CN116793346B - Improved least square based strapdown inertial navigation Doppler log calibration method, computer equipment and medium - Google Patents
Improved least square based strapdown inertial navigation Doppler log calibration method, computer equipment and medium Download PDFInfo
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Abstract
A calibration method, computer equipment and medium of a strap-down inertial navigation Doppler log based on improved least square belongs to the technical field of integrated navigation, solves the problems that the traditional least square DVL calibration method lacks treatment on pathological problems and is difficult to obtain accurate calibration parameters, and comprises the following steps: the carrier enters an integrated navigation mode after being aligned, and the carrier is calculated to obtain more accurate speed after integrated navigation filtering; and (3) carrying out improved least square estimation on the speed obtained by solving the SINS and GPS integrated navigation system and the speed of the DVL, so as to solve the pathological DVL calibration problem. The invention is suitable for underwater navigation positioning application scenes.
Description
Technical Field
The invention belongs to the technical field of integrated navigation, and particularly relates to a strapdown inertial navigation and Doppler log calibration method.
Background
In order to achieve sufficient detection and development of the ocean, the autonomous underwater vehicle needs to have deep open sea navigation capability with high precision and long navigation time, wherein underwater navigation positioning is a key technology for application of the autonomous underwater vehicle. The strapdown inertial navigation system (Strapdown Inertial Navigation System, SINS) does not radiate energy to the outside, and although navigation errors accumulate over time and cannot provide high-precision navigation information for the AUV for a long time, the navigation system is better in concealment and autonomy, so that the navigation system is commonly used as a main navigation system of the AUV. The DVL is velocity measuring equipment based on Doppler effect, has good autonomy and quick response, and can measure the velocity of the aircraft relative to the seabed and the water flow, thereby providing carrier velocity information with higher precision, and errors are not accumulated with time. At present, combined navigation of a strapdown inertial navigation system and a Doppler log is a main mode of autonomous underwater vehicle navigation. However, the SINS/DVL integrated navigation system is easy to cause spatial inconsistency of two carrier coordinate systems of the SINS and the DVL due to the introduction of the DVL system, and the installation error angle and the scale factor are required to be calibrated.
The method provided by the prior art establishes a DVL error loss function and approximates the optimal solution of the loss function based on Newton iteration method, and the method has the advantages of high convergence speed, local second-order convergence and the like, but is difficult to calculate the inverse of the Hessian matrix and consumes time and calculation resources. Besides, a three-point online calibration method is also provided in the prior art, and calibration of the scale factor error and the installation error angle can be completed only by floating the AUV twice. However, the method cannot calibrate the roll error angle, and because the pitch angle and the roll angle of the carrier are ignored in calculation, the method has higher requirements on the calibration posture of the AUV.
Disclosure of Invention
The invention aims to solve the problems that the traditional least square DVL calibration method lacks treatment on pathological problems and is difficult to obtain accurate calibration parameters, and provides a novel calibration method of a strapdown inertial navigation and Doppler log based on improved least square.
In order to solve the technical problems, the method for calibrating the strapdown inertial navigation/Doppler log based on the improved least square comprises the following steps:
Step 1: the carrier is initially aligned, enters into an SINS and GPS combined navigation mode, and obtains the speed of the carrier under a carrier coordinate system after combined navigation filtering
Step 2: constructing a DVL velocity measurement model to obtain a reverse mapping relation of the model and the velocity of the DVL under a carrier coordinate systemThe saidAnd said at least one ofResidual r of (2);
Step 3: obtaining parameters to be calibrated according to an improved least square principle
The parameters to be calibrated are obtained according to the improved least square principleComprising the following steps:
according to the principle of minimum residual r, namely r=0, the measurement equation consisting of q speed measurement values is combined to obtain a linear equation in a matrix form, a measurement matrix and measurement vectors H and Z;
singular value decomposition is carried out on the expansion matrix (H, Z), and an initial regularization parameter k is selected, wherein k is smaller than or equal to the dimension of the state vector;
Processing the singular value decomposed expansion matrix (H, Z) according to the regularization parameter k to obtain an improved least squares solution
The regularization parameter k is determined according to a generalized cross-validation method.
Further, the speed of the carrier in the carrier coordinate systemThe method comprises the following steps:
In the method, in the process of the invention, For the velocity of the carrier in the x-axis direction of the carrier coordinate system,For the velocity of the carrier in the y-axis direction of the carrier coordinate system,Is the velocity of the carrier in the z-axis direction of the carrier coordinate system.
Further, the DVL speed measurement model is as follows:
In the method, in the process of the invention, For the velocity of the DVL output in the d-frame of the DVL coordinate system, K is the scale factor,For the mounting error angular coordinate transformation matrix of the carrier coordinate system to the DVL coordinate system,Noise is measured for speed.
Further, the velocity of the DVL in the carrier coordinate systemThe method comprises the following steps:
In the method, in the process of the invention, And the parameter matrix to be calibrated.
Further, in the process of obtaining the parameter to be calibrated, the expansion matrix (H, Z) subjected to singular value decomposition is processed through the regularization parameter k, and the part of the solution corresponding to the small singular value is truncated.
Further, the linear equation is:
Z＝HX
where X is a 9-dimensional system state vector.
A computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a method for calibrating a strapdown inertial navigation doppler log based on improved least squares.
A computer readable storage medium for storing a computer program for performing a method of calibrating a strapdown inertial navigation doppler log based on improved least squares as described above.
An improved least squares based strapdown inertial navigation doppler log calibration system, the system comprising: the method is used for carrying out initial alignment on the carrier, entering an SINS and GPS combined navigation mode, and obtaining the speed of the carrier under a carrier coordinate system after combined navigation filteringIs a device of (a); the method is used for constructing a DVL velocity measurement model to obtain a reverse mapping relational expression of the model and the velocity of the DVL under a carrier coordinate systemThe saidAnd said at least one ofMeans of residual r; for obtaining parameters to be calibrated according to an improved least square principleIs provided.
The method provided by the invention can inhibit errors at two ends of the measurement equation and is suitable for treating the pathological problems.
Compared with the prior art, the invention has the beneficial effects that: when there is an error across the equivalent measurement equation, the linear least squares method is no longer optimal. The overall least squares can solve the problem of errors at both ends of the measurement equation, but cannot solve the pathological problem. The improved least square utilized by the method is a natural extension of the least square, and can be applied to the two problems.
The invention has certain engineering application value for improving the precision of parameter estimation and realizing the purpose of inhibiting random errors.
The invention is suitable for underwater navigation positioning application scenes.
Drawings
FIG. 1 is a flow chart of a method for calibrating a strapdown inertial navigation Doppler log based on improved least squares;
FIG. 2 is a flow chart of a calibration algorithm of the strap-down inertial navigation Doppler log based on improved least squares;
Detailed Description
For a better understanding of the technical content of the present invention, the following description is made with reference to the accompanying drawings, in which the main steps of the method are:
embodiment one: the specific steps of the method for improving least square based strapdown inertial navigation and Doppler log calibration in the embodiment are as follows:
step 1: after initial alignment is carried out on the carrier, starting to enter an SINS/GPS integrated navigation mode;
Step 2: after the combined navigation filtering, the speed of the carrier in the carrier coordinate system (b system) is obtained through calculation and coordinate transformation
Step 3: a velocity measurement model of DVL is established as follows
In the method, in the process of the invention,For the velocity of the DVL output in the DVL coordinate system (d-system),For the velocity of the DVL output in the carrier coordinate system, K is the scale factor,For the mounting error angular coordinate transformation matrix of the carrier coordinate system to the DVL coordinate system,Noise is measured for speed.
Step 4: after the inverse mapping is carried out on the DVL velocity measurement model, the velocity expression of the DVL in the carrier coordinate system can be obtained
In the method, in the process of the invention,And the parameter matrix to be calibrated.
Step 5: because the carrier needs to maintain a constant-speed direct navigation state during DVL calibrationIs of a constant value, i.e. has
In the method, in the process of the invention,A i, i=1, 2, …,6 are intermediate variables defined by the parameter matrix P to be calibrated.
Step 6: according to step 5, the carrier velocity in the carrier coordinate systemVelocity in carrier coordinate system with DVLR, then
In the method, in the process of the invention,A i, i=1, 2, …,6 are intermediate variables defined by the parameter matrix P to be calibrated,
ξ＝[-a1 -a2 -a3 -a4 -a5 -a6 a7 a8 a9 a10]T,ai,i＝7,8,9,10 Is based on the parameter matrix P to be calibrated and the speed measurement noiseThe intermediate variables that are defined are,
Step 7: if random error interference does not exist, residual error r=0, r epsilon n×1, and N is the number of speed data obtained through calculation. Because random error interference exists in practice, only xi can be estimated, and xi epsilon N multiplied by 1 is obtainedMinimizing the residual r, i.e. optimizing the function as
argminf(A,ξ)＝||r||2＝ξTATAξ
s.t.ξ≠0, (5)
4a1a4-(a2)2＞0.
In the formula, |·| represents modulo operation.
Step 8: as can be seen from step 6, the optimization function of equation (5) is optimized when the residual r is minimal, i.e., r=0. The following linear equation can be obtained by linearizing and developing the equation (4)
Step 9: if q velocity measurements exist, the measurement equations composed of the q velocity measurements can be combined to obtain a linear equation of the form
Z＝HX (7)
Wherein Z is a q-dimensional measurement vector, X is a 9-dimensional system state vector, and H is a measurement matrix, and the specific forms are as follows:
Wherein a i, i=7, 8,9,10 is the noise measured by the parameter matrix P to be calibrated and the speed A defined intermediate variable;
Step 10: since the number q of velocity measurements is much greater than the number of unknowns in the measurement equation, equation (7) is an overdetermined linear equation. When DVL is calibrated, the measurement matrix H and the measurement vector Z are interfered by measurement noise, so that random errors are counted as first-order approximate disturbance of H and Z obtained by (7)
Where Z and H represent error-free metrology vectors and metrology matrices, respectively, and ΔZ and ΔH are approximate perturbation terms of Z and H.
Step 11: according to step 10, the DVL calibration problem can be converted into the following:
Where F is the Frobenius modulus.
Step 12: processing the problem in step 11 by using an improved least squares method, and performing singular value decomposition on the expansion matrix (H, Z) to obtain
Wherein: σ i is the ith singular value, i=1, 2, …,10, and σ 1≥σ2≥…≥σ10;ui is the ith column vector of the matrix U,U TU＝Iq,Iq is a q-order identity matrix; v i is the ith column vector of matrix V,V TV＝I10,I10 is an identity matrix of order 10; 0 (q-10)×10 is a zero matrix of (q-10) ×10, d=diag (σ 1,…,σ10),diag(σ1,…,σm) represents a diagonal matrix composed of σ 1,…,σm elements (i.e., an m-order square matrix in which all elements except the main diagonal are zero), and m is the number of elements;
step 13: equivalent measurement equations are ill-conditioned, and the DVL calibration problem will likely be solved unreliably, even without solutions. A regularization method is introduced to obtain a stable solution, and an initial regularization parameter k is selected, wherein k is smaller than or equal to the dimension of the state vector;
Step 14: partitioning the matrix V according to the regularization parameter k to obtain
Step 15: the solution for improving the least squares can be obtained by the following formula
In the method, in the process of the invention,Is the pseudo-inverse of V 22, |·| 2 is a 2-norm.
The elements of V 22 in equation (11) cannot all be 0, but in practice the regularization parameter k can always be reduced to a sufficient extent so that V 22 possesses a sufficiently large norm.
Step 16: optimizing and selecting regularization parameters k through GCV functions;
Step 17: definition of GCV function:
Where I is the identity matrix, trace (&) represents the trace operation, and G (k) is the objective function containing the regularization parameter k.
Step 18: the optimal regularization parameters are obtained at the minimum of the GCV function, so the optimal regularization parameters are obtained according to the formula (13);
Step 19: repeating steps 14-18 until the result meets the requirement;
step 20: once the system of equations solves for the unknowns The estimated value of the parameter to be calibrated can be calculatedAnd an estimate of the speed measurement noise
The calibration method of the strapdown inertial navigation/Doppler log based on the improved least square is completed.
Embodiment two:
The embodiment performs simulation verification on the strapdown inertial navigation and Doppler log calibration method based on improved least square in the first embodiment.
The simulation conditions were set as follows:
speed of movement of the vehicle Installation deflection angle α= [0 ° 0 ° 5 ° ], scale factorMeasuring error of Doppler log
The speed measurement noise of the Doppler log isI.e.Wherein the method comprises the steps ofRepresentation ofObeying normal distribution with mean value of 0 and variance of R;
The data sampling frequency was 1Hz and the simulation time was 200 seconds.
The condition number of the measurement matrix H is 4.062 ×10 7, which indicates that the measurement equation is severely ill-conditioned. The data were processed using the conventional least squares and modified least squares methods, the results of which are shown in the following table:
Table 1: conventional least squares and improved least squares results for data processing
As can be seen from simulation results, under the condition that the measurement equation belongs to a serious pathological condition, the algorithm provided by the invention is superior to the traditional least square, and the precision is improved by about 36.1%.
Although the embodiments of the present invention and the accompanying drawings have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments and the disclosure of the drawings.
Claims (6)
1. The method for calibrating the strapdown inertial navigation Doppler log based on the improved least square is characterized by comprising the following steps of:
Step 1: the carrier is initially aligned, enters into an SINS and GPS combined navigation mode, and obtains the speed of the carrier under a carrier coordinate system after combined navigation filtering
Step 2: constructing a DVL velocity measurement model to obtain a reverse mapping relation of the model and the velocity of the DVL under a carrier coordinate systemThe saidAnd said at least one ofResidual r of (2); the DVL speed measurement model is as follows:
In the method, in the process of the invention, For the velocity of the DVL output in the DVL coordinate system,Measuring noise for the speed;
Step 3: obtaining parameters to be calibrated according to an improved least square principle Wherein, K is the scale factor,An installation error angle coordinate transformation matrix for the carrier coordinate system to the DVL coordinate system;
the parameters to be calibrated are obtained according to the improved least square principle Comprising the following steps:
According to the principle of minimum residual error r, namely r=0, the measurement equation consisting of q speed measurement values is combined to obtain a linear equation in a matrix form, a measurement matrix H and a measurement vector Z; the speed measurement value is the speed of DVL output under a DVL coordinate system;
singular value decomposition is carried out on the expansion matrix (H, Z), and an initial regularization parameter k is selected, wherein k is smaller than or equal to the dimension of the state vector;
Processing the singular value decomposed expansion matrix (H, Z) according to the regularization parameter k to obtain an improved least squares solution Specifically: after reversely mapping the DVL velocity measurement model, obtaining a velocity expression of the DVL in a carrier coordinate system
In the method, in the process of the invention,The parameter matrix is a parameter matrix to be calibrated;
Because the carrier needs to maintain a constant-speed direct navigation state during DVL calibration Is of a constant value, i.e. has
In the method, in the process of the invention,I=1, 2, …,6 is an intermediate variable defined by the parameter matrix to be calibrated P;
The speed of the carrier in the carrier coordinate system Velocity in carrier coordinate system with DVLR, then
In the method, in the process of the invention,
ξ＝[-a1 -a2 -a3 -a4 -a5 -a6 a7 a8 a9 a10]T,ai,i＝7,8,9,10 Is based on the parameter matrix P to be calibrated and the speed measurement noiseThe intermediate variables that are defined are,
The linear equation in the matrix form is z=hx, and X is a 9-dimensional system state vector;
Solving for the unknown quantity I.e. calculate the estimated value of the parameter to be calibratedAnd an estimate of the speed measurement noiseThereby obtaining
The regularization parameter k is determined according to a generalized cross-validation method.
2. The method for calibrating a strapdown inertial navigation doppler log based on improved least squares as claimed in claim 1, wherein the carrier velocity is in a carrier coordinate systemThe method comprises the following steps:
In the method, in the process of the invention, For the velocity of the carrier in the x-axis direction of the carrier coordinate system,For the velocity of the carrier in the y-axis direction of the carrier coordinate system,Is the velocity of the carrier in the z-axis direction of the carrier coordinate system.
3. The calibration method of the strapdown inertial navigation doppler log based on the least square improvement according to claim 1, wherein in the process of obtaining the parameter to be calibrated, the expansion matrix (H, Z) subjected to singular value decomposition is processed through the regularization parameter k, and the part of the solution corresponding to the small singular value is truncated.
4. A computer device comprising a memory and a processor, the memory having a computer program stored therein, the processor performing a method of calibrating a modified least squares based strapdown inertial navigation doppler log according to any one of claims 1-3 when the processor runs the computer program stored in the memory.
5. A computer readable storage medium for storing a computer program for executing a method of calibrating a strapdown inertial navigation doppler log based on improved least squares according to any one of claims 1 to 3.
6. An improved least squares based strapdown inertial navigation doppler log calibration system, wherein the system is implemented using an improved least squares based strapdown inertial navigation doppler log calibration method as claimed in any one of claims 1 to 3, the system comprising: the method is used for carrying out initial alignment on the carrier, entering an SINS and GPS combined navigation mode, and obtaining the speed of the carrier under a carrier coordinate system after combined navigation filteringIs a device of (a); the method is used for constructing a DVL velocity measurement model to obtain a reverse mapping relational expression of the model and the velocity of the DVL under a carrier coordinate systemThe saidAnd said at least one ofMeans of residual r; for obtaining parameters to be calibrated according to an improved least square principleWherein K is the scale factor,An angular coordinate transformation matrix is a mounting error of the carrier coordinate system to the DVL coordinate system.
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