High-altitude aircraft integrated navigation method based on Fourier domain computational imaging

Abstract

The invention provides a high-altitude aircraft integrated navigation method based on Fourier domain computational imaging, and relates to the technical field of aircraft positioning and navigation.The method comprises the steps that S1, a navigation coordinate system of a high-altitude aircraft is set, and an astronomy and inertia integrated navigation model is established; s2, establishing an image-free target positioning model based on Fourier single-pixel detection, and realizing large-field-of-view celestial navigation star positioning of a high-altitude aircraft; s3, analyzing the celestial navigation star map to realize celestial navigation attitude determination of the high-altitude aircraft; s4, basic parameters in the navigation process are set, and astronomical and inertial integrated navigation based on Fourier domain calculation imaging is achieved. According to the invention, the fluctuation of the light field is modulated at high frequency through the digital micromirror device, the astronomical navigation attitude determination is carried out by utilizing the relevance between the detection light field and the modulation light field on the premise of not reconstructing the total image information, the updating frequency of the large-view-field astronomical navigation information is improved to more than 20Hz, and the integrated navigation positioning precision is improved under the astronomical and inertial navigation framework.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft positioning and navigation, and in particular to a high-altitude aircraft integrated navigation method based on Fourier domain computational imaging. Background Art

[0002] With the development trend of intelligent and precise modern equipment, high-altitude aircraft are increasingly demanding high-precision and highly autonomous navigation and positioning technologies. Due to the unique advantages of their flight missions, high-altitude aircraft often use inertial navigation combined with astronomical navigation for efficient and accurate combined navigation and positioning to ensure combat performance. Inertial navigation systems have good autonomy and strong concealment, but errors accumulate over time. Celestial navigation uses navigation stars as its working objects, providing attitude information that does not change with time. It can correct the time-accumulated attitude errors of the inertial navigation system in real time and complete high-precision combined navigation and positioning tasks through information fusion. Inertial navigation systems can typically achieve an output of 100Hz-200Hz, but the attitude update frequency of traditional CCD / CMOS astronomical navigation systems is limited to seconds due to the large amount of full-image redundant information. Summary of the Invention

[0003] In order to address the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a high-altitude aircraft integrated navigation method based on Fourier domain computational imaging. By high-frequency modulating light field fluctuations with a digital micromirror device, the correlation between the detected light field and the modulated light field is utilized to perform celestial navigation attitude determination without reconstructing full-image information. The celestial navigation information update frequency is increased to above 20 Hz, thereby improving the integrated navigation positioning accuracy within the astronomical and inertial navigation framework.

[0004] Specifically, the present invention provides a high-altitude aircraft integrated navigation method based on Fourier domain computational imaging, which includes the following steps:

[0005] S1: Set the navigation coordinate system of the high-altitude aircraft and establish an astronomical and inertial combined navigation model for the high-altitude aircraft; perform optimal state estimation of the system error of the high-altitude aircraft through Kalman filtering;

[0006] S2: Establish an imageless target positioning model based on Fourier single-pixel detection to obtain celestial navigation star coordinates: Obtain celestial navigation star coordinates Constructing the speckle modulation function of the Fourier basis Calculate the structured light detection value B after Fourier base speckle modulation φ , the detection value after Fourier base speckle modulation is obtained and the Fourier coefficient F(u,v) is calculated as:

[0007]

[0008] Among them, F(u,v) is the Fourier coefficient of the current frequency; B0 is the detection value corresponding to the projected speckle with an initial phase of [0] corresponding to the current sampling frequency coefficient; B 2π / 3 is the detection value corresponding to the projected speckle with an initial phase of [2π / 3] corresponding to the current sampling frequency coefficient; B 4π / 3 is the detection value corresponding to the projected speckle with an initial phase of [4π / 3] corresponding to the current sampling frequency coefficient; j is the imaginary part in the Fourier domain; u is the horizontal coordinate parameter of the astronomical navigation star; v is the vertical coordinate parameter of the astronomical navigation star;

[0009] Based on the Fourier coefficient F(u,v), the projection of the celestial navigation star map in the current direction is obtained through inverse Fourier transform, and the coordinates of the celestial navigation star are obtained;

[0010] S3: Analyze the astronomical navigation star coordinates obtained in step S2 to obtain the panel starlight unit vector and the space starlight unit vector Set the starlight unit vector in the same space Solution and The vector group formed is used to obtain the attitude direction cosine matrix of the current astronomical navigation star sensor in the inertial navigation space

[0011] S4: Set the basic parameters in the high-altitude aircraft integrated navigation process, and convert the attitude direction cosine array of the celestial navigation star sensor obtained in step S3 in the inertial navigation space into Substitute the astronomical and inertial integrated navigation model in step S1 to achieve the optimal state estimation of the system error of the high-altitude aircraft, and then control the system error to achieve astronomical and inertial integrated navigation based on Fourier domain computational imaging.

[0012] Preferably, step S2 is specifically:

[0013] S21: Use passive mode to obtain imageless target positioning based on Fourier single pixel detection and obtain astronomical navigation star coordinates Constructing the speckle modulation function of the Fourier basis

[0014] S22: Calculate the structured light detection value B after Fourier base speckle modulation φ ;

[0015] S23: According to the detection values ​​corresponding to the projected speckles with initial phases of [0], [2π / 3], and [4π / 3] corresponding to the sampling frequency coefficients, the detection values ​​after Fourier basis speckle modulation are obtained, and the Fourier coefficients F(u,v) are calculated as the Fourier coefficients of the current frequency. The astronomical navigation star coordinates are obtained through inverse Fourier transform.

[0016] Preferably, the astronomical navigation star coordinates in step S21 Specifically:

[0017]

[0018] Among them, x ij is the horizontal coordinate of the i-th row in the matrix; y ij is the vertical coordinate of the j-th column point in the matrix; ρ is the value of the position of the astronomical navigation star; i is the row number of the transformation matrix; j is the column number of the transformation matrix.

[0019] Preferably, the speckle modulation function of the Fourier basis in step S21 is:

[0020]

[0021] in, is the speckle modulation function; is the horizontal coordinate of the astronomical navigation star; is the vertical coordinate of the astronomical navigation star; f x is the frequency value of the horizontal dimension of the star map; f y is the frequency value of the vertical dimension of the star map; a is the DC component of the Fourier series; b c is the image contrast; It is the phase of the star map for astronomical navigation.

[0022] Preferably, the method for acquiring the structured light detection value after Fourier basis speckle modulation in step S22 is:

[0023]

[0024] Among them, B φ (f x ,f y ) is the detection value corresponding to the frequency projection speckle; is the celestial navigation target star map; dx is the integral of the celestial navigation coordinate system in the X-axis direction; dy is the integral of the celestial navigation coordinate system in the Y-axis direction.

[0025] Preferably, step S3 is specifically:

[0026] S31: Calculate the panel starlight unit vector by calculating the astronomical navigation star coordinates obtained by Fourier domain imaging in step S2

[0027] S32: Based on the celestial right ascension and declination of each celestial navigation star point, the unit vector is derived from the current high-altitude aircraft's observation point to the celestial navigation star in front of it, and the space starlight unit vector is obtained.

[0028] S33: Set the high-altitude aircraft coordinate system b and the lens reference system s to coincide, that is, Get the attitude direction cosine matrix of the current astronomical navigation star sensor in the inertial navigation space

[0029] Preferably, in step S31, the panel starlight unit vector is calculated Specifically:

[0030]

[0031] in, is the panel starlight unit vector; x p is the horizontal coordinate of the panel; p is the vertical coordinate of the panel; f is the focal length of the image plane; T is the transpose sign of the matrix.

[0032] Preferably, the space starlight unit vector obtained in step S32 is Specifically:

[0033]

[0034] in, is the space starlight unit vector; α is the celestial right ascension; δ is the celestial declination.

[0035] Preferably, the attitude direction cosine array of the celestial navigation star sensor in the inertial navigation space in step S33 is In a large field of view, more than three astronomical navigation stars correspond to and The vector group is

[0036] Preferably, the system error of the high-altitude aircraft in step S1 includes: navigation attitude error δφ, velocity error δv, position error δP, gyro constant bias error ε and accelerometer bias error The state variables that constitute the system error are:

[0037]

[0038] Among them, x is the state variable of the Kalman filter system built by astronomical and inertial combined navigation; δφ is the navigation attitude error in the northeast celestial direction; δv is the velocity error in the northeast celestial direction; δP is the position error in the northeast celestial direction; ε is the gyro constant bias error in the northeast celestial direction; ▽ is the accelerometer bias error in the northeast celestial direction; and T is the transpose sign of the matrix.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] (1) The present invention realizes the extraction of coefficients of multi-directional undersampling in the Fourier domain of the celestial navigation star map, and inversely solves the projections in each direction. It can realize the rapid extraction of the coordinates of celestial navigation star points when a partial star map is generated, and provides strong technical support for improving the efficiency of celestial navigation attitude determination.

[0041] (2) The astronomical navigation method based on Fourier domain computational imaging proposed in this invention breaks through the attitude update frequency of astronomical navigation based on traditional direct imaging technology, and increases the astronomical attitude update frequency to tens of milliseconds. The error update performance of the 100Hz inertial base combined navigation is significantly improved. Based on this, a high-frequency correction astronomical and inertial combined navigation method is designed for navigation and positioning of high-altitude aircraft.

[0042] (3) The present invention is based on a high-frequency corrected astronomical and inertial combined navigation method based on Fourier domain computational imaging. By designing the light field intensity and phase fluctuations and utilizing the correlation between the detected light field and the modulated light field, astronomical attitude determination is performed without reconstructing the full image information, and the astronomical navigation information update frequency is increased to above 20 Hz. Experimental results under the inertial-based astronomical navigation framework show that the navigation positioning accuracy is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A flow chart of a high-altitude aircraft integrated navigation method based on Fourier domain computational imaging;

[0044] Figure 2 This is the Fourier spectrum diagram of the wide field of view astronomical navigation star map;

[0045] Figure 3 Schematic diagram of Fourier domain single-pixel detection of astronomical navigation stars;

[0046] Figure 4 Schematic diagram of obtaining multi-angle radial coefficients in the Fourier domain for large-field-of-view astronomical navigation following the circular law;

[0047] Figure 5 Schematic diagram of obtaining multi-angle radial coefficients in the Fourier domain for large-field-of-view astronomical navigation following the square rule;

[0048] Figure 6 A 3D trajectory comparison chart of the astronomical and inertial navigation trajectory results for 20Hz attitude correction;

[0049] Figure 7 The horizontal trajectory comparison chart of the astronomical and inertial navigation trajectory results for 20Hz attitude correction;

[0050] Figure 8 The error curve of astronomical and inertial navigation positioning results for 20Hz attitude correction;

[0051] Figure 9 Box plot of longitude displacement error for astronomical and inertial navigation with 20Hz attitude correction;

[0052] Figure 10 Box plot of latitude displacement error for astronomical and inertial navigation with 20Hz attitude correction;

[0053] Figure 11 Box plot of altitude displacement error for astronomical and inertial navigation with 20Hz attitude correction;

[0054] Figure 12 A 3D trajectory comparison chart of the astronomical and inertial navigation trajectory results with 1Hz attitude correction;

[0055] Figure 13 The horizontal trajectory comparison chart of the astronomical and inertial navigation trajectory results with 1Hz attitude correction;

[0056] Figure 14 The error curve of astronomical and inertial navigation positioning results for 1Hz attitude correction;

[0057] Figure 15 Box plot of longitude displacement error for astronomical and inertial navigation with 1Hz attitude correction;

[0058] Figure 16 Box plot of latitude displacement error for astronomical and inertial navigation with 1Hz attitude correction;

[0059] Figure 17 Box plot of altitude displacement error for astronomical and inertial navigation with 1Hz attitude correction. DETAILED DESCRIPTION

[0060] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0061] The present invention proposes a high-altitude aircraft integrated navigation method based on Fourier domain computational imaging, such as Figure 1 As shown, the navigation coordinate system of the high-altitude aircraft is set, and an astronomical and inertial combined navigation model is established; an imageless target positioning model based on Fourier single-pixel detection is established to realize astronomical navigation star positioning of the high-altitude aircraft; the astronomical navigation star map is analyzed to realize astronomical navigation attitude determination of the high-altitude aircraft; basic parameters in the navigation process are set to realize astronomical and inertial combined navigation based on Fourier domain computational imaging; the specific steps include:

[0062] Step S1: Set the navigation coordinate system of the high-altitude aircraft and establish an astronomical and inertial combined navigation model.

[0063] Step S11: Setting the navigation coordinate system of the high-altitude aircraft.

[0064] The geocentric inertial coordinate system of the high-altitude aircraft is i, and o i x i y i z i Indicates that the origin of the coordinate system is the center of the earth, o i x i Pointing to the equinox, o i z i is the Earth's rotation axis, o i x i With o i y i The axis is vertical in the plane of the Earth's equator.

[0065] The Earth-centered Earth-fixed coordinate system of the high-altitude aircraft is e, and o e x e y e z e Indicates that the origin of the coordinate system is the center of the earth, o e x e Point to the prime meridian, o e z e is the Earth's rotation axis, o e x e and o e y e The axis is vertical in the plane of the Earth's equator.

[0066] The geographic coordinate system of the high-altitude aircraft is g, and o g x g y g z g Indicates that the origin of the coordinate system is the center of the current high-altitude aircraft, o g x g Pointing to geographic east, o g y g Pointing to geographic north, o g z g Pointing to the geographic celestial direction, the geographic coordinate system is related to the current geographical location on the earth, and the position relationship relative to the geocentric earth-fixed coordinate system is expressed in longitude and latitude high geographic coordinates.

[0067] The navigation coordinate system of the high-altitude aircraft is n, with o n x n y n z n The origin of the coordinate system is the center of the current high-altitude aircraft. In this embodiment of the present invention, the n-frame and g-frame have the same orientation. Because the celestial altitude channel of pure inertial navigation theoretically diverges, this coordinate system performs horizontal navigation positioning calculations, and a barometer is introduced into the celestial channel to suppress divergence.

[0068] The high-altitude aircraft coordinate system is b, and o b xb y b z b The origin of the coordinate system is the center of the current high-altitude aircraft. b x b Pointing to the right of the high-altitude aircraft, o b y b Pointing to the front of the high-altitude aircraft, o b z b Pointing above high-altitude aircraft.

[0069] Step S12: Establishing a combined astronomical and inertial navigation model for high-altitude aircraft. Using the attitude outputs of astronomical navigation and inertial navigation as measurement values, the Kalman filter is used to perform optimal estimation of the attitude error, velocity error, and position error of the high-altitude aircraft.

[0070] Step S121: Set the navigation attitude error δφ, velocity error δv, position error δP, gyro constant bias error ε, and accelerometer bias error in the northeast direction. The 15-dimensional system error state variable is obtained as:

[0071]

[0072] Among them, x is the state variable of the Kalman filter system built by astronomical and inertial combined navigation; δφ is the navigation attitude error in the northeast sky direction; δv is the velocity error in the northeast sky direction; δP is the position error in the northeast sky direction; ε is the gyro constant zero bias error in the northeast sky direction; is the accelerometer bias error in the northeast celestial direction; T is the transpose sign of the matrix.

[0073] Step S122: Construct the state equation of the Kalman filter system for astronomical and inertial combined navigation. The standard attitude matrix from the navigation coordinate system n of the high-altitude aircraft to the high-altitude aircraft coordinate system b is Due to the influence of gyro drift and other errors, the actual attitude matrix is In order to facilitate the error accumulation of inertial navigation over time, the deviation between the optimal navigation coordinate system n′ and the initial navigation coordinate system n is corrected in real time through the state optimal estimation. The attitude error differential equation is established to describe the first-order derivative of the misalignment angle δφ of the optimal navigation coordinate system n′ relative to the initial navigation coordinate system n:

[0074]

[0075] in, is the first-order derivative of the navigation attitude error in the northeast sky direction; is the standard attitude matrix from the navigation coordinate system n to the high-altitude aircraft coordinate system b; is the rotation of the n system relative to the i system; Mav is the first parameter matrix set of the state equation; M1 is the second parameter matrix set of the state equation; M2 is the third parameter matrix set of the state equation.

[0076] The first parameter matrix set M of the state equation av The specific ones are:

[0077]

[0078] Among them, R M is the principal radius of curvature of the meridian; R N is the main curvature radius of the zodiac circle; l is the geographical latitude; h is the geographical altitude.

[0079] The second parameter matrix set M1 of the state equation is specifically:

[0080]

[0081] Among them, ω ie is the Earth's rotation speed.

[0082] The third parameter matrix set M2 of the state equation is specifically:

[0083]

[0084] Among them, v E is the eastward velocity; v N is the northbound speed.

[0085] The velocity error differential equation is established to describe the velocity error δv between the ideal velocity and the measured velocity of the high-altitude aircraft:

[0086]

[0087] in, is the speed error; f n is the accelerometer specific force; v is the geographic velocity; For the Earth's rotation; It is the n-system rotation caused by the curvature of the earth's surface when a high-altitude aircraft moves on the earth's surface.

[0088] The position error differential equation is established to describe the position error δP between the ideal position and the measured position of the high-altitude aircraft, which is composed of the latitude error δL, the longitude error δλ, and the height error δh. Specifically, it is:

[0089]

[0090] Where δL is the latitude error of the high-altitude aircraft, is its first-order derivative, L is the latitude of the high-altitude aircraft; δh is the height error of the high-altitude aircraft; δλ is the longitude error of the high-altitude aircraft, Its first-order derivative; δv E is the eastward velocity error of the high-altitude aircraft; δv N is the north velocity error of the high-altitude aircraft; δv U is the celestial velocity error of the high-altitude aircraft.

[0091] Gyro constant bias error ε and accelerometer bias error in the northeast direction of high-altitude aircraft It is established as a constant value model, specifically:

[0092]

[0093] in, is the first-order derivative of the gyro constant bias error in the northeast celestial direction; is the first-order derivative of the accelerometer bias error in the northeast celestial direction.

[0094] Step S123: Establishing a measurement equation for the Kalman filter system constructed by astronomical and inertial combined navigation.

[0095] Taking the WGS-84 geodetic coordinate system as the navigation coordinate system n of the integrated navigation system, the celestial navigation output attitude is expressed as:

[0096]

[0097] in, Output attitude for celestial navigation; is the conversion matrix from the protocol earth coordinate system e to the protocol geocentric inertial coordinate system i; is the standard attitude matrix from the Earth-centered Earth-fixed coordinate system e to the navigation coordinate system n; is the standard attitude matrix from the navigation coordinate system n to the high-altitude aircraft coordinate system b.

[0098] Affected by attitude and position errors, the inertial navigation is used to solve the platform attitude matrix and the Earth position matrix for:

[0099]

[0100] in, is the standard posture matrix The platform attitude matrix is ​​solved by inertial navigation; is the standard posture matrix The Earth position matrix for determining the position of the inertial navigation solution; Calculate the platform attitude matrix for inertial navigation; is the earth position matrix; I3 is the 3×3 identity matrix; δφ× is the cross product of the attitude error; δθ× is the cross product of the earth position attitude error.

[0101] The angular velocity of the geographic coordinate system g relative to the e system caused by the linear velocity of the high-altitude aircraft and the curvature of the earth's surface is:

[0102]

[0103]

[0104] in, is the attitude error between inertial navigation and celestial navigation; C p is the standard position attitude matrix; δθ is the earth position attitude error; is the attitude error from celestial navigation to the high-altitude aircraft coordinate system b; is the attitude error from inertial navigation to the high-altitude aircraft coordinate system b; is the transformation matrix from the navigation coordinate system n to the protocol geocentric inertial coordinate system i; I is the identity matrix.

[0105] If there is no large installation error, the corresponding attitude angle satisfies the small angle approximation. Let Z1 be the corresponding attitude angle. Then the measurement equation of astronomical and inertial combined navigation is:

[0106]

[0107] Among them, Z1 is the attitude angle of astronomical and inertial combined navigation.

[0108] To limit the divergence of inertial navigation solution in the celestial direction, a barometer is introduced and combined with inertial navigation to calculate the altitude result H ins , barometric pressure measurement value H baro The measurement equation is established as:

[0109] Z2=H ins -H baro ;

[0110] Among them, Z2 is the barometric measurement value H baro Establish the measurement equation with the state vector δH; H ins H is the height result calculated by inertial navigation; baro It is the measured value of barometric pressure.

[0111] Step S2: Establish an imageless target positioning model based on Fourier single-pixel detection to realize imageless large-field-of-view astronomical navigation star positioning of high-altitude aircraft. A combined navigation system is formed based on large-field-of-view astronomical navigation and inertial navigation, and the attitude of the inertial navigation with accumulated attitude error over time is corrected based on the astronomical navigation information with accumulated attitude error over time, so as to achieve the effect of efficient navigation and positioning. At present, conventional CCD / CMOS (Charge-Coupled Device and Complementary Metal-Oxide Semiconductor are two main image sensor technologies) astronomical navigation star sensors obtain astronomical navigation star point information from the entire image, which may contain a large amount of redundant information, affecting the output of astronomical navigation attitude information. Most existing star sensors have an information update frequency of seconds. The present invention is based on single-pixel detection technology, and performs Fourier basis F on different frequency coefficient values ​​of the horizontal and vertical spectrum diagrams of the Fourier domain of the navigation star map. ψ The speckle light field modulation, each frequency coefficient value corresponds to the Fourier basis Compared with the original astronomical navigation star map T b , the structured light detection value after light field modulation The Fourier coefficients F(u,v) are inversely resolved by modulating the Fourier basis with varying phases, as shown in step S23. Based on a series of Fourier coefficients located in the Fourier low-frequency spectrum, the original celestial navigation map can be reduced to a one-dimensional projection along multiple directions. These projections form multiple interconnected regions within the original celestial navigation map, representing the locations of celestial navigation stars. This allows for image-free navigation information acquisition while generating a partial celestial map.

[0112] Step S21: Imageless target positioning based on Fourier single-pixel detection adopts passive mode. The celestial navigation star map is illuminated on the digital micromirror device (DMD). The DMD controls the deflection of a large number of micromirrors through a built-in optical switch, and realizes the on-off state of reflection with the deflection angle to form a modulated structured light. The modulated structured light combines the star map light field information with the light field fluctuation information of the digital micromirror device itself. Finally, the bucket detector of the single-pixel detection system receives the signal and sends it to the host computer for solution to realize the celestial navigation star coordinates. The acquisition of its horizontal and vertical coordinates and Specifically:

[0113]

[0114] in, is the horizontal coordinate of the astronomical navigation star; is the vertical coordinate of the astronomical navigation star; x ij is the horizontal coordinate of the i-th row in the matrix; y ijis the vertical coordinate of the point in the jth column of the matrix; ρ is the value of the position of the astronomical navigation star.

[0115] The speckle modulation function of the Fourier basis is expressed as:

[0116]

[0117] Where a is the DC component of the Fourier series; b c is the image contrast; f x is the frequency value of the horizontal dimension of the astronomical navigation star map; f y The frequency value of the vertical dimension of the astronomical navigation star chart; It is the phase of the star chart for astronomical navigation; is the speckle modulation function.

[0118] Step S22: Obtain the structured light detection value after Fourier basis speckle modulation. The specific formula is:

[0119]

[0120] Among them, B φ (f x ,f y ) is the detection value corresponding to the frequency projection speckle; is the star map of the celestial navigation target; dx is the integral of the celestial navigation coordinate system in the X-axis direction, dy is the integral of the celestial navigation coordinate system in the Y-axis direction, and the detection value corresponding to the obtained frequency light field modulation is collected by the bucket detector.

[0121] Step S23: Calculate the Fourier coefficients based on the detected values ​​after Fourier basis speckle modulation. The specific formula is:

[0122]

[0123] Among them, B0 is the detection value corresponding to the projected speckle with an initial phase of [0] corresponding to the current sampling frequency coefficient; B 2π / 3 is the detection value corresponding to the projected speckle with an initial phase of [2π / 3] corresponding to the current sampling frequency coefficient; B 4π / 3 is the detection value corresponding to the projected speckle with an initial phase of [4π / 3] corresponding to the current sampling frequency coefficient; j is the imaginary part in the Fourier domain; F(u,v) is the Fourier coefficient of the current frequency, which is transformed by the inverse Fourier transform to obtain the celestial navigation star map projection in the current direction and the celestial navigation star coordinates; u is the horizontal coordinate parameter of the celestial navigation star; v is the vertical coordinate parameter of the celestial navigation star.

[0124] The present invention modulates the target star map with the light field in the Fourier domain, obtains coefficients at different Fourier frequencies through light field fluctuations, encodes the spatial information of the star map into a one-dimensional optical signal in a single direction, and thus obtains the projection of the star map in a single direction; at the same time, the demand for attitude determination of more than three astronomical navigation stars for large-field-of-view astronomical navigation is met, a method for obtaining coefficients in different directions in the Fourier domain is designed, star map projections in different directions are obtained, and the connected area of ​​multi-target astronomical navigation star points is obtained, thereby realizing imageless positioning of astronomical navigation stars, facilitating rapid attitude determination of astronomical navigation, and increasing the astronomical navigation attitude output period to tens of milliseconds, thereby realizing efficient error correction of imageless astronomical and inertial combined navigation.

[0125] Step S24: Undersampling the Fourier coefficients for wide-field-of-view celestial navigation. In the Fourier spectrum, low-frequency information is concentrated near the zero frequency in the center, representing the general information and slowly varying regions of the celestial navigation star chart. Due to the radial frequency attenuation characteristic, high-frequency components are distributed at the edges, corresponding to the edges, details, and texture of the celestial navigation star chart. This characteristic is exploited to develop a method for combining Fourier-domain wide-field-of-view astronomical computational imaging with inertial measurement based on single-pixel detection.

[0126] like Figure 2 The figure shows the Fourier spectrum of a large-field astronomical navigation star map. It can be clearly seen that the low-frequency information is concentrated in the center. In other words, as long as most of the coefficients in the center of the Fourier spectrum are obtained through light field modulation, most of the astronomical navigation star point information can be recovered. Figure 3 The figure shows a schematic diagram of Fourier domain single-pixel detection of astronomical navigation stars, and a flowchart of Fourier domain single-pixel detection computational imaging designed by the present invention. Using fifty sets of light field modulation at different phases in four directions, the two-dimensional image is converted into a one-dimensional projection curve according to the Fourier center slice theorem. The inverse solution obtains the projections in the four directions corresponding to the coefficients in the Fourier domain, and the connected areas are taken to obtain the slices of the current three astronomical navigation stars.

[0127] Aiming at the positioning requirements of more than three astronomical navigation stars in large field of view astronomical navigation, the present invention uses the conjugate symmetry in the Fourier domain to obtain Fourier coefficients for the right, lower right, lower left, and lower directions. The coefficients are obtained by light field fluctuation modulation in steps S21-S23 to achieve the acquisition of Fourier coefficients of different phases. Among them, the minimum number of Fourier coefficients in each direction can follow Figure 4 The circle law or Figure 5 The square rule of the present invention adopts the circle rule, such as Figure 4The figure shows a schematic diagram of obtaining the multi-angle radial coefficients in the Fourier domain for large-field-of-view astronomical navigation following the circular rule. By obtaining the Fourier coefficients in four directions and based on the Fourier slice theorem, the projection curves in the four directions are obtained, and the connected areas corresponding to each star point in the large-field-of-view astronomical navigation star map are obtained, completing the Fourier domain computational imaging positioning of the large-field-of-view astronomical navigation star. This method does not require the generation of a complete image and can theoretically achieve a coordinate positioning update frequency of tens of milliseconds. Figure 5 A schematic diagram of obtaining multi-angle radial coefficients in the Fourier domain for large-field-of-view astronomical navigation following the square rule is provided. The present invention can also use the square rule for processing.

[0128] Step S3: Analyze the astronomical navigation star map and extract the panel starlight unit vector and the space starlight unit vector Obtaining celestial navigation attitude by solving the classic Wahba problem Realize celestial navigation attitude determination of high-altitude aircraft.

[0129] Step S31: The panel starlight unit vector is calculated by Fourier domain imaging obtained by calculating the coordinates of the astronomical navigation star in step S2:

[0130]

[0131] in, is the panel starlight unit vector; x p is the horizontal coordinate of the panel; p is the vertical coordinate of the panel; f is the focal length of the image plane.

[0132] Step S32: Based on the celestial right ascension and declination of each celestial navigation star point, a unit vector is derived from the current high-altitude aircraft's observation point to the celestial navigation star in front of it, and the space starlight unit vector is obtained as:

[0133]

[0134] in, is the space starlight unit vector; α is the celestial right ascension; δ is the celestial declination.

[0135] Step S33: Set the high-altitude aircraft coordinate system b and the lens reference system s to coincide, that is, Then the attitude direction cosine matrix of the current astronomical navigation star sensor in the inertial navigation space is for:

[0136]

[0137] in, is the attitude direction cosine matrix of the current astronomical navigation star sensor in the inertial navigation space; is the starlight unit vector in the same space.

[0138] More than three astronomical navigation stars in a large field of view correspond to and The vector group is solved by the classic Wahba problem to obtain a more accurate The measured values ​​are substituted into the astronomical and inertial combined navigation model to obtain the optimal state estimation of the system error.

[0139] Step S4: Set the basic parameters in the high-altitude aircraft integrated navigation process, substitute the attitude direction cosine matrix of the celestial navigation star sensor in the inertial navigation space obtained in step S3 into the celestial and inertial integrated navigation model in step S1 to achieve the optimal state estimation of the system error of the high-altitude aircraft, and then control the system error to keep the error within a controllable range, thereby realizing astronomical and inertial integrated navigation based on Fourier domain computational imaging.

[0140] The simulation experiment process of the embodiment of the present invention is specifically as follows: the navigation initial point of the high-altitude aircraft is set at 116.3143° east longitude, 39.9589° north latitude, 30,000m above Beijing, and astronomical inertial measurement is supplemented by a barometer for combined navigation positioning. The astronomical navigation stars selected are Dubhe, Merak, and Phecda, all of which are relatively bright astronomical navigation stars with an apparent magnitude of about 2. A comparative combined navigation experiment is conducted using a 20Hz update frequency astronomical navigation method based on Fourier domain computational imaging and a 1Hz update frequency traditional CCD direct imaging astronomical navigation method. The inertial navigation gyro constant drift is 0.02° / h, and the random walk is 0.02° / h. Accelerometer constant drift 200μg, random walk

[0141] Fourier domain computational imaging is implemented in four directions, extracting 50 coefficients in each direction, and adopting a three-step phase shift reconstruction method. Based on the 32,552Hz modulation speed of the currently commonly used DMD, DLP7000, the current Fourier domain computational imaging takes 32552 / (3*4*50)≈54 frames per second, which is fully capable of achieving the current simulated 20Hz.

[0142] The aircraft movement settings are: first keep hovering for 20 seconds; then move at 1m / s 24 seconds, and then continue to move at a constant speed for 20 seconds; then, at an angular speed of 2° / s, coordinate the roll to the left, including rolling to the left for 4 seconds, turning left for 40 seconds, and rolling to the right for 4 seconds; then, continue to move at a constant speed for 20 seconds; then, climb at an angular speed of 2° / s, including raising the head for 30 seconds, constant speed for 10 seconds, and lowering the head for 30 seconds; then, continue to move at a constant speed for 20 seconds; then, at an angular speed of 2° / s, coordinate the roll to the right, including rolling to the right for 4 seconds, turning right for 40 seconds, and rolling to the left for 4 seconds; then, continue to move at a constant speed for 20 seconds; repeat the above coordinated roll to the left again, constant speed for 20 seconds, repeat the above climb at an elevation angle, constant speed for 20 seconds, repeat the above coordinated roll to the right again, constant speed for 20 seconds; finally, descend at an angular speed of 2° / s, including lowering the head for 30 seconds, constant speed for 10 seconds, raising the head for 30 seconds, constant speed for 20 seconds, and moving at a constant speed of 2m / s 2 The navigation is completed by decelerating for 30 seconds and moving at a constant speed for 20 seconds.

[0143] The experiment carried out a comparison of the astronomical and inertial combined navigation results based on 20Hz large field of view astronomical correction of Fourier domain computational imaging, such as Figure 6 The following figure shows the 3D trajectory comparison of the astronomical and inertial navigation trajectory results of the 20Hz attitude correction; it also shows the comparison of the running trajectory results of the current motion 3D image. Figure 7 The following is a comparison of the horizontal trajectory of the astronomical and inertial navigation trajectory results with 20Hz attitude correction, and the comparison of the motion plane trajectory results. It can be seen that the combined navigation result has a more obvious effect in suppressing errors than the pure inertial navigation solution result. Figure 8 The figure shows the error curve of the astronomical and inertial navigation positioning results with 20Hz attitude correction, which is the error result of the astronomical and inertial combined navigation accuracy based on Fourier domain computational imaging.

[0144] like Figure 9 The figure shows the longitude displacement error box plot of astronomical and inertial navigation with 20Hz attitude correction, and the easting navigation error box plot of astronomical and inertial combined navigation based on Fourier domain computational imaging. Figure 10 The figure shows the latitude displacement error box plot of astronomical and inertial navigation with 20Hz attitude correction, and the north navigation error box plot of astronomical and inertial combined navigation based on Fourier domain computational imaging. Figure 11 The figure shows the height displacement error box plot of astronomical and inertial navigation with 20Hz attitude correction, and the celestial navigation error box plot of astronomical and inertial integrated navigation based on Fourier domain computational imaging.

[0145] Comparison of astronomical and inertial integrated navigation results based on 1Hz conventional direct imaging astronomical correction of Fourier domain computational imaging, Figure 12The three-dimensional trajectory comparison diagram of the astronomical and inertial navigation trajectory results for 1Hz attitude correction shows the comparison of the running trajectory results of the current state motion three-dimensional image. Figure 13 The horizontal trajectory comparison diagram of the astronomical and inertial navigation trajectory results of 1Hz attitude correction is shown. Figure 7 and Figure 13 The comparison of the motion plane trajectory results shows that the combined navigation results have a more obvious effect in suppressing errors than the pure inertial navigation solution results, and the accuracy of the astronomical and inertial combined navigation based on Fourier domain computational imaging is more advantageous. Figure 14 The following is a graph showing the error curves of astronomical and inertial navigation positioning results with 1Hz attitude correction. Figure 8 and Figure 14 The displayed navigation and positioning result error curve clearly shows that the error result of the astronomical and inertial combined navigation accuracy based on Fourier domain computational imaging is much smaller than the error result of the conventional direct imaging astronomical and inertial combined navigation, indicating that the proposed method achieves a more efficient and accurate combined navigation and positioning function.

[0146] like Figure 15 The figure shows the longitude displacement error box plot of astronomical and inertial navigation with 1Hz attitude correction, and the figure shows the easting navigation error box plot of conventional direct imaging astronomical and inertial combined navigation. Figure 16 The figure shows the latitude displacement error box plot of astronomical and inertial navigation with 1Hz attitude correction, and the north navigation error box plot of conventional direct imaging astronomical and inertial combined navigation. Figure 17 The figure shows a box plot of the altitude displacement error for astronomical and inertial navigation with 1Hz attitude correction, and a box plot of the celestial navigation error for conventional direct imaging astronomical and inertial combined navigation. It can be seen that the results of both combined navigation methods are far superior to those of pure inertial navigation. The region between the upper quartile (Q3) and lower quartile (Q1) of the results of the proposed method is much smaller than that of the conventional combined navigation method, and the median (Q2) is also smaller than that of the conventional combined navigation method, further verifying the effectiveness of the proposed method in efficient and accurate navigation.

[0147] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A high-altitude aircraft integrated navigation method based on Fourier domain computational imaging, characterized in that: It includes the following steps: S1: Set the navigation coordinate system of the high-altitude aircraft and establish an astronomical and inertial combined navigation model for the high-altitude aircraft; perform optimal state estimation of the system error of the high-altitude aircraft through Kalman filtering; S2: Establish an imageless target positioning model based on Fourier single-pixel detection to obtain celestial navigation star coordinates: Obtain celestial navigation star coordinates Constructing the speckle modulation function of the Fourier basis Calculate the structured light detection value B after Fourier base speckle modulation φ , the detection value after Fourier base speckle modulation is obtained and the Fourier coefficient F(u,v) is calculated as: Among them, F(u,v) is the Fourier coefficient of the current frequency; B0 is the detection value corresponding to the projected speckle with an initial phase of [0] corresponding to the current sampling frequency coefficient; B 2π / 3 is the detection value corresponding to the projected speckle with an initial phase of [2π / 3] corresponding to the current sampling frequency coefficient; B 4π / 3 is the detection value corresponding to the projected speckle with an initial phase of [4π / 3] corresponding to the current sampling frequency coefficient; j is the imaginary part in the Fourier domain; u is the horizontal coordinate parameter of the astronomical navigation star; v is the vertical coordinate parameter of the astronomical navigation star; Based on the Fourier coefficient F(u,v), the projection of the celestial navigation star map in the current direction is obtained through inverse Fourier transform, and the coordinates of the celestial navigation star are obtained; S3: Analyze the astronomical navigation star coordinates obtained in step S2 to obtain the panel starlight unit vector and the space starlight unit vector Set the starlight unit vector in the same space Solution and The vector group formed is used to obtain the attitude direction cosine matrix of the current astronomical navigation star sensor in the inertial navigation space S4: Set the basic parameters in the high-altitude aircraft integrated navigation process, and convert the attitude direction cosine array of the celestial navigation star sensor obtained in step S3 in the inertial navigation space into Substitute the astronomical and inertial integrated navigation model in step S1 to achieve the optimal state estimation of the system error of the high-altitude aircraft, and then control the system error to achieve astronomical and inertial integrated navigation based on Fourier domain computational imaging.

2. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 1, characterized in that: Step S2 is specifically as follows: S21: Use passive mode to obtain imageless target positioning based on Fourier single pixel detection and obtain astronomical navigation star coordinates Constructing the speckle modulation function of the Fourier basis S22: Calculate the structured light detection value B after Fourier base speckle modulation φ ; S23: According to the detection values ​​corresponding to the projected speckles with initial phases of [0], [2π / 3], and [4π / 3] corresponding to the sampling frequency coefficients, the detection values ​​after Fourier basis speckle modulation are obtained, and the Fourier coefficients F(u,v) are calculated as the Fourier coefficients of the current frequency. The astronomical navigation star coordinates are obtained through inverse Fourier transform.

3. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 2, characterized in that: Celestial navigation star coordinates in step S21 Specifically: Among them, x ij is the horizontal coordinate of the i-th row in the matrix; y ij is the vertical coordinate of the j-th column point in the matrix; ρ is the value of the position of the astronomical navigation star; i is the row number of the transformation matrix; j is the column number of the transformation matrix.

4. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 2, characterized in that: The speckle modulation function of the Fourier basis in step S21 is: in, is the speckle modulation function; is the horizontal coordinate of the astronomical navigation star; is the vertical coordinate of the astronomical navigation star; f x is the frequency value of the horizontal dimension of the star map; f y is the frequency value of the vertical dimension of the star map; a is the DC component of the Fourier series; b c is the image contrast; It is the phase of the star map for astronomical navigation.

5. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 2, characterized in that: The method for obtaining the structured light detection value after Fourier basis speckle modulation in step S22 is: Among them, B φ (f x ,f y ) is the detection value corresponding to the frequency projection speckle; is the celestial navigation target star map; dx is the integral of the celestial navigation coordinate system in the X-axis direction; dy is the integral of the celestial navigation coordinate system in the Y-axis direction.

6. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 1, characterized in that: Step S3 is specifically as follows: S31: Calculate the panel starlight unit vector by calculating the astronomical navigation star coordinates obtained by Fourier domain imaging in step S2 S32: Based on the celestial right ascension and declination of each celestial navigation star point, the unit vector is derived from the current high-altitude aircraft's observation point to the celestial navigation star in front of it, and the space starlight unit vector is obtained. S33: Set the high-altitude aircraft coordinate system b and the lens reference system s to coincide, that is, Get the attitude direction cosine matrix of the current astronomical navigation star sensor in the inertial navigation space 7. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 6, characterized in that: In step S31, the panel starlight unit vector is calculated Specifically: in, is the panel starlight unit vector; x p is the horizontal coordinate of the panel; p is the vertical coordinate of the panel; f is the focal length of the image plane; T is the transpose sign of the matrix.

8. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 6, characterized in that: The space starlight unit vector obtained in step S32 Specifically: in, is the space starlight unit vector; α is the celestial right ascension; δ is the celestial declination.

9. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 6, characterized in that: In step S33, the attitude direction cosine array of the celestial navigation star sensor in the inertial navigation space In a large field of view, more than three astronomical navigation stars correspond to and The vector group is 10. The high-altitude aircraft integrated navigation method based on Fourier domain computational imaging according to claim 1, characterized in that: The system errors of the high-altitude aircraft in step S1 include: navigation attitude error δφ, velocity error δv, position error δP, gyro constant bias error ε and accelerometer bias error The state variables that constitute the system error are: Among them, x is the state variable of the Kalman filter system built by astronomical and inertial combined navigation; δφ is the navigation attitude error in the northeast sky direction; δv is the velocity error in the northeast sky direction; δP is the position error in the northeast sky direction; ε is the gyro constant zero bias error in the northeast sky direction; is the accelerometer bias error in the northeast celestial direction; T is the transpose sign of the matrix.

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