Performance evaluation method of SINS / DME / DME integrated navigation system

Abstract

The invention discloses a SINS / DME / DME integrated navigation system performance evaluation method, comprising: according to the state equation and measurement equation of the SINS / DME / DME integrated navigation system, a slant range calculated by position solution of a strapdown inertial navigation system (SINS) and slant range data measured by a distance meter (DME) are combined and a Kalman filter algorithm is adopted for fusion, specifically comprising two parts: time update and measurement update; and an actual navigation performance (ANP) calculation model based on filter covariance is used to evaluate the performance of the SINS / DME / DME integrated navigation system. The invention has the advantages of simple calculation, reliable results, and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated navigation system performance evaluation, in particular to a SINS / DME / DME integrated navigation system performance evaluation method. Background Art

[0002] In recent years, ICAO has vigorously promoted required navigation performance (RNP)-based navigation operations, covering all flight phases from en route and terminal area to approach and landing. This has supported the optimization of airspace structure, the reduction of operational separations, and the improvement of operational efficiency. Actual navigation performance (ANP) is a real-time evaluation indicator of the aircraft's navigation system and serves as a key basis for flight crews to determine whether the navigation system meets RNP requirements during flight.

[0003] Strapdown inertial navigation systems (SINS) boast strong autonomy, minimal interference, high update rates, and a rich set of output parameters. They are widely used in civil aviation and other transportation sectors. However, when used for extended periods, they require additional navigation sources to mitigate the rapid accumulation of dead reckoning errors. Distance measuring equipment (DME) uses interrogation-reply pulse pairs to measure the slant distance between an aircraft and a ground station. Due to its simple structure, ease of use, and mature technology, it is used at numerous airports both domestically and internationally. However, its positioning error approaches 0.2 nautical miles, making it difficult to meet terminal area operations requirements. When the global navigation satellite system (GNSS) signal becomes unreliable, the flight management system (FMS) adopts a degraded navigation mode, prioritizing the more accurate SINS / DME / DME combined navigation mode to output flight management position information. Its accuracy (ANP) is a key indicator in determining whether an aircraft's navigation system meets RNP operational standards.

[0004] Currently, civil airliners, both domestically and internationally, employ an integrated navigation system architecture with the SINS as the reference system and other subsystems as auxiliary systems. The integrated navigation and ANP algorithms within the flight management system are internally packaged, and there are few publicly reported publications. Traditional research has considered integrating SINS with other major auxiliary positioning systems, primarily VORs, to improve navigation performance when GNSS information is unreliable. However, there are few publicly reported studies on SINS / DME / DME integrated navigation, and even fewer studies evaluating the actual navigation performance (ANP) of integrated navigation systems using actual operational procedures. Furthermore, systematic research and validation of ANP calculation theories remain lacking. Summary of the Invention

[0005] In order to solve the problems existing in the prior art, the purpose of the present invention is to provide a SINS / DME / DME integrated navigation system performance evaluation method, which has the advantages of simple calculation and reliable results.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a SINS / DME / DME integrated navigation system performance evaluation method, comprising the following steps:

[0007] Step 1: Based on the state equation and measurement equation of the SINS / DME / DME integrated navigation system, the slant range calculated by the strapdown inertial navigation (SINS) and the slant range data measured by the range finder (DME) are combined using the Kalman filter algorithm. This process includes two parts: time update and measurement update.

[0008] Step 2: Evaluate the performance of the SINS / DME / DME integrated navigation system based on the actual navigation performance ANP calculation model of the filter covariance.

[0009] As a further improvement of the present invention, in step 1, the state equation is specifically as follows:

[0010] X k =F k,k-1 X k-1 +Γ k W k (1)

[0011] In formula (1): X k is the error state at time k, F k / k-1 is the state transition matrix from time k-1 to time k, X k-1 is the error state at the previous moment, Γ k is the noise driving matrix, W k is the system noise matrix; the system state is composed of the SINS misalignment angle, velocity error, position error, gyroscope error and accelerometer error; the 15-dimensional error state of SINS is selected as the state quantity, as follows:

[0012]

[0013] In formula (2): Φ, δv n , δp represent the misalignment angle, velocity error, and position error of SINS in the navigation coordinate system, respectively, and ε b is the projection of the gyroscope zero bias in the carrier coordinate system, is the projection of the accelerometer zero bias in the carrier coordinate system;

[0014] The state transfer matrix F k / k-1It is expressed as follows:

[0015]

[0016] As a further improvement of the present invention, in step 1, the measurement equation is specifically as follows:

[0017] Z k =H k X k +V k (4)

[0018] In formula (4), Z k is the measurement error between the two systems, H k is the measurement matrix, X k is the error state at time k, V k is the measurement noise matrix.

[0019] As a further improvement of the present invention, the step 1 is specifically as follows:

[0020] During the flight, the flight management system calculates the slant range of the aircraft relative to the two DME stations. At the same time, the DME ground station obtains the measured slant range by using a question-and-answer method with the onboard DME antenna. The measurement error of the slant range of a single DME system is expressed as:

[0021] δρ=ρ C -ρ D (5)

[0022] In formula (5), δρ is the slant range error, ρ C is the slant distance calculated by the flight management system based on the inertial navigation position, ρ D Slant range measured for the DME station;

[0023] The slant range ρ measured by the DME station D It can be expressed as the relationship between the true slant range and the DME-related noise:

[0024] ρ D =ρ+δν D (6)

[0025] In formula (6), ρ is the true slant range, δν D is the measurement noise with zero mean value of DME;

[0026] Assume that the aircraft position calculated by SINS during flight is (L P λ P ), use P(L P λ P h P ) represents the position of the aircraft in the geodetic coordinate system, where h PThe altitude of the aircraft is measured by the barometric altimeter; p'(L P λ P 0) represents the vertical projection of the aircraft position calculated by SINS on the ground; D(L D λ D h D ) represents the longitude, latitude and altitude of the DME station in the geodetic coordinate system, D′(L D λ D 0) represents the vertical projection of DME on the ground; ρ C is the slant distance from the DME station to the aircraft position resolved by SINS, S is the arc length from the DME station to the aircraft position resolved by SINS, and R is the standard earth radius;

[0027] Since the application range of the DME station is much smaller than the radius of the earth, the arc length S is approximately a straight line. D λ P 0) is the intersection of P′ and D′ on the longitude and latitude circles. Therefore, the aircraft position calculated by SINS and the projection of the DME station in space are approximately the relationship between the inner sides of the right triangle ΔP′CD′:

[0028] S 2 =P′C 2 +D′C 2 (7)

[0029] Similarly, we can get the slope distance ρ C Relationship with arc length S:

[0030]

[0031] The spatial relationship between the position solved by SINS and the DME station is decomposed in the longitude and latitude directions to obtain the longitude and latitude circle relationship between the solved position and the DME station. At the same time, let P′C = S1 and D′C = S2, and the following relationship is obtained:

[0032] S1=R(L P -L D ) (9)

[0033] S2=R(λ P -λ D )cosL P (10)

[0034] Substituting formula (9) (10) into formula (8) and differentiating it, we can obtain the following differential equation for slope distance:

[0035]

[0036] Combining formula (11) to obtain the relationship between the slant range differential and the longitude and latitude error of the aircraft position, the slant range measurement matrix H of the two DME stations is obtained. i As follows (i=1,2):

[0037]

[0038] Combined with formula (4), we can get the measurement matrix:

[0039]

[0040] For the SINS / DME / DME integrated navigation system, the slant range calculated by the SINS position solution and the slant range data measured by the DME are fused using the Kalman filter algorithm.

[0041] As a further improvement of the present invention, time update includes state update and covariance update:

[0042] X k / k-1 =F k X k-1 / k-1 (14)

[0043]

[0044] As a further improvement of the present invention, the measurement update includes filter gain, state estimation, and variance estimation:

[0045] (1) Filter gain equation:

[0046]

[0047] (2) State estimation equation:

[0048]

[0049] (3) Variance estimation equation:

[0050] P k =(IK k H k )P k / k-1 (18).

[0051] As a further improvement of the present invention, the step 2 is specifically as follows:

[0052] Assume that the positioning error result is a two-dimensional normal distribution of the errors in longitude and latitude, with a mean of E p and variance P p It is expressed as follows:

[0053] E p =[δλ δL] (19)

[0054]

[0055] Where: δλ, δL are the mean errors of longitude and latitude of aircraft navigation, σ λ ,σ L is the error of longitude and latitude, σ λL is the covariance of longitude and latitude errors;

[0056] In the process of solving the ANP, the position relationship in the horizontal rectangular coordinate system is obtained, and the transformation relationship of projecting the geodetic coordinate system into the Earth-centered Earth-fixed coordinate system is as follows:

[0057] Δx=σ λ ·(R N +h)·cos(L) (21)

[0058] Δy=σ L ·(R M +h) (22)

[0059] Where: Δx, Δy are the XY axis errors R in the Earth-centered Earth-fixed coordinate system N is the radius of curvature of the earth's circumplex, h is the altitude of the aircraft, L is the latitude of the aircraft, R M is the radius of curvature of the Earth's meridian;

[0060] Thus, the covariance matrix P in the Earth-centered Earth-fixed coordinate system is obtained xy :

[0061]

[0062] in:

[0063]

[0064] Where: are the variances of Δx and Δy respectively, is the covariance of Δx and Δy;

[0065] Obtain the eigenvalue of equation (23) and obtain the major semi-axis λ of the 1σ error ellipse max and the minor axis λ min , the relationship is as follows:

[0066]

[0067] ANP is determined by the conversion factor K and the major semi-axis λ of the 1σ error ellipse. max Obtain:

[0068] ANP=Kλ max (28)

[0069] The conversion factor K is determined by the flattening of the 1σ error ellipse. The ratio of the major and minor axes of the 1σ error ellipse is:

[0070]

[0071] K is calculated as follows:

[0072]

[0073] In the SINS / DME / DME integrated navigation system, the covariance updated at each step in the filtering algorithm is used as the variance for ANP calculation.

[0074] The beneficial effects of the present invention are:

[0075] Based on the detailed derivation of SINS and DME error models, the present invention builds a SINS / DME / DME integrated navigation implementation framework, clarifies the implementation process, and proposes an ANP calculation model based on filter covariance. The method of the present invention is simple to calculate and has reliable results, which can provide a theoretical basis for RNP operation, flight conflict warning, parallel route planning, etc. Different integrated navigation systems have different ANPs, and the ANP calculation ideas of the present invention can be used to apply to other integrated navigation systems such as GNSS / IRS, SINS / VOR / DEM, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Schematic diagram of the spatial position relationship between the aircraft position calculated by SINS and the DME station in an embodiment of the present invention;

[0077] Figure 2 Schematic diagram of the relationship between the aircraft position calculated by SINS and the longitude and latitude of the DME station in the same meridian according to an embodiment of the present invention;

[0078] Figure 3 Schematic diagram of the relationship between the aircraft position calculated by SINS and the longitude and latitude of the DME station in an embodiment of the present invention;

[0079] Figure 4 It is a diagram of the ZBAD-7D, SID, RNAV, and RWY19R procedures in the embodiment of the present invention;

[0080] Figure 5 Schematic diagram of the horizontal flight trajectory of the DOTRA-11D program in an embodiment of the present invention;

[0081] Figure 6 A schematic diagram of a three-dimensional flight trajectory of the DOTRA-11D program in an embodiment of the present invention;

[0082] Figure 7 Schematic diagram of the change of latitude and longitude errors of inertial navigation in an embodiment of the present invention;

[0083] Figure 8 Schematic diagram of DME measuring slant range error in an embodiment of the present invention;

[0084] Figure 9 A schematic diagram of a combined navigation positioning result according to an embodiment of the present invention;

[0085] Figure 10 is a schematic diagram of the change in slant range error after combined navigation in an embodiment of the present invention;

[0086] Figure 11 Schematic diagram of ANP changes after combined navigation in an embodiment of the present invention. DETAILED DESCRIPTION

[0087] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0088] Example

[0089] A SINS / DME / DME integrated navigation system performance evaluation method includes:

[0090] SINS / DME / DME integrated navigation system evaluation:

[0091] 1. Equation of state:

[0092] The system equations of SINS / DME / DME integrated navigation are described as follows:

[0093] X k =F k,k-1 X k-1 +Γ k W k (1)

[0094] In formula (1): X k is the error state at time k, F k / k-1 is the state transition matrix from time k-1 to time k, X k-1 is the error state at the previous moment, Γ k is the noise driving matrix, W k is the system noise matrix. The system state is composed of the SINS misalignment angle, velocity error, position error, gyroscope error, and accelerometer error. The 15-dimensional error state of the SINS is selected as the state quantity, as follows:

[0095]

[0096] In formula (2): Φ, δv n , δp represent the misalignment angle, velocity error, and position error of SINS in the navigation coordinate system, respectively, and ε b is the projection of the gyroscope zero bias in the carrier coordinate system, is the projection of the accelerometer zero bias in the carrier coordinate system.

[0097] The state transfer matrix F k / k-1 It can be expressed as shown in formula (3):

[0098]

[0099] 2. Measurement equation:

[0100] The measurement equation can be expressed as:

[0101] Z k =H k X k +V k (4)

[0102] In formula (4), Z k is the measurement error between the two systems, H k is the measurement matrix, X k is the error state at time k, V k is the measurement noise matrix.

[0103] During flight, the flight management system calculates the aircraft's slant range relative to the two DME stations. Simultaneously, the DME ground station uses a question-and-answer method to obtain the measured slant range from the aircraft's DME antenna. The measurement error of the slant range of a single DME system can be expressed as:

[0104] δρ=ρ C -ρ D (5)

[0105] In formula (5), δρ is the slant range error, ρ C is the slant distance calculated by the flight management system based on the position solved by the inertial navigation, ρ D The slant range measured by the DME station.

[0106] The slant range ρ measured by the DME station D It can be expressed as the relationship between the true slant range and the DME-related noise:

[0107] ρ D =ρ+δν D (6)

[0108] In formula (6), ρ is the true slant range, δν D is the measurement noise with zero mean value for DME.

[0109] Assume that the aircraft position calculated by SINS during the flight is (L P λ P ), use P(L P λ P h P) represents the position of the aircraft in the geodetic coordinate system, where h P The altitude of the aircraft is measured by the pressure altimeter. P λ P 0) represents the vertical projection of the aircraft position calculated by SINS on the ground. D λ D h D ) represents the longitude, latitude and altitude of the DME station in the geodetic coordinate system, D′(L D λ D 0) represents the vertical projection of DME on the ground. C is the slant distance from the DME station to the aircraft position resolved by SINS, S is the arc length from the DME station to the aircraft position resolved by SINS, and R is the standard earth radius. The relationship between the aircraft position resolved by SINS and the approximate spherical space position of the DME station is as follows: Figure 1 shown.

[0110] Since the application range of the DME station is much smaller than the radius of the earth, the arc length S is approximately a straight line. D λ P 0) is the intersection of P′ and D′ on the longitude and latitude circles. Therefore, the aircraft position calculated by SINS and the projection of the DME station in space are approximately the relationship between the inner sides of the right triangle ΔP′CD′:

[0111] S 2 =P′C 2 +D′C 2 (7)

[0112] Similarly, the slant distance ρ can be obtained C Relationship with arc length S:

[0113]

[0114] Decompose the spatial position relationship between the SINS solution position and the DME station in the longitude and latitude directions to obtain the longitude and latitude circle relationship between the solution position and the DME station, and set P'C = S1, D'C = S2. Figure 2 、 Figure 3 The following relationship is obtained:

[0115] S1=R(L P -L D ) (9)

[0116] S2=R(λ P -λ D )cosL P (10)

[0117] Substituting formula (9) (10) into formula (8) and differentiating it, we can obtain the following differential equation for slope distance:

[0118]

[0119] Combining formula (11) to obtain the relationship between the slant range differential and the longitude and latitude error of the aircraft position, the slant range measurement matrix H of the two DME stations can be obtained. i As follows (i=1,2):

[0120]

[0121] Combining formula (4) we can get the measurement matrix:

[0122]

[0123] For the SINS / DME / DME integrated navigation system, the slant range calculated by the SINS position solution and the slant range data measured by the DME are fused using the Kalman filter algorithm. The algorithm mainly includes two parts: time update and measurement update.

[0124] Time updates include state updates and covariance updates:

[0125] X k / k-1 =F k X k-1 / k-1 (14)

[0126]

[0127] Measurement updates include filter gain, state estimation, and variance estimation:

[0128] (1) Filter gain equation:

[0129]

[0130] (2) State estimation equation:

[0131]

[0132] (3) Variance estimation equation:

[0133] P k =(IK k H k )P k / k-1 (18)

[0134] 3. Actual Navigation Performance (ANP):

[0135] The actual navigation performance is described by the horizontal lateral position error circle under 95% probability. Under different navigation modes, the solution method of the actual navigation performance ANP is different.

[0136] During the flight, there will be errors in various navigation systems on the aircraft. When considering ANP calculation, it is assumed that the positioning error result is a two-dimensional normal distribution of errors in longitude and latitude, with a mean of E p and variance P p It is expressed as follows:

[0137] E p =[δλ δL] (19)

[0138]

[0139] Where: δλ, δL are the mean errors of longitude and latitude of aircraft navigation, σ λ ,σ L is the error of longitude and latitude, σ λL is the covariance of the longitude and latitude errors.

[0140] In the process of solving ANP, it is necessary to obtain the position relationship in the horizontal rectangular coordinate system and the transformation relationship of projecting the geodetic coordinate system into the Earth-centered Earth-fixed coordinate system, as shown below:

[0141] Δx=σ λ ·(R N +h)·cos(L) (21)

[0142] Δy=σ L ·(R M +h) (22)

[0143] Where: Δx, Δy are the XY axis errors R in the Earth-centered Earth-fixed coordinate system N is the radius of curvature of the earth's circumplex, h is the altitude of the aircraft, L is the latitude of the aircraft, R M is the radius of curvature of the Earth's meridian.

[0144] The covariance matrix P in the Earth-centered Earth-fixed coordinate system can be obtained xy :

[0145]

[0146] in:

[0147]

[0148] Where: are the variances of Δx and Δy respectively, is the covariance of Δx and Δy.

[0149] Obtain the eigenvalue of equation (23) and obtain the major semi-axis λ of the 1σ error ellipse max and the minor axis λ min, the relationship is as follows:

[0150]

[0151] ANP can be obtained by the conversion factor K and the major semi-axis λ of the 1σ error ellipse. max Obtain:

[0152] ANP=Kλ max (28)

[0153] The conversion factor K can be determined by the flattening of the 1σ error ellipse. The ratio of the major and minor axes of the 1σ error ellipse is:

[0154]

[0155] K can be calculated as follows:

[0156]

[0157] In the SINS / DME / DME integrated navigation system, the covariance updated at each step in the filtering algorithm can be used as the variance for ANP calculation.

[0158] The present embodiment is further described below through simulation:

[0159] 1. Simulation procedure: The simulation verification adopts the departure procedure of Beijing Daxing Airport published by the Civil Aviation Administration of China (AIP). The departure procedure (ZBAD-7D SIDRNAV RWY19R) includes four departure procedures: ELKUR-11D, MUGLO-11D, IDKEX-11D, and DOTRA-11D (such as Figure 4 In this embodiment, the DOTRA-11D program is selected as the simulation program for the SINS / DME / DME integrated navigation.

[0160] The DOTRA-11D program passes through six waypoints and one end point, DOTRA. Since the operating range of the DME station is 200nm, this program is within the range of three DME stations. Without considering DME station selection, only the DAXING and TIANJIN navigation stations are used. The above specific parameters are shown in Table 1, and the position information of the transmitting antenna is shown in Table 2.

[0161] Table 2 Position information of each waypoint in the DOTRA-11D procedure

[0162]

[0163] Table 2 Transmitting antenna location information

[0164]

[0165] The simulation starts from waypoint AD711. The distances between the waypoints and the DME stations on the DOTRA-11D departure procedure and the starting point AD711 (see Figure 5 In this program, the aircraft's movements include three basic movements: climbing, turning, and constant speed. The ideal inertial attitude information of the aircraft without inertial error during the program flight can be obtained through the inversion algorithm. Figure 6 This is an ideal inertial three-dimensional flight trajectory and can be used as a benchmark for simulation results.

[0166] 2. Simulation parameter setting: This embodiment does not consider the aircraft taxiing and taking off from the airport runway, and only simulates the flight trajectory of the aircraft starting from waypoint AD711.

[0167] Assume that the initial position of the aircraft is 39°29′26″N, 116°38′29″E, altitude 600m, initial speed 200kt, and initial heading 70°; the initial position error in the northeast and celestial directions is 30m, the initial misalignment angle is 0.5°, and the initial speed error is 0.1m / s. The total error of the DME ground transmitter error and the onboard interrogator is 0.2nm, which is calculated by the white noise error ν with zero mean. δD and a constant bias δD, where

[0168] The SINS update frequency is 10 Hz, and only four parameters are considered: gyro bias eb, gyro random walk web, accelerometer bias db, and accelerometer random walk wdb. The specific parameter settings are summarized below (see Table 3).

[0169] Table 3 Simulation parameter settings

[0170]

[0171] Then the system measurement noise matrix R is:

[0172] R=diag([ρ1k ρ2k hk] T ) 2 (31)

[0173] The system noise matrix Q is:

[0174] Q=diag([web wdb zeros(9,1)] T ) 2 (32)

[0175] The mean square error matrix P of the initial system state is:

[0176] P=diag([ak vk rk eb db]T ) 2 (33)

[0177] 3. Simulation analysis: Based on the ideal inertial trajectory parameters, the ideal angular velocity will be obtained Compared with ideal i b On this basis, the gyro error and accelerometer error are superimposed to obtain the angular velocity with gyroscope error Comparison with accelerometer error Then and Substitute into equations (1)-(3) to obtain the position, attitude and velocity parameters solved by SINS. The slant range data generated by the DME / DME navigation method can be measured and updated based on the obtained ideal trajectory parameters through the relationship between the measurement equation (equation (4)), the measurement matrix (equation (13)), and the measurement noise (equation (6)) to serve as the slant range data of the simulated DME / DME. The latitude and longitude of pure inertial navigation should be in a divergent state (such as Figure 7 The slant range error measured by DME is randomly distributed within 0.16NM (as shown in Figure 8 As shown in Figure 3, the simulation results of a single navigation source are consistent with the actual state.

[0178] The simulation results of SINS / DME / DME integrated navigation are further analyzed, and the position change of the integrated navigation trajectory is compared with the ideal trajectory to obtain the change diagram of the longitude and latitude positioning result error (see Figure 9 ). The height error does not change in the figure because the slant range does not correct the height error (Equation (12)). In the simulation from 100s to 400s, the north error is kept in the range of 50m-100m, and the east error is controlled within the range of 50m. In the simulation from 1300s to 1600s, the north and east errors are both kept within the range of 50m. By comparing the difference between the slant range measured by the fused DME and the ideal slant range (see Figure 10 ), it can be seen that after the fluctuation caused by the initial value, the slant range error is maintained within 50m in the simulation 100s-400s, and the slant range error is quickly stabilized within 20m in the simulation 1300s-1700s, showing a better performance than Figure 8 The DME / DME measurement is more excellent.

[0179] In order to verify that the effect of the SINS / DME / DME integrated navigation method meets the RNP standard of PBN operation, it is necessary to calculate and evaluate the actual navigation performance of the SINS / DME / DME integrated navigation method. The ANP calculation steps of the SINS / DME / DME integrated navigation method are as follows: (19)-(30), and the results can be obtained (see Figure 11), the results show that the ANP values ​​during the entire departure procedure are much less than 1NM, which meets the RNP 1 standard departure operation requirements.

[0180] The above-described embodiments merely represent specific implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A SINS / DME / DME integrated navigation system performance evaluation method, characterized in that: The following steps are involved: Step 1: Based on the state equation and measurement equation of the SINS / DME / DME integrated navigation system, the slant range calculated by the strapdown inertial navigation (SINS) and the slant range data measured by the range finder (DME) are combined using the Kalman filter algorithm. This process includes two parts: time update and measurement update. The step 1 is specifically as follows: During the flight, the flight management system calculates the slant range of the aircraft relative to the two DME stations. At the same time, the DME ground station obtains the measured slant range by using a question-and-answer method with the onboard DME antenna. The measurement error of the slant range of a single DME system is expressed as: δρ=ρ C -r D (5) In formula (5), δρ is the slant range error, ρ C is the slant distance calculated by the flight management system based on the inertial navigation position, ρ D Slant range measured for the DME station; The slant range ρ measured by the DME station D It can be expressed as the relationship between the true slant range and the DME-related noise: r D =p+sn D (6) In formula (6), ρ is the true slant range, δν D is the measurement noise with zero mean value of DME; Assume that the aircraft position calculated by SINS during the flight is (L P λ P ), use P(L P λ P h P ) represents the position of the aircraft in the geodetic coordinate system, where h P The altitude of the aircraft is measured by the barometric altimeter; p'(L P λ P 0) represents the vertical projection of the aircraft position calculated by SINS on the ground; D(L D λ D h D ) represents the longitude, latitude and altitude of the DME station in the geodetic coordinate system, D′(L D λ D 0) represents the vertical projection of DME on the ground; ρ C is the slant distance from the DME station to the aircraft position resolved by SINS, S is the arc length from the DME station to the aircraft position resolved by SINS, and R is the standard earth radius; Since the application range of the DME station is much smaller than the radius of the earth, the arc length S is approximately a straight line. D λ P 0) is the intersection of P′ and D′ on the longitude and latitude circles. Therefore, the aircraft position calculated by SINS and the projection of the DME station in space are approximately the relationship between the inner sides of the right triangle ΔP′CD′: S 2 =P′C 2 +D′C 2 (7) Similarly, we can get the slope distance ρ C Relationship with arc length S: The spatial relationship between the position solved by SINS and the DME station is decomposed in the longitude and latitude directions to obtain the longitude and latitude circle relationship between the solved position and the DME station. At the same time, let P′C = S1 and D′C = S2, and the following relationship is obtained: S1=R(L P -L D ) (9) S2=R(λ P -λ D )cosL P (10) Substituting formula (9) (10) into formula (8) and differentiating it, we can obtain the following differential equation for slope distance: Combining formula (11) to obtain the relationship between the slant range differential and the longitude and latitude error of the aircraft position, the slant range measurement matrix H of the two DME stations is obtained. i As follows, where i = 1, 2: Combined with formula (4), we can get the measurement matrix: For the SINS / DME / DME integrated navigation system, the slant range calculated by the SINS position solution and the slant range data measured by the DME are fused using the Kalman filter algorithm; Step 2: Evaluate the performance of the SINS / DME / DME integrated navigation system based on the actual navigation performance ANP calculation model of the filter covariance.

2. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 1, characterized in that: In step 1, the state equation is as follows: X k =F k,k-1 X k-1 +Γ k W k (1) In formula (1): X k is the error state at time k, F k / k-1 is the state transition matrix from time k-1 to time k, X k-1 is the error state at the previous moment, Γ k is the noise driving matrix, W k is the system noise matrix; the system state is composed of the SINS misalignment angle, velocity error, position error, gyroscope error and accelerometer error; the 15-dimensional error state of SINS is selected as the state quantity, as follows: In formula (2): Φ, δv n , δp represent the misalignment angle, velocity error, and position error of SINS in the navigation coordinate system, respectively, and ε b is the projection of the gyroscope zero bias in the carrier coordinate system, b is the projection of the accelerometer zero bias in the carrier coordinate system; The state transfer matrix F k / k-1 It is expressed as follows:

3. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 2, characterized in that: In step 1, the measurement equation is as follows: Z k =H k X k +V k (4) In formula (4), Z k is the measurement error between the two systems, H k is the measurement matrix, X k is the error state at time k, V k is the measurement noise matrix.

4. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 1, characterized in that: Time updates include state updates and covariance updates: X k / k-1 =F k X k-1 / k-1 (14) 5. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 4, characterized in that: The measurement update includes filter gain, state estimation, and variance estimation: (1) Filter gain equation: (2) State estimation equation: (3) Variance estimation equation: P k =(I-K k H k )P k / k-1 (18)。 6. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 5, characterized in that: The step 2 is specifically as follows: Assume that the positioning error result is a two-dimensional normal distribution of the errors in longitude and latitude, with a mean of E p and variance P p It is expressed as follows: E p =[δλδL] (19) Where: δλ, δL are the mean errors of longitude and latitude of aircraft navigation, σ λ ,σ L is the error of longitude and latitude, σ λL is the covariance of longitude and latitude errors; In the process of solving the ANP, the position relationship in the horizontal rectangular coordinate system is obtained, and the transformation relationship of projecting the geodetic coordinate system into the Earth-centered Earth-fixed coordinate system is as follows: Δx=σ λ ·(R N +h)·cos(L) (21) Δy=σ L ·(R M +h) (22) Where: Δx, Δy are the XY axis errors R in the Earth-centered Earth-fixed coordinate system N is the radius of curvature of the earth's circumplex, h is the altitude of the aircraft, L is the latitude of the aircraft, R M is the radius of curvature of the Earth's meridian; Thus, the covariance matrix P in the Earth-centered Earth-fixed coordinate system is obtained xy : in: Where: are the variances of Δx and Δy respectively, is the covariance of Δx and Δy; Obtain the eigenvalue of equation (23) and obtain the major semi-axis λ of the 1σ error ellipse max and the minor axis λ min , the relationship is as follows: ANP is determined by the conversion factor K and the major semi-axis λ of the 1σ error ellipse. max Obtain: ANP=Kλ max (28) The conversion factor K is determined by the flattening of the 1σ error ellipse. The ratio of the major and minor axes of the 1σ error ellipse is: K is calculated as follows: In the SINS / DME / DME integrated navigation system, the covariance updated at each step in the filtering algorithm is used as the variance for ANP calculation.

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