduct the corresponding generation and emission of interrogation rangefinder signals, and the output results are presented in the form of an updated position of the aircraft at the same time, an additional database is formed, including radiation patterns of the antenna of the satellite receiver and the onboard antennas of the transceiver of rangefinder signals, after receiving the NS signals in parallel with the determination of navigation parameters on the SSN, the constellation of the working constellation and the angular coordinates of the NS are extracted, the signal-to-noise ratio of the satellite receiver is extracted and formed correlation matrix of errors CCH, then form the direction vectors of the NS and determine the weight coefficients of the NS from the composition of the working constellation in orientation the aircraft, the correct position of the aircraft, the angular coordinates of the NS and the antenna radiation pattern of the satellite receiver, adjust the composition of the working constellation of satellites according to the weight coefficients of the NS, adjust the navigation parameters according to the adjusted composition of the working constellation of the NS, then form an oriented correlation matrix of errors of the SSN, taking into account the orientation of the aircraft, to On the basis of the adjusted composition of the working constellation and taking into account NS weight coefficients, a correlation error matrix of the SDS, f form the direction vectors and determine the weight coefficients of the NRM from the working composition of the NRM according to the orientation of the aircraft, the correct position of the aircraft, the coordinates of the NRM from the working composition of the NRM and the radiation pattern of the aforementioned onboard antenna of the transceiver, adjust the working composition of the NRM by the weight coefficients of the NRM, form an oriented correlation matrix of errors of the SDL, taking into account the orientation of the aircraft, based on the adjusted working composition of the NRM and taking into account the weight coefficients of the NRM, form accordingly oriented navigation nnye parameters for CLO and SDS and their use in avionic computer to form a complex navigational parameters, the results are output as a position proximate the aircraft, corrected for aircraft orientation.

A variant of the method is proposed that discloses operations when generating data on aircraft orientation, which consists in calculating the orientation operator in the ISN according to the readings of inertial sensors in the form of angular velocities in the ISN, and forming directional vectors in the SSN for the NS angular coordinates in the navigation system coordinates, then, using the orientation operator, the NS direction vectors are formed in the associated coordinate system and, using the antenna pattern of the satellite receiver, the weight NS coefficients, in parallel in the SDS, the angular coordinates of the NRM are calculated from the database and the updated position of the aircraft, form the NRM direction vectors in the navigation coordinate system, then, using the orientation operator, form the NRM direction vectors in the associated coordinate system and, using the airborne radiation pattern antennas of the transceiver of ranging signals, determine the weighting coefficients of the NRM, while in the IOS using the orientation operator calculate the acceleration vector of the aircraft in the navigation system rdinat, by which the position of the aircraft is determined by the ISN.

A method variant is also proposed in which, after the formation of the directional direction vectors, the gain of each of the airborne antennas of the transceiver of the ranging signals is additionally determined, and the antenna pattern with the highest gain is selected, and for similar amplitudes of the mentioned airborne antennas, the antenna pattern is selected in accordance with the movement of the vector directions of NRM.

A variant of the method is also proposed in which an LA multipath diagram is introduced into the additional database, additional NS weight coefficients are determined from the composition of the working constellation according to the aircraft orientation and the multipath diagram, after determining the NS weight coefficients, the weight coefficients are adjusted to determine the resulting NS weight coefficient, for example as the sum of the weight coefficient and the additional weight coefficient, and is introduced when forming an oriented correlation matrix shibok CCH resultant weighting factor.

The essence of the proposed method is illustrated using FIG. 1, 2, 3, 4 and 5.

In FIG. 1 is an illustration of the relative position of the radiation patterns of the onboard antennas used in the SSN and SDS.

In FIG. 2 presents a block diagram of the main sequence of operations of the proposed method for integrated navigation of the aircraft.

In FIG. 3, a sequence of operations is disclosed when generating data on aircraft orientation to determine direction vectors and weighting factors of NS and NRM.

In FIG. 4 shows a variant of the method for determining the weighting coefficients of the NRM in the case of several onboard antennas of the transceiver of ranging signals.

In FIG. 5 shows a variant of the method that takes into account the multipath effect in determining the weight coefficients of NS.

In addition, Appendix 1 discloses a block diagram of the main sequence of operations performed in the prototype, and Appendix 2 presents typical radiation patterns of onboard antennas of a rangefinder signal transceiver.

FIG. 1 illustrates the change in the position of the central axes of the antenna patterns in the CLS and LTOs and, accordingly, the change in information about the navigation signals when the aircraft orientation changes (in this case, the pitch angle).

The essence of the proposed method is illustrated using FIG. 2, which presents a flowchart of the implementation of an integrated navigation method.

The following is a description of the symbols in FIG. 2:

1. Determination of navigational parameters and the position of the aircraft on the ISN.

2. Reception of aircraft signals on the aircraft.

3. Determination of navigation parameters by SSN with data on the position of the aircraft in the form of pseudorange and pseudo-speeds.

4. The formation and emission on the aircraft of interrogative rangefinder signals (ZDS).

5. Reception of ZDS on NRM, formation and radiation of response range-finding signals (ODS).

6. Reception of SLM in the aircraft.

7. Determination of navigation parameters by SDS (range).

8. Formation of complex navigation parameters and a complex correlation matrix (CM) for SSN and SDS.

9. Evaluation of errors in the position of the aircraft on the ISN.

10. Determination of the specified position of the aircraft.

11. The selection of the working composition of the NRM.

12. The database.

13. The allocation of the composition of the working constellation and angular coordinates of the NS.

14. The allocation of signal-to-noise (s / w) and the formation of CM errors SSN.

15. The formation of vectors of the direction of the national Assembly and the determination of the weighting coefficients of the national Assembly.

16. Correction of the composition of the working constellation of the National Assembly.

17. Correction of navigation parameters according to the SSN according to the adjusted composition of the working constellation.

18. The formation of oriented CM errors SSN.

19. The formation of KM errors SDS.

20. Formation of direction vectors and determination of weighting coefficients of the NRM.

21. Adjustment of the working composition of the NRM.

22. The formation of the oriented CM errors SDS.

23. The formation of oriented navigation parameters on the SSN.

24. The formation of oriented navigation parameters for the SDS.

The method includes operations typical for the prototype method (see Appendix 1 and Fig. 2): determining the navigation parameters and the position of the aircraft on the ISN 1, receiving the signals of the NS 2 on the aircraft, determining the navigation parameters on the SSN with data on the position of the aircraft in the form of pseudo-ranges and pseudo-speeds 3, generation and emission of interrogative rangefinder signals 4, reception of the interrogated signals to the receiver, generation and emission of interfaced rangefinder signals 5, reception of the response signals to the LA 6, determination of navigation parameters by SDS in the range to L NRM 7, the formation in the on-board computer of the integrated navigation parameters of the aircraft and the complex correlation matrix of position errors of the aircraft, as determined by SSN and SDS 8, the estimation of position errors by ISN 9, the determination of the corrected position of the aircraft 10, the choice of the working composition of the NRM 11, the base data 12.

The following signals are applied to inputs “a”, “b”, “c”:

a) aircraft orientation data,

b) the antenna pattern of the satellite receiver,

c) the radiation pattern of the on-board antenna of the ZDS transceiver.

Offered operations that implement the claimed method (Fig. 2). After calculating the navigation parameters on the SSN, the composition of the working constellation and the angular coordinates of NS 13 are extracted, the signal-to-noise ratios of the satellite receiver are extracted and the CM errors of the SSN 14 are generated, the direction vectors and the determination of the weight coefficients of the NS 15 are formed, the composition of the working constellation of the satellites is determined by the weight coefficients of the NS 16, adjustment of navigation parameters for SSN 17, the formation of oriented CM errors SSN 18, the formation of CM errors SDS 19, the formation of direction vectors and determine the weighting factors of the NRM 20, the adjustment of the working composition of the NRM according to the weighting coefficients of the NRM 21, the formation of oriented KM errors SDS 22, the formation, respectively, oriented navigation parameters for SSN 23 and SDN 24 and their use in the on-board computer for the formation of complex navigation parameters of the aircraft for SSN and SDS 8.

The operation of the proposed method is as follows.

Actions 1-12 are performed completely similar to the prototype. In this case, the determination of the navigation parameters and the position of the aircraft according to ISN 1 consists in integrating the readings of the inertial sensors ID and involves the calculation of the spatial coordinates of the aircraft that make up the velocity vector and angular coordinates [2]. Reception of NS 2 signals to the aircraft ends with the determination of navigation parameters by SSN 3, which implies the determination of position data in the form of pseudo-ranges and pseudo-velocities, as well as the composition of the working constellation and signal-to-noise ratios [3, 4]. To determine the navigation parameters for SDS 7, the formation and emission of interrogated rangefinder signals (ZSD) 4 is performed, reception of the WHSDs on the receiver, the formation and emission of response rangefinder signals (ODS) 5, the reception of the ODS on the aircraft 6. At the same time, the determination of the navigation parameters for the SDS 7 involves the determination of the time delays of the ODS relative to the ZDS and the calculation of the ranges to the NRM. Processing of navigation parameters obtained by radio-technical navigation methods (SSN and SDS) is carried out by forming complex navigation parameters of the aircraft from the navigation parameters determined by SSN and SDS, and the formation of a complex correlation matrix of errors SSN and SDS 8, with which the position errors of the aircraft are estimated determined by the ISN, and by correcting the position determined by the ISN of the aircraft, the specified position of the aircraft by the ISN 9 is determined. Complex processing uses a compensation method that implements the principle invariance to aircraft dynamics [11]. For this purpose, the position errors of the aircraft according to the ISS are estimated and these errors are compensated, as a result of which the specified position of the aircraft is determined 10. The calculator also selects the working composition of the MPM 11 using database 2, which determines the formation and emission of the airborne laser.

In parallel with the determination of navigation parameters for SSN 3, the following operations are performed: separation of the composition of the working constellation and angular coordinates of NS 13, separation of signal-to-noise ratios and generation of CM errors of SSN 14, formation of satellite direction vectors and determination of satellite weights 15 and correction of the composition of the working constellation 16 .

The separation of the composition of the working constellation and the angular coordinates of the NS 13 is performed when receiving signals 2 in the satellite receiver [3, 4]. When forming the direction vectors of NS 15, orientation data (signal “a”) are used, which can be generated in various ways. An example is considered below when the NS angular coordinates (elevation and azimuth angles) are used in the navigation coordinate system (NSC). Then the vectors of the NS directions are formed in the associated coordinate system (SSC) taking into account the aircraft orientation (these operations will be described in more detail below).

и, при корректировке состава рабочего созвездия 16 оставляются спутники, для которых коэффициент усиления антенны превышает указанный порог. Для оставшихся в корректируемом составе рабочего созвездия спутников коэффициент усиления антенны определяет информационный вес данного спутника при решении навигационной задачи. С этой целью после определения навигационных параметров по ССН 3 выполняется выделение отношений сигнал/шум спутникового приемника и формирование КМ ошибок ССН 14.When determining the weights of the satellites 15, the antenna pattern of the satellite receiver mounted on the aircraft (signal "b") is used. The antenna pattern is usually given in azimuth-elevation coordinates (in CCK). After determining the direction vectors of the NS, the gain of the antenna of the satellite receiver in the direction to the satellite K _{ant.s is} compared with the threshold $$K_{\mathrm{but}nt.\mathrm{from}}^{m\mathrm{and}n}$$

and, when adjusting the composition of the working constellation 16, satellites are left for which the antenna gain exceeds the specified threshold. For those remaining in the corrected composition of the working constellation of satellites, the antenna gain determines the information weight of this satellite when solving a navigation problem. For this purpose, after determining the navigation parameters for SSN 3, the signal-to-noise ratios of the satellite receiver are extracted and CM errors of SSN 14 are generated.

In the formation of CM errors, the SNS takes into account the noise errors of the measurements of pseudorange (PD) and pseudo-velocity (PS) in the satellite receiver. Evaluation of the accuracy of the measurements of the PD in relation to the noise error in the satellite receiver is performed using the formula for calculating the variance of the measurement error [11]:

where Δf is the bandwidth of the tracking system for the delay of the ranging code; τ is the duration of the elementary symbol of the code; In-bandwidth of the satellite receiver; Q is the signal-to-noise ratio, i.e. ratio of satellite signal power and noise in the 1 Hz band (Q value is measured in a satellite receiver).

For example, for GLONASS, τ = 2 μs. At Q = 40 dB Hz, Δf = 1 Hz and B = 15 MHz, we have the mean square value of the measurement error of a PD of 2.5 nsec or 0.75 m.

для каждого спутникового канала располагаются на главной диагонали корреляционной матрицы ошибок по ССН 14.Values $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PD}^{}$$

for each satellite channel are located on the main diagonal of the correlation matrix of errors according to SSN 14.

Next, the formation of the oriented KM errors of the SSN 18 is performed. In order to determine the information weight (NM) of the NS remaining after adjustment 16, a functional transformation of the value of K _{ant.s is used} , for example, of the form:

- пороговое значение для величины K_ант.с; a ₁ - масштабный коэффициент, обеспечивающий плавное выключение спутника из решения навигационной задачи при близких к порогу значениях K_ант.с.where D _nq - information on the weight of the NA PD $$K_{\mathrm{but}nt.\mathrm{from}}^{m\mathrm{and}n}$$

- threshold value for the value of K _ant.s ; a ₁ - scale factor, providing a smooth shutdown of the satellite from the solution of the navigation problem at close to the threshold values of K _ant.s.

и D_ПД формируются значения первых (N-M) диагональных элементов ориентированной КМ ошибок ССН 18, соответствующих ошибкам ПД, в виде $${\sigma }_{ПД}^2+D_{ПД}^{-1}$$

(D_ПД>0)(дисперсия ошибки измерения псевдодальности обратно пропорциональна информационному весу измерений).After calculating $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PD}^{}$$

and D _PD , the values of the first (NM) diagonal elements of the oriented KM errors of SSN 18 corresponding to PD errors are formed, in the form $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PD}^{}+D_{PD}^{-\mathrm{one}}$$

(D _PD > 0) (the variance of the pseudorange measurement error is inversely proportional to the information weight of the measurements).

[11]. Тогда полоса пропускания по выходу частоты следящей системы равна Δf^ω=0.5(Δf^φ)³ и оценка точности измерений ПС по отношению к шумовой ошибке в спутниковом приемнике (оценка дисперсии измерения доплеровской частоты) выполняется с помощью формулы:When forming the values of the diagonal elements of the CM, the errors of the SSN corresponding to the PS errors do the same. If the parameters of the carrier tracking system (PLL) in the satellite receiver are optimized under the influence of noise, then the bandwidth of the second-order loop is determined from the expression $$\Delta f^{\varphi }=K_a^{0.5}$$

[eleven]. Then the passband at the output of the tracking system frequency is Δf ^ω = 0.5 (Δf ^φ ) ³ and the accuracy of measurements of the PS with respect to the noise error in the satellite receiver (estimation of the variance of the Doppler frequency measurement) is estimated using the formula:

where Δf ^ω is the passband of the PLL system.

In order to determine the information weight (NM) of the NS remaining after adjustment 16, a functional transformation of the value of K _{ant.s is also used} , similar to that given earlier (2):

Where: D _ps - informational weight of the PS for PS,

and ₂ is a scale factor (in general, different from a ₁ ), providing a smooth shutdown of the satellite from the solution of the navigation problem.

, и D_ПС формируются значения последующих после (N-M) диагональных элементов с (N-М+1)до 2(N-M)) ориентированной КМ ошибок ССН 18, соответствующих ошибкам ПС, в виде $${\sigma }_{ПC}^2+D_{ПС}^{-1}$$

(D_ПС>0) (дисперсия ошибки измерения псевдоскорости обратно пропорциональна информационному весу измерений).After calculating $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; C"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PC}^{}$$

, and D _PS , the values of the subsequent after (NM) diagonal elements are formed from (N-М + 1) to 2 (NM)) oriented CM errors CCH 18, corresponding to PS errors, in the form $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; C"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PC}^{}+D_{P\mathrm{FROM}}^{-\mathrm{one}}$$

(D _PS > 0) (the variance of the measurement error of the pseudo-velocity is inversely proportional to the information weight of the measurements).

Correction of the navigation parameters of the aircraft according to SSN 17 is carried out after determining the navigation parameters according to SSN 3 and adjusting the composition of the working constellation 16, and these navigation parameters include pseudorange and pseudo-speeds. This excludes the navigation parameters of satellites for which the antenna gain does not exceed the set threshold.

The formation of oriented navigation parameters by SSN 23 combines two information flows: navigation parameters of an SS by SSN in the form of pseudo-ranges and pseudo-velocities (vector size 2 (WM)), as well as the accuracy characteristics of these parameters in the form of oriented CM errors on SSN (matrix size 2 (NM ) × 2 (NM)). Additionally, the rejection of the NS by the value of the elements of the oriented CM is performed. The need for this operation is due to the fact that at small elevation angles it is difficult to have accurate data on the antenna gain due to the influence of reflections from the surface of the aircraft body and changes in the geometry of the aircraft during flight. During operation, the aircraft body is repeatedly repainted, and the surface condition depends on weather conditions. During flight, the shape of the hull, and in particular the deflection of the wing, depends on the load, fuel consumption and maneuvering. Therefore, additional rejection of NS according to the size of the elements of oriented CM is required.

After determining the navigation parameters for SDS 7, the following operations are performed: the formation of direction vectors and determination of the weight coefficients of the NRM 20 and the adjustment of the working composition of the NRM 21. The selection of the working composition of the NRM 11 in the prototype method [10] is performed in the on-board computer based on the coordinates of the NRM contained in the database, and the updated position (coordinates) of the aircraft. This takes into account the distance of the aircraft relative to the receiver and the geometric factor [6]. The orientation of the aircraft is not taken into account. The formation of the ZDS is performed on the frequency-code channels of only those NRMs that are included in the current operating structure. In the proposed method, the adjustment of the working composition of the NRM 21.

To do this, the formation of direction vectors and determination of weight coefficients 20. When forming the direction vectors NRM 20, using the data on the coordinates of the NRM and the correct position of the aircraft, the angular coordinates (elevation and azimuth angles) of the working NRMs in the NSC are calculated. Then, the direction vectors of the NRM in the SSK are formed taking into account the orientation of the aircraft (these operations will be described in more detail below).

и при корректировке рабочего состава НРМ 21 оставляются те НРМ, для которых коэффициент усиления антенны превышает порог. Если коэффициент усиления антенны для какого-либо НРМ не превышает порог, то передача ЗДС для этого НРМ не выполняется.When determining the weighting coefficients 20, the directivity pattern of the onboard antenna of the transceiver of rangefinder signals installed on the aircraft is used (at small ranges, the directivity pattern of the antenna of the responder HPM can be taken into account). The antenna pattern is usually given in azimuth-elevation coordinates (in CCK). In this case, the gain of the antenna of the receiver of the ODS K _ant.d in the direction on the receiver is compared with the threshold $$K_{\mathrm{but}nt.d}^{m\mathrm{and}n}$$

and when adjusting the working composition of the NRM 21, those NRMs for which the antenna gain exceeds the threshold are left. If the antenna gain for any of the NRM does not exceed the threshold, then the transmission of the ZDS for this NRM is not performed.

For those remaining in the adjusted working composition of the NRM, the antenna gain determines the information weight of the given NRM when solving the navigation problem. For this purpose, after determining the navigation parameters for the SDS 7, CM errors are generated for the SDS 19. When generating the correlation matrix of errors for the SDS, the noise errors of the measurement of the delay time in the ODS receiver, depending on the distance of the aircraft relative to the receiver, are taken into account:

where b ₁ - the variance of the instrumental error of range measurement; r is the range of the NRM relative to the aircraft; b ₂ - scale factor.

для каждого НРМ располагаются на главной диагонали (позиции диагональных элементов с 1 до L) корреляционной матрицы ошибок по ДСН 19.Values $${\sigma }_D^{}$$$${}_2^{}$$

for each NRM are located on the main diagonal (positions of diagonal elements from 1 to L) of the correlation matrix of errors according to the SDS 19.

Next, the formation of the oriented CM errors for SDS 22 is performed. In order to determine the information weight of the signal of this NRM when solving the navigation problem, the functional conversion of the gain of the antenna antenna of the receiver of the ODS K _ant.d , for example, is used:

- пороговое значение для величины K_ант.д; а ₃ - масштабный коэффициент, обеспечивающий плавное выключение НРМ из решения навигационной задачи при близких к порогу значениях K_ант.д.Where $$K_{\mathrm{but}nt.d}^{m\mathrm{and}n}$$

- the threshold value for the value of K _ant.d ; and ₃ is a scale factor that provides smooth shutdown of the receiver from the solution of the navigation problem at close to the threshold values of K _ant.d.

и D_Д формируются значения диагональных элементов ориентированной КМ ошибок по ДСН 22, соответствующих ошибкам измерения дальности Д, в виде $${\sigma }_{Д}^2+D_{Д}^{-1}$$

(D_Д>0) (дисперсия ошибки измерения дальности обратно пропорциональна информационному весу измерений).After calculating $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; D"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_D^{}$$

and D _D the values of the diagonal elements of the oriented CM errors are formed according to the SDS 22 corresponding to the measurement errors of the range D, in the form $${\sigma }_D^{}$$$${}_2^{}+D_D^{-\mathrm{one}}$$

(D _D > 0) (the variance of the range measurement error is inversely proportional to the information weight of the measurements).

The formation of oriented navigation parameters by DSP 24 combines two information streams: navigation parameters of an aircraft according to SDS in the form of ranges (a vector of size L), as well as the accuracy characteristics of these parameters in the form of oriented CM errors on an SDS (matrix of size L × L). In this case, the same considerations are used as in the implementation of step 23 and an additional rejection of the NRM is performed according to the size of the elements of the oriented CM.

To evaluate errors in the position of the aircraft according to ISN 9, the Kalman filtering algorithm is used. At the same time, the oriented navigation parameters for SSN and SDS, together with the results of calculating the position of the aircraft for SSI, are used in the error estimation algorithm of the inertial navigation method with the advanced Kalman filter. The operations of forming the integrated navigation parameters of the aircraft by CCH and SDS 8 combine the following information flows: oriented correlation matrices of errors by CCH and SDS are combined in the form of one diagonal matrix R of size (2 (N-M) + L) × (2 (NM) + L ), the navigation parameters of the aircraft along the SSN and SDS are combined in the form of a single vector Z (i) of size 2 (N-M) + L.

Errors in calculating the position (coordinates) of the aircraft ISN X are described by the vector difference equation [1,2]:

where X is the error state vector; U is the error vector of inertial sensors; F is the matrix of the system of differential equations; W is the transformation matrix.

Said state vector contains errors of measurement of position, velocity and angular orientation:

where Δх, Δy, Δz are measurement errors of rectangular navigation coordinates, with the x axis pointing to the North, the y axis pointing to the East, the z axis pointing down; Δv _x , Δv _y , Δv _z - errors of speed measurement; Δα, Δβ, Δγ - errors of the angular orientation of the ANN.

The matrix of the system of differential equations F is selected depending on the class of the inertial navigation system. In tactical class systems with limited accuracy of angular velocity sensors, the angular velocity of the Earth’s rotation is not taken into account [1]. Then the matrix can be represented as:

where μ = (R + h) ^-1 ; η = -tgB (R + h) ^-1 ; R is the Earth's radius for the selected reference ellipsoid; h is the height of the aircraft; B is the latitude of the aircraft; and _N , and _E , and _D are the components of the aircraft acceleration vector in the NSC.

The vector U contains errors of the acceleration and angular velocity sensors in the associated coordinate system:

.

.

.The transformation matrix is

.

The vector X (i) is supplemented by errors of inertial sensors, as well as an error in measuring the time t and the departure speed of the clock v _{t of the} satellite receiver. As a result, a new n-dimensional (n = 17) state vector Y (i) is formed:

The difference equation of state in discrete time i has the form:

Y (i + 1) = ФY (i) + V (i),

- матрица перехода, причем Ф₁=I+ΔtF; Ф₂ - матрица модели ошибок инерциальных датчиков [1] и $${Ф}_3=\left[\begin{array}{cc}1& \Delta t\\ 0& 1\end{array}\right]$$

- матрица модели ухода часов спутникового приемника; Δt - интервал временной дискретизации.where V (i) is the n-dimensional vector of discrete white noise with the known correlation matrix Q _v ; $$F=\left(\begin{array}{ccc}{F}_{\mathrm{one}}& \mathrm{<figure-callout\; id="0"\; label="\Delta \; t\; W"\; filenames="00000077.png,00000078.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}tW& 0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="00000072.png"\; state="\{\{state\}\}">F</figure-callout>}}_2& 0\\ 0& 0& F_3\end{array}\right)$$

is the transition matrix, with Ф ₁ = I + ΔtF; F ₂ - matrix model errors inertial sensors [1] and $${\mathrm{<figure-callout\; id="3"\; label="F"\; filenames="00000072.png"\; state="\{\{state\}\}">F</figure-callout>}}_3=\left[\begin{array}{cc}\mathrm{one}& \mathrm{<figure-callout\; id="0"\; label="\Delta \; t"\; filenames="00000077.png,00000078.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}t\\ 0& \mathrm{one}\end{array}\right]$$

- matrix of the model of watch drift of the satellite receiver; Δt is the time sampling interval.

The observed value contains the navigation parameters calculated by the satellite receiver: pseudorange (PD) and pseudo-speed (PS) relative to the (N-M) NS, as well as calculated by the receiver of the rangefinding range system (D) relative to L NRM and, therefore, has the form:

,

,

where Z _PD (i) is the vector of measurements of PD; Z _PS (i) - vector measurement PS; Z _D (i) is the vector of range measurements.

Note that the vector Z (i) represents the complex (oriented) navigation parameters of the aircraft according to the SSN and SDS and has a size of 2 (N-M) + L.

The PD vector consists of (N-M) elements of the form

- дискретный белый шум с известной дисперсией, определенной для каждой из N-M ПД при формировании корреляционной матрицы ошибок ССН в виде $${\sigma }_{ПД}^2+D_{ПД}$$

.where x _and (i), y _and (i) and z _and (i) are the elements of the coordinate vector measured in an inertial manner; k is the satellite number k = 1 ... NM; x _k (i), y _k (i) and z _k (i) are the coordinates of the k-th satellite; $$n_{\mathrm{to}}^{Pd}(i)$$

- discrete white noise with a known dispersion defined for each of the NM PD during the formation of the correlation matrix of errors in the SSN in the form $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PD}^{}+D_{PD}$$

.

The PS vector also contains N-M elements of the form

, $${\dot{y}}_k(i)$$

и $${\dot{z}}_k(i)$$

- элементы вектора скорости k-го спутника; cos_xk, cos_yk и cos_zk - направляющие косинусы k-го спутника; f_н - несущая частота; Δf=v_tf_н - уход частоты; $$n_{к}^{пс}(i)$$

- дискретный белый шум с известной дисперсией, определенной для каждой из N-М ПС при формировании корреляционной матрицы ошибок ССН в виде $${\sigma }_{ПC}^2+D_{ПC}$$

.where v _x (i), v _y (i) and v _z (i) are elements of the velocity vector measured in an inertial manner; $${\dot{x}}_k(i)$$

, $${\dot{y}}_k(i)$$

and $${\dot{z}}_k(i)$$

- elements of the velocity vector of the kth satellite; cos _xk , cos _yk and cos _zk are the direction cosines of the k-th satellite; f _n - carrier frequency; Δf = v _t f _n - frequency drift; $$n_{\mathrm{to}}^{P\mathrm{from}}(i)$$

- discrete white noise with a known dispersion defined for each of the N-M PS in the formation of the correlation matrix of errors CCH in the form $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; C"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PC}^{}+D_{PC}$$

.

The range measurement vector consists of L elements of the form

,

,

- дискретный белый шум с известной дисперсией, определенной для каждой из L дальности при формировании корреляционной матрицы ошибок ДСН в виде $${\sigma }_{Д}^2+D_{Д}$$

.where x _and (i), y _and (i) and z _and (i) are the elements of the coordinate vector measured in an inertial manner; j is the number of the receiver array j = 1 ... L; x _j (i), y _j (i) and z _j (i) are the coordinates of the j-th NRM; $$n_j^d(i)$$

- discrete white noise with a known dispersion defined for each of the L ranges during the formation of a correlation matrix of SDS errors in the form $${\sigma }_D^{}$$$${}_2^{}+D_D$$

.

формируется в соответствии с алгоритмом [1, 2]:Optimal estimation of the state vector $$\stackrel{\wedge }{Y}(i)$$

formed in accordance with the algorithm [1, 2]:

, $${\stackrel{\wedge }{Z}}_{\stackrel{-}{П}С}(i)$$

и $${\stackrel{\wedge }{Z}}_{\stackrel{-}{Д}}(i)$$

- векторы, построенные с использованием экстраполированных оценок вектора состояния $${\stackrel{\wedge }{Y}}_{\stackrel{-}{}}(i)$$

; элементы вектора $${\stackrel{\wedge }{Z}}_{\stackrel{-}{П}Д}(i)$$

для k-го спутника равны:Where $${\stackrel{\wedge }{Z}}_{\stackrel{-}{P}D}(i)$$

, $${\stackrel{\wedge }{Z}}_{\stackrel{-}{P}\mathrm{FROM}}(i)$$

and $${\stackrel{\wedge }{Z}}_{\stackrel{-}{D}}(i)$$

- vectors constructed using extrapolated estimates of the state vector $${\stackrel{\wedge }{Y}}_{\stackrel{-}{}}(i)$$

; vector elements $${\stackrel{\wedge }{Z}}_{\stackrel{-}{P}D}(i)$$

for the k-th satellite are equal:

;

;

равны:vector elements $${\stackrel{\wedge }{Z}}_{\stackrel{-}{P}\mathrm{FROM}}(i)$$

equal to:

;

;

для j-го НРМ равны:vector elements $${\stackrel{\wedge }{Z}}_{\stackrel{-}{D}}(i)$$

for the j-th NRM are:

K (i) is the optimal gain.

The value of K (i) is determined by the expressions:

- производные нелинейных функций наблюдения, содержащихся в Z(i).where P (i) and P ^- (i) are the correlation matrices of filtering errors and extrapolation of the object state vector; $$H_l=\frac{\partial H}{\partial Y}|{\widehat{Y}}^{-}(i)$$

- derivatives of nonlinear observation functions contained in Z (i).

Note that the matrix R is now a complex correlation matrix of errors according to SSN and SDS, taking into account the orientation of the aircraft, and has a size of (2 (N-M) + L) × (2 (N-M) + L).

на выходе расширенного Фильтра Калмана (ФК), причем в этой оценке учтено влияние изменения ориентации ЛА.After evaluating the errors in the position of the aircraft by the satellite, the navigation parameters are corrected by the satellite and the updated position of the aircraft is determined 10. In this case, the values of the corresponding estimates of the errors of the satellite (coordinates and speed measurements) contained in the vector estimate are subtracted from the estimates of the navigation parameters of the aircraft obtained inertially state $$\widehat{Y}(i)$$

at the output of the extended Kalman Filter (FC), moreover, this assessment takes into account the influence of changes in aircraft orientation.

Below are considered options that develop and clarify the proposed method.

. Тогда преобразование вектора ускорения a ^b, измеренного в ССК, в НСК a ⁿ выполняется с помощью выражения $$a^n=C_b^n{a}^b$$

, а обратное преобразование имеет вид $$a^b={(C_b^n)}^T{a}^n$$

. После преобразования координат выполняется интегрирование преобразованного вектора ускорений $$a^n=C_b^n{a}^b$$

с учетом поправок на ускорение силы тяжести и угловую скорость вращения Земли [1, 2]. При этом также учитываются начальные условия (координаты и скорость ЛА). В результате рассмотренных навигационных вычислений данные, получаемые от инерциальных датчиков, преобразуются в координаты, вектор скорости и углы ориентации ЛА. Рассмотренное преобразование координат всегда выполняется в БИНС, поэтому оператор ориентации ЛА предлагается после формирования векторов направления НС в НСК 26 использовать при формировании векторов направления НС в ССК 27 и последующим определением весовых коэффициентов с учетом влияния диаграммы направленности антенны спутникового приемника (Фиг. 3). Аналогично это преобразование можно использовать при формировании векторов направления НРМ в ССК 31 и последующим определением весовых коэффициентов с учетом влияния диаграммы направленности антенны приемопередатчика ДСН. Рассмотрим эти операции подробнее.Option corresponding to paragraph 2 of the formula. When calculating the position of the aircraft according to ISN 1 (Fig. 2), it is assumed that a strapdown inertial navigation system (SINS) is used. In such a system, an inertial sensor unit mounted on the aircraft’s hull produces an angular velocity vector ω ^b and acceleration vector a ^b in a linked coordinate system (SSC), for example: Roll-Pitch-Yaw - RPY. The determination of the coordinates and the velocity vector of the aircraft is then performed in the navigation coordinate system (NSC), for example: "North-East-Down" - NED. To calculate the position of the aircraft according to the ISN (Fig. 3), the following operations are performed: determining the angular velocity and acceleration vectors in the SSC (readings of inertial sensors), calculating the orientation operator of the aircraft 25, which provides coordinate conversion. Next, the position of the aircraft is calculated according to ISN 33 by converting the acceleration vector from the SSC to the NSC and calculating the speed and coordinates of the aircraft [2, 9]. As an aircraft orientation operator, for example, one can use the matrix of guiding cosines $$C_b^n$$

. Then, the conversion of the acceleration vector a ^b measured in SSC to NSC a ⁿ is performed using the expression $$a^n=C_b^n{a}^b$$

, and the inverse transformation has the form $$a^b={(C_b^n)}^T{a}^n$$

. After coordinate transformation, the converted acceleration vector is integrated $$a^n=C_b^n{a}^b$$

subject to corrections for the acceleration of gravity and the angular velocity of rotation of the Earth [1, 2]. In this case, the initial conditions (coordinates and speed of the aircraft) are also taken into account. As a result of the considered navigation calculations, the data obtained from inertial sensors are converted into coordinates, velocity vector and aircraft orientation angles. The considered coordinate transformation is always performed in the SINS, therefore, it is proposed to use the aircraft orientation operator after generating the NS direction vectors in the NSC 26 when forming the NS direction vectors in the SSK 27 and then determining the weight coefficients taking into account the influence of the antenna radiation pattern of the satellite receiver (Fig. 3). Similarly, this transformation can be used in the formation of directional vectors of the NRM in SSK 31 and the subsequent determination of weight coefficients, taking into account the influence of the radiation pattern of the antenna of the transceiver SDS. Let's consider these operations in more detail.

When forming the direction vectors of the NS in the NSC 26 (Fig. 3), the angular coordinates of the NS (elevation and azimuth angles) in the NSC are used. The satellite elevation angle φ in the NSC is measured relative to the horizontal plane, and the azimuth angle ϕ is relative to the direction to the North. The direction to the satellite in the NSC is characterized by the vector

.

.

:Then, NS direction vectors are formed in SSK 27 using the transposed matrix $${(C_b^n)}^T$$

:

.

.

When determining the weighting coefficients of satellites 28 (Fig. 3), the antenna pattern of the satellite receiver mounted on the aircraft is used. The antenna pattern is usually given in azimuth-elevation coordinates (in CCK). For example, if the direction vector N ^b = (n ₁ n ₂ n ₃ ) ^T is determined, then the elevation angle of the satellite in the SSC is -arcsinn ₃ and the azimuth is arctg (n ₂ / n ₁ ). Further, as described above, the antenna gain of the satellite receiver K _ant.s in the direction of with NRM N ^{b is} compared with a threshold and the composition of the working NRM 21 is adjusted. After the correction, (NM) satellites remain. For the remaining satellites in the corrected composition of the working constellation, weights 32 are determined (this operation has been described previously).

When forming the direction vectors of the NRM 30 (Fig. 3), the angular coordinates of the NRM 29 (elevation and azimuth angles for working NRMs in the NSC) are preliminarily calculated using data on the coordinates of the NRM and the updated position of the aircraft. The elevation angle φM in the NSC is measured relative to the horizon, and the azimuth angle ϕ is relative to the direction to the North. The direction to the NRM in the navigation coordinate system is characterized by a vector (the formation of the NRM direction vectors in SSK 30)

.

.

:Then, the direction vectors of the NRM are formed in SSK 31 using the transposed matrix $${(C_b^n)}^T$$

:

.

.

When determining the weighting coefficients of the HPM 32 (Fig. 3), the directivity pattern of the onboard antenna of the transceiver of the rangefinder signals mounted on the aircraft is used. The antenna pattern is usually given in azimuth-elevation coordinates (in CCK). For example, if the direction vector N ^b = (n ₁ n ₂ n ₃ ) ^T is determined, then the elevation angle is -arcsinn ₃ and the azimuth is arctg (n ₂ / n ₁ ). Further, as described above, the gain of the antenna of the transceiver of the ranging signals K _ant.d in the direction to the NRM N ^{b is} compared with the threshold and the working composition of the NRM 21 is adjusted. After the correction, the (NM) NRM will remain. For those remaining in the adjusted working composition of the NRM, weights 32 are determined (this operation has been described previously).

с последующим определением весового коэффициента D_Д выбранного источника (НРМ) 32.Option corresponding to paragraph 3 of the formula. Since it is impossible for an SDS to build an omnidirectional antenna, several antennas are installed on the aircraft, for example, the nose and tail [12]. The radiation patterns of these antennas are shown in Appendix 2 in Figure 1. If you use the total output of these antennas, interference occurs in a wide sector of angles, and reliable communication is provided only in the bow and tail sectors (Appendix 2 of Fig. 2). You can use the independent outputs of these antennas and search for strong signals. But with this search, time is lost and the continuity of communication with the NRM is disrupted. Due to the presence of SINS, it is possible to implement the optimal method for selecting a DSP antenna (Figure 4), which includes the formation of directional vectors of the NRM in SSK 31, determining the gain of the antennas and vectors combined with the maximum radiation patterns of the antennas 34, comparing the gain of the antennas and selecting the largest 35, with the presence of which the antenna pattern is selected 37 with the highest gain $$K_{\mathrm{but}nt}^{m\mathrm{but}\mathrm{to}\mathrm{from}}$$

with the subsequent determination of the weight coefficient D _{D of the} selected source (NRM) 32.

возможна такая ситуация, когда антенны имеют равные или близкие коэффициенты усиления. Тогда целесообразно выбрать антенну, максимум диаграммы направленности которой находится в соответствии с перемещением вектора направления НРМ. Определение перемещения вектора направления НРМ 36 осуществляется следующим способом (Фиг. 4). Угол между вектором направления N^b и вектором, совмещенным с максимумом диаграммы N^макс, определяется выражениемWhen choosing the antenna pattern with the highest gain $$K_{\mathrm{but}nt}^{m\mathrm{but}\mathrm{to}\mathrm{from}}$$

such a situation is possible when the antennas have equal or close gain factors. Then it is advisable to choose an antenna whose maximum radiation pattern is in accordance with the movement of the direction vector of the NRM. The determination of the displacement of the direction vector НРМ 36 is carried out in the following way (Fig. 4). The angle between the direction vector N ^b and the vector combined with the maximum of the diagram N ^max is determined by the expression

The movement towards the maximum corresponds to a decrease in the angle γ and an increase in the product N ^b N ^max and, accordingly, a positive value of the derivative of this quantity. To determine the direction, we calculate the derivative N ^b N ^max with respect to time.

и известное уравнение $${\dot{C}}_b^n=C_b^n\times {\omega }^b$$

, где ω^b - вектор угловой скорости. Тогда получим окончательное выражение для производной:Next we use the transformation $${\dot{N}}^b={({\dot{C}}_b^n)}^T{N}^n$$

and the famous equation $${\dot{C}}_b^n=C_b^n\times {\omega }^b$$

where ω ^b is the angular velocity vector. Then we get the final expression for the derivative:

The resulting expression depends on the direction vector of the NRM in the SSC, the angular rotation vector of the aircraft and the orientation operator. When selecting the antenna, the aforementioned derivative is calculated and the antenna 37 is selected with a positive derivative value.

Option corresponding to paragraph 4 of the formula. In the formation of the oriented CM errors of the SSN errors, it is possible to take into account the effects of multipath propagation of radio signals (hereinafter, the multipath effects).

, и должна быть также задана в координатах азимут-угол места.The effects of multipath lead to an increase in the error in measuring data on the position of the aircraft on the SSN. In this case, the influence of the spatial orientation of the aircraft during its maneuvering can have a significant effect on the level of the indicated error. To identify such effects, it is necessary to have a diagram of the bistatic effective scattering surface (volumetric multipath diagram [13]) of the aircraft hull elements and data on the angular position of the hull relative to the direction to the satellite. Therefore, it is proposed to determine the additional weighting coefficients of NS 38 (Fig. 5) taking into account the orientation operator and the 3D multipath diagram stored in the database and characteristic for this type of aircraft. This diagram contains the variances of the multipath error, for example pseudorange $${\sigma }_{\mathrm{<figure-callout\; id="2"\; label="M\; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">M\; </figure-callout>}PD}^2$$

, and should also be given in the coordinates of the azimuth-elevation angle.

, и формируются значения первых N-M диагональных элементов ориентированной КМ ошибок по ССН 19, соответствующих ошибкам ПД, в виде: $${\sigma }_{ПД}^2+{\sigma }_{МПД}^2+D_{ПД}^{-1}$$

. Формирование элементов ориентированной КМ ошибок по ССН 19, соответствующих ошибкам ПС выполняется аналогично. Таким образом, в предложенном способе соединены принципиально новые операции (действия), связанные с учетом влияния ориентации на определение положения ЛА:Next, the adjustment of the weight coefficients of the HC 39 (Fig. 5), for example in the form of: $${\sigma }_{\mathrm{<figure-callout\; id="2"\; label="M\; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">M\; </figure-callout>}PD}^2+D_{PD}^{-\mathrm{one}}$$

, and the values of the first NM diagonal elements of the oriented KM errors are formed according to SSN 19, corresponding to PD errors, in the form: $${\mathrm{<figure-callout\; id="2"\; label="\sigma \; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">\sigma \; </figure-callout>}}_{PD}^{}+{\sigma }_{\mathrm{<figure-callout\; id="2"\; label="M\; P\; D"\; filenames="00000072.png"\; state="\{\{state\}\}">M\; </figure-callout>}PD}^2+D_{PD}^{-\mathrm{one}}$$

. The formation of the elements of the oriented CM errors on SSN 19, corresponding to the errors PS is performed similarly. Thus, in the proposed method connected fundamentally new operations (actions) associated with taking into account the influence of orientation on determining the position of the aircraft:

- the formation of oriented correlation error matrices of satellite and rangefinding navigation methods;

- the formation of oriented navigation parameters of the aircraft, determined by each of the above methods.

Moreover, it is essential:

- when forming oriented navigation parameters of the aircraft according to the SSN, the navigation parameters are adjusted taking into account the changing composition of the working constellation of the NS and the oriented correlation matrix of errors of the SSN;

- in the formation of oriented navigation parameters of the aircraft according to the SDS, the changing working composition of the NRM is constantly monitored and taken into account.

These actions determine the significant novelty of the proposed method. The effectiveness of the proposed method is confirmed by the results of digital and semi-natural simulation on integrated stands during the development and debugging of software for on-board navigation and landing complexes of promising aircraft.

The flight tests conducted on the Yak-42 aircraft and the Mi-8 helicopter showed the technical feasibility and effectiveness of the proposed method.

Thus, the claimed invention is promising for solving problems of increasing the reliability and accuracy of advanced navigation systems, ultimately, reducing the likelihood of aircraft accidents.

Appendix 3 contains a list of abbreviations accepted in the text.

Literature

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Claims (4)

1. An integrated method of navigation of aircraft (LA), which provides for the use of inertial, satellite and rangefinding navigation methods to determine the position of an aircraft, while the inertial navigation method (INS) determines the navigation parameters and position of the aircraft according to the readings of inertial sensors, in the satellite navigation method ( SSN) on N navigation satellites (NS), they receive NS signals on an aircraft, determine navigation parameters on SSN with data on the position of the aircraft in the form of pseudo-ranges and pseudo-velocities, and in the ranging method of navigation (SDS) generate and emit interrogation rangefinder signals on an aircraft, receive the aforementioned interrogation signals on ground beacons with known coordinates, generate and emit a response rangefinder signals, receive the aforementioned response signals on an aircraft and determine the navigation parameters in the form of ranges to L NRM, and then in the on-board computer form the integrated navigation parameters of the aircraft from the navigation parameters determined by the SSN and the SDS, and form a complex matrix of OSh Ibok CLO and SDS through which evaluate aircraft position error determined by SRI, and by correcting the specified on IOS aircraft position define a refined position of the aircraft, in addition, the onboard computer selects a working composition HPM on the updated position of the aircraft and coordinates HPM from the database data associated with the on-board computer, while the working composition of the NRM conducts the corresponding formation and emission of interrogation rangefinder signals, and the output results are presented in the form of an updated position of the aircraft, In that they form an additional database, including radiation patterns of the satellite receiver antenna and the onboard antennas of the rangefinder signal transceiver, after receiving the NS signals in parallel with the determination of the navigation parameters on the SSN, the constellation of the working constellation and the angular coordinates of the NS are isolated, the signal-to-noise ratios of the satellite receiver are extracted and form a correlation matrix of errors CCH, then form the direction vectors of the NS and determine the weight coefficients of the NS from the composition of the working constellation orientation of the aircraft, the correct position of the aircraft, the angular coordinates of the NS and the antenna radiation pattern of the satellite receiver, adjust the composition of the working constellation of satellites according to the weight coefficients of the NS, adjust the navigation parameters according to the adjusted composition of the working constellation of the NS, then form an oriented correlation matrix of errors of the SSN, taking into account the orientation of the aircraft, based on the adjusted composition of the working constellation and taking into account the weight coefficients of the NS, in parallel along the SDS form a correlation matrix erroneously directional signals, form direction vectors and determine the weighting factors of the NRM from the working composition of the NRM according to the orientation of the aircraft, the correct position of the aircraft, the coordinates of the NRM from the working composition of the NRM and the radiation pattern of the aforementioned onboard antenna of the transceiver, adjust the working composition of the NRM by the weight coefficients of the NRM, form an oriented correlation matrix SDS errors that take into account the orientation of the aircraft, based on the adjusted working composition of the NRM and taking into account the weight coefficients of the NRM, form accordingly oriented to navigation parameters according to SSN and SDS and use them in the on-board computer to form integrated navigation parameters, while the output results are presented in the form of an updated position of the aircraft, adjusted for the orientation of the aircraft. 2. The complex method according to claim 1, characterized in that, according to the readings of inertial sensors in the form of angular velocities in the associated coordinate system, the orientation operator is calculated in the ISN, the direction vectors of the NS are formed in the SSN by the angular coordinates of the NS in the navigation coordinate system, then using the operator orientation, form the direction vectors of the NS in the associated coordinate system and, using the radiation pattern of the antenna of the satellite receiver, determine the weight coefficients of the NS, in parallel to the SDS according to the coordinates of the NRM from the database and to the correct position of the aircraft, the angular coordinates of the NRM are calculated, the direction vectors of the NRM are generated in the navigation coordinate system, then, using the orientation operator, the direction vectors of the NRM are formed in the associated coordinate system and, using the directional diagram of the onboard antenna of the transceiver of rangefinder signals, the weight coefficients of the NRM are determined, while AIS using the orientation operator calculates the acceleration vector of the aircraft in the navigation coordinate system, which determines the position of the aircraft according to the ISN. 3. The method according to PP. 1,2, characterized in that after the formation of the direction vectors NRM determine the gain of each of the airborne antennas of the transceiver of rangefinder signals and select the antenna pattern with the highest gain, and at close gains of the mentioned airborne antennas choose the radiation pattern of the antenna in accordance with the movement of the vector directions of NRM. 4. The method according to p. 1, characterized in that an additional multipath diagram of the aircraft is introduced into the additional database, additional weight coefficients of the NS are determined from the composition of the working constellation according to the orientation of the aircraft and the mentioned multipath diagram, after determining the weight coefficients of the NS, weight coefficients are adjusted, determining the resulting NS weight coefficient, for example, as the sum of a weight coefficient and an additional weight coefficient, and is introduced when forming an oriented correlation matrix of SS errors the resulting weighting factor.

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