A compact inertial / spectral redshift navigation method assisted by starlight direction vector

Abstract

The present invention relates to a starlight direction vector-assisted tightly combined inertial / spectral redshift combined navigation method, which establishes a spectral redshift navigation model and calculates the speed and position information of an aircraft through spectral redshift information. Then, a starlight direction vector-assisted spectral redshift navigation model is established. The starlight direction vector of the same observed star body is introduced into the spectral redshift navigation model of step one, and the measurement information is fully utilized. At the same time, the direction vector measurement is used to calculate the position information of the aircraft, thereby reducing the number of stars required to be observed. A starlight direction vector-assisted tightly combined inertial / spectral redshift combined navigation system model is established. A tightly combined navigation system model is established, including a state equation and a measurement equation. At the same time, through a volumetric Kalman-based federal filtering, the starlight direction vector-assisted spectral redshift navigation in step two is subjected to information fusion with the inertial navigation system, thereby further reducing the number of observed celestial bodies and ensuring the stability and reliability of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of spectral redshift navigation and relates to a tightly combined inertial / spectral redshift combined navigation method assisted by a starlight direction vector. Background Art

[0002] The spectral redshift navigation system is a novel autonomous astronomical navigation system with advantages such as high velocity measurement accuracy and wide applicability, promising broad applications in deep space exploration. This method uses the redshift values ​​of the spectra of stars or solar system objects as a navigation information source. Based on the principle of spectral redshift, it calculates the radial velocity of the probe relative to the navigation object. Then, combined with an orbital dynamics model, it performs a filtered estimate of navigation parameters such as the probe's position and velocity. While spectral redshift navigation systems have traditionally been used for deep space navigation, with the improvement of spectrometer spectral resolution, their application in near-space vehicles and cruise missiles is also being explored.

[0003] Current research on spectral-redshift integrated navigation primarily encompasses inertial / spectral-redshift integrated navigation and inertial / astronomical / spectral-redshift integrated navigation. Inertial / spectral-redshift integrated navigation systems improve vehicle navigation reliability without sacrificing autonomy. However, these systems still operate in a loosely coupled mode, resulting in poor interference immunity. Furthermore, spectral-redshift navigation fails to fully utilize star sensor measurements and can only directly correct inertial navigation velocity errors using proposed measurement equations. This can lead to divergence in the inertial navigation output even after long navigation periods. Inertial / astronomical / spectral-redshift integrated navigation further improves the accuracy and reliability of the navigation system's position error by integrating astronomical navigation into inertial / spectral-redshift integrated navigation. However, currently studied astronomical navigation systems still have their own limitations. For example, astronomical navigation systems based on altitude and azimuth cannot measure altitude, and astronomical navigation systems based on starlight refraction are affected by atmospheric concentration. Therefore, obtaining reliable and stable navigation information using existing methods is a current research priority. Summary of the Invention

[0004] Technical problems to be solved

[0005] In order to avoid the shortcomings of the prior art, the present invention proposes a tightly combined inertial / spectral redshift combined navigation method assisted by starlight direction vector, which fully utilizes sensor measurement information to obtain reliable and stable navigation information.

[0006] This paper establishes a measurement equation based on the redshift navigation equation assisted by the starlight direction vector. This equation, combined with the INS error equation, forms a tight combination model that directly corrects the INS's velocity and position errors and improves navigation reliability and anti-interference capabilities. Finally, simulations and comprehensive analysis demonstrate that the improved spectral redshift measurement-assisted inertial navigation / star sensor integrated navigation system can generate reliable and stable navigation information.

[0007] Technical Solution

[0008] A starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method is characterized by the following steps:

[0009] Step 1: Establish a spectral redshift navigation model and calculate the radial velocity and position information of the spacecraft using the spectral redshift information:

[0010] Spectral redshift navigation model:

[0011] Where p i represents the position of the aircraft and p c Indicates the position of a celestial body, measured, c is the speed of light, v i is the velocity vector of the aircraft in the inertial system, i.e., system i, v c is the speed of the celestial body; z is the redshift value of the celestial body spectrum obtained on the target spacecraft;

[0012] Step 2: Introduce the starlight direction vector of the same observed star into the spectral redshift navigation model of step 1:

[0013]

[0014]

[0015] Utilize the measurement information and use the direction vector measurement to calculate the position information of the aircraft, reducing the number of stars required to be observed.

[0016] Step 3: Establish a compact inertial / spectral redshift integrated navigation system model assisted by the starlight direction vector, including the navigation system state equation, redshift measurement equation, and starlight direction vector measurement equation:

[0017] The navigation system state equation: X k =F k X k-1 +W k

[0018] Where F is the state transfer matrix of the inertial navigation system, and X is the state vector of the inertial navigation system;

[0019] The redshift measurement equation:

[0020] Among them, V z =Δz-Δz(Δu)

[0021] The starlight direction vector measurement equation:

[0022]

[0023] Step 4: Implement information fusion based on cubature Kalman filtering. The process is as follows:

[0024] a. First, initialize the system parameters;

[0025] b. Use CKF to filter the state equation and measurement data:

[0026] Filtering the state equation, the state update is as follows:

[0027]

[0028] Filter the redshift and direction vector measurement equations to obtain the measurement prediction:

[0029]

[0030] Input redshift and direction vector measurements are filtered and subsystem measurements are updated:

[0031]

[0032] c. Use federated filtering to achieve the above information fusion and obtain the INS error state estimate of the feedback estimate:

[0033]

[0034]

[0035] d. Feed the INS error state estimate back to the INS sensor and output navigation information after subtracting the sensor signal;

[0036] Repeat steps a to d until the navigation is complete.

[0037] The process of establishing the spectral redshift navigation model:

[0038] According to the principle of generalized Doppler effect

[0039]

[0040] Where: v i is the velocity vector of the aircraft in the inertial system, i.e., system i, v cis the velocity of the celestial body, c is the speed of light, and θ is the angle between the direction of the velocity vector of the aircraft in the inertial coordinate system and the straight line from the celestial body to the aircraft; |v i -v c |cosθ=v r Indicates the radial velocity from the target spacecraft to the observed celestial body;

[0041] The spectral redshift is defined as: z = λ / λ0-1 (2)

[0042] Where: z is the redshift value of the celestial body spectrum obtained on the target spacecraft, λ0 is the wavelength of the spectral line from the celestial body when the celestial body is stationary, and λ is the wavelength of the spectral line from the celestial body observed in the target spacecraft;

[0043] Combining formula (1) and formula (2), we can get:

[0044] The radial velocity of the aircraft is:

[0045] The spectral redshift navigation model is:

[0046] Where p i represents the position of the aircraft and p c Indicates the position of a celestial body, measured, c is the speed of light, v i is the velocity vector of the aircraft in the inertial system, i.e., system i, v c is the velocity of the celestial body; z is the redshift value of the celestial body spectrum obtained on the target spacecraft.

[0047] The process of introducing the starlight direction vector of the same observed star into the spectral redshift navigation model of step 1:

[0048] The starlight direction vector measurement obtained by the star sensor is expressed as

[0049]

[0050] Where: u c Represents the unit vector of the position from the celestial body to the center of the vehicle body in the i coordinate system, is the transformation matrix from the body coordinate system b to the i system; x b and y b represents the projection of the position vector from the target spacecraft to the observed celestial body on the imaging plane, and f is the focal length of the star sensor;

[0051] According to the geometric relationship between the observed celestial body and the spacecraft,

[0052] v r =(v i -v c )·u c (7)

[0053] Then, substitute formula (7) into formula (3) to obtain

[0054]

[0055]

[0056] In the navigation system state equation, X is the state vector of the inertial navigation system, specifically:

[0057]

[0058] Where, Φ=(φ E ,φ N ,φ H ) represents the platform misalignment angle under the navigation system; δv n =(δv E ,δv N ,δv H ) represents the velocity error in the navigation system; δp n =(δL,δλ,δh) represents the position error in the navigation system; ε =(ε x ,ε y ,ε z )and They represent the gyro random drift and accelerometer random bias respectively.

[0059] In the navigation system state equation, W is the system noise matrix, which obeys the Gaussian distribution N(0,Q), and is specifically expressed as:

[0060]

[0061] Where, represents the random error of the gyroscope, Indicates accelerometer drift.

[0062] The establishment of the redshift measurement equation:

[0063] According to the starlight direction vector-assisted spectral redshift navigation formula, the system establishes the direction vector-assisted spectral redshift measurement equation to correct the INS velocity deviation as follows:

[0064] The redshift measurement is expressed as

[0065]

[0066] Where z m is the measured redshift of the celestial body, u m,c is the corresponding direction vector measurement value, Δz is the redshift measurement error of the redshift navigation system; Δz(Δu) represents the error caused by the direction vector measurement error Δu;

[0067] have to

[0068]

[0069] Where, is the velocity information in the inertial system output by INS, δv i is the velocity error of the inertial navigation system;

[0070] Substituting formula (14) into formula (13) we get

[0071]

[0072] Also known

[0073]

[0074] Where, and The conversion matrices from the navigation coordinate system to the earth coordinate system and from the earth coordinate system to the inertial coordinate system are:

[0075]

[0076]

[0077] Further based on the redshift measurement equation, we can get

[0078]

[0079] Among them, V z =Δz-Δz(Δu) is the redshift measurement noise.

[0080] The establishment of the starlight direction vector measurement equation:

[0081] The starlight direction vector measurement is expressed as

[0082]

[0083] Further expressed as

[0084]

[0085] at the same time,

[0086]

[0087] in

[0088]

[0089] Combining equations (21), (22) and (23), we can get the starlight direction vector measurement equation as follows:

[0090]

[0091] Where, Indicates the position information of the inertial navigation output in the inertial system, δp i It represents the inertial navigation position error in the inertial system.

[0092] Beneficial effects

[0093] The present invention proposes a starlight direction vector-assisted tightly combined inertial / spectral redshift combined navigation method, which adopts a technical solution: first, a spectral redshift navigation model is established. A spectral redshift navigation model is established, and the speed and position information of the aircraft are calculated through the spectral redshift information. Then, a spectral redshift navigation model assisted by a starlight direction vector is established. The starlight direction vector of the same observed star body is introduced into the spectral redshift navigation model of step one, and the measurement information is fully utilized. At the same time, the direction vector measurement is used to calculate the position information of the aircraft, thereby reducing the number of stars required to be observed. A tightly combined inertial / spectral redshift combined navigation system model assisted by a starlight direction vector is established. A tightly combined navigation system model is established, including a state equation and a measurement equation. At the same time, through a volumetric Kalman-based federal filtering, the starlight direction vector-assisted spectral redshift navigation in step two is information fused with the inertial navigation system, thereby further reducing the number of observed celestial bodies and ensuring the stability and reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 A spectral redshift navigation system assisted by the starlight direction vector.

[0095] Figure 2 Geometric relations for spectral redshift navigation.

[0096] Figure 3 Structure diagram of the inertial / spectral redshift tightly integrated navigation system assisted by the starlight direction vector.

[0097] Figure 4 This is the trajectory diagram of the aircraft.

[0098] Figure 5 Velocity error diagram at different spectral resolutions.

[0099] Figure 6 Position error diagram at different spectral resolutions.

[0100] Figure 7 Velocity error diagram under different star sensor accuracies.

[0101] Figure 8 This is the position error diagram under different star sensor accuracies.

[0102] Figure 9Velocity error diagram for different numbers of observable celestial bodies.

[0103] Figure 10 This is a diagram of position errors under different numbers of observable celestial bodies.

[0104] Figure 11 Velocity error diagram under different ephemeris errors.

[0105] Figure 12 This is the position error diagram under different ephemeris errors. DETAILED DESCRIPTION

[0106] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0107] The implementation of step one is as follows:

[0108] First, according to the principle of generalized Doppler effect, we can get

[0109]

[0110] Where: λ0 is the wavelength of the spectral line from the celestial body when the celestial body is stationary, λ is the wavelength of the spectral line from the celestial body observed by the target spacecraft, v i is the velocity vector of the aircraft in the inertial system (i system), v c is the velocity of the celestial body, c is the speed of light, and θ is the angle between the direction of the velocity vector of the aircraft in the inertial coordinate system and the straight line from the celestial body to the aircraft. i -v c |cosθ=v r It represents the radial velocity from the target spacecraft to the observed celestial body.

[0111] It is also known that the spectral red shift is defined as

[0112] z=λ / λ0-1 (2)

[0113] Where: z is the redshift value of the celestial body spectrum obtained on the target spacecraft.

[0114] Secondly, combining formula (1) and formula (2), we can get

[0115]

[0116] Since the radial velocity can also be expressed as

[0117]

[0118] Where p i and p c They represent the position of the spacecraft and the position of the celestial body in the inertial system respectively.

[0119] Finally, substituting equation (4) into equation (3), we can get the complete spectral redshift navigation principle equation:

[0120]

[0121] Equation (5) shows that it is the principle equation of the spectral redshift navigation system. Through this equation, the spectral redshift navigation system can calculate the speed and position information of the aircraft through the observed spectral redshift information.

[0122] The implementation of step 2 is as follows:

[0123] Introducing the starlight direction vector measurement into the spectral redshift combined navigation equation can, on the one hand, reduce the number of celestial bodies required for spectral redshift navigation and improve the reliability of spectral redshift navigation under poor observation conditions; on the other hand, it makes full use of the starlight direction vector information to ensure that the spectral redshift navigation equation assisted by the starlight direction vector can still solve the velocity and position information. The navigation system structure is as follows Figure 1 shown.

[0124] The starlight direction vector measurement obtained by the star sensor can be expressed as

[0125]

[0126] Where: u c Represents the unit vector of the position from the celestial body to the center of the vehicle body in the i coordinate system, is the transformation matrix from the body coordinate system b to the i system. b and y b It represents the projection of the position vector from the target spacecraft to the observed celestial body on the imaging plane, and f is the focal length of the star sensor.

[0127] according to Figure 2 The geometric relationship between the observed celestial body and the spacecraft is shown in

[0128] v r =(v i -v c )·u c (7)

[0129] Then, substituting formula (7) into formula (3) yields

[0130]

[0131]

[0132] Equations (8) and (9) are the principle equations of the starlight direction vector-assisted spectral redshift navigation system. It can be seen that by introducing the starlight direction vector of the same observed star, the improved starlight direction vector-assisted spectral redshift navigation only needs to simultaneously observe the redshift values ​​of three celestial bodies in the solar system to calculate the spacecraft's velocity information. In addition, the improved spectral redshift navigation fully utilizes the measurement information and can also use the direction vector measurement to calculate the spacecraft's position information.

[0133] The implementation of step three is as follows:

[0134] The equations of the tightly combined inertial / spectral redshift integrated navigation system assisted by the starlight direction vector include state equations and measurement equations.

[0135] (1) Establishing the equation of state

[0136] According to the inertial navigation system error model, the state equation of the integrated navigation system can be expressed as

[0137] X k =F k X k-1 +Γ k W k (10)

[0138] Where F is the state transfer matrix of the inertial navigation system, Γ represents the noise driving matrix, and X is the state vector of the inertial navigation system, specifically:

[0139]

[0140] Where, Φ=(φ E ,φ N ,φ H ) represents the platform misalignment angle of inertial navigation under the navigation system; δv n =(δv E ,δv N ,δv H ) represents the velocity error of inertial navigation under the navigation system; δp n =(δL,δλ,δh) represents the position error of inertial navigation under the navigation system; ε =(ε x ,ε y ,ε z )and They represent the gyro random drift and accelerometer random bias of inertial navigation respectively.

[0141] W is the system noise matrix, which obeys the Gaussian distribution N(0,Q), specifically expressed as

[0142]

[0143] Where, represents the random error of the gyroscope, Indicates accelerometer drift.

[0144] (2) Establishing the measurement equation

[0145] First, based on the starlight direction vector-assisted spectral redshift navigation formula, the system can establish the direction vector-assisted spectral redshift measurement equation to correct the INS velocity deviation as follows:

[0146] According to formula (8), the redshift measurement value can be expressed as

[0147]

[0148] Where z m is the measured redshift of the celestial body, u m,c is the corresponding direction vector measurement value, Δz is the redshift measurement error of the redshift navigation system, and Δz(Δu) represents the error caused by the direction vector measurement error Δu.

[0149] It can be seen that

[0150]

[0151] Where, is the velocity information in the inertial system output by INS, δv i is the velocity error of the inertial navigation in the inertial system.

[0152] Substituting formula (14) into formula (13) yields

[0153]

[0154] Also known

[0155]

[0156] Where, and They are the transformation matrices from the navigation coordinate system to the earth coordinate system and the transformation matrix from the earth coordinate system to the inertial coordinate system, which can be written as

[0157]

[0158]

[0159] We can further obtain the redshift measurement equation as follows:

[0160]

[0161] Among them, V z =Δz-Δz(Δu) is the redshift measurement noise.

[0162] Furthermore, according to the spectral redshift navigation formula assisted by the starlight direction vector, the system continues to establish the measurement equation based on the starlight direction vector. The details are as follows:

[0163] According to formula (9), the starlight direction vector measurement can be expressed as

[0164]

[0165] Similar to formula (16), formula (20) can be further expressed as

[0166]

[0167] at the same time,

[0168]

[0169] in

[0170]

[0171] Combining equations (21), (22) and (23), the starlight direction vector measurement equation can be obtained as follows:

[0172]

[0173] Where, Indicates the position information of the inertial navigation output in the inertial system, δp i Indicates the inertial position error in the inertial system

[0174] It can be seen from Equations (19) and (24) that, in the tightly coupled mode, even if only one celestial body has observations, the measurement equations can still be established to correct the errors of the inertial navigation system.

[0175] (3) Inertial / spectral redshift tight integration navigation system assisted by starlight direction vector

[0176] Combining the above-established integrated navigation system equations and the federated filtering method based on cubature Kalman, the overall working structure of the starlight direction vector-assisted inertial / spectral redshift tight integrated navigation system is as follows: Figure 3 shown.

[0177] The overall workflow of the starlight direction vector-assisted inertial / spectral redshift tight integration navigation system is as follows:

[0178] a. First, initialize the system parameters and obtain the outputs of the inertial navigation, star sensor and spectrometer.

[0179] b. According to the state equation, each sub-filter performs state prediction as follows

[0180]

[0181] Where, X k|k-1 represents the state prediction at time k, P k-1 represents the k-1 time state covariance matrix, P k|k-1 represents the one-step predicted state covariance matrix at time k, Q k represents the state noise matrix.

[0182] c. According to the redshift and direction vector measurement equation, each sub-filter is updated

[0183]

[0184] Where ξ represents the volume matrix, represents the volume sampling point at time k, represents the measurement volume sampling point at time k, h j () represents the measurement equation used by the j-subfilter. represents the measurement prediction of the j-subfilter, represents the one-step prediction measurement covariance matrix of the j-subfilter.

[0185]

[0186] Where, K represents the one-step prediction covariance matrix of the j-subfilter measurement and state. j,k represents the filter gain of the j-th sub-filter, X j,k represents the state estimate of the j-subfilter, P j,k Represents the state covariance matrix estimate of the j-subfilter.

[0187] d. Realize information fusion based on the state estimation of sub-filters by federated filtering [4]

[0188]

[0189]

[0190] Where, X k represents the fused state estimate, P k Represents the estimated state covariance matrix after fusion.

[0191] e. Feedback the fused INS error state estimate to correct the INS and output the final INS navigation information.

[0192] f. Repeat steps b to e until the navigation is complete.

[0193]

Experimental verification

[0194] This patent mainly verifies the performance of the proposed starlight direction vector assisted inertial / spectral redshift tight integrated navigation system through ground simulation experiments. In the simulation, the total flight time is set to 2 hours, and the aircraft flight trajectory is generated as follows Figure 4 The spectral signal is primarily based on the Gaia database spectral signal, and the observed spectrum of the corresponding resolution is generated through interpolation. The cross-correlation method is used to measure the spectral redshift. The reference system used in the simulation experiment is the Northeast Navigation Coordinate System. The sensor parameters used in the simulation are generally shown in Table 1. The initial error settings are shown in Table 2.

[0195] The mean absolute error (MAE) is defined as:

[0196]

[0197] Where ΔX, ΔY, and ΔZ represent the three-dimensional errors in velocity or position, respectively.

[0198] In a tightly integrated inertial / spectral redshift navigation system assisted by a starlight direction vector, the main factors affecting navigation accuracy include sensor accuracy, ephemeris errors of observed objects, the number of observable objects, and the observation period. Therefore, to verify the performance of this tightly integrated inertial / spectral redshift navigation system, a simulation experiment compared the effects of different navigation parameters on the performance and accuracy of this tightly integrated inertial / spectral redshift navigation system.

[0199] Figure 5 and Figure 6 The velocity and position errors at different spectral resolutions are given. -7 When the spectral resolution is 10, the absolute error of velocity and position is the largest. As the resolution increases, the error decreases. Table 3 lists the average absolute error corresponding to different spectral resolutions. -7 When the spectral resolution increases to 10 -8 and 10 -9 When the spectral resolution is reduced, the average velocity and absolute position errors are reduced to 0.44 m / s and 182.39 m, and 0.11 m / s and 153.12 m, respectively. It can be seen that as the spectral resolution decreases, the navigation error fluctuation increases. In particular, the velocity error is significantly affected.

[0200] Figure 7 and Figure 8Table 4 lists the corresponding mean absolute errors (MAEs) for velocity and position at different star sensor accuracies. It can be seen that star sensor accuracy also affects the proposed navigation accuracy, particularly the position error. When the star sensor accuracy is 10″, the mean velocity and position absolute errors are 0.48 m / s and 368.33 m. When the star sensor accuracy is reduced to 20″ and 40″, the mean velocity and position absolute errors decrease to 0.53 m / s and 715.66 m, and 0.79 m / s and 1240.24 m, respectively.

[0201] Summarize Figure 5-8 From the results in Table 3-4, it can be seen that without considering other factors, the spectral resolution (10 -8 ) and the star sensor accuracy (less than 10″), the proposed navigation system can theoretically meet the navigation needs of near-space vehicles.

[0202] Figure 9 and Figure 10 The velocity and position errors for different numbers of observable objects are presented, and the corresponding mean absolute errors are listed in Table 5. First, it can be seen that, compared to loose combinations, the proposed inertial / spectral redshift navigation system, through its tight combination, can provide redshift and direction vector measurement information to correct inertial navigation errors when the number of observable objects is less than three. When the number of observable objects is one throughout the simulation, there is a divergence trend during the simulation, with the average velocity and position absolute errors within one hour being 1.39 m / s and 1029.36 m. However, when the number of observable objects increases to two, the divergence trend is no longer significant, and the average velocity and position absolute errors decrease to 0.72 m / s and 223.45 m, respectively. When the number of observable objects increases to three, the average velocity and position absolute errors further decrease to 0.43 m / s and 196.39 m.

[0203] Figure 11 and Figure 12 Table 6 lists the corresponding mean absolute errors for velocity and position under different ephemeris errors. It can be seen that ephemeris error significantly affects navigation accuracy. When the ephemeris error for all celestial bodies is 5 km, the average velocity and position absolute errors are the largest, at 4.32 m / s and 1358.02 m. When the ephemeris error for all celestial bodies is reduced to 1 km and 500 m, the average velocity and position absolute errors decrease to 1.16 m / s, 389.44 m, and 0.72 m / s, 275.24 m, respectively. Since the lunar ephemeris error is approximately 1 m, the Venus ephemeris error is less than 200 m, the Mars ephemeris error is less than 1 km, and the Mercury ephemeris error is within 5 km, the above ephemeris error analysis shows that a tightly integrated inertial / spectral redshift navigation system using the starlight direction vectors of the planets in the solar system as observational objects can obtain relatively accurate navigation information.

[0204] Table 1 Sensor simulation parameter settings

[0205]

[0206] Table 2 Initial navigation error

[0207]

[0208] Table 3 Average absolute error at different spectral resolutions

[0209]

[0210] Table 4 Mean absolute error of different star sensor accuracies

[0211]

[0212] Table 5 Mean absolute error under different numbers of observable celestial bodies

[0213]

[0214] Table 6 Mean absolute error under different ephemeris errors

[0215]

Claims

1. A starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method, characterized in that Here are the steps: Step 1: Establish a spectral redshift navigation model and calculate the radial velocity and position information of the spacecraft using the spectral redshift information: Spectral redshift navigation model: Where p i represents the position of the aircraft and p c Indicates the position of a celestial body, measured, c is the speed of light, v i is the velocity vector of the aircraft in the inertial system, i.e., system i, v c is the speed of the celestial body; z is the redshift value of the celestial body spectrum obtained on the target spacecraft; Step 2: Introduce the starlight direction vector of the same observed star into the spectral redshift navigation model of step 1: Utilize the measurement information and use the direction vector measurement to calculate the position information of the aircraft, reducing the number of stars required to be observed. Step 3: Establish a compact inertial / spectral redshift integrated navigation system model assisted by the starlight direction vector, including the navigation system state equation, redshift measurement equation, and starlight direction vector measurement equation: The navigation system state equation: X k =F k X k-1 +W k Where F is the state transfer matrix of the inertial navigation system, and X is the state vector of the inertial navigation system; The redshift measurement equation: is the velocity information in the inertial system output by INS, δv n =(δv E ,δv N ,δv H ) represents the velocity error in the navigation system; and They are the transformation matrix from the navigation coordinate system to the earth coordinate system and the transformation matrix from the earth coordinate system to the inertial coordinate system respectively; Among them, V z =Δz-Δz(Δu) Δz(Δu) represents the error caused by the direction vector measurement error Δu; The starlight direction vector measurement equation: δp n =(δL,δλ,δh) represents the position error in the navigation system, Indicates the position information of the inertial navigation output in the inertial system, δp i It represents the inertial position error in the inertial system, Step 4: Implement information fusion based on cubature Kalman filtering. The process is as follows: a. First, initialize the system parameters; b. Use CKF to filter the state equation and measurement data: Filtering the state equation, the state update is as follows: Filter the redshift and direction vector measurement equations to obtain the measurement prediction: represents the volume sampling point at time k, represents the measurement volume sampling point at time k, Q k represents the state noise matrix, h j () represents the measurement equation used by the j-subfilter, represents the measurement prediction of the j-subfilter, Input redshift and direction vector measurements are filtered and subsystem measurements are updated: represents the one-step prediction covariance matrix of the j-subfilter measurement and state, K j,k represents the filter gain of the j-subfilter c. Use federated filtering to achieve the above information fusion and obtain the INS error state estimate of the feedback estimate: d. Feed the INS error state estimate back to the INS sensor, subtract it from the sensor signal, and output navigation information; Repeat steps a to d until the navigation is complete.

2. The starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method according to claim 1, characterized in that: The process of establishing the spectral redshift navigation model: According to the principle of generalized Doppler effect Where: v i is the velocity vector of the aircraft in the inertial system, i.e., system i, v c is the velocity of the celestial body, c is the speed of light, and θ is the angle between the direction of the velocity vector of the aircraft in the inertial coordinate system and the straight line from the celestial body to the aircraft; |v i -v c |cosθ=v r Indicates the radial velocity from the target spacecraft to the observed celestial body; The spectral redshift is defined as: z = λ / λ0-1 (2) Where: z is the redshift value of the celestial body spectrum obtained on the target spacecraft, λ0 is the wavelength of the spectral line from the celestial body when the celestial body is stationary, and λ is the wavelength of the spectral line from the celestial body observed in the target spacecraft; Combining formula (1) and formula (2), we can get: The radial velocity of the aircraft is: The spectral redshift navigation model is: Where p i represents the position of the aircraft and p c Indicates the position of a celestial body, measured, c is the speed of light, v i is the velocity vector of the aircraft in the inertial system, i.e., system i, v c is the velocity of the celestial body; z is the redshift value of the celestial body spectrum obtained on the target spacecraft.

3. The starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method according to claim 1, characterized in that: The process of introducing the starlight direction vector of the same observed star into the spectral redshift navigation model of step 1: The starlight direction vector measurement obtained by the star sensor is expressed as Where: u c Represents the unit vector of the position from the celestial body to the center of the vehicle body in the i coordinate system, is the transformation matrix from the body coordinate system b to the i system; x b and y b represents the projection of the position vector from the target spacecraft to the observed celestial body on the imaging plane, and f is the focal length of the star sensor; According to the geometric relationship between the observed celestial body and the spacecraft, v r =(v i -v c )·u c (7) Then, substitute formula (7) into formula (3) to obtain 4. The starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method according to claim 1, characterized in that: In the navigation system state equation, X is the state vector of the inertial navigation system, specifically: Where, Φ=(φ E ,φ N ,φ H ) represents the platform misalignment angle under the navigation system; δv n =(δv E ,δv N ,δv H ) represents the velocity error in the navigation system; δp n =(δL,δλ,δh) represents the position error in the navigation system; ε =(ε x ,ε y ,ε z )and They represent the gyro random drift and accelerometer random bias respectively.

5. The starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method according to claim 1, characterized in that: In the navigation system state equation, W is the system noise matrix, which obeys the Gaussian distribution N(0,Q), and is specifically expressed as: Where, represents the random error of the gyroscope, Indicates accelerometer drift.

6. The starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method according to claim 1, characterized in that: The establishment of the redshift measurement equation: According to the starlight direction vector-assisted spectral redshift navigation formula, the system establishes the direction vector-assisted spectral redshift measurement equation to correct the INS velocity deviation as follows: The redshift measurement is expressed as Where z m is the measured redshift of the celestial body, u m,c is the corresponding direction vector measurement value, Δz is the redshift measurement error of the redshift navigation system; Δz(Δu) represents the error caused by the direction vector measurement error Δu; have to Where, is the velocity information in the inertial system output by INS, δv i is the velocity error of the inertial navigation system; Substituting formula (14) into formula (13) we get Also known Where, and They are the conversion matrices from the navigation coordinate system to the earth coordinate system and the conversion matrices from the earth coordinate system to the inertial coordinate system: Further based on the redshift measurement equation, we can get Among them, V z =Δz-Δz(Δu) is the redshift measurement noise.

7. The starlight direction vector-assisted tightly combined inertial / spectral redshift navigation method according to claim 1, characterized in that: The establishment of the starlight direction vector measurement equation: The starlight direction vector measurement is expressed as Further expressed as at the same time, in Combining equations (21), (22) and (23), we can get the starlight direction vector measurement equation as follows: Where, Indicates the position information of the inertial navigation output in the inertial system, δp i It represents the inertial navigation position error in the inertial system.

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