A method for generating inertial information suitable for integrity testing of integrated navigation systems

Abstract

This invention proposes an inertial information generation method suitable for integrated navigation integrity testing. The method includes: generating local standard gravity values ​​using a global high-precision gravity field model; generating gravity disturbance values ​​using a vehicle velocity and gravity vertical deviation error model; generating local true gravity values ​​from the local standard gravity values ​​and gravity disturbance values; and finally generating inertial information suitable for integrated navigation integrity testing. This method can be used to test the performance of integrated navigation integrity algorithms under extreme gravity environments. It considers the error between the global high-order gravity field model and true gravity, ensuring the accuracy of inertial information output and demonstrating strong practicality.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation technology, and specifically relates to an inertial information generation method suitable for integrated navigation integrity testing. Background Technology

[0002] Currently, most gravity compensation models in inertial navigation algorithms adopt the normal gravity field model, which describes the Earth's gravity field under the assumption of a regular Earth. However, the Earth is not actually regular, and the normal gravity field can only approximate the Earth's true gravity field. Accurately and meticulously characterizing the Earth's true gravity field is of great significance for high-precision inertial navigation. Statistics show that compared to the normal gravity model, applying a high-precision gravity field model can improve inertial navigation accuracy by approximately 0.1 nautical miles per hour (1 nautical mile = 1.852 km); simultaneously, a 1 mGal horizontal gravity disturbance causes approximately 0.2 arcseconds of horizontal attitude error (horizontal gravity disturbances are typically tens to 100 mGal).

[0003] Therefore, to ensure the reliability of inertial reference system services, it is necessary to evaluate the algorithm performance under extreme gravity environments during the testing and verification of civil aviation integrated navigation integrity algorithms. Under extreme gravity environments, even high-precision spherical harmonic function models differ significantly from actual gravity values; however, most existing inertial information simulation schemes do not consider the impact of this difference on inertial information. Summary of the Invention

[0004] The purpose of this invention is to provide an inertial information generation method suitable for integrated navigation integrity testing. In order to obtain the most realistic inertial measurement information, this method considers the difference between the higher-order spherical harmonic function gravity model and the actual gravity.

[0005] The technical solution of this invention: This invention provides an inertial information generation method suitable for integrity testing of integrated navigation systems in civil aircraft. Addressing the testing and verification requirements of integrated navigation integrity algorithms, the method first determines a high-precision gravity model and acquires the motion information of the carrier. Second, it uses the Yule-Walker equations and a discretized second-order system transfer function to determine the parameters of a continuous vertical deviation error model. Next, the continuous vertical deviation error model is discretized to facilitate computer processing. This process fully considers the errors introduced by discretization, reducing discretization errors by setting a threshold for the error coefficients. Subsequently, the gravity disturbance value is calculated using the discretized vertical deviation model, and the gravity value obtained from the high-precision gravity spherical harmonic function model is added to the gravity disturbance value calculated by the discretized vertical deviation error model to obtain the true gravity value. Finally, the obtained true gravity value is used to simulate inertial information, which will be used for testing the integrated navigation integrity algorithm.

[0006] The advantages of this invention may be:

[0007] 1. This invention improves the accuracy of inertial information simulation by utilizing a vertical deviation error model;

[0008] 2. A method for determining the parameters of the continuous vertical deviation error model based on real gravity data is proposed.

[0009] 3. It ensures the accuracy of the discretization of the continuous vertical deviation error model and avoids gravity disturbance caused by the discretization error of the model;

[0010] 4. High versatility: This scheme can be used for testing and verification of different types of integrated navigation algorithms. Attached Figure Description

[0011] To more clearly illustrate the technical solutions implemented in this invention, a simple explanation of the accompanying drawings used in the description of this invention will be provided below. Obviously, the drawings described below are merely some embodiments of this invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0012] Figure 1 This is a schematic diagram of the inertial information simulation process according to a preferred embodiment of the present invention; Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] The features and illustrative embodiments of various aspects of the present invention will now be described in detail. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention. The invention is by no means limited to any specific setup and method set forth below, but covers any improvements, substitutions, and modifications to the structures, methods, and devices without departing from the spirit of the invention.

[0015] It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other, and the various embodiments can be referenced and cited in each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0016] Example 1

[0017] This invention provides a method for generating inertial information suitable for integrated navigation integrity testing, wherein the inertial information refers to specific force measurement. In this embodiment, it is assumed that the carrier is flying horizontally in a due east direction without any attitude change, and both the carrier coordinate system and the track coordinate system coincide with the navigation coordinate system. It is assumed that the carrier is currently at [34°, 120°, 1000m], and its speed is [200, 0, 0] m / s (in the track coordinate system), with the speed increment... The speed is [5, 0, 0] m / s (in the track coordinate system). For example... Figure 1 As shown, the method includes the following steps:

[0018] Step 101: Derive the parameters required for calculation from the specific force equation;

[0019] Given the specific force equation:

[0020]

[0021] in The coordinate transformation matrix represents the coordinate transformation between the navigation coordinate system (n-frame) and the vehicle coordinate system (b-frame) at time t. v is the projection of the vehicle velocity increment at time t onto the navigation coordinate system; n (t) represents the projection of the vehicle's velocity (speed) at time t onto the navigation coordinate system; g n (t) is the projection of the actual gravity value of the carrier at time t onto the navigation coordinate system; Let t be the projection of the specific force measurement in the navigation coordinate system. Let be the projection of the angular velocity of the Earth system (e-frame) relative to the inertial frame at time t onto the navigation coordinate system, which can be expressed as:

[0022] [0,ω ie cos(L), ω ie sin(L)]

[0023] Where L is the latitude of the current location of the carrier; ω ie The Earth's rotational angular velocity is 7.2921151467e-05 rad / s; Let be the projection of the angular velocity of the navigation coordinate system relative to the Earth coordinate system at time t onto the navigation coordinate system, which can be expressed as:

[0024] [-v N / (R M +h),v E / (R N +h),v E tan(L)I(R N+h)]

[0025] Where h is the height of the carrier, v N With v E R represents the northward and eastward velocities of the carrier, respectively; N Let be the radius of curvature of the zonal loop, and its calculation formula is:

[0026]

[0027] R e ε is the semi-major axis of the Earth ellipsoid, with a value of 6,378,137 m; e is the eccentricity of the Earth ellipse, with a value of 0.0818.

[0028] For the true gravity value g n (t), which can be represented as:

[0029]

[0030] in Let t be the projection of the standard gravity value at time t onto the navigation frame; Let t be the projection of the gravity disturbance value in the navigation system at time t.

[0031] Step 102: Based on the carrier trajectory and motion state during the simulation process, obtain the carrier motion information required in the specific force equation;

[0032] The velocity V of the carrier at time t is [200, 0, 0] m / s (in the track coordinate system (g system));

[0033] The position of the carrier at time t [34°, 120°, 1000m];

[0034] The velocity increment of the carrier at time t [5, 0, 0] m / s (in the track coordinate system (g frame))

[0035] The rotation matrix from the track coordinate system to the navigation coordinate system is:

[0036]

[0037] The rotation matrix from the vehicle coordinate system to the navigation coordinate system (East-North-Sky) is:

[0038]

[0039] Step 103: Calculate the standard gravity value at time t;

[0040] The position information of the carrier at time t is input into the spherical harmonic function calculation module, and the standard gravity value at time t is calculated using the EGM-2008 gravity field model. The gravity value in the navigation system is calculated using the EGM-2008 gravity model at [34°, 120°, 1000m]. The value is [0.00035499, 0.00011356, -9.79345341] m / s 2 .

[0041] Step 104: Calculate the gravitational disturbance value at time t;

[0042] The gravity disturbance value is calculated based on the vertical deviation error model; the vertical deviation measures the difference in direction between the standard gravity vector and the true gravity vector; the vertical deviation error model describes the difference between the gravity value output by the high-precision gravity field and the true gravity value; since the vertical deviation can be decomposed into east-west and north-south directions, the gravity disturbance described in this example will also be divided into east-west and north-south directions.

[0043] The vertical deviation error model can be modeled as a continuous second-order Markov process:

[0044]

[0045] Where x(t) is the vertical deviation value at time t, ω0 is the coherence frequency, which can be expressed as ω0 = 2πV / d0; where V is the speed of the carrier, d0 is the coherence length of the model, which represents the spatial correlation of the vertical deviation model; q(t) is the driving white noise of the second-order Markov process, which represents the drastic change in the vertical deviation in the current region, and the variance of q(t) is set to Q. Only when the value of d0 and the statistical characteristics of q(t) are determined does the continuous second-order Markov process of vertical deviation have practical significance.

[0046] This example demonstrates the method for determining d0 and q(t).

[0047] First, obtain actual gravity data (with a resolution of at least 1 arcminute) within the range of the carrier's motion. If actual gravity data within this range cannot be obtained, consider using a region with similar or more drastic gravity changes as a substitute.

[0048] Secondly, simulate and generate uniform running trajectories along the east-west or north-south direction (at least 10 trajectories in the east-west or north-south direction);

[0049] Subsequently, the differences between the vertical deviation of the actual data and the vertical deviation of EGM-2008 in the east-west and north-south directions were calculated based on different running trajectories. Let the actual gravity measured at time t be... The actual vertical deviations of the north-south and east-west data can be expressed as:

[0050] North-South actual data vertical deviation:

[0051] East-west true data vertical deviation: Meanwhile, let the standard gravity at time t be [value]. The north-south and east-west vertical deviations of EGM-2008 can be expressed as:

[0052] EGM-2008 North-South Vertical Deviation:

[0053] EGM-2008 East-West Vertical Deviation: The difference between the vertical deviation of the actual data and the vertical deviation of EGM-2008 in the east-west and north-south directions can be expressed as:

[0054] North-South Difference: x SN -x SN,2008

[0055] East-West Difference: x EW -x EW,2008

[0056] The above process only shows the vertical deviation difference at time t. For any simulated trajectory, the vertical deviation difference on its trajectory constitutes a sequence, the length of which is determined by the resolution of the real data.

[0057] Next, a second-order autoregressive model (AR(2)) was used to fit the vertical deviation difference sequences in the east-west and north-south directions, respectively. The AR(2) model can be expressed as:

[0058] X k =aX k-1 +bX k-2 +w

[0059] Where X k Let be the vertical deviation difference value at the k-th point; a and b are the coefficients of the AR(2) model, respectively; w is the driving noise of the model. Using the Yule-Walker equation, a and b can be determined. The Yule-Walker equation for solving a and b can be expressed as:

[0060]

[0061] ρ x (p) represents the autocorrelation coefficient, and its calculation process is as follows:

[0062]

[0063] Where M is the length of the vertical deviation difference sequence. Let a and b be the mean of the vertical deviation difference sequence. Once a and b are determined, the amplitude of the driving white noise can be determined. The formula for determining the variance of the driving white noise is as follows:

[0064]

[0065] Where γ0 is the variance of the vertical deviation difference sequence.

[0066] Finally, using the discretized transfer function of the second-order Markov process, the parameters of the continuous model are determined, and their correspondence can be expressed as:

[0067] a=(2+2ω0ΔT)

[0068] b = 1 + 2ω0ΔT + (ω0ΔT) 2

[0069]

[0070] Where ΔT is the sampling time, expressed as Δf / V. Here, Δf is the spatial resolution of the real data, and V is the speed of the simulated vehicle. Thus, all parameters of the continuous second-order Markov process have been solved.

[0071] Since continuous second-order Markov processes cannot be directly processed by computers, they need to be discretized.

[0072] Discretization processes can be divided into first-order discretization and higher-order discretization. To clearly describe the discretization process, we first rewrite the continuous second-order Markov process in state equation form:

[0073]

[0074] Where x1(t) = x(t); x2(t) are intermediate quantities. In the discretization process of the state equation, the discretized expression of A is... It can be obtained from the expansion formula of the exponential matrix:

[0075]

[0076] Where I is the identity matrix; Δ is the interval between two adjacent gravity output moments; the first-order discretization process refers to... During the discretization process, the required discretization scheme varies significantly depending on the Δ value under different scenarios. In this example, Δ is set to 5s, the coherence length to 10km, and the noise variance Q to 25arcsec. 2 To determine the specific discretization scheme, the discretization error coefficient λ is calculated:

[0077]

[0078] When λ < 0.01, the discretization order can be determined to be n-1. In this example, the discretization order is 6. The expression is:

[0079]

[0080] Therefore, the discretized state equation can be expressed as:

[0081]

[0082] Where x1(k) and x2(k) are the state values ​​at time k after discretization. For discretized white noise, its variance is approximately: Based on the discretized state equations, we can derive:

[0083]

[0084] After simplification, the discretized model can be obtained:

[0085]

[0086] It can be seen that the above formula is a second-order autoregressive model AR(2), and its driving noise variance is: Letting x1(k+1) = x(k+1) yields the final discretized vertical deviation error model. When calculating the (k+1)th vertical deviation error, the magnitudes of the kth and (k-1)th vertical deviation errors need to be known; these values ​​are derived from actual gravity data. and standard gravity If real gravity data is unavailable, x(k) = x(k-1) = 0 can be preset. Therefore, the discretized perpendicular deviation error model for the east-west and north-south directions can be expressed as:

[0087] East-west vertical deviation error:

[0088]

[0089] North-South vertical deviation error:

[0090]

[0091] In this example, the error x in the perpendicular deviation along the east-west direction is... EW (k) and x EW (k-1) is preset to 5 arcsec; for the north-south vertical deviation error x SN (k) and x SN (k-1) is preset to 1 arcsec. Based on the preset vertical deviation error x... EW (k+1) is 7.30 arcsec; x SN(k+1) is -3.34 arcsec. Based on the small-angle assumption, the gravitational perturbation can be obtained as:

[0092]

[0093]

[0094] Step 104: Generate the actual gravity value;

[0095] Given the standard gravity value in the navigation system at [34°, 120°, 1000m] calculated using the EGM-2008 gravity model. The value is [0.00035499, 0.00011356, -9.79345341] m / s 2 The true gravity value g can be obtained using the gravity perturbation value. n for:

[0096] Step 105: Generate specific force measurement value;

[0097] The specific force value was calculated using the specific force equation as: [4.9999, -2.7356×10]. -4 9.7935 m / s 2 .

Claims

1. A method for generating inertial information suitable for integrity testing of integrated navigation systems, characterized in that, include: The motion trajectory of the carrier is simulated to obtain the carrier's motion information; Establish a high-precision gravity model and a continuous vertical deviation error model; Discretize the continuous vertical deviation error model; The gravity residual value is calculated using a discretized vertical deviation error model; The true gravity value is obtained by adding the gravity residual value to the value calculated by the high-precision global gravity model; Inertial information is generated based on the actual gravity value and the carrier's motion information.

2. The inertial information generation method for integrated navigation integrity testing according to claim 1, characterized in that, The carrier motion information includes the following data: The carrier's position, its operating speed, its acceleration, and its attitude.

3. The inertial information generation method for integrated navigation integrity testing according to claim 1, characterized in that, The high-precision gravity model is the high-order spherical harmonic function model of the Earth's gravity field, EGM-2008.

4. The inertial information generation method for integrated navigation integrity testing according to claim 1, characterized in that, The continuous vertical deviation error model is a stationary second-order Gaussian Markov random process, whose parameters can be determined by the Yule-Walker equation and the discretized transfer function of the second-order Markov process; the discrete vertical deviation error model is a second-order autoregressive model, whose parameters are determined by the continuous vertical deviation error model.

5. The inertial information generation method for integrated navigation integrity testing according to claim 4, characterized in that, The parameters of the continuous vertical deviation error model include the following information: The model's spatial wavelength information and the variance information of the driving noise.

6. The inertial information generation method for integrated navigation integrity testing according to claim 1, characterized in that, The discretization process employs an infinite series expansion of an exponential matrix.

7. The inertial information generation method for integrated navigation integrity testing according to claim 6, characterized in that, Based on the carrier's movement speed, the discretization order is adjusted by setting a threshold for the discretization error coefficient, thereby avoiding errors caused by low-order discretization.

8. The inertial information generation method for integrated navigation integrity testing according to claim 1, characterized in that, The generated inertial information is a specific force measurement.

Images