Dual-array navigation and directional joint estimation method and system

Abstract

The application provides a double-array navigation and orientation joint estimation method and system, and relates to the technical field of satellite navigation and orientation. The method obtains two-end observation data and actual complex weight vectors and nominal channel responses, constructs inter-satellite differential observation vectors; unifies additional phase differences, channel deviations, time deviations and near-field wave front deviations into a low-dimensional non-ideal parameter vector with a dimension less than the observation number, and establishes an observation mapping from the low-dimensional non-ideal parameter vector to the observation vector; establishes a joint estimation model taking the baseline direction, integer ambiguity and low-dimensional parameter as unknown quantities with the known baseline length as a constraint; constructs a whitening Jacobian matrix, and performs identifiability gating by using the rank and minimum eigenvalue criterion, so that fixed solutions are output when the gating is satisfied, and floating point solutions are output when the gating is not satisfied. The application solves the problem of orientation deviation and integer fixing rate decline caused by interference. Effective separation of additional phase and baseline direction and online quantitative gating of identifiability are realized under non-ideal conditions.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and orientation technology, and specifically to a dual-array navigation and orientation joint estimation method and system. Background Technology

[0002] Satellite navigation dual-antenna or multi-antenna orientation determines the vehicle's heading, pitch, or three-dimensional attitude by measuring the carrier phase difference between the two ends of a known baseline. It is widely used in unmanned platforms, vehicle navigation, and measurement equipment. In environments with strong electromagnetic interference, each antenna is typically connected to an independent array, and adaptive spatial processing is applied to suppress interference and protect satellite signals.

[0003] Existing technologies mainly develop along two routes. One route, represented by single-baseline carrier phase attitude measurement, performs single-difference between antennas and double-difference between satellites on the carrier phase observations at both ends, and uses LAMBDA-type integer least squares search to recover integer ambiguity, thereby solving for the baseline pointing. This route assumes that the RF links at both ends are strictly synchronized, the channel phase is pre-calibrated, and the additional phase introduced by array processing cancels each other out in the differential as a common mode. The other route, represented by array anti-interference processing, applies weights such as power inversion, minimum variance distortion-free response, linear constraint minimum variance, or space-time adaptive processing to each array to suppress interference and output a synthesized signal. In practical systems, the two routes are usually used in combination: each end performs spatial anti-interference processing independently, and then the output signal is sent to a classical dual-antenna orientation model to solve for the attitude.

[0004] However, the above-mentioned combined approach faces the following problems in engineering: the weights of the two arrays are calculated independently based on their respective interference situations, and the added phases of the weights are different and vary with the direction and power of the interference, making them unable to be canceled out as common modes in differential calculations; the receivers at both ends are driven by independent crystal oscillators and use independent time bases, resulting in millisecond-level deviations and slow drift in the hardware timestamps; when the interference source is located in the near field of the array, the wavefronts observed at both ends do not satisfy the far-field plane wave assumption. All of these factors cause the added phase to be mixed into the baseline geometric phase or integer ambiguity term, leading to a systematic shift in the orientation results and a decrease in the integer fixity rate. In addition, the existing model lacks a quantitative means to determine whether the current satellite geometric and temporal excitation is sufficient to separate the above error sources, and may output false fixed solutions when observation conditions are insufficient. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a joint estimation method and system for dual-array navigation and orientation. It solves the problem that existing dual-antenna orientation methods, under the condition that the array space processing is performed independently at both ends, cannot use the weighted additional phase as a common mode to cancel each other, and that various interference factors are coupled, leading to the deviation of the orientation results.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A joint estimation method for navigation and orientation using dual arrays includes the following steps: Obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observations, hardware timestamps, complex weight vectors actually used for array spatial processing, and nominal channel responses output by both ends; Inter-satellite differential observation vectors are constructed based on the carrier phase observation values ​​output from both ends; the inter-satellite differential observation is obtained by taking the difference between the carrier phase observation values ​​at both ends of the same satellite to obtain the inter-antenna single difference, and then subtracting the inter-antenna single differences of different satellites; The effects of additional phase difference introduced by the spatial processing of the two-end arrays, channel offset at both ends, reception time offset at both ends, and near-field wavefront offset of interference sources on the inter-satellite differential observation vector are uniformly parameterized into a low-dimensional non-ideal parameter vector. An observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established based on the complex weight vector and the nominal channel response. The dimension of the low-dimensional non-ideal parameter vector is smaller than the dimension of the inter-satellite differential observation vector. Using the known baseline length as a constraint, a joint estimation model is established with the carrier baseline unit direction vector, integer ambiguity vector, and the low-dimensional non-ideal parameter vector as unknowns; Construct a whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, perform integer fuzzy search and continuous parameter optimization on the joint estimation model and output a fixed solution; otherwise, output a floating-point solution.

[0007] In one embodiment of the present invention, the selection of reference satellites in the construction of the inter-satellite differential observation vector includes: among visible satellites that meet the carrier-to-noise ratio threshold, the one with the highest elevation angle is selected first, or the one that minimizes the condition number of the inter-satellite differential matrix is ​​selected, and satellites falling near the null trap of the array space processing weights are not used as reference satellites.

[0008] In one embodiment of the present invention, the step of establishing the observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector based on the complex weight vector and the nominal channel response includes: The receiver channel response matrix is ​​expressed as the product of its nominal response matrix and the bias matrix, wherein the bias matrix is ​​determined by a low-dimensional bias parameter vector; The additional phase difference is expanded in first order Taylor at the identity matrix of the deviation matrix to obtain the known terms calculated analytically from the complex weight vector and the nominal channel response, as well as the linear sensitivity term of the deviation parameter vector. The sensitivity term is used to construct the Jacobian matrix of the observation map.

[0009] In one embodiment of the present invention, the time deviation is parameterized as a low-dimensional time-varying function including constant components and drift components; the contribution of the time deviation to the inter-satellite differential observation vector is incorporated into the observation mapping after being modulated by the Doppler frequency of each satellite.

[0010] In one embodiment of the present invention, the near-field wavefront deviation of the interference source is represented by the interference source orientation angle and inverse distance parameter, wherein the inverse distance parameter is proportional to the reciprocal of the distance from the interference source to the array reference element; A second-order expansion of the relative phase of the spherical wave yields a plane wave term, a curvature term linearly related to the inverse distance parameter, and higher-order terms. When the inverse distance parameter approaches zero, the near-field model continuously degenerates into a far-field plane wave model. The range of values ​​for the inverse distance parameter is limited by box constraints.

[0011] In one embodiment of the present invention, the rank determination of the whitened Jacobian matrix adopts a singular value decomposition with tolerance, and the singular value to the maximum singular value is judged as zero if the ratio of the singular value to the maximum singular value is lower than the set tolerance.

[0012] In one embodiment of the present invention, the integer fuzziness search and continuous parameter optimization include: First, relax the integer ambiguity vector to a real number, and then solve it together with the carrier baseline unit direction vector and the low-dimensional non-ideal parameter vector to obtain the floating-point solution and its covariance. After performing a downcorrelation transformation on the ambiguity sub-blocks of the covariance, integer candidates are searched. Given integer candidates, the Jacobian block corresponding to the low-dimensional non-ideal parameter vector is eliminated to obtain the reduction equation only for the tangent space increment of the carrier baseline unit direction vector, and the carrier baseline unit direction vector is updated on the unit spherical tangent space.

[0013] The present invention also provides a dual-array navigation and orientation joint estimation system, comprising: The observation and acquisition module is used to obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observation values, hardware timestamps, complex weight vectors actually used for array spatial processing, and nominal channel responses output by both ends; The observation construction module is used to construct inter-satellite differential observation vectors based on the carrier phase observation values ​​output from both ends. The inter-satellite differential observation is obtained by taking the difference between the carrier phase observation values ​​at both ends of the same satellite to obtain the inter-antenna single difference, and then subtracting the inter-antenna single differences of different satellites. The parameterized modeling module is used to uniformly parameterize the effects of additional phase difference introduced by the spatial processing of the arrays at both ends, channel deviation at both ends, reception time deviation at both ends, and near-field wavefront deviation of interference sources on the inter-satellite differential observation vector into a low-dimensional non-ideal parameter vector. Based on the complex weight vector and the nominal channel response, an observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established; the dimension of the low-dimensional non-ideal parameter vector is less than the dimension of the inter-satellite differential observation vector. The model building module is used to establish a joint estimation model with the known baseline length as a constraint and the carrier baseline unit direction vector, integer ambiguity vector and the low-dimensional non-ideal parameter vector as unknowns. The output module is used to construct a whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, integer fuzzy search and continuous parameter optimization are performed on the joint estimation model, and a fixed solution is output; otherwise, a floating-point solution is output.

[0014] The present invention also provides an electronic device, the electronic device including a memory and a processor, the memory storing program instructions; the processor being used to run the program instructions to perform the dual-array navigation orientation joint estimation method as described above.

[0015] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program causes a computer to perform the dual-array navigation orientation joint estimation method as described above.

[0016] This invention provides a joint estimation method and system for dual-array navigation and orientation. Compared with existing technologies, it has the following advantages: By unifying the additional phase difference, channel bias, time bias, and near-field wavefront bias of the array spatial processing at both ends into a low-dimensional non-ideal parameter vector with a dimension much smaller than the number of observations, and solving it in the same joint estimation model as the baseline direction and integer ambiguity, reliable separation of the additional phase from the baseline geometric phase is achieved under non-ideal conditions such as independent weights at both ends, inconsistent channels, asynchronous time, and near-field interference. This does not require the assumption of identical weights at both ends or common-mode cancellation of the additional phase, nor does it require an external synchronization link. At the same time, the known baseline length constraint is used to prevent the absorption of the baseline scale by the channel bias, and the rank sum minimum eigenvalue of the whitened Jacobian matrix is ​​used as the identifiability criterion to perform online quantitative gating to determine whether the current observation conditions are sufficient to support parameter separation and integer fixation. When the conditions are insufficient, floating-point solutions are automatically output, avoiding spurious fixed solutions and ensuring the reliability of the orientation results. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A flowchart of the dual-array navigation orientation joint estimation method provided in this application embodiment; Figure 2 This is a diagram illustrating the joint estimation structure of dual-array navigation and orientation provided in an embodiment of this application. Figure 3 A schematic diagram of known baseline lengths and multi-star geometry provided for embodiments of this application; Figure 4 Asynchronous time alignment and channel difference state diagram provided for embodiments of this application; Figure 5 A schematic diagram of the near-field spherical wave array response provided in an embodiment of this application; Figure 6 A flowchart of mixed integer joint estimation and identifiability gating provided for embodiments of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This application provides a dual-array navigation orientation joint estimation method and system, which solves the problem that under conditions of independent array weights at both ends, inconsistent channels, asynchronous time, and coexistence of near-field interference, the array additional phase is mixed with the baseline geometric phase and integer ambiguity, leading to systematic shift in orientation results and a decrease in integer fixation rate. It achieves joint separation of baseline direction, integer ambiguity, and difference terms at both ends under non-ideal conditions, as well as reliability gating of fixed solution output.

[0021] As attached Figure 1 As shown, the technical solution in this application embodiment is to solve the above-mentioned technical problems by providing a dual-array navigation orientation joint estimation method. This method is performed according to the following steps: Obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observations, hardware timestamps, complex weight vectors actually used for array spatial processing, and nominal channel responses output by both ends; Inter-satellite differential observation vectors are constructed based on the carrier phase observation values ​​output from both ends; the inter-satellite differential observation is obtained by taking the difference between the carrier phase observation values ​​at both ends of the same satellite to obtain the inter-antenna single difference, and then subtracting the inter-antenna single differences of different satellites; The effects of additional phase difference introduced by the spatial processing of the two-end arrays, channel offset at both ends, reception time offset at both ends, and near-field wavefront offset of interference sources on the inter-satellite differential observation vector are uniformly parameterized into a low-dimensional non-ideal parameter vector. An observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established based on the complex weight vector and the nominal channel response. The dimension of the low-dimensional non-ideal parameter vector is smaller than the dimension of the inter-satellite differential observation vector. Using the known baseline length as a constraint, a joint estimation model is established with the carrier baseline unit direction vector, integer ambiguity vector, and the low-dimensional non-ideal parameter vector as unknowns; Construct a whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, perform integer fuzzy search and continuous parameter optimization on the joint estimation model and output a fixed solution; otherwise, output a floating-point solution.

[0022] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0023] S1: Observation, data collection and reporting.

[0024] That is, to obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observation value, hardware timestamp, complex weight vector actually used for array space processing, and nominal channel response output by both ends.

[0025] Please see Figure 2 Here, A and B represent two antenna arrays and their receiving channels, respectively. A and B independently perform array space processing, such as power inversion and minimum variance distortionless response (MVDR), to suppress interference. The receivers at both ends are driven by their respective crystal oscillators, have independent hardware timestamp references, and the amplitude and phase responses of the RF channels at both ends are not necessarily consistent. A joint observation model is constructed, defining the reference point baseline vectors of antennas or arrays A and B. for: (Equation 1) The baseline vector L·q connects the reference points of the two arrays, where L is the known or highly calibrated baseline length, and q is the unit direction vector to be estimated (i.e., the carrier baseline unit direction vector). The input consists of the raw observations output by receivers A and B at their respective hardware timestamps, including: Both ends A and B conduct observations and data acquisitions under their respective time bases. Specifically: Obtain the carrier phase observation values ​​of each satellite, denoted as... and In this context, subscripts A and B represent end A and end B respectively, s represents satellite serial number, and k represents epoch serial number; Obtain pseudorange observations ( , Doppler or carrier phase change rate observation ( , ), carrier-to-noise ratio and lockout flag; Obtain the hardware timestamps of both receivers and ; Obtain the complex weight vectors actually used by the array processing units at both ends A and B in the current epoch. and and the nominal channel response at both ends as specified by the manufacturer. and The nominal channel response includes the amplitude, phase, and group delay information of the radio frequency channel; At the same time, it also obtains satellite positions given by broadcast ephemeris or precise ephemeris. And related calibration information such as array element positions, mutual coupling nominal values, and temperature sensor readings.

[0026] S2: Time alignment and observation construction.

[0027] That is, construct the inter-satellite differential observation vector based on the carrier phase observation values ​​output from both ends.

[0028] Furthermore, the time deviation is parameterized as a low-dimensional time-varying function including constant and drift components; the contribution of the time deviation to the inter-satellite differential observation vector is incorporated into the observation mapping after being modulated by the Doppler frequency of each satellite.

[0029] First, based on the difference between the hardware timestamps at both ends - Using these as initial values, and combining code observations (pseudorange) and frequency observations (Doppler), the relative time deviation between points A and B is estimated. This relative time deviation is modeled as a low-dimensional time-varying function, namely: in, The relative time deviation between the two ends of epoch k. For constant time deviation components, For the drift rate component, For common reference time, The reference starting epoch is used. This model contains only two unknown parameters and can effectively characterize timestamp deviations and slow drifts on the order of milliseconds.

[0030] It should be noted that, for each satellite, the impact of this time deviation on carrier phase observation is Doppler frequency modulation, that is, the phase error introduced by the time deviation for the s-th satellite is... Due to the different Doppler frequencies of different satellites They are all different, and the influence of the baseline direction on the observation is achieved through the line-of-sight geometry matrix. Upon entering, the corresponding Jacobian sequences are linearly independent when the number of satellites is sufficient, thus the time bias and baseline direction can be separated in the joint estimation.

[0031] Subsequently, after time alignment is completed, the difference in carrier phase between the two ends is taken for the same satellite s: The single difference between antennas is obtained, which eliminates satellite clock errors and most of the common errors in the ionosphere and troposphere.

[0032] In one embodiment, the selection of reference satellites in the construction of the inter-satellite difference observation vector includes: among visible satellites that meet the carrier-to-noise ratio threshold, the one with the highest elevation angle is selected first, or the one that minimizes the condition number of the inter-satellite difference matrix is ​​selected, and satellites falling near the null trap of the array space processing weights are not used as reference satellites.

[0033] Specifically, a reference satellite is selected from the set of visible satellites. The selection criteria for reference satellites are as follows: the satellite with the highest elevation angle is selected first to reduce multipath and atmospheric residuals; if there are multiple satellites with similar elevation angles, the satellite with the smallest condition number of the inter-satellite difference matrix is ​​selected to improve numerical conditions; satellites falling near the null weight trap of the local or remote array shall not be used as reference satellites.

[0034] Subtracting the inter-antenna single difference of the reference satellite from the inter-antenna single difference of each non-reference satellite yields the inter-satellite differential observation vector. This process eliminates the clock difference between the receivers at both ends and the common overall phase offset between the two ends.

[0035] Let the line-of-sight unit vector of satellite s relative to the carrier at epoch k be... Then construct a geometric matrix. , The i-th action The transpose of , where i traverses all satellites except the reference satellite (dimension is S-1 rows, 3 columns, where S is the number of visible satellites participating in the solution). Thus, the inter-satellite difference observation vector... It can be modeled as: (Equation 2) Where λ is the carrier wavelength, and L is the known or high-precision calibrated baseline length. For geometric matrices, Let be the unit direction vector to be estimated. This is the inter-antenna / inter-satellite differential integer ambiguity vector. That is, by All A column vector (dimension) formed by multiplying by the wavelength λ and stacking them in satellite number order. ), Design a matrix for ambiguity, i.e. Each row corresponds to a non-reference satellite, and its elements are determined by the inter-satellite difference relationship between the satellite and the reference satellite (i.e., the corresponding position of the satellite is 1, the corresponding position of the reference satellite is -1, or an equivalent linear combination after the transformation of the reference satellite). It is a low-dimensional, non-ideal parameter vector; The observation mapping (i.e., observation mapping) is the mapping from low-dimensional non-ideal parameters to inter-satellite difference observation vectors. To observe noise.

[0036] As attached Figure 2 The diagram shown is a high-level flowchart of a dual-array navigation and orientation joint estimation system. It illustrates the overall flow of the attitude determination algorithm based on a dual-array system. The input is array A (actual complex weights). timestamp ) and array B (actual weighted values) timestamp ), and the known baseline length L; the carrier phase observations at both ends and the nominal channel response are input into the "multi-satellite differential observation model" module, and the observation model is expressed by equation (2), that is ,in Design a matrix for ambiguity. The result is an integer ambiguity vector; then it enters the "mixed integer spherical constraint estimation" module, which includes rank and minimum information feature value gating (i.e., discriminability determination); finally, it outputs fixed / floating solutions for heading, pitch, and three-dimensional attitude, as well as integrity indices.

[0037] As attached Figure 3The figure shows a geometrical diagram of dual-array satellite observation. It illustrates the geometrical layout for receiving signals from multiple satellites using a dual-array system. The top section shows four satellites: s1, s2, s3, and s4, with s1 designated as the reference satellite. Below are arrays A and B, each consisting of four receiving elements. Solid lines represent the line-of-sight connections between the reference satellite s1 and arrays A and B, as well as the baseline connections between arrays A and B (thick solid lines). Dashed lines represent the line-of-sight connections between the other satellites (s2, s3, s4) and arrays A and B, respectively. This geometric relationship is used to construct the geometric matrix in equation (2). The i-th row is the difference between the line-of-sight unit vectors of the non-reference satellite and the reference satellite.

[0038] S3: Low-dimensional parametric modeling (constructing observation maps) ).

[0039] The effects of additional phase difference, channel offset, receiving time offset, and near-field wavefront offset of interference sources introduced by the spatial processing of the two arrays on the inter-satellite differential observation vector are uniformly parameterized into a low-dimensional non-ideal parameter vector. An observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established based on the complex weight vector and the nominal channel response.

[0040] The core of this invention lies in unifying and parameterizing various non-ideal factors into a low-dimensional non-ideal parameter vector. And construct its mapping to the observation space. . The dimension is strictly smaller than the current observation vector. The dimension of the parameter is a prerequisite for ensuring parameter identifiability and numerical stability. This step is achieved through the following three types of sub-models (i.e., parametric modeling): (I) Channel bias at both ends and additional phase linearization In one embodiment, establishing the observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector based on the complex weight vector and the nominal channel response includes: The receiver channel response matrix is ​​expressed as the product of its nominal response matrix and the bias matrix, wherein the bias matrix is ​​determined by a low-dimensional bias parameter vector.

[0041] The additional phase difference is expanded in first order Taylor at the identity matrix of the deviation matrix to obtain the known terms calculated analytically from the complex weight vector and the nominal channel response, as well as the linear sensitivity term of the deviation parameter vector. The sensitivity term is used to construct the Jacobian matrix of the observation map.

[0042] Specifically, the complex responses (equivalent gain after array spatial processing) of A and B for satellite s are written as follows: (Equation 3) where, , are conjugate transposes of the complex weight vectors practically used at the two ends; , are channel response matrices; , are array manifold vectors. The additional phase difference of the two ends for this satellite is exactly .

[0043] In order to convert the above additional phase difference into an identifiable low-dimensional parameterized model, the present invention decomposes the channel response matrix into a product form of a nominal part and a low-dimensional deviation part: where, is the nominal channel response matrix given by factory calibration (regarded as a known quantity), is an identity matrix, denotes a diagonal matrix of corresponding dimensions constituted by the channel deviation parameter vector (the diagonal matrix is equivalent to a preferred implementation form of the deviation matrix), belongs to the d-dimensional real number space, and d is much smaller than the observation number n (i.e., d<<n). Physically, each component of corresponds to the amplitude or phase deviation of one radio frequency channel, whose dimension is determined by the number of channels and the deviation type, and is much smaller than the number of satellites.

[0044] Performing a first-order Taylor expansion on the additional phase difference at = 0, we can obtain: , (Equation 3-1) where, is a known term calculated from the actual weight and the nominal channel, which is calculated and derived from the actual weight , and the nominal channel through analytical calculation; and are respectively the sensitivity row vectors of the additional phases at end A and end B to their respective channel deviation parameter vectors , , whose calculation expression is , which can be analytically obtained by derivation.

[0045] The core significance of this linearized model lies in that it compresses the original problem of "one unknown additional phase for each satellite" into "a set of low-dimensional channel deviation parameters shared by all satellites". Through this processing, the additional phase no longer enters the equation as an overall unknown quantity, but is separated from the baseline geometric phase in the same joint estimation process.

[0046] As shown in the attached Figure 4 The diagram shown illustrates time synchronization and deviation. It illustrates the time axis relationship between points A and B, and the sources of error. The upper and lower horizontal lines represent the time axes of points A and B, respectively; the middle label reads "Relative Time Deviation". “” indicates that there is a misalignment between the two time bases; the vertical dashed line marks “common reference time”, indicating that the observations at both ends are converted to a unified time base; the upper right corner is marked “channel difference → low-dimensional additional phase”, indicating that the hardware channel difference at both ends is parameterized into a low-dimensional additional phase term after linearization processing by equation (3-1).

[0047] To ensure numerical stability, a zero-trap gating mechanism must be implemented. Let... This refers to the nominal amplitude response modulus output after the satellite signal has undergone space processing. When the value falls below a set threshold (e.g., less than 10% of the nominal average amplitude response), it indicates that the satellite has fallen into a null trap near its local weights, and the noise in the phase observations will be extremely amplified. In this case, the satellite should be directly removed, or its weights should be adjusted accordingly. Reduce the weight until it reaches zero. If the satellite falls below the rejection threshold, it will be directly rejected and prohibited from serving as a reference satellite.

[0048] (ii) Asynchronous Time Deviation Parameterization The time deviation is parameterized as a low-dimensional time-varying function including constant and drift components; the contribution of the time deviation to the inter-satellite differential observation vector is incorporated into the observation mapping after being modulated by the Doppler frequency of each satellite.

[0049] As described in step S2 above, time deviation Using a two-parameter model Characterization. The contribution of this parameter to the differential phase between the s-th stars is: In constructing the observation mapping At that time, the contribution will be regarded as The mapping terms corresponding to the time components. It should be noted that within a short time window, and Highly correlated (collinear). Therefore, the system adaptively determines whether to enable it based on the window length. The minimum eigenvalue of the whitening Jacobian only when the window length exceeds a set threshold and is enabled. Only when the increase exceeds a preset threshold will it be... Incorporate the parameter vector, or otherwise fix it to the prior value (usually set to 0) to avoid ill-conditioned normal equations.

[0050] (III) Parameterization of Near-Field Interference Spherical Wavefront The near-field wavefront deviation of the interference source is represented by the interference source's direction angle and inverse distance parameter, which is proportional to the reciprocal of the distance from the interference source to the array reference element.

[0051] A second-order expansion of the relative phase of the spherical wave yields a plane wave term, a curvature term linearly related to the inverse distance parameter, and higher-order terms. When the inverse distance parameter approaches zero, the near-field model continuously degenerates into a far-field plane wave model. The range of values ​​for the inverse distance parameter is limited by box constraints.

[0052] Specifically, when the interference source is located in the near field of the array, its wavefront cannot be approximated as a plane wave. This applies to the location of the interference source. (Position vector of the j-th interference source) and array element position (Position vector of the m-th element), the relative phase of the spherical wave can be precisely expressed as: (Equation 4) in, For the number of interference sources, For the wavenumber of the interference signal, Let be the position vector of the array reference element, and ||·|| denote the vector 2 norm, i.e., the Euclidean norm.

[0053] If directly based on the distance of the interference source As a parameter to be estimated, there are two inherent difficulties: first, the phase pair partial derivatives according to The inverse square decays, and when the interference source is located at a medium to long distance, this parameter becomes almost unobservable, causing the normal equation to become ill-conditioned; secondly, The value range of is a semi-infinite interval, making it difficult to impose bounded constraints. Therefore, this invention uses inverse distance parameterization instead.

[0054] To overcome the direct estimation of the absolute distance to the interference source = Existing pathological problems (phase pairs) The partial derivative with The square inverse decays (becoming nearly unobservable at long distances), this invention employs inverse distance parameterization, defined as: (Equation 5) Inverse distance parameter of the j-th interference source It has the following properties: First, its values ​​are definitely bounded, that is... ,in The minimum allowable disturbance distance for the system allows for direct optimization using box constraints (i.e., upper and lower bound constraints); secondly, when When the distance approaches zero, the interference source degenerates to infinity, and the model automatically degenerates into a far-field plane wave model.

[0055] Perform a second-order Fresnel expansion on the path difference in equation (4), and use... From the definition, we can obtain: (Equation 6) Substituting into equation (4), we can obtain the additional phase of array element m relative to the reference array element: (Equation 7) in, = - Let m be the position vector of the array element relative to the reference array element; = ( ) / The unit vector is the direction of the interference source; It is the identity matrix; The projection matrix; This represents the vertical component of the array element's deviation from the direction of the interference source; This represents a higher-order infinitesimal term whose modulus is no greater than a certain constant multiplied by 1. The square of.

[0056] The physical meaning of equation (7) is very clear: the first term on the right-hand side The first term is the plane wave term (far-field steering vector phase); the second term... The curvature term characterizes the deviation of the spherical wavefront from the planar wavefront. Note that the curvature term only relates to... The curvature term is proportional to the square of the component perpendicular to the direction of arrival. When the array elements are arranged along the direction of arrival (the vertical component is zero), the spherical wavefront does not produce an additional curvature phase; only when the array elements are spread out in a direction perpendicular to the direction of arrival does the curvature term increase with the square of the spread. The conditions for equations (6) and (7) to hold are as follows: <<1, meaning the distance to the interference source is much greater than the array aperture D. If higher-order terms... If the magnitude of the noise is higher than the current phase observation noise standard deviation, then the third-order term should be retained or the pre-established spherical wave response dictionary interpolation should be used instead.

[0057] As attached Figure 5 As shown, this is a schematic diagram of the wavefront of a near-field interference source. This figure illustrates the influence model of the near-field interference source on the dual arrays. The black dot in the upper left corner represents the near-field interference source; multiple rays emanate from the interference source and point to the receiving elements of arrays A and B respectively; the dashed arc represents the spherical wavefront, indicating that when the interference source is located in the near field of the array, the wavefront is a curved sphere rather than a plane wave. This geometric relationship corresponds to the inverse distance parameterization model of equations (5) to (7), where the curvature term in equation (7) accurately characterizes the deviation of the spherical wavefront relative to the plane wavefront.

[0058] After the parameterization described above, the parameters to be estimated for each near-field interference source are only the two angles (azimuth and elevation) of the direction of arrival and the inverse range parameter. There are three in total, and they are independent of the number of array elements M. When there are J interference sources, the total number of introduced parameters is 3J. Each end A and B has its own independent reference array element, range, and direction of arrival; therefore, their difference is the contribution of the near-field wavefront to the phase difference between the two ends.

[0059] (iv) Adaptive selection of parameter subsets The system only uses a subset of parameters that are identifiable under the current observation conditions and contribute to the residuals. This selection employs a greedy forward selection algorithm: starting from an empty set, candidate components are temporarily incorporated into the set during each calculation. Its whitened Jacobian minimum eigenvalue The improvement amount is selected, and the candidate component with the largest improvement amount is incorporated. Until the increase falls below a set increment threshold (e.g., relative to the current...). The mechanism ensures that the improvement rate is less than 5% or the number of conditions exceeds the limit (e.g., 1000). dimensionality (dim( The value is always much smaller than the number of observations n, which avoids ill-conditioned and overfitting of the normal equation, while not ignoring significant differences between the two ends.

[0060] In each iteration, the system is based on the values ​​determined in the previous round. Based on this, recalculate the temporary merged value for each candidate component that has not yet been activated. Increase the quantity, rather than sorting all at once using the initial values.

[0061] Finally, the above three types of parameters ( Includes channel bias parameters Time parameters / Near-field parameters / (etc.) and their corresponding mapping terms are uniformly assembled into the observation mapping. And its analytical Jacobian matrix is ​​given.

[0062] S4: Construct a joint estimation model.

[0063] That is, using the known baseline length as a constraint, a joint estimation model is established with the carrier baseline unit direction vector, integer ambiguity vector and the low-dimensional non-ideal parameter vector as unknowns.

[0064] Stack K epoch observations, including the current epoch, and use the known baseline length L as a hard constraint (or a high-weight calibration constraint) to establish a vector q (the unit direction vector of the carrier baseline). Integer ambiguity vector and low-dimensional non-ideal parameter vectors This is a joint estimation model for unknowns. The objective function of this model is to minimize the sum of squared whitening residuals with added prior regularization terms, i.e., to solve for: (Equation 8) in, To observe the inverse of the noise covariance matrix, For regularization terms (by) (Given the prior covariance). for The feasible region (defined by box constraints, prior range, and physical boundary), i.e. Depend on The physical boundaries of each component are defined together with the box constraints, such as the inverse distance parameter. The box constraint is The boundaries of the channel bias parameter are determined by its physical range. The known length L is used as a hard constraint in the solution. This constraint, together with the unit direction constraint, defines the direction and scale of the baseline, thereby eliminating trivial solutions that arbitrarily absorb the baseline scale due to channel bias or additional phase.

[0065] S5: Identifiability determination (gating).

[0066] That is, construct a whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, perform integer fuzzy search and continuous parameter optimization on the joint estimation model and output a fixed solution; otherwise, output a floating-point solution.

[0067] Take a unit spherical tangent space basis near a given integer candidate. Construct a continuous parameter Jacobian matrix: (Equation 9) in, The Jacobian block in the tangent space corresponding to the baseline direction (dimension is (S-1)×2); To observe the Jacobian blocks of the mapping on a low-dimensional parameter vector (with dimensions of (S-1)×dim( Each column of the partial derivative corresponds to The sensitivity of one component is obtained by assembling the Jacobians of the three sub-models in S3.

[0068] Will Stacked according to epochs and whitened using the observation noise covariance (i.e., left-multiplied) ), to obtain the whitened Jacobian matrix Determine whether the identifiability condition is met: (Equation 10) Where rank(·) represents the rank of the matrix, 2 is the local degree of freedom of the carrier baseline unit direction vector (the tangent space dimension of the three-dimensional unit vector is 2), and dim(ξ) is the dimension of the currently enabled low-dimensional non-ideal parameter vector. (·) indicates finding the minimum eigenvalue of a matrix; Let be the inner product matrix of the whitened Jacobian; This is a preset information threshold.

[0069] As the time window slides, for An incremental update and rank reduction update strategy is adopted, that is, only the Jacobian block of the newly added epoch is calculated and the matrix is ​​updated, avoiding the need to perform a complete singular value decomposition on the entire window again, so as to reduce the amount of computation.

[0070] In one embodiment, The value is 1.0 (this value can be determined by gradually increasing the threshold under static scenarios with a fixed success rate of no less than 95% as the indicator. The specific value can be adjusted according to the system's accuracy requirements). Dimensions and Consistency (dimensionless or equivalent to the information content after normalization of observation noise) represents the information content threshold of the weakest observable direction, which can be determined in static calibration based on fixed success rate requirements in engineering. The physical meaning of this criterion is: the estimated variance of the weakest observable direction is not inferior to the observation noise level.

[0071] In one embodiment, the rank determination of the whitened Jacobian matrix employs a tolerable singular value decomposition, where a singular value whose ratio to the largest singular value is less than a set tolerance is judged as zero.

[0072] The rank determination employs Singular Value Decomposition (SVD) with tolerance, where a singular value whose ratio to the largest singular value is less than a set tolerance (e.g., machine precision multiplied by the maximum dimension) is considered zero, thus avoiding misclassification of rank due to floating-point errors. The smallest eigenvalue is obtained through symmetric eigenvalue decomposition or exponential iteration.

[0073] When equation (10) is satisfied, it is determined that the current satellite geometry and time excitation are sufficient to support parameter separation and integer fixation, and proceeds to the subsequent execution steps; when not satisfied, the historical epochs are incorporated forward to reconstruct the whitened Jacobian matrix and the determination is made again. If the condition is still not satisfied after being incorporated into the maximum time window (for example, preset to 5 seconds or 10 seconds according to the dynamic characteristics of the carrier), the satellite geometry is determined to be degraded. At this time, the system skips integer fixation, directly outputs the floating-point direction solution, and sets the gating flag to "not allow integer fixation" to prevent the output of false fixed attitude.

[0074] S6: Joint solution of mixed integers and continuous layer optimization.

[0075] In one embodiment, the integer fuzziness search and continuous parameter optimization include: First, relax the integer ambiguity vector to a real number, and then solve it together with the carrier baseline unit direction vector and the low-dimensional non-ideal parameter vector to obtain the floating-point solution and its covariance.

[0076] After performing a downcorrelation transformation on the ambiguity sub-block of the covariance, integer candidates are searched.

[0077] Given integer candidates, the Jacobian block corresponding to the low-dimensional non-ideal parameter vector is eliminated to obtain the reduction equation only for the tangent space increment of the carrier baseline unit direction vector, and the carrier baseline unit direction vector is updated on the unit spherical tangent space.

[0078] Specifically, this step uses a three-layer structure to solve equation (8).

[0079] First layer (constraint layer): The known baseline length L is used as a hard constraint in the solution; if L is obtained from calibration and has calibration uncertainty, then a high-weight constraint consistent with that uncertainty is used instead. The unit direction constraint is applied as a manifold constraint, that is, q is always kept on the unit sphere.

[0080] The second layer (integer layer): First, the integer ambiguity vector N is relaxed to real numbers and solved jointly with q and ξ to obtain floating-point solutions and their covariance. Then, a decorrelation transformation is performed on the ambiguity sub-blocks of the covariance, for example, using integer whitening filtering in the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) algorithm to compress the search space; then, integer candidates are enumerated by ellipsoidal search in the transformed space, and the first few candidates are retained according to the objective function value.

[0081] The third layer (continuous layer): Given integer candidates, the continuous subproblems with respect to q and ξ are solved using Gauss-Newton iterations. In each iteration, the block corresponding to ξ is first eliminated, resulting in the tangent space increment only with respect to the unit direction vector of the carrier baseline. The reduced equation: (Equation 11) The weighted elimination matrix P is: (Equation 12) in, For whitening Jacobian blocks with tangent spatial increments in the baseline direction. For whitening Jacobian blocks with low-dimensional non-ideal parameters, The whitening residual vector, The Tikhonov regular matrix (by The prior covariance and the second derivative of the regularization term in the objective function are given together, and I is the identity matrix.

[0082] It should be noted that: only when When P is a zero matrix, then P is the one that reaches zero. Orthogonal projection matrix of the orthogonal complement of column space; when When P is non-zero, it no longer satisfies idempotency; its effect is to apply the a priori strength to... Weighted elimination in all directions, when When P is non-zero, its function is equivalent to, while preserving prior information, to... The uncertainty in direction is removed from the direction estimate, and then the direction increment is calculated. (Introduction) It can be guaranteed Strictly positive definite, so that elimination occurs in It remains numerically feasible even when the excitation in certain directions is insufficient. In the implementation of Equations (11) and (12), the Jacobian matrix is ​​decomposed into orthogonal triangular decomposition (QR decomposition) without explicitly forming the product of its transpose and itself, so as to avoid the condition number being squared.

[0083] After obtaining the tangent space increment η, the carrier baseline unit direction vector is updated in the unit spherical tangent space using an exponential mapping: (Equation 13) in, and Let represent the unit direction vector of the carrier baseline before and after the iteration (i.e., the nth iteration and the (n+1th iteration), respectively. It forms a basis for the tangent space (two orthogonal column vectors). To map the tangent vector to a three-dimensional Cartesian space, This update method avoids singularities in Euler angle parameterization at specific poses and eliminates the need for renormalization after each iteration, thus preventing module drift. The third iteration uses incremental module... |The convergence criterion is that the decrease in the objective function is simultaneously less than a set threshold, and an upper limit is set for the maximum number of iterations.

[0084] After all integer candidates have been solved, they are sorted in ascending order of weighted residual sum of squares. A residual test (e.g., chi-square test, where the whitened residual sum of squares follows a chi-square distribution with degrees of freedom equal to the number of observations minus the number of parameters, with a significance level of 0.01) is performed on the best candidate to determine if the model is compatible with the observations. Then, a ratio test (with an example threshold of 3.0) is performed using the ratio of the weighted residual sum of squares of the second-best candidate to the best candidate to determine if the best candidate is significantly better than the others. If both tests pass, a fixed solution and its covariance are output; otherwise, a floating-point solution is output and observations continue to accumulate.

[0085] As attached Figure 6The diagram shows a detailed flowchart of attitude calculation and integrity monitoring. It illustrates the specific execution steps and logical judgments of the algorithm. Step 1: Obtain the carrier phase observations at both ends, the actual complex weight vector, channel state information, and hardware timestamps, corresponding to step S1 in the implementation method. Step 2: Perform time alignment and construct a multi-satellite differential observation model (where multi-epoch stacking is performed in step S4 of the implementation method, and single-epoch observation construction is performed in step S2), corresponding to steps S2 and S4 in the implementation method. Step 3: Perform outer-layer integer ambiguity search using LAMBDA decorrelation search, corresponding to the second layer of step S6 in the implementation method. Step 4: Jointly estimate the baseline direction and low-dimensional parameters under inner-layer unit spherical constraints, corresponding to the third layer of step S6 in the implementation method. Step 5: Construct and whiten the stacked Jacobian matrix, calculate the rank and minimum information eigenvalue, corresponding to step S5 in the implementation method. This judgment can be performed before the integer search for admission control, or after obtaining the floating-point solution and before fixing the integer candidates for fixing control. Step 6: Determine whether the rank is full and... If the value is not less than the threshold, the process returns to the inner layer estimation and iterates again with measures such as extending the observation window and reducing parameters until the maximum window still does not meet the requirement. Then, a floating-point solution is output, which corresponds to the rollback strategy at the end of step S5 in the implementation method. Step 7 performs an integer integrity check (i.e., residual check and ratio check). If it fails, measures such as reducing parameters, adding satellites, extending the window, and maintaining the floating-point solution are taken, and the process returns to the inner layer estimation. This corresponds to the parameter subset adjustment in step S3 (IV) and the check strategy at the end of step S6 in the implementation method. If it passes, the fixed solutions for heading, pitch, and three-dimensional attitude, as well as the integrity index, are output.

[0086] It should be noted that this method ensures the integrity of the vehicle's true attitude motion when performing the joint solution of S6. The baseline geometric phase changes generated by the vehicle during turning, rolling, or pitching are entirely determined by the true baseline direction term in the model. This indicates that the system only handles additional factors caused by spatial processing, channels, time, and interference at both ends. Estimation and compensation will not misjudge the actual rotation of the carrier as channel drift or parameter change. This characteristic is naturally guaranteed by the structural division of labor in the model of this invention: the baseline direction q and the low-dimensional non-ideal parameters Occupying different column spaces in the Jacobian matrix, the change in q is represented by the movement of the direction angle across the unit sphere, while The changes manifest as alterations in the additional phase mapping, and there is no ambiguous coupling between the two. Therefore, this invention does not eliminate the changed signal through differential or filtering methods, but rather retains the true geometric phase changes as a source of directional information. The geometric carrier phase generated by the true turning, roll, and pitch will not be mistakenly eliminated.

[0087] S7: Reference star switching processing.

[0088] When the elevation angle of the original reference satellite falls below a set threshold, is lost, or is determined to be under interference, the system selects a new reference satellite. At this point, a single-modulus integer linear transformation is performed on the integer ambiguity vector: Where T is the integer transformation matrix from the old reference star to the new reference star, and its absolute determinant is 1 (i.e., This property guarantees the equivalence of integer lattices before and after the transformation.

[0089] The specific construction method is as follows: Let the old reference star be s1, and the new reference star be s. m (The r-th component in the original ambiguity vector corresponds to satellite s) m When the j-th row of the transformation matrix T is multiplied by the original vector, if the new vector corresponds to the old reference star in that row, then the matrix row element takes -1 at position r and 0 for the rest; if the new vector corresponds to a common non-reference star i, then the matrix row element takes 1 at position i, -1 at position r, and 0 for the rest. This matrix is ​​an integer matrix with an absolute determinant of 1, therefore it is a single-mode transformation. Simultaneously, a corresponding transformation is performed on the ambiguity covariance: This process ensures that integer solutions are equivalent before and after the switch, and fixed integer solutions do not need to be searched again; if the identifiability criterion is no longer met after the switch, the system will automatically fall back to the floating-point solution output.

[0090] After the reference star is switched, the system automatically returns to S5 to re-execute the identifiability determination; if the criterion of equation (10) is no longer satisfied, the system will fall back to the floating-point solution output.

[0091] Several specific embodiments are provided below to better help understand the method provided by the present invention.

[0092] Example 1: Asynchronous Dual-Array Orientation Both ends A and B perform power inversion (PI) space processing and output the actual weights, frequency-locked loop (FLL) and phase-locked loop (PLL) states, and carrier phase. The initial synchronization error, sub-milliseconds, is obtained at both ends using hardware timestamps, and the remaining error is estimated using code and frequency observations. and The system constructs a multi-satellite antenna differential at a common reference time and incorporates the satellite-by-satellite PI response difference, channel phase difference, and τ at both ends. The outer LAMBDA layer generates integer candidates, while the inner layer optimizes q on the unit sphere. In this embodiment, the subset of parameters enabled by S3 is the relative deviation between the two channels. and Relative time deviation and The integer fixing is only performed after the requirement (10) in step S5 is met. This embodiment provides a usable fixed solution under the condition that the weights at both ends are different and the time bases are independent, and its additional phase is no longer misinterpreted as the baseline geometric phase.

[0093] Example 2: Near-field interference The distance to the interference source and the array aperture do not satisfy the far-field condition. The system adopts the spherical wave array manifold described in equations (5) to (7), with two angles and inverse distance parameters in the interference direction. These are low-dimensional parameters. If the estimated values ​​are... The Jacobian and baseline direction Jacobian are highly correlated (correlation coefficient exceeds the threshold), indicating that they are inseparable under the current geometry. Based on this, the system extends the time window to wait for the carrier motion to provide excitation, or pauses integer fixed and high-precision attitude output, providing only floating-point solutions. In this embodiment, each interference source only needs to estimate three parameters (two incoming angles + one inverse distance), and... exist The inner box is constrained, when When the model approaches zero, it continuously degenerates into a far-field model without the need for threshold switching.

[0094] Example 3: Online calibration of known installation posture and channel There is a known installation rotation matrix between the two arrays. The system uses this as a priori constraint, but allows for small-angle installation error states. Group delay and phase deviation are estimated jointly using multi-frequency carrier and code observations; a channel drift model is established using a temperature sensor. The prior covariance of the channel state is automatically adjusted with temperature changes and restart time. In this embodiment, the nominal installation rotation matrix is ​​used as a strong prior in modeling in step S4, while the three small-angle installation errors are used as additional components of ξ; group delay and phase deviation are separated using a linear combination of multi-frequency carrier and code observations; the prior covariance of ξ is adjusted online by temperature sensor readings, with the prior relaxed during the initial power-on phase and tightened after entering steady state.

[0095] Example 4: Minimum number of satellites and adaptive window The system progressively incorporates historical epochs from the current epoch and reconstructs the stacked whitened Jacobian matrix until the rank criterion and minimum eigenvalue criterion of equation (10) are satisfied. If the epochs are not satisfied after adding epochs, the system determines that the satellite is geometrically degraded, triggering a reference star switch or outputting a floating-point direction. In this embodiment, a tolerable singular value decomposition is performed again after each inclusion; if the epochs are not satisfied after inclusion to the maximum allowable window, the system attempts to change the reference star and introduce an independent phase anchor point in sequence. If the epochs are still not satisfied, only the floating-point direction is output and the gating flag is set to not allow integer fixation. In this embodiment, the admission criteria for the number of satellites and the time window are changed from calculation based on the number of observations to quantitative determination based on the Jacobian rank and minimum information eigenvalue, thereby avoiding the output of false fixed attitudes during geometric degradation. The system simultaneously outputs the gating conclusion and test statistics (such as the sum of squares of whitened residuals and the ratio test statistics) as a quantitative basis for the reliability of the orientation results.

[0096] In summary, this application's embodiments use the unified observation model of equation (2) as the core. Through the three types of low-dimensional parameterization modeling in S3 (channel deviation and additional phase linearization, asynchronous time deviation dual parameterization, and near-field interference inverse distance parameterization), various end-to-end difference terms are compressed into low-dimensional non-ideal parameter vectors much smaller than the number of observations. This avoids the dependence of existing technologies on ideal assumptions such as equal weights, consistent channels, strict synchronization, and far-field interference. A joint estimation model is established with the known baseline length as a hard constraint. Combined with the rank and minimum information feature value gating in S5 and the three-layer mixed integer solution structure in S6, a safe mechanism for automatically backing up floating-point solutions under satellite geometric degradation or parameter coupling conditions is realized, ensuring the reliability of the output results. Embodiments 1 to 4 respectively verify the applicability in typical scenarios such as asynchronous dual arrays, near-field interference, online channel calibration, and minimum number of satellites and window adaptation. Each embodiment can be run independently or in combination within the same process framework. Technical details not described in detail in the above specific embodiments can be implemented with reference to common knowledge in the field or the full text of this specification.

[0097] This application also provides a dual-array navigation and orientation joint estimation system, including: The observation and acquisition module is used to obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observation values, hardware timestamps, complex weight vectors actually used for array spatial processing, and nominal channel responses output by both ends; The observation construction module is used to construct inter-satellite differential observation vectors based on the carrier phase observation values ​​output from both ends. The inter-satellite differential observation is obtained by taking the difference between the carrier phase observation values ​​at both ends of the same satellite to obtain the inter-antenna single difference, and then subtracting the inter-antenna single differences of different satellites. The parameterized modeling module is used to uniformly parameterize the effects of additional phase difference introduced by the spatial processing of the arrays at both ends, channel deviation at both ends, reception time deviation at both ends, and near-field wavefront deviation of interference sources on the inter-satellite differential observation vector into a low-dimensional non-ideal parameter vector. Based on the complex weight vector and the nominal channel response, an observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established; the dimension of the low-dimensional non-ideal parameter vector is less than the dimension of the inter-satellite differential observation vector. The model building module is used to establish a joint estimation model with the known baseline length as a constraint and the carrier baseline unit direction vector, integer ambiguity vector and the low-dimensional non-ideal parameter vector as unknowns. The output module is used to construct a whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, integer fuzzy search and continuous parameter optimization are performed on the joint estimation model, and a fixed solution is output; otherwise, a floating-point solution is output.

[0098] The dual-array navigation and orientation joint estimation system provided in this embodiment belongs to the same inventive concept as the above-described method embodiment, and includes: an observation acquisition module, an observation construction module, a parameterized modeling module, a model construction module, an identifiability determination module, and a solution output module.

[0099] The connection relationships and data processing flow of each module are as follows: The observation and acquisition module is connected to both the first and second array receivers. It acquires the known baseline length between them, the carrier phase observations output from both ends, the hardware timestamp, the complex weight vector actually used for array spatial processing, and the nominal channel response. This data is then transmitted to the observation construction module. This module corresponds to step S1 and is the input source for all subsequent processing.

[0100] The observation construction module, connected to the observation acquisition module, is used to construct inter-satellite differential observation vectors based on the carrier phase observation values ​​at both ends. Specifically, for the same satellite, the difference between the carrier phases at both ends is taken to obtain the inter-antenna single difference, and the difference between the inter-antenna single differences of different satellites is calculated to obtain the inter-satellite differential observation vector. Simultaneously, the reference satellite identifier and geometric matrix are output. This module corresponds to method step S2.

[0101] The parameterized modeling module, connected to the observation construction module, is used to uniformly parameterize the effects of additional phase difference introduced by the spatial processing of the arrays at both ends, channel offset at both ends, receiving time offset at both ends, and near-field wavefront offset of interference sources on the inter-satellite differential observation vector into a low-dimensional non-ideal parameter vector. It also receives the actual complex weighted vector and nominal channel response provided by the observation acquisition module, and establishes an observation mapping from this low-dimensional parameter vector to the inter-satellite differential observation vector. This module ensures that the dimension of the low-dimensional non-ideal parameter vector is less than the dimension of the inter-satellite differential observation vector. This module corresponds to step S3 of the method.

[0102] The model building module, connected to both the observation construction module and the parametric modeling module, receives inter-satellite difference observation vectors, observation mappings, and the known baseline length. Using the baseline length as a constraint, it establishes a joint estimation model with the carrier baseline unit direction vector, integer ambiguity vector, and low-dimensional non-ideal parameter vector as unknowns. This module corresponds to method step S4.

[0103] The identifiability determination module, connected to the model construction module, is used to construct a whitening Jacobian matrix based on the Jacobian matrix of the joint estimation model, and to determine whether the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and whether the minimum eigenvalue is not less than a preset threshold, and outputs an identifiability gating flag. This module corresponds to method step S5.

[0104] The output module, connected to both the model building module and the identifiability determination module, receives the joint estimation model and a gating flag. When the gating flag satisfies the identifiability condition, it performs integer fuzzy search and continuous parameter optimization on the joint estimation model, outputting a fixed solution; when the gating flag is not satisfied, it outputs a floating-point solution. This module corresponds to step S6 of the method.

[0105] Each of the above modules can be implemented collaboratively by one or more processors (such as FPGA, DSP, or ARM), or can be implemented using discrete hardware circuits; data transfer between modules is accomplished through a data bus or shared memory. Since this system embodiment and the aforementioned method embodiment are based on the same inventive concept, and their implementation principles and beneficial effects are the same as those of the method embodiment, the specific mathematical processing details in the system will not be repeated here; please refer to the aforementioned method embodiment.

[0106] An electronic device provided in this application includes a memory and a processor; the memory is a computer-readable storage medium used to store computer programs; the processor is used to implement the above-described dual-array navigation orientation joint estimation method when executing the computer program.

[0107] In this embodiment, the beneficial effects of the electronic device and the computer-readable storage medium are similar to those of the dual-array navigation orientation joint estimation method described above, and will not be repeated here.

[0108] The present invention describes electronic devices that can serve as servers or clients of this application, which are examples of hardware devices applicable to various aspects of this application. Electronic devices are intended to represent various forms of digital electronic computer devices. Electronic devices can also represent various forms of mobile devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present application described and / or claimed herein.

[0109] Electronic devices include a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM can also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0110] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. The storage medium can be a read-only memory (ROM) or a random access memory (RAM), etc. The integrated units described above can be implemented in hardware or as software functional units.

[0111] In summary, compared with existing technologies, it has the following beneficial effects: 1. By performing low-dimensional parameterization of the additional phase difference at both ends, the unknown additional phase that was originally one per satellite is compressed into a low-dimensional parameter shared by all satellites. Under the condition that the weights at both ends are independent and the channels are inconsistent, the additional phase and the baseline geometric phase can still be separated in a unified model; achieving independence from the assumption that the weights at both ends are the same or that the additional phases are common-mode cancellation.

[0112] 2. By incorporating channel bias, time bias, and near-field wavefront bias into the same low-dimensional parameter vector and solving them all at once in the joint estimation model, the error propagation of item-by-item correction is avoided, and no external synchronization link or common-mode assumption is required; thus, it can jointly handle channel inconsistency, time asynchrony, and near-field interference.

[0113] 3. By using the known baseline length as a hard constraint and combining the identifiability criterion, it quantitatively determines online whether the current satellite geometric and temporal excitation is sufficient to support parameter separation and integer fixation. When the observation conditions are insufficient, it automatically falls back to the floating-point solution, thus avoiding the output of spurious fixed solutions.

[0114] 4. By parameterizing the near-field disturbance with inverse distance and characterizing the spherical wavefront with a second-order expansion, only 3 bounded parameters are introduced for each disturbance source. The parameter dimension does not increase with the number of array elements, and it can continuously degenerate into a far-field model when the inverse distance parameter approaches zero, without the need for model switching decision.

[0115] 5. By adopting a hybrid solution structure that combines integer relaxation, decorrelation search, and continuous optimization, and obtaining a second-order reduction equation with respect to direction only by eliminating low-dimensional parameter blocks in the continuous layer, the numerical conditions of the direction subproblem are not infected by the ill-conditioned blocks of low-dimensional parameters, thus improving the solution stability. At the same time, the geometric phase change generated by the actual rotation of the carrier is retained in the baseline direction term, while the low-dimensional parameters only represent the difference terms at both ends. Therefore, the turning, rolling, and pitching motions of the carrier will not be mistakenly eliminated or misjudged as channel drift.

[0116] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A joint estimation method for navigation and orientation using dual arrays, characterized in that, Includes the following steps: Obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observations, hardware timestamps, complex weight vectors actually used for array spatial processing, and nominal channel responses output by both ends; Inter-satellite differential observation vectors are constructed based on the carrier phase observation values ​​output from both ends; the inter-satellite differential observation is obtained by taking the difference between the carrier phase observation values ​​at both ends of the same satellite to obtain the inter-antenna single difference, and then subtracting the inter-antenna single differences of different satellites; The effects of additional phase difference introduced by the spatial processing of the two-end arrays, channel offset at both ends, reception time offset at both ends, and near-field wavefront offset of interference sources on the inter-satellite differential observation vector are uniformly parameterized into a low-dimensional non-ideal parameter vector. An observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established based on the complex weight vector and the nominal channel response. The dimension of the low-dimensional non-ideal parameter vector is smaller than the dimension of the inter-satellite differential observation vector. Using the known baseline length as a constraint, a joint estimation model is established with the carrier baseline unit direction vector, integer ambiguity vector, and the low-dimensional non-ideal parameter vector as unknowns; Construct a whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, perform integer fuzzy search and continuous parameter optimization on the joint estimation model to output a fixed solution. Otherwise, output the floating-point solution.

2. The method according to claim 1, characterized in that, In the construction of the inter-satellite differential observation vector, the selection of reference satellites includes: among visible satellites that meet the carrier-to-noise ratio threshold, the one with the highest elevation angle is selected first, or the one that minimizes the condition number of the inter-satellite differential matrix is ​​selected, and satellites that fall near the null trap of the array space processing weights are not used as reference satellites.

3. The method according to claim 1, characterized in that, The observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector based on the complex weighted vector and the nominal channel response includes: The receiver channel response matrix is ​​expressed as the product of its nominal response matrix and the bias matrix, wherein the bias matrix is ​​determined by a low-dimensional bias parameter vector; The additional phase difference is expanded in first order Taylor at the identity matrix of the deviation matrix to obtain the known terms calculated analytically from the complex weight vector and the nominal channel response, as well as the linear sensitivity term of the deviation parameter vector. The sensitivity term is used to construct the Jacobian matrix of the observation map.

4. The method according to claim 1, characterized in that, The time deviation is parameterized as a low-dimensional time-varying function including constant and drift components; the contribution of the time deviation to the inter-satellite differential observation vector is incorporated into the observation mapping after being modulated by the Doppler frequency of each satellite.

5. The method according to claim 1, characterized in that, The near-field wavefront deviation of the interference source is represented by the interference source orientation angle and inverse distance parameter, which is proportional to the reciprocal of the distance from the interference source to the array reference element; A second-order expansion of the relative phase of the spherical wave yields a plane wave term, a curvature term linearly related to the inverse distance parameter, and higher-order terms. When the inverse distance parameter approaches zero, the near-field model continuously degenerates into a far-field plane wave model. The range of values ​​for the inverse distance parameter is limited by box constraints.

6. The method according to claim 1, characterized in that, The rank determination of the whitened Jacobian matrix adopts a singular value decomposition with tolerance, and a singular value is judged to be zero if the ratio of the singular value to the largest singular value is lower than the set tolerance.

7. The method according to claim 1, characterized in that, The integer fuzziness search and continuous parameter optimization include: First, relax the integer ambiguity vector to a real number, and then solve it together with the carrier baseline unit direction vector and the low-dimensional non-ideal parameter vector to obtain the floating-point solution and its covariance. After performing a downcorrelation transformation on the ambiguity sub-blocks of the covariance, integer candidates are searched. Given integer candidates, the Jacobian block corresponding to the low-dimensional non-ideal parameter vector is eliminated to obtain the reduction equation only for the tangent space increment of the carrier baseline unit direction vector, and the carrier baseline unit direction vector is updated on the unit spherical tangent space.

8. A dual-array navigation and orientation joint estimation system, characterized in that, include: The observation and acquisition module is used to obtain the known baseline length between the first array receiver and the second array receiver, as well as the carrier phase observation values, hardware timestamps, complex weight vectors actually used for array spatial processing, and nominal channel responses output by both ends; The observation construction module is used to construct inter-satellite differential observation vectors based on the carrier phase observation values ​​output from both ends. The inter-satellite differential observation is obtained by taking the difference between the carrier phase observation values ​​at both ends of the same satellite to obtain the inter-antenna single difference, and then subtracting the inter-antenna single differences of different satellites. The parameterized modeling module is used to uniformly parameterize the effects of additional phase difference introduced by the spatial processing of the arrays at both ends, channel deviation at both ends, reception time deviation at both ends, and near-field wavefront deviation of interference sources on the inter-satellite differential observation vector into a low-dimensional non-ideal parameter vector. Based on the complex weight vector and the nominal channel response, an observation mapping from the low-dimensional non-ideal parameter vector to the inter-satellite differential observation vector is established; the dimension of the low-dimensional non-ideal parameter vector is less than the dimension of the inter-satellite differential observation vector. The model building module is used to establish a joint estimation model with the known baseline length as a constraint and the carrier baseline unit direction vector, integer ambiguity vector and the low-dimensional non-ideal parameter vector as unknowns. The determination output module is used to construct the whitening Jacobian matrix. When the rank of the whitening Jacobian matrix is ​​equal to the sum of the local degrees of freedom of the carrier baseline unit direction vector and the dimension of the low-dimensional non-ideal parameter vector, and the minimum eigenvalue of the whitening Jacobian matrix is ​​not less than a preset threshold, the module performs integer fuzzy search and continuous parameter optimization on the joint estimation model and outputs a fixed solution. Otherwise, output the floating-point solution.

9. An electronic device, characterized in that, The electronic device includes: A memory, wherein the memory stores program instructions; A processor for executing the program instructions to perform the dual-array navigation orientation joint estimation method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores a computer program, wherein the computer program causes the computer to perform the dual-array navigation orientation joint estimation method as described in any one of claims 1 to 7.

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