CN115683092B - Repositioning method for DME/DME/SINS (symmetric multi-user navigation system/strapdown inertial navigation system) - Google Patents
Repositioning method for DME/DME/SINS (symmetric multi-user navigation system/strapdown inertial navigation system) Download PDFInfo
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Abstract
The repositioning method of the DME/DME/SINS tightly combined navigation system disclosed by the invention has the anti-interference capability and can meet the navigation instantaneity and reliability. The invention is realized by the following technical scheme: finishing SINS navigation calculation according to the measurement output value of the inertial device, outputting the attitude, the speed and the position of the aircraft, calculating the pseudo-slope distance from the aircraft to the DME station according to the calculated pseudo-slope distance, forming slope distance measurement information by making a difference between the calculated pseudo-slope distance and the slope distance obtained by the DME airborne equipment, and forming altitude measurement information by making a difference between the altitude and the altitude output by the atmosphere data machine; based on SINS attitude, speed and position error equation, establishing Kalman filtering state equation and mathematical relationship between slant distance, altitude error and state variable, thereby establishing Kalman filtering measurement equation; and correcting the SINS posture, speed and position by using the estimated posture, speed and position error feedback, so as to inhibit SINS navigation error and output navigation information with higher precision.
Description
Technical Field
The invention relates to a rapid repositioning technology of a DME/DME/SINS tightly combined navigation system of a carrier in the flight process under working environments of high dynamic state, weak signals and the like.
Background
With the continuous development of navigation technology, requirements on the aspects of navigation system precision, stability and the like are higher and higher. Modern aviation industry involves more and more technology, and aircraft are not simple vehicles, but rather are an aggregate of multiple technologies, and the performance of a single navigation system has a certain limitation, which often cannot meet the positioning requirements in a special environment. The combined navigation system can fully exert the advantages of each system, and the advantages of each navigation system are complementary, so that the stability of the system is improved while the accuracy of the whole system is ensured, and the combined navigation system is rapidly developed in view of the advantages. Among them, strapdown Inertial Navigation System (SINS) and GNSS integrated navigation system are most widely used. The GNSS has the defects of poor dynamic response capability, easy electronic interference, easy signal shielding and poor integrity, GNSS signals have poor quality under certain special environments, in this case, GNSS/SINS integrated navigation cannot work normally, the system enters a pure SINS resolving working mode, and navigation positioning errors accumulate with time due to the existence of error sources such as inertial device measurement errors and the like, and the requirement of long-time navigation cannot be met by means of independent operation of the SINS. Therefore, there is a need to design a backup navigation system of the GNSS/SINS integrated navigation system to meet the navigation requirements of the aircraft under the GNSS rejection condition.
The land-based radio navigation system is an international universal civil aviation navigation system, and is a basic system for civil aviation organization and implementation of flight, and safety production and operation management. The land-based radio navigation system has the advantages of poor positioning accuracy, high signal transmitting power, difficult interference, high data updating rate and the like, which are not possessed by the satellite navigation system. The range finder (DME) is a high-precision non-autonomous time ranging short-range navigation system, is a land-based ranging navigation system important for civil aviation, and can provide an airplane with a slant range to a DME station. The DME rangefinder employs an inquiry-response ranging method, which is a universal ranging guide device for civil aviation worldwide, and can be used as both an airline navigation device and an airport navigation device. The DME acquires distance information by measuring the propagation time of electric waves in space, and the distance measurement process is divided into a searching, tracking and memorizing stage. The DME system consists of an airborne interrogator and a ground transponder, and the distance information from the aircraft to the ground DME platform is calculated by accurately measuring the total time of receiving and transmitting signals and the fixed time delay of the ground response part. DME/DME navigation is widely used in the course navigation phase in performance-based navigation applications. DME/DME navigation belongs to a positioning mode, and the positioning error of DME/DME is also limited based on the limitation of DME measurement skew. The inertial navigation system is a navigation parameter resolving system of a sensor by using an assembled triaxial gyroscope and an accelerometer, and the system establishes a navigation coordinate system according to the output of the gyroscope and resolves the speed and the position of a carrier according to the output of the accelerometer. The inertial navigation system can be divided into two types of platform type and strapdown type according to different methods for constructing the navigation coordinate system, wherein the system for determining the navigation coordinate system by adopting a mathematical algorithm is called a strapdown inertial navigation system, namely SINS. When the interference quality of the GNSS signals in a special environment is reduced, the navigation precision of the GNSS/SINS integrated navigation system is reduced, and the requirement of navigation on the navigation path cannot be met.
Most of domestic civil airliners are assembled with foreign produced flight management systems, wherein part of the model flight management systems already have DME/DME/SINS integrated navigation functions, but specific technical details cannot be known, and related technical data are difficult to find. There is little research performed on the DME/DME/SINS integrated navigation system in China, and only one literature has developed the research. Under the condition of high reference, the integrated navigation problem is simplified into two-dimensional plane integrated navigation. Obviously, due to the fact that the earth is locally simplified to be a plane, a principle error is brought to the modeling layer of the state space model, the principle error directly influences navigation precision, and therefore the practical application value of the research is low. In view of the above, it is necessary to develop a more intensive study on the integrated navigation system with a wide application prospect. The DME/DME/SINS integrated navigation system is researched, the simplest direct mode is to form measurement information by making a difference between a DME/DME positioning position result and an SINS calculated position, a Kalman filtering state space model is built on the basis of an SINS error propagation equation, and then the navigation error of the system is estimated and compensated through a Kalman filter so as to realize integrated navigation. The combined mode is usually called a loose combined navigation mode, and the mode is completely consistent with a GNSS/SINS loose combined mode, and has the advantages of simple implementation, insufficient algorithm navigation precision, serious navigation precision loss under the condition of abrupt measurement noise interference and incapability of meeting navigation requirements even in a certain time, so that the loose combined navigation mode is not an ideal working mode of DME/DME/SINS combined navigation. In order to solve the problem of loose combination, a great deal of researches are carried out by a great deal of researchers aiming at the filtering algorithm of the integrated navigation information fusion, however, the related filtering algorithm provided can improve the performance of the integrated navigation system to a certain extent on a theoretical level, but brings other problems: firstly, setting initial parameters of filtering is very severe to ensure the effect of a filtering algorithm; secondly, the improved filtering algorithm greatly increases the operand, which presents a new challenge for the real-time performance of the algorithm operation. Therefore, the feasibility of the strategy for optimizing the performance of the loosely-combined navigation system through the improved filtering algorithm in practical application still needs to be verified in a large quantity. Besides the research of filtering algorithms, some researchers apply related methods of fault diagnosis and isolation to loose combination navigation systems, such as wavelet transformation, M estimation and the like, and the methods have the same problem on the real-time performance of algorithm operation.
The tightly combined navigation mode is the most practical working mode of the GNSS/SINS combined navigation system, and the tightly combined mode can be adopted to design the DME/DME/SINS combined navigation system. The tight-fitting uses deeper observables to form measurement information, such as pseudoranges and pseudorange rates, relative to the loose-fitting mode using external position or velocity assistance. As the combination is performed by adopting the more advanced observables, the integrated navigation system in the tightly combined working mode has stronger anti-interference capability and higher navigation precision in practical application. However, the DME/SINS tight integrated navigation system cannot be designed by directly referencing the GNSS/SINS tight integrated navigation mode, because the former combination often requires the use of external observation information such as pseudorange rate, while the latter has no measurement information such as pseudorange rate during the combination. Aiming at the DME/DME/SINS tightly integrated navigation system, the integrated navigation cannot be realized by only depending on two pseudo-range observation information, and the airborne altitude information provided by the atmosphere data machine can be used as additional observation information in combination with the actual airborne navigation equipment, so that the integrated navigation can be assisted by the double pseudo-range observation information to realize the tightly integrated navigation of the SINS. The DME/DME/SINS integrated navigation system suppresses the navigation error accumulated by the SINS along with time mainly by establishing three aspects of a Kalman filtering state equation and a measurement equation, kalman filtering state estimation and a navigation parameter error correction mode.
In summary, in view of less research on the DME/SINS integrated navigation system in China, considering that the DME/SINS has important application prospect as a backup of the GNSS/SINS integrated navigation system, it is necessary to research the deployment system. In the implementation process, in consideration of the engineering implementation difficulty of the system and the anti-interference capability and navigation precision of the combined navigation system, intensive research on a tight combined navigation mode of the DME/DME/SINS combined navigation system should be conducted.
Disclosure of Invention
In order to ensure the navigation precision of an on-board navigation system under the GNSS refusal condition, the invention provides a DME/DME/SINS tight combination navigation scheme which has anti-interference capability and can meet the requirements of navigation instantaneity and reliability, and aims to provide a reliable backup navigation system for the GNSS/SINS combination navigation system under the GNSS refusal condition and ensure the flight safety of an aircraft in the flight phase of a navigation path.
The above object of the present invention can be achieved by a DME/DME/SINS tightly integrated navigation system repositioning method characterized by comprising the steps of: based on a north-orientation SINS attitude error equation, a speed error equation and a position error equation, establishing a Kalman filtering state equation based on a triaxial attitude error, a northeast-day speed error, a position error, a gyro constant drift and an accelerometer constant zero bias as state variables; calculating a pseudo-slope distance from the aircraft to a DME double station of a range finder according to the SINS calculated position of the strapdown inertial navigation system, forming slope distance measurement information by making a difference between the slope distance measured by the DME airborne measurement equipment and the pseudo-slope distance, and forming height measurement information by making a difference between the height measured by the atmospheric data machine and the height output by the SINS; deducing a conversion relation between measurement information and state variables, and establishing a Kalman filtering measurement equation; performing SINS navigation calculation according to the measured value output by the inertial device, and outputting navigation parameters; under the assistance of two navigation information of the slope distance output by the DME and the altitude of the atmospheric data machine, the real-time estimation of the system state variable is realized through a Kalman filter, the Kalman filter adopts a feedback correction strategy, the attitude error, the speed error and the position error are corrected through feedback, the SINS navigation error is corrected in real time, the final position, the speed and the attitude of the airplane are determined, the establishment of a Kalman filtering state equation and a measuring equation, the calculation of the measuring information and the Kalman filtering state estimation and the feedback correction are integrated, the results of the data acquisition, the data processing, the information fusion and the repositioning of the navigation sensor of the DME/DME/SINS tightly combined navigation system are obtained, the estimated attitude, the estimated speed and the estimated position error are utilized for feedback correction of the SINS attitude, the estimated speed and the estimated position error, the estimated SINS navigation error are restrained, and the navigation information with higher precision is output and displayed.
The invention has the following beneficial effects:
Aiming at the DME/DME/SINS tightly combined navigation system, the invention has no complete scheme which can be implemented in practical application, adopts DME/DME to replace GNSS, and utilizes the better error smoothing characteristic of SINS to effectively smooth the DME/DME positioning error.
According to the invention, the DME+DME+SINS tightly combined navigation scheme is adopted, the theoretical framework is complete, the algorithm content is simple and reliable, the performance of the airborne navigation system under the GNSS rejection condition is improved, and a foundation is laid for further research of the subsequent DME/DME/SINS combined navigation scheme.
The system has stronger anti-interference capability and higher navigation precision. The DME/DME/SINS integrated navigation scheme designed by the invention adopts a tightly integrated navigation mode. Compared with a loose combination navigation mode that the position of the airplane is obtained by adopting the DME/DME through a positioning mode, and the position is differenced with the SINS solved position to form measurement information, the invention has stronger anti-interference capability and higher navigation precision in practical application because a tight combination mode that the measurement information is formed by adopting the difference between the deeper inclined distance and the pseudo inclined distance.
An important backup is provided for the GNSS/SINS integrated navigation system. The execution of the DME/DME/SINS integrated navigation scheme provided by the invention is completely independent from the GNSS/SINS integrated navigation system, and can refer to the navigation result given by the GNSS/SINS integrated navigation system under the condition of good GNSS signals, and the DME/DME/SINS integrated navigation system can provide important backup for the GNSS/SINS integrated navigation system under the condition of GNSS signal rejection, thereby meeting the flight safety of the aircraft in the flight phase of the aircraft route under the condition of GNSS rejection.
The invention can realize the information fusion of the navigation data output by the SINS and the DME, improve the anti-interference capability and the navigation precision of the integrated navigation system, and provide important backup for the GNSS/SINS integrated navigation system under the GNSS signal rejection condition.
The method is suitable for the navigation information fusion of the original data output by the DME double station, the atmosphere data machine and the inertial device in the aircraft application process, can effectively realize the DME/DME/SINS combined navigation, and has low external dependence and strong anti-interference capability. The method has stronger anti-interference capability and higher navigation precision, can be used as an important backup of the GNSS/SINS integrated navigation system under the GNSS rejection condition, and provides reliable navigation information for the course flight stage.
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The invention is further described below with reference to the drawings and examples.
FIG. 1 is a schematic diagram of a DME/DME/SINS tightly integrated navigation scheme of the present invention;
FIG. 2 is a schematic diagram of a scenario in which the present invention implements a DME/DME/SINS tightly integrated navigation scheme.
Detailed Description
See fig. 1 and 2. According to the invention, based on a north-orientation SINS attitude error equation, a speed error equation and a position error equation, a Kalman filtering state equation is established based on a triaxial attitude error, a northeast-to-north speed error, a position error, a gyro constant drift and an accelerometer constant zero bias as state variables; calculating a pseudo-slope distance from the aircraft to a DME double station of a range finder according to the SINS calculated position of the strapdown inertial navigation system, forming slope distance measurement information by making a difference between the slope distance measured by the DME airborne measurement equipment and the pseudo-slope distance, and forming height measurement information by making a difference between the height measured by the atmospheric data machine and the height output by the SINS; deducing a conversion relation between measurement information and state variables, and establishing a Kalman filtering measurement equation; performing SINS navigation calculation according to the measured value output by the inertial device, and outputting navigation parameters; under the assistance of two navigation information of the slope distance output by the DME and the altitude of the atmospheric data machine, the real-time estimation of the system state variable is realized through a Kalman filter, the Kalman filter adopts a feedback correction strategy, the attitude error, the speed error and the position error are corrected through feedback, the SINS navigation error is corrected in real time, the final position, the speed and the attitude of the airplane are determined, the establishment of a Kalman filtering state equation and a measuring equation, the calculation of the measuring information and the Kalman filtering state estimation and the feedback correction are integrated, the results of the data acquisition, the data processing, the information fusion and the repositioning of the navigation sensor of the DME/DME/SINS tightly combined navigation system are obtained, the estimated attitude, the estimated speed and the estimated position error are utilized for feedback correction of the SINS attitude, the estimated speed and the estimated position error, the estimated SINS navigation error are restrained, and the navigation information with higher precision is output and displayed.
Under the normal working state, the aircraft-mounted GNSS receiver receives the lowest 4 satellite navigation signals, and under the condition of completing positioning, the aircraft-mounted GNSS receiver outputs the position, the speed and the gesture of the aircraft through a loose combination navigation mode with the strapdown inertial navigation system SINS. When the situation shown in the figure occurs, that is, when the navigation signals of the satellite 2 and the satellite 4 are refused (the satellite is attacked or the signals are artificially interfered), the navigation parameters of the aircraft cannot be output continuously in a GNSS/SINS combined navigation mode, and the navigation parameters of the system can be output only by means of SINS self navigation solution. With the extension of time, due to the existence of error sources such as inertial device measurement errors, SINS navigation errors are accumulated seriously with time until the requirements of airplane navigation on the way of the airplane for flight navigation cannot be met. If the DME airborne equipment sends an inquiry signal when the satellite navigation signal is refused, the response signals of the DME station 1 and the DME station 2 (at least two DME stations) can be received, and at the moment, the position, the speed and the gesture of the aircraft can be output in a DME/DME/SINS combined navigation mode, so that backup is provided for the aircraft route navigation under the GNSS signal refusing condition.
The inertial device comprises a gyroscope and an accelerometer, wherein the gyroscope outputs an angular velocityThe accelerometer outputs a specific force angular velocity f b. The strapdown inertial navigation system SINS performs navigation solution according to the output measurement value of the inertial device, wherein the navigation solution comprises attitude solution, speed solution and position solution, and outputs the position, speed and attitude of the airplane. And according to the position output by the airborne SINS at the current moment, simultaneously combining the positions of the two ground DME stations to calculate the pseudo-slope distance from the aircraft to the ground DME stations.
The DME on-board measurement device includes: a DME terrestrial transponder and DMEDME on-board interrogator that perform bi-directional interrogation response interactions. The latitude, longitude and altitude of SINS output are respectivelyLambda s and h s, the positions of the ground DME station under the geocentric and geodetic fixed coordinate system are x D、yD and z D, the positions output by the SINS (strapdown inertial navigation system) are x s、ys and z s, and the pseudo-skew l s is calculated according to a pseudo-skew calculation formula in the following manner:
If the DME on-board interrogator transmits an interrogation signal at GNSS signal rejection, at least two DME station DME terrestrial transponder reply signals may be received. Assuming that the DME airborne interrogator can receive the response signals of the DME ground transponders of the two ground DME stations of the DME station 1 and the DME station 2, according to the position information output by the SINS, pseudo-slant distances l s1 and l s2 from the aircraft to the two ground DME stations can be calculated according to the above pseudo-slant distance calculation formula, and then the pseudo-slant distances enter a kalman filter.
The Kalman filter constructs a Kalman filter state space model according to the h a and two slant distance values output by the atmospheric modem, and calculates a measurement value Z entering the Kalman filter as follows: Establishing a state matrix F, a system noise driving matrix G and a measuring matrix H, and obtaining a state equation of a Kalman filter state space model according to a system excitation noise sequence w, a measuring noise sequence v and a state variable X And measurement equationWherein: phi E、φN and phi U represent attitude errors, δv E、δvN and δv U represent velocity errors, δx, δy and δz represent position errors,AndIndicating the drift of the spinning top,AndIndicating the accelerometer zero offset.
Establishing a Kalman filtering state matrix shown in the following formula according to the SINS attitude error equation, the speed error equation and the position error equation:
Wherein:
Map＝M1+M2
Mva＝fn×
Mvp＝(vn×)(2M1+M2)
Wherein: is a strapdown matrix; omega ie is the earth rotation angular velocity; r M and R N are the radii of curvature of the meridian and the mortise circle respectively; v n is speed, v E and v N are northeast and north speeds; The projection of the rotation angular velocity of the earth under a navigation coordinate system; for the projection of the angular velocity of the navigational coordinate system relative to the earth coordinate system under the navigational coordinate system, The projection of the rotation angular velocity of the navigation coordinate system relative to the inertial system under the navigation coordinate system; f n represents the projection of the specific force under the navigational coordinate system; x represents the vector-wise antisymmetric matrix.
In an alternative embodiment, a geographic coordinate system is selected as a navigation coordinate system, and a system noise driving array G shown in the following formula is obtained:
Through a series of mathematical derivations, a measurement matrix H is obtained having the following form:
Where matrix n=pm, where: the matrices P and M are calculated as follows:
Wherein: x D1、yD1 and z D1 are the locations of ground DME station 1; x D2、yD2 and z D2 are the locations of ground DME station 2; e is the elliptical eccentricity.
The estimated value of the 15-dimensional state variable can be obtained at each filtering moment, and only the attitude error, the speed error and the position error can be accurately estimated according to the result obtained by the observability analysis, so that the attitude, the speed and the position of the SINS are corrected by using only the estimated attitude error, the estimated speed error and the estimated position error at the filtering estimation moment, and the navigation error accumulated by the SINS along with time is restrained.
The foregoing describes in detail embodiments of the present invention, which are described herein using specific embodiments, the description of the embodiments being merely intended to aid in the understanding of the methods and apparatus of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (10)
1. A repositioning method of a DME/DME/SINS tightly-integrated navigation system is characterized by comprising the following steps: based on a north-orientation SINS attitude error equation, a speed error equation and a position error equation, establishing a Kalman filtering state equation based on a triaxial attitude error, a northeast-day speed error, a position error, a gyro constant drift and an accelerometer constant zero bias as state variables; calculating a pseudo-slope distance from the aircraft to a DME double station of a range finder according to the SINS calculated position of the strapdown inertial navigation system, forming slope distance measurement information by making a difference between the slope distance measured by the DME airborne measurement equipment and the pseudo-slope distance, and forming height measurement information by making a difference between the height measured by the atmospheric data machine and the height output by the SINS; deducing a conversion relation between measurement information and state variables, and establishing a Kalman filtering measurement equation; SINS navigation solution is carried out according to the measured value output by the inertial device, and navigation parameters are output; under the assistance of two navigation information of DME station position pseudo-slope distance calculation and atmospheric data machine height, real-time estimation of system state variables is realized through a Kalman filter, a feedback correction strategy is adopted, attitude errors, speed errors and position errors are corrected through feedback, SINS navigation errors are corrected in real time, final positions, speeds and attitudes of the aircraft are determined, the establishment of Kalman filtering state equations and measuring equations, calculation of measuring information and Kalman filtering state estimation and feedback correction are integrated, the results of data acquisition, data processing, information fusion and repositioning of a DME/SINS tightly combined navigation system navigation sensor are obtained, SINS attitude, speed and position are corrected through feedback of the estimated attitude, speed and position errors, SINS navigation errors are restrained, and higher-precision navigation information is output.
2. The DME/SINS tight integrated navigation system repositioning method according to claim 1, wherein: the method comprises the steps that an aircraft-mounted GNSS receiver receives the lowest 4 satellite navigation signals, and under the condition that positioning is completed, a strapdown inertial navigation system SINS outputs the position, the speed and the gesture of an aircraft in a loose combined navigation mode.
3. The DME/SINS tightly coupled navigation system repositioning method of claim 2 wherein: when the navigation signals of the satellite 2 and the satellite 4 are refused, namely the satellite is attacked or the signals are artificially interfered, the navigation parameters of the system are calculated and output by means of SINS self navigation.
4. A DME/SINS tightly coupled navigation system relocation method as claimed in claim 3, wherein: if the DME airborne equipment transmits an inquiry signal when the satellite navigation signal is refused and receives response signals of the DME station 1 and the DME station 2, outputting the position, the speed and the attitude of the aircraft in a DME/DME/SINS combined navigation mode, so that backup is provided for aircraft route navigation under the GNSS signal refusing condition.
5. The DME/SINS tight integrated navigation system repositioning method according to claim 1, wherein: the inertial device comprises a gyroscope and an accelerometer, wherein the gyroscope outputs an angular velocityThe accelerometer outputs a specific force angular velocity f b.
6. The DME/SINS tight integrated navigation system repositioning method according to claim 1, wherein: the strapdown inertial navigation system SINS performs navigation calculation according to the output measured value of the inertial device, and comprises attitude calculation, speed calculation and position calculation, and outputs the position, speed and attitude of the aircraft.
7. The DME/SINS tight integrated navigation system repositioning method according to claim 1, wherein: the DME on-board measurement device includes: DME ground transponder and DME airborne interrogator for bidirectional interrogation response interaction, SINS output latitude, longitude and altitude are respectivelyLambda s and h s, the positions of the ground DME station under the geocentric fixed coordinate system are x D、yD and z D, the position information of the DME station is converted into the geocentric fixed coordinate system, the pseudo-skew l s is calculated according to the pseudo-skew calculation formula of the strapdown inertial navigation system SINS output positions are x s、ys and z s as follows:
8. The DME/SINS tightly coupled navigation system repositioning method of claim 7 wherein: the DME airborne interrogator can receive response signals of the two ground DME station ground transponders of the DME station 1 and the DME station 2, then according to the position information output by the SINS, pseudo-slant distances l s1 and l s2 from the aircraft to the two ground DME stations are calculated according to a pseudo-slant distance calculation formula, and the two slant distances l D1 and l D2 of the DME station 1 and the DME station 2 are calculated.
9. The DME/SINS tight integrated navigation system repositioning method according to claim 1, wherein: the Kalman filter constructs a Kalman filter state space model according to the height h a and two slant distance values output by the atmospheric modem, and calculates a measurement value Z entering the Kalman filter as follows:
Establishing a state matrix F, a system noise driving matrix G and a measuring matrix H, and obtaining a state equation of a Kalman filter state space model according to a system excitation noise sequence w, a measuring noise sequence v and a state variable X And measurement equation
Where phi E、φN and phi U represent attitude errors, δv E、δvN and δv U represent velocity errors, δx, δy and δz represent position errors,AndIndicating the drift of the spinning top,AndIndicating the accelerometer zero offset.
10. The DME/SINS tightly coupled navigation system repositioning method of claim 9 wherein: establishing a Kalman filtering state matrix shown as follows according to the SINS attitude error equation, the speed error equation and the position error equation: And is also provided with
Map＝M1+M2,Mva＝fn×
Mvp＝(vn×)(2M1+M2)，
Wherein: Representing latitude; n represents a navigation coordinate system; is a strapdown matrix; omega ie is the earth rotation angular velocity; r M and R N are the radii of curvature of the meridian and the mortise circle respectively; v n is speed, v E and v N are northeast and north speeds; The projection of the rotation angular velocity of the earth under a navigation coordinate system; for the projection of the angular velocity of the navigational coordinate system relative to the earth coordinate system under the navigational coordinate system, The projection of the rotation angular velocity of the navigation coordinate system relative to the inertial system under the navigation coordinate system; f n represents the projection of the specific force under the navigational coordinate system; x represents the vector-wise antisymmetric matrix.
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| CN119255192B (en) * | 2024-10-10 | 2025-10-03 | 中国人民解放军空军工程大学 | A multi-positioning method and system based on time-sharing query |
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