An unmanned aerial vehicle transfer alignment method based on a relative installation error analytical expression model

Abstract

The present application relates to a kind of unmanned plane transfer alignment method based on relative installation error analytical expression model, belong to unmanned plane transfer alignment technical field, including the following steps: S1, the relative installation error analytical expression model between main inertial navigation system and sub inertial navigation system is constructed;S2, based on the relative installation error analytical expression model of step S1 construction, relative installation error is obtained;S3, using the relative installation error of step S2, initial self-alignment error is obtained;S4, based on the relative installation error and initial self-alignment error of step S3 acquisition, transfer alignment is carried out.The method provided by the present application is high in reliability, strong in universality, high in the running efficiency of algorithm, simple in operation, high in precision, and good in practicability.

Description

Technical Field

[0001] This invention belongs to the field of UAV transfer alignment technology, specifically relating to a UAV transfer alignment method based on an analytical model of relative installation error. Background Technology

[0002] Before launch, unmanned aerial vehicles (UAVs) need to acquire accurate initial attitude information. However, due to payload limitations, UAVs can only be equipped with low-cost, miniaturized inertial navigation systems (INS). Generally, miniaturized INS have low accuracy, making it impossible for self-alignment to meet the initial attitude accuracy requirements before launch. Currently, the method to improve the initial attitude accuracy of UAVs is the transfer alignment method. This method relies on the high-precision INS (main INS) of the ship to correct the initial attitude of the low-precision INS (sub-INS) of the UAV through transfer alignment. For example, Chinese invention patent publication CN111707292A provides a fast transfer alignment method with adaptive filtering; Chinese invention patent publication CN109612499A discloses a transfer alignment method based on adaptive compensation H-infinite filtering; and Chinese invention patent publication CN114786128A provides an adaptive switching method for ship INS transfer alignment based on data quality control.

[0003] However, since relative attitude includes relative installation error and self-alignment error, and the two errors are coupled with each other, existing transfer alignment methods mostly rely on filtering algorithms. The filtering parameters need to be adjusted for different levels of inertial navigation systems. In addition, during the transfer alignment process, the ship needs to perform some special maneuvers to assist in the convergence of the filter estimate. When the system is affected by colored noise, the filter will diverge. Furthermore, the existing transfer alignment time is relatively long, which cannot meet the needs of carrier-based aircraft to perform emergency missions. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a UAV transfer alignment method based on an analytical model of relative installation error. This method is highly reliable, versatile, has high algorithm efficiency, is simple to operate, has high accuracy, and is highly practical.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a UAV transfer alignment method based on an analytical model of relative installation error, comprising the following steps:

[0006] S1. Construct an analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system;

[0007] S2. Based on the analytical model of relative installation error constructed in step S1, obtain the relative installation error;

[0008] S3. Using the relative installation error obtained in step S2, obtain the initial self-alignment error;

[0009] S4. Based on the relative installation error and initial self-alignment error obtained in step S3, perform transfer alignment.

[0010] Furthermore, in step S1, the analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system is constructed as follows:

[0011]

[0012] In the formula, Main inertial navigation in t m-1 to t m The angular increment vector at time t.

[0013] Main inertial navigation in t m-1 to t m The angular increment of the X-gyroscope at time t, Main inertial navigation in t m-1 to t m The angular increment of the Y-gyroscope at time t. Main inertial navigation in t m-1 to t m The angular increment of the Z-gyroscope at time t;

[0014] for antisymmetric matrix,

[0015]

[0016] The relative installation error vector between the master and sub-inertial navigation systems. Δβ 1,2 The pitch relative installation error of the master and slave inertial navigation systems, Δγ 1,2 The relative roll installation error of the master and sub-inertial navigation systems, Δα 1,2 The relative installation error of the heading of the main and sub-inertial navigation systems;

[0017] The relative attitude error vector caused by self-alignment error is determined by the following formula:

[0018]

[0019] In the formula, For t m The self-alignment error vector at time t.

[0020] δβ 1,2 (t m ) for tm The pitch relative attitude error at any given time, δγ 1，2 (t m ) for t m The relative roll attitude error at time δα 1，2 (t m ) for t m The relative attitude error of the heading at any given moment;

[0021] antisymmetric matrix,

[0022]

[0023] For t m The relative attitude error vector at time t.

[0024] yes antisymmetric matrix,

[0025] Furthermore, in step S2, the specific method for obtaining the relative installation error based on the analytical model of relative installation error constructed in step S1 includes the following steps:

[0026] S201. Collect the attitude vector ψ1 output by the main inertial navigation system, the attitude vector ψ2 output by the sub-inertial navigation system, and the angular increment vector Δθ output by the main inertial navigation system within a time interval T. b2 ;

[0027] Where s≥3, ψ1=[β1,γ1,α1] T ψ2=[β2,γ2,α2] T β1 is the pitch angle output by the main inertial navigation system, γ1 is the roll angle output by the main inertial navigation system, α1 is the yaw angle output by the main inertial navigation system, β2 is the pitch angle output by the sub-inertial navigation system, γ2 is the roll angle output by the sub-inertial navigation system, and α2 is the yaw angle output by the sub-inertial navigation system.

[0028] S202. Based on the attitude vector ψ1 output by the main inertial navigation system and the attitude vector ψ2 output by the sub-inertial navigation system obtained in step S201, use the formula... Obtain the relative attitude error vector Right now

[0029]

[0030] In the formula, β1(t) m ) for t m The pitch angle output by the master inertial navigation system at time t, γ1(t) m ) for t m The roll angle output by the master inertial navigation system at time t, α1(t) m) for t m The heading angle output by the master inertial navigation system at time t, β2(t) m ) for t m The pitch angle output by the sub-inertial navigation system at time t, γ2(t) m ) for t m The roll angle output by the sub-inertial navigation system at time t, α2(t) m ) for t m The heading angle output by the sub-inertial navigation system at any given moment;

[0031] S203. Based on step S1, construct an analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system, and use the attitude vectors output by the main inertial navigation system, the attitude vectors output by the sub-inertial navigation system, the angular increment vector output by the main inertial navigation system, and the relative attitude error vector obtained in step S201, and solve for the relative installation error vector.

[0032] Specifically, the attitude vectors output by the main inertial navigation system (INS), the attitude vectors output by the sub-INS, the angular increment vector output by the main INS, and the relative attitude error vectors obtained in step S201 within a time period T are substituted into the analytical model of relative installation error to obtain s sets of equations:

[0033]

[0034] An equation has three variables: Δβ 1,2 ,Δγ 1,2 and Δα 1,2 Since s≥3 is guaranteed in step S201, the solution is obtained by the least squares method. The relative installation error vector can then be obtained.

[0035] Furthermore, in step S3, the specific method for obtaining the initial self-alignment error using the relative installation error obtained in step S2 includes the following steps:

[0036] S301. Collect the attitude vector ψ1(0) output at the initial moment after the main inertial navigation system is aligned and the attitude vector ψ2(0) output at the initial moment after the sub-inertial navigation system is aligned.

[0037] Where ψ1(0)=[β1(0),γ1(0),α1(0)] T ,ψ2(0)=[β2(0),γ2(0),α2(0)] Tβ1(0) is the pitch angle output at the initial moment of the main inertial navigation system's alignment completion, γ1(0) is the roll angle output at the initial moment of the main inertial navigation system's alignment completion, α1(0) is the heading angle output at the initial moment of the main inertial navigation system's alignment completion, β2(0) is the pitch angle output at the initial moment of the sub-inertial navigation system's alignment completion, γ2(0) is the roll angle output at the initial moment of the sub-inertial navigation system's alignment completion, and α2(0) is the heading angle output at the initial moment of the sub-inertial navigation system's alignment completion.

[0038] S302. Based on the attitude vector ψ1(0) output at the initial moment of the main inertial navigation system alignment completion and the attitude vector ψ2(0) output at the initial moment of the sub-inertial navigation system alignment completion obtained in step S301, using the formula... Obtain the self-alignment error vector at the initial moment after alignment completion, i.e.

[0039]

[0040] Furthermore, in step S4, the specific method for performing transfer alignment based on the relative installation error and initial self-alignment error obtained in step S3 includes the following steps:

[0041] S401. Collect the attitude vector ψ1(0) output at the initial moment after the main inertial navigation system alignment is completed;

[0042] S402, Using the formula Obtain the sub-INS correction attitude of the transfer alignment; where ψ2'(0) is the sub-INS correction attitude of the transfer alignment.

[0043] Compared with existing technologies, the present invention has the following advantages: The method provided by the present invention establishes an analytical model of the relative installation error between the main inertial navigation system (main inertial navigation system) and the sub-inertial navigation system (sub-inertial navigation system). First, the relative installation error is obtained based on the analytical model of the relative installation error. Then, the self-alignment error is obtained based on coordinate transformation using the obtained relative installation error. Finally, the relative attitude between the main and sub-inertial navigation systems is obtained. This method has high reliability, strong versatility, high algorithm efficiency, simple operation, high accuracy, and good practicality. The method provided by the present invention solves the problems that existing transfer alignment methods rely heavily on filtering algorithms, require adjustment of filtering parameters for different levels of inertial navigation systems, and require ships to perform special maneuvers during the transfer alignment process to assist in the convergence of the filtered estimates. When the system is affected by colored noise, filtering divergence will occur. Furthermore, existing transfer alignment methods have long times, which cannot meet the needs of carrier-based aircraft performing emergency missions. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating a UAV alignment method based on an analytical model of relative installation error according to the present invention. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0046] like Figure 1 As shown, a specific embodiment of the present invention provides a UAV transfer alignment method based on a relative installation error analytical model, comprising the following steps:

[0047] S1. Construct an analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system;

[0048] S2. Based on the analytical model of relative installation error constructed in step S1, obtain the relative installation error;

[0049] S3. Using the relative installation error obtained in step S2, obtain the initial self-alignment error;

[0050] S4. Based on the relative installation error and initial self-alignment error obtained in step S3, perform transfer alignment.

[0051] In this embodiment, in step S1, the analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system is constructed as follows:

[0052]

[0053] In the formula, Main inertial navigation in t m-1 to t m The angular increment vector at time t.

[0054] Main inertial navigation in t m-1 to t m The angular increment of the X-gyroscope at time t, Main inertial navigation in t m-1 to t m The angular increment of the Y-gyroscope at time t. Main inertial navigation in t m-1 to t m The angular increment of the Z-gyroscope at time t;

[0055] for antisymmetric matrix,

[0056]

[0057] The relative installation error vector between the master and sub-inertial navigation systems. Δβ 1,2 The pitch relative installation error of the master and slave inertial navigation systems, Δγ 1,2The relative roll installation error of the master and sub-inertial navigation systems, Δα 1,2 The relative installation error of the heading of the main and sub-inertial navigation systems;

[0058] The relative attitude error vector caused by self-alignment error is determined by the following formula:

[0059]

[0060] In the formula, For t m The self-alignment error vector at time t.

[0061] δβ 1,2 (t m ) for t m The pitch relative attitude error at any given time, δγ 1，2 (t m ) for t m The relative roll attitude error at time δα 1，2 (t m ) for t m The relative attitude error of the heading at any given moment;

[0062] for antisymmetric matrix,

[0063]

[0064] For t m The relative attitude error vector at time t.

[0065] yes antisymmetric matrix,

[0066] In this embodiment, in step S2, the specific method for obtaining the relative installation error based on the analytical model of relative installation error constructed in step S1 includes the following steps:

[0067] S201. Collect the attitude vector ψ1 output by the main inertial navigation system, the attitude vector ψ2 output by the sub-inertial navigation system, and the angular increment vector Δθ output by the main inertial navigation system within a time interval T. b2 ;

[0068] Where s≥3, ψ1=[β1,γ1,α1] T ψ2=[β2,γ2,α2] Tβ1 is the pitch angle output by the main inertial navigation system, γ1 is the roll angle output by the main inertial navigation system, α1 is the yaw angle output by the main inertial navigation system, β2 is the pitch angle output by the sub-inertial navigation system, γ2 is the roll angle output by the sub-inertial navigation system, and α2 is the yaw angle output by the sub-inertial navigation system.

[0069] S202. Based on the attitude vector ψ1 output by the main inertial navigation system and the attitude vector ψ2 output by the sub-inertial navigation system obtained in step S201, use the formula... Obtain the relative attitude error vector Right now

[0070]

[0071] In the formula, β1(t) m ) for t m The pitch angle output by the master inertial navigation system at time t, γ1(t) m ) for t m The roll angle output by the master inertial navigation system at time t, α1(t) m ) for t m The heading angle output by the master inertial navigation system at time t, β2(t) m ) for t m The pitch angle output by the sub-inertial navigation system at time t, γ2(t) m ) for t m The roll angle output by the sub-inertial navigation system at time t, α2(t) m ) for t m The heading angle output by the sub-inertial navigation system at any given moment;

[0072] S203. Based on step S1, construct an analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system, and use the attitude vectors output by the main inertial navigation system, the attitude vectors output by the sub-inertial navigation system, the angular increment vector output by the main inertial navigation system, and the relative attitude error vector obtained in step S201, and solve for the relative installation error vector.

[0073] Specifically, the attitude vectors output by the main inertial navigation system (INS), the attitude vectors output by the sub-INS, the angular increment vector output by the main INS, and the relative attitude error vectors obtained in step S201 within a time period T are substituted into the analytical model of relative installation error to obtain s sets of equations:

[0074]

[0075] An equation has three variables: Δβ 1,2 ,Δγ 1,2 and Δα 1,2 Since s≥3 is guaranteed in step S201, the solution is obtained by the least squares method. The relative installation error vector can then be obtained.

[0076] In this embodiment, the specific method for obtaining the initial self-alignment error using the relative installation error obtained in step S2 in step S3 includes the following steps:

[0077] S301. Collect the attitude vector ψ1(0) output at the initial moment after the main inertial navigation system is aligned and the attitude vector ψ2(0) output at the initial moment after the sub-inertial navigation system is aligned.

[0078] Where ψ1(0)=[β1(0),γ1(0),α1(0)] T ,ψ2(0)=[β2(0),γ2(0),α2(0)] T β1(0) is the pitch angle output at the initial moment of the main inertial navigation system's alignment completion, γ1(0) is the roll angle output at the initial moment of the main inertial navigation system's alignment completion, α1(0) is the heading angle output at the initial moment of the main inertial navigation system's alignment completion, β2(0) is the pitch angle output at the initial moment of the sub-inertial navigation system's alignment completion, γ2(0) is the roll angle output at the initial moment of the sub-inertial navigation system's alignment completion, and α2(0) is the heading angle output at the initial moment of the sub-inertial navigation system's alignment completion.

[0079] S302. Based on the attitude vector ψ1(0) output at the initial moment of the main inertial navigation system alignment completion and the attitude vector ψ2(0) output at the initial moment of the sub-inertial navigation system alignment completion obtained in step S301, using the formula... Obtain the self-alignment error vector at the initial moment after alignment completion, i.e.

[0080]

[0081] In this embodiment, the specific method for performing transfer alignment based on the relative installation error and initial self-alignment error obtained in step S3 in step S4 includes the following steps:

[0082] S401. Collect the attitude vector ψ1(0) output at the initial moment after the main inertial navigation system alignment is completed;

[0083] S402, Using the formula Obtain the sub-INS correction attitude of the transfer alignment; where ψ2'(0) is the sub-INS correction attitude of the transfer alignment.

[0084] To verify the correctness of the present invention, a simulation experiment was conducted below. The parameters of the inertial navigation system selected for the simulation experiment are shown in Table 1. Table 1 shows the gyroscope and accelerator accuracy of the main and sub-inertial navigation systems.

[0085] Table 1: Accuracy of gyroscope and dialing in the master inertial navigation system during simulation experiments

[0086] Inertial navigation system spinning top accelerometer Main Inertial Navigation 0.05° / h 100ug Sub-inertial navigation 0.5° / h 300ug

[0087] Based on the inertial navigation system parameters in Table 1, six sets of inertial navigation system (INS) sea roll data were simulated, with roll amplitudes of ±10° for yaw and ±6° for pitch. Then, initial attitude error parameters, as shown in Tables 2 and 3, were set according to the INS device accuracy, the machining accuracy of the mounting plane, and manual installation errors. The initial attitude information of the main INS is shown in Table 2, and the initial attitude information of the sub-INS is shown in Table 3.

[0088] Table 2: Initial attitude error settings of the main inertial navigation system in the simulation experiment

[0089]

[0090] Table 3: Initial attitude error settings of the sub-inertial navigation system in the simulation experiment

[0091]

[0092] The above data were processed using the method provided by this invention, and the processing results are shown in Table 4.

[0093] Table 4 presents the actual relative installation error and the actual relative self-alignment error angle of the main and sub-inertial navigation systems, as well as the relative installation error and the relative self-alignment error angle estimated by the algorithm.

[0094] Table 4: Relative error estimation results of the main and sub-inertial navigation systems in the simulation experiment

[0095]

[0096] As can be seen from the results of the six simulation experiments in Table 4, the method proposed in this invention achieves an accuracy better than 3% (3σ) in estimating the relative error between the main and sub-inertial navigation systems. The relative installation error, as a deterministic error, is valuable for accurately estimating to separate the relative self-alignment error between the main and sub-inertial navigation systems. According to the principle of limit alignment, the self-alignment accuracy is determined by the device accuracy, which in turn determines navigation performance. Estimating and compensating for the relative self-alignment error can effectively improve the navigation performance of the inertial navigation system. Table 4 shows that the method presented in this paper can effectively compensate for more than 98% of the heading error. Therefore, the effectiveness and correctness of the method provided in this paper are verified.

[0097] The parts of this invention not disclosed in detail are well-known technologies in the field.

[0098] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes will be obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

Claims

1. A UAV transfer alignment method based on an analytical model of relative installation error, characterized in that, Includes the following steps: S1. The analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system is as follows: ； In the formula, Δθ b2 (t m ) as the main inertial navigation system in t m-1 to t m The angular increment vector at time Δθ b2 (t m )=[Δθ b2x (t m ) Δθ b2y (t m ) Δθ b2z (t m )],Δθ b2x (t m ) as the main inertial navigation system in t m-1 to t m The angular increment of the X-gyroscope at time Δθ b2y (t m ) as the main inertial navigation system in t m-1 to t m The angular increment of the Y-gyroscope at time Δθ b2z (t m ) as the main inertial navigation system in t m-1 to t m The angular increment of the Z-gyroscope at time t; [Δθ b2 (t m )×] is Δθ b2 (t m The antisymmetric matrix of ) ; φ is the relative installation error vector between the main and sub-inertial navigation systems, φ=[Δβ] 1,2 ,Δγ 1,2 ,Δα 1,2 ] T Δβ 1,2 The pitch relative installation error of the master and slave inertial navigation systems, Δγ 1,2 The relative roll installation error of the master and sub-inertial navigation systems, Δα 1,2 The relative installation error of the heading of the main and sub-inertial navigation systems; The relative attitude error vector caused by self-alignment error is determined by the following formula: ； In the formula, For t m The self-alignment error vector at time t. ,δβ 1,2 (t m ) for t m The pitch relative attitude error at any given time, δγ 1,2 (t m ) for t m The relative roll attitude error at time δα 1,2 (t m ) for t m The relative attitude error of the heading at any given moment; for antisymmetric matrix, ; For t m The relative attitude error vector at time t. ; yes antisymmetric matrix, ; S2. Based on the analytical model of relative installation error constructed in step S1, obtain the relative installation error; S3. Using the relative installation error obtained in step S2, obtain the initial self-alignment error; S4. Based on the relative installation error and initial self-alignment error obtained in step S3, perform transfer alignment.

2. The UAV transfer alignment method based on an analytical model of relative installation error according to claim 1, characterized in that, In step S2, based on the analytical model of relative installation error constructed in step S1, the specific method for obtaining the relative installation error includes the following steps: S201. Collect the attitude vectors output by the main inertial navigation system, the attitude vectors output by the sub-inertial navigation system, and the angular increment vector output by the main inertial navigation system within a time period T. Where s≥3, ψ1=[β1,γ1,α1] T ψ2=[β2,γ2,α2] T β1 is the pitch angle output by the main inertial navigation system, γ1 is the roll angle output by the main inertial navigation system, α1 is the yaw angle output by the main inertial navigation system, β2 is the pitch angle output by the sub-inertial navigation system, γ2 is the roll angle output by the sub-inertial navigation system, and α2 is the yaw angle output by the sub-inertial navigation system. S202. Based on the attitude vector ψ1 output by the main inertial navigation system and the attitude vector ψ2 output by the sub-inertial navigation system obtained in step S201, use the formula... Obtain the relative attitude error vector ,Right now ; In the formula, β1(t) m ) for t m The pitch angle output by the master inertial navigation system at time t, γ1(t) m ) for t m The roll angle output by the master inertial navigation system at time t, α1(t) m ) for t m The heading angle output by the master inertial navigation system at time t, β2(t) m ) for t m The pitch angle output by the sub-inertial navigation system at time t, γ2(t) m ) for t m The roll angle output by the sub-inertial navigation system at time t, α2(t) m ) for t m The heading angle output by the sub-inertial navigation system at any given moment; S203. Based on step S1, construct an analytical model of the relative installation error between the main inertial navigation system and the sub-inertial navigation system, the attitude vector output by the main inertial navigation system collected in step S201, the attitude vector output by the sub-inertial navigation system, the angular increment vector output by the main inertial navigation system, and the relative attitude error vector obtained in step S202, and solve to obtain the relative installation error vector φ. Specifically, the attitude vectors output by the main inertial navigation system (INS), the attitude vectors output by the sub-INS, the angular increment vector output by the main INS, and the relative attitude error vectors obtained in step S201 within a time period T are substituted into the analytical model of relative installation error to obtain s sets of equations: ； An equation has three variables: Δβ 1,2 ,Δγ 1,2 and Δα 1,2 Since s≥3 is guaranteed in step S201, the solution is obtained by the least squares method. The relative installation error vector φ=[Δβ] can then be obtained. 1,2 ,Δγ 1,2 ,Δα 1,2 ] T .

3. The UAV transfer alignment method based on an analytical model of relative installation error according to claim 2, characterized in that, In step S3, the specific method for obtaining the initial self-alignment error using the relative installation error obtained in step S2 includes the following steps: S301. Collect the attitude vector ψ1(0) output at the initial moment after the main inertial navigation system is aligned and the attitude vector ψ2(0) output at the initial moment after the sub-inertial navigation system is aligned. Where ψ1(0)=[β1(0),γ1(0),α1(0)] T ,ψ2(0)=[β2(0),γ2(0),α2(0)] T β1(0) is the pitch angle output at the initial moment of the main inertial navigation system's alignment completion, γ1(0) is the roll angle output at the initial moment of the main inertial navigation system's alignment completion, α1(0) is the heading angle output at the initial moment of the main inertial navigation system's alignment completion, β2(0) is the pitch angle output at the initial moment of the sub-inertial navigation system's alignment completion, γ2(0) is the roll angle output at the initial moment of the sub-inertial navigation system's alignment completion, and α2(0) is the heading angle output at the initial moment of the sub-inertial navigation system's alignment completion. S302. Based on the attitude vector ψ1(0) output at the initial moment of the main inertial navigation system alignment completion and the attitude vector ψ2(0) output at the initial moment of the sub-inertial navigation system alignment completion obtained in step S301, using the formula... Obtain the self-alignment error vector at the initial moment after alignment completion, i.e. .

4. The UAV transfer alignment method based on a relative installation error analytical model according to claim 3, characterized in that: In step S4, the specific method for transferring alignment based on the relative installation error and initial self-alignment error obtained in step S3 includes the following steps: S401. Collect the attitude vector ψ1(0) output at the initial moment after the main inertial navigation system alignment is completed; S402, Using the formula Obtain the sub-INS correction attitude of the transfer alignment; where ψ2'(0) is the sub-INS correction attitude of the transfer alignment.

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