A combined navigation method based on single base station spatial difference

Abstract

The invention discloses a combined navigation method based on single base station spatial difference, comprising the steps of Step 1. converting the longitude, latitude and altitude information of a base station and a system to be combined into xyz coordinates of an earth-centered earth-fixed coordinate system under a GNSS denial condition; Step 2. calculating the distance between the longitude and latitude of the base station and the system to be combined; Step 3. constructing equations of the error of the system to be combined and the error of the ranging system based on the single base station spatial difference; Step 4. solving and obtaining the positioning error of the system to be combined; Step 5. converting the positioning error into longitude and latitude errors to obtain the covariance matrix of the error; Step 6. estimating the error of the system to be combined based on an error propagation model of inertial navigation, embedding the observation covariance matrix, and realizing combined navigation; the method can effectively suppress the error of the inertial navigation system by introducing inertial navigation information, reducing the requirement on the number of base stations, and has the characteristics of low cost and high reliability.

Description

Technical Field

[0001] The present invention relates to the technical field of navigation precise speed measurement and positioning, and in particular to a combined navigation method based on single base station spatial difference. Background Art

[0002] Navigation technology is a technology that can provide different platforms such as vehicles, ships and aircraft with relevant motion status information such as position, speed, attitude and time during movement. Due to its close relationship with the safety of different military and civilian carriers in completing specific tasks, navigation technology has become one of the key research areas in recent years.

[0003] At present, manned-unmanned collaborative systems mainly rely on GNSS navigation signals to achieve relative positioning functions, thereby forming the ability of manned-unmanned systems to collaboratively complete common tasks; however, given the technical disadvantages of GNSS navigation signals in terms of concealment, stability and anti-interference, exploring the relative positioning solution of manned-unmanned collaborative systems in a GNSS navigation signal denial environment has become one of the technical problems that urgently need to be solved in military applications in various countries around the world at present and in the future.

[0004] Although the inertial navigation system has become an essential navigation system for most moving vehicles due to its advantages such as complete autonomy and all-weather operation, its method based on dead reckoning will inevitably cause the navigation error to increase with the working time, making it difficult to meet the high-precision navigation requirements when working alone for a long time.

[0005] Therefore, in order to meet the needs of long-duration and high-precision navigation, designers need to seek a combination of other navigation systems and inertial navigation systems; at this stage, the dynamic-to-dynamic relative positioning can refer to the existing GNSS satellite positioning principles and models; GNSS single-point positioning adopts the principle of three-sphere intersection method, and measures the distance from the receiver to multiple satellites through navigation signals, and then calculates the satellite position in combination with the ephemeris to determine the position of the receiver; each member is equipped with a special transceiver, broadcasts continuous information, receives response information from other members to complete ranging, and broadcasts response information after receiving information broadcast by other members; the distance between the two receivers is determined by the time difference between the transmission and return of the ranging signal, and at the same time, each member will broadcast the distance information measured by itself and all other members; through this mechanism, each member can know the distance information between each member, thereby completing relative positioning;

[0006] Based on the principle of moving-to-moving positioning, it is known that if the relative positioning of a three-dimensional space carrier is to be achieved, no less than three mobile base stations are required; this conflicts with the safety and economy in military and civil applications. In addition, the lack of attitude information in the multi-base station solution is not conducive to the acquisition of control information for the platform;

[0007] Therefore, how to achieve high-precision and long-duration navigation based on a single base station under GNSS denial conditions is one of the technical challenges that urgently needs to be solved in current relative navigation applications. Summary of the invention

[0008] In view of the above-mentioned problems, the present invention aims to provide a combined navigation method based on single base station spatial difference. This method aims at the relative positioning problem of a single base station under GNSS denial conditions in relative navigation. By introducing inertial navigation information, the error suppression of the inertial navigation system can be effectively achieved, and the requirement on the number of base stations is effectively reduced. It has the characteristics of low cost and high reliability.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0010] A combined navigation method based on single base station spatial difference, comprising the steps of

[0011] Step 1. Under GNSS denial conditions, convert the longitude, latitude and altitude information of the base station and the system to be combined into the xyz coordinates of the Earth-centered Earth-fixed coordinate system;

[0012] Step 2. Calculate the distance between the base station and the longitude and latitude of the system to be combined in the xyz coordinate system of the Earth-centered Earth-fixed coordinate system;

[0013] Step 3. After obtaining the distance between the base station and the longitude and latitude of the system to be combined, the equation of the error of the system to be combined and the error of the ranging system is constructed based on the single base station spatial difference method;

[0014] Step 4. Based on the equation of the error of the system to be combined and the error of the ranging system, solve and obtain the positioning error of the system to be combined;

[0015] Step 5. Convert the calculated positioning error into longitude and latitude error and obtain the error covariance matrix;

[0016] Step 6. Based on the error propagation model of inertial navigation, embed the observation covariance matrix to estimate the error of the system to be combined and realize integrated navigation.

[0017] Preferably, the process of converting the longitude, latitude and altitude information of the base station and the system to be combined into the xyz coordinates of the earth-centered earth-fixed coordinate system described in step Step 1 includes:

[0018] Step 101. Assume that the algebraic relationship between the xyz coordinate system based on the WGS84 reference ellipsoid and the Earth-centered Earth-fixed coordinate system is as follows:

[0019]

[0020] In equation (4), x, y, and z are the xyz values ​​of the Earth-centered Earth-fixed coordinate system, and RN is the radius of curvature of the ellipsoid at the location of the carrier, h is the height of the ellipsoid, L is the geographic latitude of the location of the carrier, λ is the geographic longitude of the location of the carrier, and e is the eccentricity of the WGS84 reference ellipsoid;

[0021] Step 102. Convert the latitude, longitude and altitude of the base station using formula (4) to obtain the real-time geocentric coordinates of the base station. and the Earth-centered Earth-fixed coordinate system of the system to be combined with errors

[0022] Preferably, the process of calculating the distance between the base station and the longitude and latitude of the system to be combined in step 2 includes:

[0023] Based on the xyz coordinate result of the earth-centered earth-fixed system converted in step 102, the distance between the base station and the system to be combined based on the coordinate value can be calculated as follows:

[0024]

[0025] Wherein, formula (5) is the distance calculation result including the positioning error of the inertial navigation system, and the definition of the variables is the same as that in step 1.

[0026] Preferably, the process of constructing the equation of the system error to be combined and the ranging system error based on the single base station spatial difference in step 3 includes:

[0027] Step 301. Define the positioning error of the system to be combined as follows:

[0028]

[0029] Among them, x k ,y k ,z k is the true value of the coordinates of the system to be combined at the kth sampling moment, δx k ,δy k ,δz k is the positioning error;

[0030] Step 302. Substitute the above formula into Step 2 and define

[0031]

[0032] Step 303. Available

[0033]

[0034] Expand both ends of the above equation and define the distance between the mobile base station and the system to be combined

[0035]

[0036] Available,

[0037]

[0038] That is, the equation of the system error to be combined and the ranging system error is obtained.

[0039] Preferably, the process of calculating and obtaining the positioning error of the system to be combined in step 4 includes:

[0040] Step 401. In the update cycle of the adjacent 6 ranging systems, the positioning error of the combined system remains unchanged, then the following can be obtained based on the result of Step 3:

[0041]

[0042] Subtracting (1) from (2), (3) from (4), and (5) from (6) from the above equations will give us three equations, which can be rearranged to get:

[0043]

[0044] Step 402. Define the coefficient matrix

[0045]

[0046]

[0047] Step 403. By inverting the matrix, the error estimate is as follows:

[0048]

[0049] in, is the error estimate, T is the transpose of the matrix, is the inverse matrix of the coefficient matrix.

[0050] Preferably, the specific process of converting the positioning error into longitude and latitude errors and obtaining the covariance matrix of the position error by calculation in step 5 includes:

[0051] Step 501. Obtain the xyz coordinate error estimate and the included error estimate of the system to be combined from step 403, and obtain the estimate of the true value of the coordinates as follows:

[0052]

[0053] The formula for converting the xyz coordinate system to longitude and latitude is as follows:

[0054]

[0055] Among them, in formula (17), x, y and z are the xyz values ​​of the Earth-centered Earth-fixed coordinate system, R N is the radius of curvature of the ellipsoid at the location of the carrier, h is the height of the ellipsoid, L is the geographic latitude of the location of the carrier, λ is the geographic longitude of the location of the carrier, and e is the eccentricity of the WGS84 reference ellipsoid;

[0056] Step 502. Obtain the longitude, latitude and altitude of the system to be combined after compensation by using the xyz coordinate system to longitude and latitude formula, and obtain the longitude and latitude errors by subtracting the position information of the system to be combined before compensation as follows:

[0057]

[0058] Among them, in formula (18), L k ,λ k is the longitude and latitude of the system to be combined at the kth sampling time before error compensation, The longitude and latitude of the system to be combined at the kth sampling moment after error compensation;

[0059] Step 503. Assume that the ranging result obtained by the ranging system obeys Gaussian distribution, that is

[0060]

[0061] Then the covariance matrix of the xyz error estimate is as follows:

[0062]

[0063] The variance of the longitude error is given by:

[0064]

[0065] Where D(·) is the variance of the random variable;

[0066] The variance of the latitude error is given by:

[0067]

[0068] Preferably, the error propagation model based on inertial navigation described in step 6 embeds the observation covariance matrix to estimate the error of the system to be combined, and the process of realizing combined navigation includes:

[0069] Step 601. Based on the variance of the longitude and latitude errors obtained in step 5, assume that the observation value of the navigation system to be combined is

[0070]

[0071] Then, the observation noise covariance matrix

[0072]

[0073] Then the observation matrix

[0074]

[0075] Step 602. Time update using the formula:

[0076]

[0077] In equation (26), Φ is the discretization matrix of matrix F, the discretization period is the filter update period, and Q k is the covariance matrix of the process noise, which is determined by the random errors of the inertial measurement elements of the combined system, P k-1 is the covariance matrix of the state estimation deviation at time k-1, is the estimated value of the system state at time k, P k，k-1 is its covariance matrix;

[0078] Step 603. Observation update using the formula:

[0079]

[0080] Among them, in formula (27), is the estimated value of the system state at time k, P k，k-1 is its covariance matrix; is the estimated value of the state at time k, P k K is the covariance matrix of the state estimation deviation at time k; k is the Kalman filter gain.

[0081] The beneficial effects of the present invention are as follows: the present invention discloses a combined navigation method based on single base station spatial difference. Compared with the prior art, the improvements of the present invention are as follows:

[0082] (1) In view of the problem that the error of the inertial navigation system cannot be suppressed when the base station cannot meet the minimum base station number requirement under GNSS denial conditions in relative navigation, the present invention proposes a combined navigation method based on single base station spatial difference under GNSS denial conditions. By introducing inertial navigation information, the error suppression of the inertial navigation system can be effectively achieved, the requirement on the number of base stations is effectively reduced, and the method has the advantages of low cost and high reliability.

[0083] (2) The combined navigation method based on single-base station spatial difference can realize the inertial navigation system error suppression function under GNSS denial conditions, thereby improving the long-term stability and navigation accuracy of the combined system, thereby solving the problem that the positioning error of the inertial navigation system of vehicles, ships and aircraft increases with the working time;

[0084] (3) This method only requires a single base station based on the time-space difference method to achieve error suppression of the inertial navigation system, which effectively reduces the number of base stations required, can effectively reduce the cost of the entire system and increase the reliability of the system;

[0085] (4) In situations where the concealment of the system is required to be high (for example, cluster / swarm drones in military applications), the single base station solution described in the present invention can effectively reduce the probability of the combined platform being discovered by the enemy and can effectively improve the security of the system's mission-performing devices;

[0086] (5) The principle of the single-base station combined navigation system based on the spatial difference method adopted in the present invention has a certain degree of universality, and the implementation process is based on the iterative recursive form, which is conducive to computer application; and the numerical calculations of the calculation process are all based on the matrix form, the calculation form is simple, easy to promote and apply, and has good engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 The figure is an algorithm flow chart of the combined navigation method based on single base station spatial difference of the present invention.

[0088] Figure 2 This is a schematic diagram of the rolling angle errors before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0089] Figure 3 This is a schematic diagram of the pitch angle errors before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0090] Figure 4 This is a schematic diagram of the heading angle errors before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0091] Figure 5 This is a schematic diagram of the north velocity error before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0092] Figure 6 This is a schematic diagram of the eastward velocity error before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0093] Figure 7 This is a schematic diagram of the latitude errors before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0094] Figure 8 This is a schematic diagram of the longitude errors before and after the inertial navigation system to be combined in Example 2 of the present invention.

[0095] Among them: Figure 2 In the figure, Figure (a) is a schematic diagram of the roll angle error before the combination, and Figure (b) is a schematic diagram of the roll angle error after the combination;

[0096] exist Figure 3 In the figure, Figure (a) is a schematic diagram of the pitch angle error before the combination, and Figure (b) is a schematic diagram of the pitch angle error after the combination;

[0097] exist Figure 4 In the figure, Figure (a) is a schematic diagram of the heading angle error before the combination, and Figure (b) is a schematic diagram of the heading angle error after the combination;

[0098] exist Figure 5 In the figure, Figure (a) is a schematic diagram of the north velocity error before the combination, and Figure (b) is a schematic diagram of the north velocity error after the combination;

[0099] exist Figure 6 In the figure, (a) is a schematic diagram of the eastward velocity error before the combination, and (b) is a schematic diagram of the eastward velocity error after the combination;

[0100] exist Figure 7 In the figure, Figure (a) is a schematic diagram of the latitude error before the combination, and Figure (b) is a schematic diagram of the latitude error after the combination;

[0101] exist Figure 8 In the figure, Figure (a) is a schematic diagram of the longitude error before the combination, and Figure (b) is a schematic diagram of the longitude error after the combination. DETAILED DESCRIPTION

[0102] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0103] The basic principles of this method are:

[0104] Embodiment 1: refer to the attached Figure 1 The combined navigation method based on single base station spatial difference shown in the figure comprises the steps of

[0105] First, in this embodiment, in order to facilitate the description of the implementation process of the combined navigation method based on single base station spatial difference under GNSS denial conditions, the navigation error propagation model and related definitions of the system to be combined are given:

[0106] The inertial navigation system navigation error propagation model used in the method described in this embodiment is as follows:

[0107]

[0108] Among them, in formula (1),

[0109] x=[φ E φ N φ U δV E δV N δL δλ] T (2)

[0110] ω n =[ε E ε N ε U ▽ E ▽ N 0 0] T (3)

[0111] In equations (2) and (3), φ E is the pitch angle error, φ N is the roll angle error, φ U is the heading angle error, δV E is the eastward velocity error, δV N is the north velocity error, δL is the latitude error, δλ is the longitude error, ▽ E is the equivalent east angular velocity meter error, ▽ N is the equivalent north accelerometer error, ε E is the equivalent east gyro error, ε N is the equivalent north gyro error, ε U is the equivalent azimuth gyro error:

[0112]

[0113] In the above formula, ω ie is the Earth's rotation angular velocity, L is the geographic latitude of the carrier's location, g is the gravitational acceleration, R M R is the radius of curvature of the meridian at the carrier location. N is the radius of curvature of the circle at the position of the carrier, v E is the eastward velocity, v N is the north velocity, h is the ellipsoid height, f E is the eastward specific force component, f N is the north specific force component, f U It is the weight of the force in the direction of the sky;

[0114] The purpose of the combined navigation method is to find an auxiliary system that is not homogeneous with the inertial navigation system, and to seek characteristics that navigation information such as position, velocity or attitude does not diverge over time, so as to damp the inertial navigation system, and to achieve error estimation of the inertial navigation system by designing a reasonable combined navigation method, so as to achieve the longitude improvement of the position, velocity and attitude of the corrected combined navigation system;

[0115] The ranging information provided by the single-base station ranging system is only related to the designed ranging principle, carrier wavelength, measurement environment and other characteristics. Since it is independent of the measurement time, it meets the requirement of non-homogeneity with the inertial navigation system error and can be used as an external damping information source for the inertial navigation system.

[0116] Step 1. Under GNSS denial conditions, convert the longitude, latitude and altitude information of the base station and the system to be combined into the xyz coordinates of the Earth-centered Earth-fixed coordinate system;

[0117] Step 2. Calculate the distance between the base station and the longitude and latitude of the system to be combined in the xyz coordinate system of the Earth-centered Earth-fixed coordinate system;

[0118] Step 3. After obtaining the distance between the base station and the longitude and latitude of the system to be combined, the equation of the error of the system to be combined and the error of the ranging system is constructed based on the single base station spatial difference method;

[0119] Step 4. Based on the equation of the error of the system to be combined and the error of the ranging system, solve and obtain the positioning error of the system to be combined;

[0120] Step 5. Convert the calculated positioning error into longitude and latitude error and obtain the error covariance matrix;

[0121] Step 6. Based on the error propagation model of inertial navigation, embed the observation covariance matrix to estimate the error of the system to be combined and realize integrated navigation.

[0122] Preferably, the principle of converting the longitude, latitude and altitude information of the base station and the system to be combined into the xyz coordinates of the earth-centered earth-fixed coordinate system described in step Step 1 is that the system to be combined can obtain the longitude, latitude and altitude information of the base station by demodulating the ranging message, and the system to be combined is equipped with an inertial navigation system, which can obtain the longitude, latitude and altitude information containing errors through inertial navigation solution based on historical navigation information, and the specific process includes:

[0123] Step 101. Assume that the algebraic relationship between the xyz coordinate system based on the WGS84 reference ellipsoid and the Earth-centered Earth-fixed coordinate system is as follows:

[0124]

[0125] In equation (4), x, y, and z are the xyz values ​​of the Earth-centered Earth-fixed coordinate system, and R N is the radius of curvature of the ellipsoid at the location of the carrier, h is the height of the ellipsoid, L is the geographic latitude of the location of the carrier, λ is the geographic longitude of the location of the carrier, and e is the eccentricity of the WGS84 reference ellipsoid;

[0126] Step 102. Convert the latitude, longitude and altitude of the base station using formula (4) to obtain the real-time geocentric coordinates of the base station. and the Earth-centered Earth-fixed coordinate system of the system to be combined with errors

[0127] Preferably, the process of calculating the distance between the base station and the longitude and latitude of the system to be combined in step 2 includes:

[0128] Step 201. Based on the xyz coordinate result of the earth-centered earth-fixed system converted in step Step 102, the distance between the base station and the system to be combined based on the coordinate value can be calculated as follows:

[0129]

[0130] The above formula is the distance calculation result including the positioning error of the inertial navigation system, and the definition of the variables is the same as that in step 1.

[0131] Preferably, the principle of constructing the equation of the system error to be combined and the ranging system error based on the single base station spatial difference in step 3 includes: is the positioning result of the system to be combined, which contains positioning and navigation errors. Therefore, it is necessary to combine the result of step 2 with the relationship between the distance information between the mobile base station and the system to be combined obtained by the ranging system to obtain the error estimation value in the result to be combined. The specific process is:

[0132] Step 301. Define the positioning error of the system to be combined as follows:

[0133]

[0134] Among them, x k ,y k ,z k is the true value of the coordinates of the system to be combined at the kth sampling moment, δx k ,δy k ,δz k is the positioning error;

[0135] Step 302. Substitute the above formula into Step 201 and define

[0136]

[0137] Step 303. It can be obtained.

[0138]

[0139] Expand both ends of the above equation and define the distance between the mobile base station and the system to be combined

[0140]

[0141] Available

[0142]

[0143] That is, the equation of the system error to be combined and the ranging system error is obtained.

[0144] Preferably, the process of calculating and obtaining the positioning error of the system to be combined in step 4 includes:

[0145] Step 401. Since the update rate of the ranging system is high and the short-term positioning accuracy of the inertial navigation system is high, this embodiment assumes that the positioning error of the system to be combined remains unchanged within the update cycles of the adjacent 6 ranging systems. Based on the result of Step 3, the following can be obtained recursively:

[0146]

[0147] Subtracting (1) from (2), (3) from (4), and (5) from (6) from the above equations will give us three equations, which can be rearranged to get:

[0148]

[0149] Step 402. Define the coefficient matrix

[0150]

[0151]

[0152] Step 403. By inverting the matrix, the error estimate is as follows:

[0153]

[0154] Among them, in formula (15), is the error estimate, T is the transpose of the matrix, is the inverse matrix of the coefficient matrix.

[0155] Preferably, the specific process of converting the positioning error into longitude and latitude errors and obtaining the covariance matrix of the position error by calculation in Step 5 includes:

[0156] Step 501. Obtain the xyz coordinate error estimate and the included error estimate of the system to be combined from step 403, and obtain the estimate of the true value of the coordinates as follows:

[0157]

[0158] The formula for converting the xyz coordinate system to longitude and latitude is as follows:

[0159]

[0160] Among them, in formula (17), x, y and z are the xyz values ​​of the Earth-centered Earth-fixed coordinate system, RN is the radius of curvature of the ellipsoid at the location of the carrier, h is the height of the ellipsoid, L is the geographic latitude of the location of the carrier, λ is the geographic longitude of the location of the carrier, and e is the eccentricity of the WGS84 reference ellipsoid;

[0161] Step 502. The latitude, longitude and altitude of the system to be combined after compensation can be obtained by converting the xyz coordinate system to the longitude and latitude formula. The longitude and latitude errors can be obtained by subtracting the position information of the system to be combined before compensation as follows:

[0162]

[0163] Among them, in formula (18), L k ,λ k is the longitude and latitude of the system to be combined at the kth sampling time before error compensation, The longitude and latitude of the system to be combined at the kth sampling moment after error compensation;

[0164] Step 503. Assume that the ranging result obtained by the ranging system obeys Gaussian distribution, that is

[0165]

[0166] Then the covariance matrix of the xyz error estimate is as follows:

[0167]

[0168] The variance of the longitude error is given by:

[0169]

[0170] Where D(·) is the variance of the random variable;

[0171] The variance of the latitude error is given by:

[0172]

[0173] Preferably, the error propagation model based on inertial navigation described in step 6 embeds the observation covariance matrix to estimate the error of the system to be combined, and the process of realizing integrated navigation includes:

[0174] Step 601. Based on the variance of the longitude and latitude errors obtained in step 5, assume that the observation value of the navigation system to be combined is

[0175]

[0176] Then, the observation noise covariance matrix

[0177]

[0178] Then the observation matrix

[0179]

[0180] Step 602. Time update using the formula:

[0181]

[0182] In equation (26), Φ is the discretization matrix of matrix F, the discretization period is the filter update period, and Q k is the covariance matrix of the process noise, which is determined by the random errors of the inertial measurement elements of the combined system, P k-1 is the covariance matrix of the state estimation deviation at time k-1, is the estimated value of the system state at time k, P k，k-1 is its covariance matrix;

[0183] Step 603. Observation update using the formula:

[0184]

[0185] Among them, in formula (27), is the estimated value of the system state at time k, P k，k-1 is its covariance matrix; is the estimated value of the state at time k, P k K is the covariance matrix of the state estimation deviation at time k; k is the Kalman filter gain.

[0186] Preferably, the basic principle of the combined navigation method based on single base station spatial difference described in this embodiment is: taking into account that the single base station error realizes three-dimensional position solution through a single moment, this embodiment proposes a method for solving the position error of the system to be combined based on spatial difference based on the short-time high-precision characteristics of the inertial navigation system included in the system to be combined, assuming that the error is unchanged in a short time, and based on the spatial difference at different times combined with the high-precision characteristics of the ranging system. In order to achieve high-precision combined navigation, a method for calculating the position error covariance matrix is ​​proposed while solving the system position error, and a combined navigation method based on the embedded observation covariance matrix is ​​constructed based on the inertial navigation error propagation model.

[0187] Example 2: To verify the effectiveness of the combined navigation method based on single base station spatial difference described in Example 1, the initial conditions of the simulation test are as follows:

[0188] The initial attitude, velocity and position errors of the inertial navigation system (elevation depends on other elevation information sources, this simulation only considers horizontal velocity and position errors) equipped with the integrated navigation system are 0, the gyroscope constant zero bias is 0.1° / h, the random error is 0.1° / h (1s average), the accelerometer constant zero bias is 100ug, the random error is 100ug (1s average), the update rate of the ranging system is 1Hz, the ranging accuracy is 5m (standard deviation), the update rate of the integrated navigation is iterative update, and the update period is 4 seconds. The simulation results are shown in the figure below. Figure 2-Figure 8 shown.

[0189] pass Figure 2-Figure 8 From the simulation results, it can be seen that: compared with the navigation information output of the inertial navigation system, after the inertial navigation systems to be combined are combined by the combined navigation method based on single base station spatial difference described in the present invention, the roll angle, pitch angle, heading angle, north speed, east speed, latitude and longitude errors output by the combined system are all reduced, further improving the accuracy and reliability of the output parameters of the navigation system, indicating that the method can effectively realize the error suppression of the inertial navigation system, thereby improving the long-term stability and navigation accuracy of the combined system.

[0190] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A combined navigation method based on single base station spatial difference, characterized in that: Included steps Step 1. Under GNSS denial conditions, convert the longitude, latitude and altitude information of the base station and the system to be combined into the xyz coordinates of the Earth-centered Earth-fixed coordinate system; Step 2. Calculate the distance between the base station and the longitude and latitude of the system to be combined in the xyz coordinate system of the Earth-centered Earth-fixed coordinate system; Step 3. After obtaining the distance between the base station and the longitude and latitude of the system to be combined, the equation of the error of the system to be combined and the error of the ranging system is constructed based on the single base station spatial difference method; Step 4. Based on the equation of the error of the system to be combined and the error of the ranging system, solve and obtain the positioning error of the system to be combined; Step 5. Convert the calculated positioning error into longitude and latitude error and obtain the error covariance matrix; The specific process of converting the positioning error into longitude and latitude errors and obtaining the covariance matrix of the position error by calculation includes: Step 501. Obtain the xyz coordinate error estimate and the included error estimate of the system to be combined from step 403, and obtain the estimate of the true value of the coordinates as follows: The formula for converting the xyz coordinate system to longitude and latitude is as follows: Among them, in formula (17), x, y and z are the xyz values ​​of the Earth-centered Earth-fixed coordinate system, R N is the radius of curvature of the ellipsoid at the location of the carrier, h is the height of the ellipsoid, L is the geographic latitude of the location of the carrier, λ is the geographic longitude of the location of the carrier, and e is the eccentricity of the WGS84 reference ellipsoid; Step 502. Obtain the longitude, latitude and altitude of the system to be combined after compensation by using the xyz coordinate system to longitude and latitude formula, and obtain the longitude and latitude errors by subtracting the position information of the system to be combined before compensation as follows: Among them, in formula (18), L k ,λ k is the longitude and latitude of the system to be combined at the kth sampling time before error compensation, The longitude and latitude of the system to be combined at the kth sampling moment after error compensation; Step 503. Assume that the ranging result obtained by the ranging system obeys Gaussian distribution, that is Then the covariance matrix of the xyz error estimate is as follows: The variance of the longitude error is given by: Where D(·) is the variance of the random variable; The variance of the latitude error is given by: Step 6. Based on the error propagation model of inertial navigation, embed the observation covariance matrix to estimate the error of the system to be combined and realize integrated navigation; The error propagation model based on inertial navigation embeds the observation covariance matrix to estimate the error of the system to be combined, and the process of realizing integrated navigation includes: Step 601. Based on the variance of the longitude and latitude errors obtained in step 5, assume that the observation value of the navigation system to be combined is Then, the observation noise covariance matrix Then the observation matrix Step 602. Time update using the formula: In equation (26), Φ is the discretization matrix of matrix F, the discretization period is the filter update period, and Q k is the covariance matrix of the process noise, which is determined by the random errors of the inertial measurement elements of the combined system, P k-1 is the covariance matrix of the state estimation deviation at time k-1, is the estimated value of the system state at time k, P k，k-1 is its covariance matrix; Step 603. Observation update using the formula: Among them, in formula (27), is the estimated value of the system state at time k, P k，k-1 is its covariance matrix; is the estimated value of the state at time k, P k K is the covariance matrix of the state estimation deviation at time k; k is the Kalman filter gain.

2. The integrated navigation method based on single base station spatial difference according to claim 1, characterized in that: The process of converting the longitude, latitude and altitude information of the base station and the system to be combined into the xyz coordinates of the earth-centered earth-fixed coordinate system as described in step 1 includes: Step 101. Assume that the algebraic relationship between the xyz coordinate system based on the WGS84 reference ellipsoid and the Earth-centered Earth-fixed coordinate system is as follows: In equation (4), x, y, and z are the xyz values ​​of the Earth-centered Earth-fixed coordinate system, and R N is the radius of curvature of the ellipsoid at the location of the carrier, h is the height of the ellipsoid, L is the geographic latitude of the location of the carrier, λ is the geographic longitude of the location of the carrier, and e is the eccentricity of the WGS84 reference ellipsoid; Step 102. Convert the latitude, longitude and altitude of the base station using formula (4) to obtain the real-time geocentric coordinates of the base station. and the Earth-centered Earth-fixed coordinate system of the system to be combined with errors 3. The integrated navigation method based on single base station spatial difference according to claim 2, characterized in that: The process of calculating the distance between the base station and the longitude and latitude of the system to be combined in step 2 includes: Based on the xyz coordinate result of the earth-centered earth-fixed system converted in step 102, the distance between the base station and the system to be combined based on the coordinate value can be calculated as follows: Wherein, formula (5) is the distance calculation result including the positioning error of the inertial navigation system, and the definition of the variables is the same as that in step 1.

4. The integrated navigation method based on single base station spatial difference according to claim 3, characterized in that: The process of constructing the equation of the system error to be combined and the ranging system error based on the single base station spatial difference described in step 3 includes: Step 301. Define the positioning error of the system to be combined as follows: Among them, x k ,y k ,z k is the true value of the coordinates of the system to be combined at the kth sampling moment, δx k ,δy k ,δz k is the positioning error; Step 302. Substitute the above formula into Step 2 and define Step 303. Available Expand both ends of the above equation and define the distance between the mobile base station and the system to be combined Available, That is, the equation of the system error to be combined and the ranging system error is obtained.

5. The integrated navigation method based on single base station spatial difference according to claim 4, characterized in that: The process of solving and obtaining the positioning error of the system to be combined described in step 4 includes: Step 401. In the update cycle of the adjacent 6 ranging systems, the positioning error of the combined system remains unchanged, then the following can be obtained based on the result of Step 3: Subtracting (1) from (2), (3) from (4), and (5) from (6) from the above equations will give us three equations, which can be rearranged to get: (12) Step 402. Define the coefficient matrix Step 403. By inverting the matrix, the error estimate can be obtained as follows: in, is the error estimate, T is the transpose of the matrix, is the inverse matrix of the coefficient matrix.

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