A method for real-time estimation of remaining time for satellite-assisted inertial navigation alignment

Abstract

This invention provides a method for real-time estimation of the remaining time for satellite-assisted inertial navigation system (INS) alignment. Traditional methods for determining the completion of satellite-assisted alignment are generally the same as those for ground-based static base self-alignment, i.e., fixed time or statistical filtering counts. However, in reality, the accuracy of satellite-assisted alignment is related to the latitude and motion during the alignment process. This invention designs a method for calculating the remaining time for fine satellite-assisted INS alignment without changing the satellite-assisted alignment algorithm. Using a Kalman filter as a mathematical tool, and taking the diagonal elements Pk_yaw of the covariance matrix corresponding to the heading error during uniform level flight and the number of filtering counts as references, a relationship is established between the estimated remaining time for fine alignment and the real-time Pk_yaw and the real-time number of filtering counts, enabling real-time calculation of the remaining time for satellite-assisted fine alignment.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation precision alignment remaining time calculation technology, and in particular relates to a method for real-time estimation of satellite-assisted inertial navigation alignment remaining time. Background Technology

[0002] Initial alignment of the inertial navigation system is the process of establishing the initial values ​​of the navigation mathematical platform, that is, the transformation relationship between the carrier coordinate system b and the navigation coordinate system n (which can be described by pitch angle, roll angle, and azimuth angle). Acceleration measurements are projected onto the navigation frame using the mathematical platform, and integration can complete the velocity and position calculations.

[0003] Initial alignment generally consists of two stages: coarse alignment and fine alignment. In the coarse alignment stage, rough values ​​for pitch, roll, and azimuth angles are obtained through autonomous calculation (GC self-alignment) or binding methods (transfer alignment). In the fine alignment stage, initial mathematical platform values ​​are established using the coarse alignment results for navigation calculations. Then, using an inertial navigation error propagation model, the mathematical platform error is estimated from the rates of change of velocity and position errors, and compensation is used to improve the accuracy of the mathematical platform. Fine alignment is generally achieved using a Kalman filter.

[0004] For ground-based GC alignment, the measurements (velocity error, position error) of the Kalman filter are directly calculated using inertial navigation based on stationary ground conditions (velocity is 0, position remains unchanged), without requiring additional reference information. The ground-based GC alignment accuracy convergence process is less affected by the working environment and is typically designed with a fixed alignment time, with a typical value of 8 minutes.

[0005] Satellite-assisted alignment is used for aligning moving bases, where the carrier's velocity and position change constantly. Therefore, to obtain measurements of inertial navigation velocity and position errors, reference velocity and position information is needed from satellite navigation. This involves subtracting the velocity and position from the onboard inertial navigation data from the satellite navigation data to obtain the measurements. The completion determination method for traditional satellite-assisted alignment is generally the same as that for ground-based static base self-alignment, i.e., fixed time or statistical filtering counts.

[0006] However, the accuracy of satellite-assisted alignment is related to the latitude and the motion during the alignment process. The higher the latitude, the smaller the northward component of the Earth's rotational angular velocity, which is less conducive to alignment and thus affects the alignment time. Real-time estimation of the remaining time required for the inertial navigation system to switch to navigation state during the inertial navigation alignment process is very important for pilots to understand the inertial navigation alignment state, for the execution of flight missions, the formulation of flight strategies, and flight decisions in emergency situations. Summary of the Invention

[0007] The purpose of this invention is to provide a method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment. By estimating the current alignment accuracy of the fine alignment filter online, the remaining time required for the inertial navigation system to switch to navigation mode can be estimated, which can help pilots understand the working status of the inertial navigation system and provide a basis for the execution of flight missions and the formulation of flight strategies.

[0008] The technical solution of this invention is as follows: In order to achieve the above-mentioned objective, a method for real-time estimation of the remaining time of satellite-assisted inertial navigation alignment is proposed. Based on the navigation error model of the inertial navigation system and the information of the satellite navigation receiver, an inertial navigation fine alignment Kalman filter is established; the convergence degree of the filter estimation error variance matrix Pk is used as a measure of alignment accuracy to realize real-time estimation of the remaining time of inertial navigation alignment.

[0009] Specifically, the steps include the following:

[0010] S1, Obtain the satellite-assisted inertial navigation fine alignment design time T FINE Precise alignment filter period T 滤波 ;

[0011] S2. Create a typical trajectory with a reference latitude of zero and a flight path that flies northward at a constant speed;

[0012] S3. Based on the information from inertial navigation and satellite navigation receivers, establish a satellite-assisted inertial navigation precision alignment Kalman filter;

[0013] S4. Under the flight trajectory conditions created in step S2, perform satellite-assisted inertial navigation fine alignment simulation using the Kalman filter established in step S3, within the satellite-assisted fine alignment design time T. FINE Within, the mean square error matrix P of the filter state estimation error is... k The diagonal elements corresponding to the misalignment angle error of the Zhongtian platform are denoted as the analog array Pk_yaw_array, including T. FINE / T 滤波 Each element in the array is sequentially labeled with its array element number.

[0014] S5. During actual flight, the satellite-assisted inertial navigation precision alignment Kalman filter established in step S3 is used to obtain the current filtering count N in real time during actual flight. flter And the recently updated Kalman filter state estimation error mean square matrix P of satellite-aided inertial navigation precision alignment k The diagonal element Pk_yaw_real_time corresponding to the misalignment angle error of the Zhongtian platform; using the simulation array Pk_yaw_array obtained in step S4, the remaining time for satellite-assisted inertial navigation alignment is estimated in real time according to the following formula:

[0015]

[0016] Where, when N filter When the value is greater than 15, Pk_yaw_real_time is compared with the value in the simulated array Pk_yaw_array. If Pk_yaw_real_time is smaller than the smallest value in the simulated array Pk_yaw_array, it means that the heading has converged; otherwise, the heading has not converged. iax is the index of the first array element in the simulated array Pk_yaw_array that is less than or equal to Pk_yaw_real_time.

[0017] In one possible embodiment, during step S5, the actual predetermined precision alignment time is taken during the actual flight. Take the actual precise alignment filter period Where Lat is the initial latitude.

[0018] In one possible embodiment, during the actual flight of step S5, the remaining time for satellite-assisted inertial navigation alignment is estimated in real time using the actual predetermined fine alignment time and the actual fine alignment filter period according to the following formula:

[0019]

[0020] In one possible embodiment, in step S2, the reference coordinate systems that need to be established for a typical trajectory of uniform northward flight include a navigation reference system, denoted as n; an aircraft body reference system, denoted as b; an inertial navigation IMU reference system, denoted as s; a fixed Earth coordinate system, denoted as e; and a geocentric inertial coordinate system, denoted as i.

[0021] In one possible embodiment, the process of establishing the satellite-assisted inertial navigation precision alignment Kalman filter in step S3 includes: establishing an inertial navigation system navigation error model; which consists of differential equations of platform misalignment angle error, velocity error, and position error.

[0022] In one possible embodiment, step S3 further includes establishing a state space model for the transmission of satellite-assisted inertial navigation precision alignment error based on the inertial navigation system navigation error model; the state variables of the state space model include: the state space model for the transmission of satellite-assisted inertial navigation precision alignment error is selected as a combination of the inertial navigation system navigation error model, gyroscope drift error, accelerator zero position error and lever arm residual error.

[0023] In one possible embodiment, in step S3, a system equation is constructed using a state-space model of satellite-assisted inertial navigation (INS) alignment error propagation. Using real-time position and velocity information from satellite positioning as an external reference, the INS velocity and position errors are calculated, measurement equations are constructed, and a Kalman filter for satellite-assisted INS alignment is established. In this method, the Kalman filter measurement values ​​are the differences between the INS velocity and position information and the velocity and position information of the time-synchronized satellite navigation receiver. The satellite navigation receiver velocity and position information should first be compensated for the lever arm error between the satellite navigation receiver and the INS.

[0024] In one possible embodiment, in step S5, the remaining time for satellite-assisted inertial navigation alignment is estimated using the fine alignment filter period or the actual fine alignment filter period as the period until the fine alignment is completed.

[0025] If the actual flight is at approximately a constant speed, the estimated remaining time is generally close to the preset time. If the aircraft maneuvers, the estimated time will generally decrease rapidly.

[0026] The actual flight of the aircraft includes maneuvers such as S-shaped flight or figure-eight flight.

[0027] The beneficial effects of this invention are:

[0028] This invention establishes a Kalman filter for inertial navigation system (INS) fine alignment based on the navigation error model and satellite navigation receiver information. The convergence of the filter's estimation error variance matrix Pk is used as a measure of alignment accuracy, enabling real-time estimation of the remaining INS alignment time. Taking the slowest-converging heading error as the evaluation object, and using the diagonal elements of the fine alignment filter's covariance matrix Pk as a measure of alignment accuracy, offline simulation yields the covariance corresponding to the heading error under typical flight trajectories. This covariance is compared with the filter's heading estimation covariance in real-time flight, and the influence of latitude on alignment is comprehensively considered, allowing for real-time prediction of the remaining fine alignment time. This method enables real-time prediction of the remaining time required for INS to transition to navigation mode during INS alignment, helping pilots understand the INS alignment status and providing a basis for flight mission execution, flight strategy formulation, and emergency flight decisions. Attached Figure Description

[0029] Figure 1 This is a flowchart of a preferred embodiment of the present invention;

[0030] Figure 2A A schematic diagram illustrating the convergence of heading error under aircraft maneuvering conditions;

[0031] Figure 2B A schematic diagram illustrating the remaining time for precise alignment under aircraft maneuvering conditions;

[0032] Figure 3AA schematic diagram illustrating the convergence of heading error under the condition of level flight to the west;

[0033] Figure 3B A schematic diagram showing the estimated remaining time for precise alignment under westward level flight conditions. Detailed Implementation

[0034] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings:

[0035] like Figure 1 As shown, a method for real-time estimation of the remaining time of satellite-assisted inertial navigation alignment is proposed. Based on the navigation error model of the inertial navigation system and the information of the satellite navigation receiver, a fine alignment Kalman filter is established. The convergence degree of the filter estimation error variance matrix Pk is used as the criterion for the completion of fine alignment, thereby realizing the estimation of the remaining time of fine alignment.

[0036] Example 1

[0037] The more specific implementation steps are as follows:

[0038] Step 1: Determine the design time T for satellite-assisted fine alignment. FINE =400s, fine alignment filter period T 滤波 =2s.

[0039] Step 2: Design typical flight trajectories

[0040] Step 2.1: Establish a reference coordinate system

[0041] These include: navigation reference frame (n frame), aircraft body reference frame (b frame), inertial navigation IMU reference frame (s frame), Earth-fixed coordinate system (e frame), and geocentric inertial coordinate system (i frame).

[0042] a) Navigation coordinate system OX n Y n Z n The local northeast-central geographic coordinate system is used as the navigation coordinate system, OX. n OY n OZ n They point to the east, north, and sky directions respectively;

[0043] b) Aircraft body coordinate system OX b Y b Z b Fixed to the aircraft fuselage, OX b OY b OZ b These point to the right, forward, and upward directions of the aircraft fuselage, respectively, corresponding to the aircraft's longitudinal axis, transverse axis, and vertical axis.

[0044] c) Inertial navigation IMU reference frame OX s Ys Z s Fixed to the inertial navigation IMU, OX s OY s OZ s These point to the right, forward, and upward directions of the inertial navigation IMU, respectively.

[0045] d) Earth-fixed coordinate system OX e Y e Z e The origin is located at the Earth's center, OX o Pointing to the intersection of the Prime Meridian and the Equator, OZ o Pointing to the North Pole, OY e With OX e OZ e Forming a right-handed orthogonal system;

[0046] e) Geocentric inertial coordinate system OX t Y t Z t The origin is located at the Earth's center, OX t Pointing to the vernal equinox, OZ i Along the Earth's axis of rotation, OY i With OX i OZ i They form a right-handed orthogonal system.

[0047] Step 2.2: Design typical flight trajectories as simulation inputs.

[0048] In the reference coordinate system established in step 2.1, a flight trajectory of uniform northward flight in the navigation coordinate system is designed as a typical flight trajectory, and the attitude, velocity, position, gyroscope angle increment, and accelerometer velocity increment of the inertial navigation system are obtained through simulation.

[0049] Step 3: Establish a state-space model for the propagation of satellite-assisted inertial navigation alignment errors.

[0050] Establish a navigation error model for the inertial navigation system, based on the platform's misalignment angle error. speed error Position error The differential equations are structured as follows:

[0051]

[0052]

[0053]

[0054] In the formula:

[0055] The symbol δ represents the error of the relevant parameters; E, N, and U represent east, north, and celestial directions, respectively; δv EIndicates the eastward velocity error, δv N Indicates the northward velocity error, δv U Indicates the upward velocity error; φ E Indicates the platform's eastward misalignment angle, φ N Indicates the platform's northward misalignment angle, φ U This indicates the platform's inaccuracy angle. These are the latitude, longitude, and altitude errors, respectively. latitude, λ s For longitude, h s R represents height; N and R E Here, f represents the radius of curvature of the Earth's meridian and circumference, respectively; f is the specific force; and v is the velocity. It is the coordinate transformation matrix from the IMU reference frame to the geographic frame;

[0056] The projection of the rotational angular velocity of system b relative to system a onto system c, such as This represents the projection of the rotational angular velocity of the Earth-fixed coordinate system relative to the inertial frame onto the navigation coordinate system.

[0057] D s and This represents the gyroscope drift error and accelerator null error of the inertial navigation IMU;

[0058] D s Model as random constant and white noise The superposition model, Model as random constant and white noise Superposition model:

[0059]

[0060] in

[0061]

[0062]

[0063] q D Measure the variance of noise for the gyroscope. The variance of noise measured for the accelerometer.

[0064] The residual error δL of the lever arm relative to the phase center of the inertial navigation system antenna is... b =[δL x δL y δL z ] T Model as random constant error

[0065]

[0066] The state-space model for the propagation of satellite-assisted inertial navigation alignment errors is selected as a synthesis of the inertial navigation system navigation error model, gyroscope drift error, accelerator null error, and lever arm residual error, totaling 18 dimensions:

[0067]

[0068] Step 4: Construct system equations using the state-space model of satellite-assisted inertial navigation precision alignment error propagation from Step 3. Using the real-time position and velocity information of satellite positioning as an external reference, calculate the velocity and position errors of the inertial navigation system, construct measurement equations, and establish a Kalman filter for satellite-assisted inertial navigation precision alignment.

[0069] The system equations of a continuous domain Kalman filter are as follows:

[0070]

[0071] In the formula, F matrix is ​​the transfer matrix of the continuous domain Kalman filter system, which is constructed from the error differential equations in equations (2), (3), and (4), and w is the system noise, which is derived from the gyroscope noise. and added noise constitute;

[0072] The Kalman filter measures the velocity error of the inertial navigation system. and position error δp s

[0073] z k =H k x k +v k

[0074] In the formula H k Let v be the measurement matrix of the filter. k For measuring noise;

[0075] H k Related to speed error, position error, and residual lever arm error, specifically:

[0076]

[0077] In the formula, This is the expression of the angular velocity of the b-system relative to the e-system in the b-system. express The antisymmetric matrix, I 3×3 It is a 3-order identity matrix. It is the attitude transformation matrix from the machine system to the navigation system, C p The transformation matrix representing the error from east, north, and sky to latitude, longitude, and altitude is as follows:

[0078]

[0079] The three components, R N and R E denoted by , respectively, the radii of curvature of the Earth's meridian and circumference, and h is the altitude.

[0080] Measurement z j The specific construction formula is based on the inertial navigation velocity. Position p s With satellite navigation receiver speed v n The result is obtained by subtracting the position p (compensation lever arm compensation), i.e.

[0081]

[0082] In the formula

[0083]

[0084]

[0085] Kalman filtering calculations are divided into prediction updates and measurement updates. At time K, during the prediction phase, the system prediction equation obtained from the system model is:

[0086]

[0087]

[0088]

[0089]

[0090] Where T F It is the transition period, F is the continuous domain system matrix, Φ k，k-1 It is the discrete-domain state transition matrix. Indicates t k-1 The state estimate of the system state X at time X. Indicates based on t k-1 State estimate at time 1 Make a prediction to obtain t k The predicted state value at time P. k-1 It is t k-1 The covariance of the system state X at time X, P k / k-1 Q is the one-step predictive covariance of the system state X. K-1 It is t k-1 Time-based system noise.

[0091] During the measurement update phase, the state estimate and covariance estimate are updated using predicted and observed values. The update equation is as follows:

[0092]

[0093]

[0094]

[0095] P k =(IK k H k )P k / k-1

[0096] in H represents the difference between the observed and predicted values, and can also be seen as the measurement estimation error caused by the prediction error. k It is a measurement matrix.

[0097] K k It's called Kalman gain, a weight matrix that determines... What percentage of the gain is accepted by the system? Gain matrix K k It is derived based on the minimum mean square error criterion.

[0098] Precisely aligned Kalman filters require adjustments to Pk, Q, R, and x. k Initialize the matrices: Pk is the mean square error matrix of the filter state estimation, Q is the noise variance matrix of the filter system, and R is the measurement noise variance matrix of the filter. State variable x k The initial value is set to 0; taking a medium-precision inertial device as an example, the Kalman filter parameters are initialized as follows:

[0099]

[0100]

[0101] R = diag{(0.2m / s)} 2 (0.2m / s) 2 (0.2m / s) 2 ,(0.5″) 2 ,(0.5″) 2 (10m) 2}

[0102] P k Let be the mean square error matrix of the filter state estimation, Q be the variance matrix of the filter system noise, and R be the variance matrix of the filter measurement noise. State variable x k The initial value is set to 0.

[0103] The attitude error, velocity error, position error, and gyroscope and accelerator errors estimated by the Kalman filter correspond to the first 15 dimensions of the state variables, while the lever residual error corresponds to the last 3 dimensions of the state variables. These can be used to provide feedback and correct navigation results and device errors of the inertial navigation unit (IMU). The transfer period is set to 1 second; in this example, the filtering period is T. 滤波 =2s.

[0104] Step 5: Under the flight trajectory conditions designed in Step 2, perform satellite-assisted inertial navigation fine alignment simulation using the Kalman filter established in Step 4.

[0105] Step 5.1 Inertial Navigation Fine Alignment Initialization

[0106] The inertial navigation system (INS) completes horizontal alignment using accelerometer data during level flight, initializes the INS' heading angle using the horizontal track angle calculated by satellite positioning, completes the heading setting, and sets the INS' position and velocity using the position and velocity from satellite positioning, thus achieving the initialization of precise INS alignment.

[0107] Step 5.2 Inertial Navigation Update Calculation

[0108] After initialization, the inertial navigation system (INS) updates its navigation parameters using a standard strapdown inertial navigation update algorithm. The input information consists of the angular increment Δθ and velocity increment Δv of the s-frame relative to the i-frame measured by the INS IMU. The output information is the INS's position at time t. k Attitude matrix at time step speed latitude Longitude λ k ,high

[0109] Step 5.3 Criteria for Satellite-Aided Inertial Navigation Fine Alignment

[0110] Satellite-assisted inertial navigation precision alignment uses a Kalman filter as the implementation tool, and the convergence degree of the filter is used as the criterion for accuracy. The specific design is as follows:

[0111] a. The convergence degree of the diagonal element Pk(N, N) of the filter Pk array corresponding to the inertial navigation platform misalignment angle error is used as the criterion for judging the convergence of the inertial navigation platform misalignment angle, that is, the criterion for the accuracy of the alignment, where N is the index of the inertial misalignment angle in the state variable x of the Kalman filter. The reason for choosing the inertial navigation platform misalignment angle error is that, under level flight conditions, the inertial navigation platform misalignment angle error is comparable to the heading error, and its convergence speed is the slowest.

[0112] b. Using the typical flight trajectory designed in step 2 as simulation conditions, and the Kalman filter designed in step 4 as the tool, the alignment time is T. FINE The diagonal elements Pk(N, N) corresponding to the heading error in the covariance matrix Pk during the simulation filtering process are saved as T.FINE / T 滤波 An array of elements, denoted as Pk_yaw_array, is used to estimate the remaining alignment time during real-time flight.

[0113] Step 6: During the actual flight, take the actual predetermined precision alignment time. Take the actual precise alignment filter period Where Lat is the initial latitude;

[0114] Step 7: Calculation of remaining alignment time during actual flight using satellite-assisted inertial navigation fine alignment.

[0115] The precision alignment algorithm in actual flight is consistent with the offline simulation described above, that is, it uses the Kalman filter described in step 4 as the implementation tool. Let N be the current filtering iteration number during actual flight. filter The estimated remaining alignment time is calculated using the diagonal element Pk(N, N) (denoted as Pk_yaw_real_time) corresponding to the heading error in the covariance matrix Pk of the alignment filter during actual flight as the criterion. The specific design is as follows:

[0116] During actual flight, after each Kalman filter calculation, the actual flight process covariance matrix is ​​calculated and updated in real time based on the Kalman filter calculation equation. The number of filtering iterations N is... filter When the remaining alignment time is less than or equal to 15, the estimated remaining alignment time is reduced by T with each filter. step ; Number of filtering iterations N filter When the value is greater than 15, compare Pk_yaw_real_time with the value in Pk_yaw_array, where Pk_yaw_real_time is the diagonal element corresponding to the heading error in the covariance matrix Pk of the current alignment filter. If Pk_yaw_real_time is smaller than the minimum value in Pk_yaw_array, it means the heading has converged and alignment is complete. Otherwise, it is determined that the heading has not converged, and the index of the first element in Pk_yaw_array that is less than or equal to Pk_yaw_real_time is found, and the remaining alignment time is estimated to be T. REMAIN =T FINE_lat -idx·T step The above judgment logic can be summarized as follows:

[0117]

[0118] Specifically, a specific aircraft trajectory was designed, and a simulation of the remaining alignment time was performed to verify the effectiveness of the invention.

[0119] Aircraft maneuvers such as speed changes, turns, and banking can improve the observability and convergence speed of the Kalman filter. However, flying westward at a specific speed causes the aircraft's linear motion to cancel out the Earth's rotation, and higher latitudes reduce the northward component of the Earth's rotation; both of these conditions negatively impact heading error convergence. These changes in state result in irregular variations in the remaining time required for alignment.

[0120] Using the method described in this invention, with an error set according to a medium-precision inertial navigation system, take T... FINE =400s, T 滤波 =2s, simulating two motions: aircraft maneuvering and counteracting the Earth's rotation. Figure 2A It is evident that the heading error converges faster under maneuvering conditions than under uniform motion. Figure 2B It is evident that the estimated alignment time is correspondingly shorter than that for uniform motion. From Figure 3A It is evident that the heading error converges more slowly under westward flight conditions compared to uniform motion. Figure 3B It is evident that the estimated alignment time is correspondingly longer than that during uniform motion. The estimated remaining alignment time calculation results described in this invention reflect the influence of these two types of motion on the convergence speed of alignment accuracy.

[0121] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate and not limit the technical solutions of the present invention. All modifications or partial substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment, characterized in that, Includes the following steps: S1. Obtain the design time for satellite-assisted inertial navigation precision alignment. Precise alignment filter period T 滤波 ; S2. Create a typical trajectory with a reference latitude of zero and a flight path that flies northward at a constant speed; S3. Based on the information from inertial navigation and satellite navigation receivers, establish a satellite-assisted inertial navigation precision alignment Kalman filter; S4. Under the flight trajectory conditions created in step S2, perform satellite-assisted inertial navigation fine alignment simulation using the Kalman filter established in step S3, within the satellite-assisted fine alignment design time. Within, the mean square error matrix P of the filter state estimation error is... k The diagonal elements corresponding to the misalignment angle error of the Zhongtian platform are denoted as the simulated array Pk_yaw_array, including... / T 滤波 Each element in the array is sequentially labeled with its array element number. S5. During actual flight, the satellite-assisted inertial navigation precision alignment Kalman filter established in step S3 is used to obtain the current number of filters during actual flight in real time. And the recently updated Kalman filter state estimation error mean square matrix P of satellite-aided inertial navigation precision alignment k The diagonal element Pk_yaw_real_time corresponding to the misalignment angle error of the Zhongtian platform; using the simulated array Pk_yaw_array obtained in step S4, the remaining time for satellite-assisted inertial navigation alignment is estimated in real time according to the following formula: Among them, when When the value is greater than 15, compare Pk_yaw_real_time with the value in the simulation array Pk_yaw_array. If Pk_yaw_real_time is smaller than the smallest value in the simulation array Pk_yaw_array, the heading has converged; otherwise, the heading has not converged. This is the index of the first array element in the simulated array Pk_yaw_array that is less than or equal to Pk_yaw_real_time.

2. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment, characterized in that, Includes the following steps: S1. Obtain the design time for satellite-assisted inertial navigation precision alignment. Precise alignment filter period T 滤波 ; S2. Create a typical trajectory with a reference latitude of zero and a flight path that flies northward at a constant speed; S3. Based on the information from inertial navigation and satellite navigation receivers, establish a satellite-assisted inertial navigation precision alignment Kalman filter; S4. Under the flight trajectory conditions created in step S2, perform satellite-assisted inertial navigation fine alignment simulation using the Kalman filter established in step S3, within the satellite-assisted fine alignment design time. Within, the mean square error matrix P of the filter state estimation error is... k The diagonal elements corresponding to the misalignment angle error of the Zhongtian platform are denoted as the simulated array Pk_yaw_array, including... / T 滤波 Each element in the array is sequentially labeled with its array element number. S5. During actual flight, the satellite-assisted inertial navigation precision alignment Kalman filter established in step S3 is used to obtain the current number of filters during actual flight in real time. Take the actual scheduled precise alignment time Take the actual precise alignment filter period ,in This is the initial latitude; using the actual predetermined fine alignment time and the actual fine alignment filter period, the remaining time for satellite-assisted inertial navigation alignment is estimated in real time according to the following formula: 。 3. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment according to any one of claims 1 or 2, characterized in that, In step S2, the typical trajectory of a flight moving north at a constant speed requires the establishment of a reference coordinate system, including a navigation reference system, denoted as... Aircraft airframe reference frame, denoted as . Frame; Inertial navigation IMU reference frame, denoted as System; Earth-fixed coordinate system, denoted as System; geocentric inertial coordinate system, denoted as Tie.

4. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment according to any one of claims 1 or 2, characterized in that, In step S3, the process of establishing the satellite-assisted inertial navigation precision alignment Kalman filter includes: establishing the navigation error model of the inertial navigation system; which consists of differential equations of platform misalignment angle error, velocity error, and position error.

5. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment according to any one of claims 1 or 2, characterized in that, In step S3, a state-space model for the propagation of satellite-assisted inertial navigation precision alignment error is also established based on the inertial navigation system navigation error model. The state variables of the state space model include: the state space model for the transmission of satellite-assisted inertial navigation precision alignment error is selected as a combination of the inertial navigation system navigation error model, gyroscope drift error, accelerator zero position error and lever arm residual error.

6. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment according to any one of claims 1 or 2, characterized in that, In step S3, the system equations are constructed using the state-space model of satellite-assisted inertial navigation precision alignment error propagation. The real-time position and velocity information of satellite positioning is used as an external reference to calculate the velocity error and position error of the inertial navigation system, construct the measurement equations, and establish the satellite-assisted inertial navigation precision alignment Kalman filter.

7. A method for real-time estimation of the remaining time for satellite-assisted inertial navigation alignment according to any one of claims 1 or 2, characterized in that, In step S5, the remaining time for satellite-assisted inertial navigation alignment is estimated using the fine alignment filter period or the actual fine alignment filter period as the period until the fine alignment is completed.

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