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

Abstract

The invention discloses an SINS / DME / DME integrated navigation system performance evaluation method, which comprises the following steps: according to a state equation and a measurement equation of an SINS / DME / DME integrated navigation system, calculating slope distance data calculated by a position through a strapdown inertial navigation system SINS and slope distance data measured by a distance meter DME, and fusing by adopting a Kalman filtering algorithm, specifically comprising two parts of time updating and measurement updating; evaluating the performance of the SINS / DME / DME integrated navigation system based on the actual navigation performance ANP calculation model of the filtering covariance; the method has the advantages of simple calculation, credible result and the like.

Description

Technical Field

[0001] The 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 navigation operations based on required navigation performance (RNP), covering all flight phases from airways, terminal areas to approach and landing, providing support for optimizing airspace structure, reducing operation intervals, and improving operation efficiency. Actual navigation performance (ANP) is a real-time evaluation indicator of the aircraft navigation system and is the key basis for the crew to determine whether the navigation system meets the RNP operation during flight.

[0003] The strapdown inertial navigation system (SINS) has the advantages of strong autonomy, low external interference, high update rate, and rich output parameters. It is widely used in civil aviation and other transportation fields. However, when used for a long time, it needs other navigation sources to suppress the rapid accumulation of dead reckoning errors. The distance measuring equipment (DME) measures the slant distance between the aircraft and the ground station through the interrogation-reply pulse pair. Due to its simple structure, convenient use, and mature technology, it is used in many airports at home and abroad, but the positioning error is close to 0.2 nautical miles, which is difficult to meet the terminal area operation requirements. When the global navigation satellite system (GNSS) signal is unreliable, the flight management system (FMS) adopts the navigation degradation mode and preferentially switches to the higher-precision SINS / DME / DME combined navigation mode to output flight management position information. Its ANP is the key indicator to determine whether the aircraft navigation system meets the RNP operation standard.

[0004] At present, civil airliners at home and abroad all adopt a combined navigation system architecture with SINS as the reference system and other subsystems as auxiliary. The combined navigation and ANP algorithms in the flight management system are all encapsulated internally, and there are few publicly reported documents. Traditional studies have considered the use of SINS and other major auxiliary positioning systems, mainly VOR, to improve navigation performance when GNSS information is unreliable. However, there are few publicly reported studies on SINS / DME / DME combined navigation, and there are very few evaluations of the actual navigation performance (ANP) of the combined navigation system combined with actual operating procedures. There is still a lack of systematic research and verification on the calculation theory of ANP. Summary of the invention

[0005] 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: According to 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 rangefinder DME are fused using the Kalman filter algorithm, which specifically 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 state of the system is composed of the misalignment angle, velocity error, position error, gyroscope error and accelerometer error of SINS; 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, ▽ b 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 distance of the aircraft relative to the two DME stations respectively. At the same time, the DME ground station obtains the measured slant distance by question-and-answer method with the DME antenna on the aircraft. The measurement error of the slant distance 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 is 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 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 PThe pressure altimeter measures the aircraft's altitude; 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 solved by SINS, S is the arc length from the DME station to the aircraft position solved 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 solved 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 get the slope distance ρ C Relationship with arc length S:

[0030]

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

[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, the differential equation of slope range is as follows:

[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] Combining formula (4) to obtain 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 updating includes state updating and covariance updating:

[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 ) 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 error in longitude and latitude, with a mean value of E p and variance P p It is expressed as follows:

[0053] E p =[δλδL] (19)

[0054]

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

[0056] In the process of solving ANP, the position relationship in the horizontal rectangular coordinate system is obtained, and the transformation relationship of projecting the geodetic coordinate system to 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 height 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 Find:

[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 of the ANP calculation.

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

[0075] The invention builds a SINS / DME / DME integrated navigation implementation framework on the basis of detailed derivation of SINS and DME error models, clarifies the implementation process, and proposes an ANP calculation model based on filter covariance; the method of the invention is simple to calculate and the result is credible, and 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 invention can all be used for reference in other integrated navigation systems such as GNSS / IRS, SINS / VOR / DEM, etc. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0077] Figure 2 A schematic diagram of the relationship between the aircraft position solved by SINS and the latitude and longitude of the DME station in the same meridian in an embodiment of the present invention;

[0078] Figure 3 A 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 program diagram of ZBAD-7D, SID, RNAV, and RWY19R 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] Fig. 9 A schematic diagram of a combined navigation positioning result in an embodiment of the present invention;

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

[0086] Fig.11 It is a schematic diagram of the change of ANP 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, comprising:

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

[0091] 1. State equation:

[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 state of the system consists of the misalignment angle, velocity error, position error, gyroscope error and accelerometer error of SINS. The 15-dimensional error state of 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, ▽ bis 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 the flight, the flight management system calculates the slant distance of the aircraft relative to the two DME stations. At the same time, the DME ground station obtains the measured slant distance by questioning the DME antenna on the aircraft. The measurement error of the slant distance 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 inertial navigation position, ρ D Slant range measured by the DME station.

[0106] The slant range ρ measured by the DME station is 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 pressure altimeter measures the aircraft's altitude. 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 solved by SINS, S is the arc length from the DME station to the aircraft position solved by SINS, and R is the standard earth radius. The relationship between the aircraft position solved 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 solved 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 slope 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, the differential equation of slope range is as follows:

[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] The measurement update includes 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 ) 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 value of E p and variance P p It is expressed as follows:

[0137] E p =[δλδL] (19)

[0138]

[0139] Where: δλ, δL are the mean errors of longitude and latitude of aircraft navigation, σ λ , σ L is the error in longitude and latitude, σ λL is the covariance of precision and dimensionality 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 to 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 height 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 Find:

[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 of the 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 6 waypoints and one end point DOTRA. Since the working range of the DME station is 200nm, the program is within the range of 3 DME stations. Without considering the DME station selection, only the DAXING and TIANJIN navigation stations are used. The above specific parameters are shown in Table 1, and the location information of the transmitting antenna is shown in Table 2.

[0161] Table 1 Position information of each waypoint in DOTRA-11D program

[0162]

[0163] Table 2 Transmitting antenna location information

[0164]

[0165] The simulation starts from waypoint AD711. The distances between waypoints and DME stations on the DOTRA-11D departure procedure and the starting point AD711 (see Figure 5 ). In this program, the aircraft's actions include three basic actions: climbing, turning, and constant speed. The inversion algorithm can be used to obtain the ideal inertial attitude information of the aircraft without inertial error during the program flight. Figure 2 is the ideal inertial three-dimensional flight trajectory (see Figure 6 ), which 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, 600m altitude, 200kt initial speed, and 70° initial heading; the initial position error of the northeast celestial direction 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 airborne interrogator is 0.2nm, which is calculated by the white noise error ν with a mean of zero. δD and constant zero bias δD

[10] , here the command The update frequency of SINS is 10Hz, and only four parameters are considered: gyro bias eb, gyro random walk web, accelerometer bias db, and accelerometer random walk web. The specific parameter settings are summarized as follows (see Table 3).

[0168] Table 3 Simulation parameter settings

[0169]

[0170] Then the system measurement noise matrix R is:

[0171] R=diag([ρ1kρ2k hk] T ) 2 (31)

[0172] The system noise matrix Q is:

[0173] Q = diag ([web wdb zeros (9, 1)] T ) 2 (32)

[0174] The mean square error matrix P of the initial system state is:

[0175] P=diag([ak vk rk eb db] T ) 2(33)

[0176] 3. Simulation analysis: Based on the ideal inertial trajectory parameters, the ideal angular velocity ω will be obtained. i b Compared with the ideal i b On this basis, the gyro error and accelerometer error are superimposed to obtain the angular velocity with gyro 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 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 The simulation results of a single navigation source are consistent with the actual state.

[0177] 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 Fig. 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 within 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 Fig.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 has better results.

[0178] 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 shown in equations (19)-(30), and the results can be obtained (see Fig.11), the results show that the ANP value during the entire departure procedure is much less than 1NM, which meets the RNP 1 standard departure operation requirements.

[0179] The above-mentioned embodiments only express the specific implementation of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope 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: According to 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 rangefinder DME are fused using the Kalman filter algorithm, which specifically includes two parts: time update and measurement update. 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 state of the system is composed of the misalignment angle, velocity error, position error, gyroscope error and accelerometer error of SINS; 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, 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 3, characterized in that: The step 1 is specifically as follows: During the flight, the flight management system calculates the slant distance of the aircraft relative to the two DME stations respectively. At the same time, the DME ground station obtains the measured slant distance by question-and-answer method with the DME antenna on the aircraft. The measurement error of the slant distance 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 is 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 pressure altimeter measures the aircraft's altitude; 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 solved by SINS, S is the arc length from the DME station to the aircraft position solved 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 solved 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 get the slope distance ρ C Relationship with arc length S: The relationship between the position solved by SINS and the spatial position of the DME station is decomposed in the longitude and latitude directions to obtain the relationship between the solved position and the longitude and latitude circles of the DME station. At the same time, let P′C=S1, D′C=S2, and get the following relationship: S1=R(L P -L D ) (9) S2=R(λ P -λ D )whatsL P (10) Substituting formula (9) (10) into formula (8) and differentiating it, the differential equation of slope range is as follows: 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): Combining formula (4) to obtain 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.

5. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 4, characterized in that: Time updates include state updates and covariance updates: X k / k-1 =F k X k-1 / k-1 (14) 6. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 5, 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)。 7. The SINS / DME / DME integrated navigation system performance evaluation method according to claim 6, characterized in that: The step 2 is specifically as follows: Assume that the positioning error result is a two-dimensional normal distribution of the error in longitude and latitude, with a mean value of E p and variance P p It is expressed as follows: E p =[δλ δL] (19) Where: δλ, δL are the mean errors of longitude and latitude of aircraft navigation, σ λ , σ L is the error in longitude and latitude, σ λL is the covariance of precision and dimensionality errors; In the process of solving ANP, the position relationship in the horizontal rectangular coordinate system is obtained, and the transformation relationship of projecting the geodetic coordinate system to 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 height 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 Find: 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 of the ANP calculation.

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