CN114777762A - Inertial navigation method based on Bayesian NAS - Google Patents

Inertial navigation method based on Bayesian NAS Download PDF

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CN114777762A
CN114777762A CN202210700859.8A CN202210700859A CN114777762A CN 114777762 A CN114777762 A CN 114777762A CN 202210700859 A CN202210700859 A CN 202210700859A CN 114777762 A CN114777762 A CN 114777762A
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CN114777762B (en
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付博
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Beijing Shendao Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD

Abstract

The invention provides an inertial navigation method based on Bayes NAS, which adopts an inertial/milemeter combined navigation mode, introduces Bayes optimization to search a neural framework, assists an integrated navigation system to further improve navigation accuracy, anti-jamming capability and stability under a satellite rejection environment, completes the Bayes optimization by extracting an upper computer for realizing the scheme on low-cost equipment, and dynamically optimizes delay, computing capability, FLAH, SRAM resources and the like of the system at the same time, has high accuracy and reliability, is mainly applied to inertial navigation systems with limited resources such as ground traveling vehicles, intelligent robots and the like, has deep learning capability, realizes high-efficiency algorithms on low-cost equipment, reduces equipment cost using deep learning, can only carry out conventional operation on a lower computer, and transfers a large amount of convolution type operation to the upper computer for carrying out, meanwhile, one upper computer can simultaneously support several navigation devices, and even the capability can be further improved by using a cloud computing mode.

Description

Inertial navigation method based on Bayesian NAS
Technical Field
The invention relates to the technical field of measurement and testing, in particular to an inertial navigation method based on Bayesian NAS.
Background
The combined navigation system of the inertia/mileometer is widely used in the satellite rejection environment, and compared with the combined navigation method based on dead reckoning, the combined navigation system based on the neural network deep learning has higher precision, resolution and stability. However, the existing neural network inertia/odometer combined navigation framework has high requirements on hardware resources, and is not suitable for being applied to low-resource and low-cost equipment.
At present, the application of the deep learning neural network on the inertial navigation system is mainly BPNN in China, and no precedent of adopting a Bayesian neural framework is searched. In general, most of the predicted values of the latter are closer to the true values than the former, and the prediction effect is better. Such as: an inertial navigation indoor positioning method based on a BP neural network (patent) is invented in patent CN201910067512.2, an indoor inertial navigation method improved based on the BP neural network (patent) is invented in patent CN201611020582.5, and an MEMS inertial navigation system positioning enhancement method based on an LSTM neural network model (patent) is invented in patent CN202110798898.1 and the like.
The existing inertial navigation system based on deep learning usually needs a computer equipped with strong hardware resources, and cannot be widely applied to low-cost and miniaturized equipment, or needs post-processing, and cannot meet the real-time requirement. Such as: a vehicle track estimation method and device based on a neural network model is disclosed in the patent CN 202110597498.4.
Taking a patent of 'an indoor inertial navigation method based on improvement of a bp neural network' as an example, a method for combining a human body advancing step length with an inertial system is provided. Only aiming at the partial advancing characteristics of the pedestrians, the device is easy to be interfered and has poor stability.
Therefore, a navigation method with high precision and reliability is needed.
Disclosure of Invention
The invention provides an inertial navigation method based on Bayesian NAS (network attached storage), aiming at solving the problems of navigation precision and reliability, wherein an inertial/mileometer combined navigation mode is adopted, Bayesian optimization is introduced to search a neural framework, an auxiliary combined navigation system further improves the navigation precision, the anti-interference capability and the stability in a satellite rejection environment, and in order to realize the scheme on low-cost equipment, the Bayesian optimization is extracted to be completed by an upper computer, and dynamic optimization is carried out on the delay, the computing capability, the FLAH, the SRAM (static random access memory) resources and the like of the system.
The invention provides an inertial navigation method based on Bayesian NAS, which comprises the following steps:
s1, signal acquisition: the inertial/odometer combined navigation module simultaneously outputs the measured angular speed signal, the measured acceleration signal and the measured mileage pulse signal to a navigation computer and an upper computer;
s2, resolving a basic attitude: the navigation computer comprises an attitude calculation module, a navigation computer neural network module and a control module which are electrically connected, wherein the attitude calculation module performs basic attitude calculation according to an angular velocity signal, an acceleration signal and a mileage pulse signal, obtains attitude information and motion metadata and outputs the attitude information and the motion metadata to the navigation computer neural network module, the motion metadata is used for eliminating noise by judging the motion state of the inertia/mileage meter combined navigation module, the motion state comprises acceleration, deceleration, constant speed and stillness, the motion metadata comprises a speed increment, and the noise comprises drift and abnormal value interference of the inertia/mileage meter combined navigation module;
s3, neural architecture search: the upper computer searches and searches for an optimal neural network which improves the utilization rate of the navigation computer hardware SRAM and FLASH and reduces delay by using a Bayesian neural architecture, and outputs a control command, correction information and a hardware model to the control module;
s4, model control: the control module performs memory allocation, model loading, instruction response and model updating on the navigation computer neural network module, and the navigation computer neural network module performs noise filtering, dynamic noise reduction, data anomaly prediction and drift prediction by combining attitude information and motion metadata and then outputs corrected three-dimensional angle information, northeast speed and longitude and latitude information.
The invention relates to an inertial navigation method based on Bayesian NAS, which is used as an optimal mode, wherein an inertial/mileometer combined navigation module comprises an accelerometer and a mileometer;
the navigation computer neural network module uses a deep neural network;
the upper computer comprises a Bayesian neural architecture searching module electrically connected with the control module, and a machine learning platform, a hardware simulation module and a design space which are electrically connected with the Bayesian neural architecture searching module, wherein the Bayesian neural architecture searching module uses a Bayesian neural architecture searching and Monte Carlo sampling method, the machine learning platform uses a deep neural network, the machine learning platform is electrically connected with the inertia/mileometer combined navigation module, and the hardware simulation module is connected with the control module through a real-time system timer;
the motion metadata includes: a forward speed increment, a side speed increment, and a tip speed increment.
In the inertial navigation method based on bayesian NAS of the present invention, as a preferable mode, step S3 includes the following steps:
s31, training a machine learning platform: constructing a backbone neural network architecture, using navigation training information including routes and road conditions to train a machine learning platform, and enabling a hardware simulation module to establish a hardware simulation model;
s32, sending a control command: when the hardware simulation module is communicated with a real-time system timer and the machine learning platform is communicated with the inertia/mileometer combined navigation module, the inertia/mileometer combined navigation module outputs an angular velocity signal, an acceleration signal and a mileometer pulse signal to the machine learning platform, and the Bayesian neural architecture search module searches a design space according to the hardware simulation model and then sends a control command to the machine learning platform;
s33, Bayesian optimization: the machine learning platform performs attitude calculation according to the angular velocity signal, the acceleration signal and the mileage pulse signal to obtain attitude information and motion element data, performs precision judgment on the angular velocity signal, the acceleration signal and the mileage pulse signal according to the navigation training information and the motion element data, and returns the precision condition to the Bayesian neural architecture searching module;
and S34, the Bayesian neural architecture searching module searches for an optimal neural network by using Bayesian neural architecture searching and Monte Carlo sampling and outputs a control command, correction information and a hardware model to the control module.
The inertial navigation method based on Bayesian NAS is a preferred mode, and in the step S31, the method for constructing the backbone neural network architecture is to model f by using TCN and process layered spatial and temporal characteristics in a combined manner:
Figure DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 762222DEST_PATH_IMAGE002
for the receptive field of each cell in the ith layer in the TCN,
Figure 604276DEST_PATH_IMAGE003
the kernel size is k × k, p is the expansion factor,
Figure 733906DEST_PATH_IMAGE004
in order to expand the nucleus p times later,
Figure 876174DEST_PATH_IMAGE002
size i x (k-1) + k;
z=tanh(
Figure 433058DEST_PATH_IMAGE005
*
Figure 355883DEST_PATH_IMAGE006
)⊙𝜎（
Figure 758046DEST_PATH_IMAGE007
）；
wherein z is a switch type residual block, tanh and𝜎is the function of the activation of the function,xw is a weight matrix of a convolution filter, h and g are filters and gates, k is a layer index, x is convolution operation, and l is element-by-element multiplication operation;
the two dilated causal convolution layers are fused together by a switched-mode residual block z for modeling the bounded non-linearity and the time dependence of the input sequence.
The inertial navigation method based on the Bayesian NAS is an optimal mode, and in step S34, the Bayesian neural architecture search module finds out the inertial navigation method from the TCN
Figure 20400DEST_PATH_IMAGE008
，
Figure 748184DEST_PATH_IMAGE008
Is an optimal neural network;
Figure 830410DEST_PATH_IMAGE009
；
wherein f is an objective function, fError ofTo characterize the error objective function, ftlaylag is the objective function characterizing the delay, fflashTo characterize the capacity objective function of FLASH, fSRAMTo characterize the objective function of SRAM usage capacity,𝜆is a random scalar domain, and Q is a search space;
Figure 446984DEST_PATH_IMAGE008
to seek in competition with each other
Figure 596468DEST_PATH_IMAGE010
Is determined as a function of the pareto optimal solution of (a).
The inertial navigation method based on the Bayesian NAS is an optimal method,
Figure 823050DEST_PATH_IMAGE011
；
Figure 658151DEST_PATH_IMAGE012
；
Figure 667695DEST_PATH_IMAGE013
；
Figure 373483DEST_PATH_IMAGE014
；
Figure 708649DEST_PATH_IMAGE015
；
wherein w is the weight of the neural network,𝛾Is a super-parameter,
Figure 968729DEST_PATH_IMAGE016
Is directed acyclic graph, E is activation graph edge, V is activation graph vertex,𝛿for convolution and batch normalization, the HIL information is corresponding usage information output by a search hardware simulation module;
Figure 906598DEST_PATH_IMAGE017
is a tensrflow model of FLASH,
Figure 873417DEST_PATH_IMAGE018
is the maximum capacity of the hardware FLASH,
Figure 970031DEST_PATH_IMAGE019
is the maximum capacity of a hardware SRAM,
Figure 655090DEST_PATH_IMAGE020
is to ask for
Figure 396650DEST_PATH_IMAGE021
0The norm of (a) of (b),
Figure 811451DEST_PATH_IMAGE022
t is the input column vector, theta is the computational load,
Figure 957261DEST_PATH_IMAGE023
the operation load after expanding for p times is obtained;
monte carlo sampling is used in the bayes signaling up interval.
The inertial navigation method based on the Bayesian NAS is used as a preferred mode,
Figure 988671DEST_PATH_IMAGE024
obtaining by using a method for verifying mean square error;
Figure 878130DEST_PATH_IMAGE025
obtaining by using a RAM (random access memory) model, and storing an intermediate layer activation graph and tensor in an SRAM (static random access memory);
Figure 678595DEST_PATH_IMAGE026
using the floating point arithmetic capability of the processor.
As an optimal mode, when the HIL information of the hardware simulation module is effective,
Figure 260887DEST_PATH_IMAGE025
、
Figure 451696DEST_PATH_IMAGE027
and
Figure 738321DEST_PATH_IMAGE026
obtained from the implementing operating system of the target compiler.
The invention relates to an inertial navigation method based on Bayesian NAS, as a preferred mode, in step S4, three-dimensional angle information comprises an attitude angle phi, northeast speed v and longitude and latitude height information P;
Figure 862135DEST_PATH_IMAGE028
；
Figure 739961DEST_PATH_IMAGE029
；
Figure 355750DEST_PATH_IMAGE030
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 980154DEST_PATH_IMAGE031
in order to be the attitude angle of the robot,
Figure 896158DEST_PATH_IMAGE031
the update is obtained by the equivalent rotation metric method from the angular increment of the angular velocity signal,
Figure 148147DEST_PATH_IMAGE032
true angular velocity, exp (x) is an exponential function of an antisymmetric matrix,
Figure 641446DEST_PATH_IMAGE033
satisfy the requirement of
Figure 676398DEST_PATH_IMAGE034
；
Figure 305962DEST_PATH_IMAGE035
For the speed of the northeast day under the navigation coordinate system,
Figure 400957DEST_PATH_IMAGE035
the update is obtained from the acceleration integral after subtracting the gravitational acceleration g,
Figure 381552DEST_PATH_IMAGE036
is a specific force truth value;
Figure 220195DEST_PATH_IMAGE037
is a longitude and latitude high position, and is characterized in that,
Figure 704266DEST_PATH_IMAGE037
obtained from the northeast velocity integral.
The inertial navigation method based on the Bayesian NAS is used as a preferred mode,
Figure 235741DEST_PATH_IMAGE038
；
Figure 641315DEST_PATH_IMAGE039
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 142703DEST_PATH_IMAGE040
is the actual output of the gyroscope,
Figure 622226DEST_PATH_IMAGE041
is the actual output of the accelerometer,
Figure 633258DEST_PATH_IMAGE042
is the white noise of the gyroscope,
Figure 526127DEST_PATH_IMAGE043
is the white noise of the accelerometer and,
Figure 706573DEST_PATH_IMAGE044
and
Figure 430815DEST_PATH_IMAGE045
is a zero offset and is set to zero,
Figure 38514DEST_PATH_IMAGE044
and
Figure 949838DEST_PATH_IMAGE045
is related to temperature;
Figure 933975DEST_PATH_IMAGE046
；
Figure 778303DEST_PATH_IMAGE047
；
wherein the content of the first and second substances,
Figure 556903DEST_PATH_IMAGE048
and
Figure 958453DEST_PATH_IMAGE049
is gaussian white noise.
The invention aims to provide an inertial navigation method based on Bayesian neural architecture search, which adopts an inertial/mileometer combined navigation mode, introduces Bayesian optimization to the neural architecture search, assists a combined navigation system to further improve navigation accuracy, anti-interference capability and stability in a satellite rejection environment, extracts the Bayesian optimization to an upper computer to complete in order to realize the scheme on low-cost equipment, and dynamically optimizes delay, computing capability, FLAH, SRAM resources and the like of the system.
To achieve these objects and advantages in accordance with the present invention, there is provided an inertial navigation method based on bayesian neural architecture search, comprising:
firstly, an IMU is modeled, and the output of a gyroscope and an accelerometer is decomposed into three parts of a true value, a zero offset and Gaussian noise. As shown in equation 1:
Figure 215122DEST_PATH_IMAGE050
Figure 648377DEST_PATH_IMAGE039
(formula 1)
Wherein the content of the first and second substances,
Figure 597879DEST_PATH_IMAGE040
and
Figure 14954DEST_PATH_IMAGE041
is the actual output of the gyroscope and accelerometer,
Figure DEST_PATH_IMAGE051
and
Figure 668789DEST_PATH_IMAGE052
the true values of the angular velocity and the specific force,
Figure 97496DEST_PATH_IMAGE042
and
Figure 76954DEST_PATH_IMAGE043
is the white noise of the gyro and accelerometer,
Figure 325532DEST_PATH_IMAGE044
and
Figure 579796DEST_PATH_IMAGE045
it is zero bias that is generally temperature dependent, so the change in zero bias can be modeled as follows:
Figure 863010DEST_PATH_IMAGE053
Figure 278948DEST_PATH_IMAGE047
(formula 2)
Wherein the content of the first and second substances,
Figure 14823DEST_PATH_IMAGE048
and
Figure 807198DEST_PATH_IMAGE049
is gaussian white noise.
Then, the inertial motion is modeled, and divided into attitude solution (azimuth, pitch and roll), velocity solution and position solution, specifically as follows:
Figure 679339DEST_PATH_IMAGE054
Figure DEST_PATH_IMAGE055
Figure 325565DEST_PATH_IMAGE056
(formula 3)
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE057
exp (x) is an exponential function of the antisymmetric matrix for the attitude angle updated by the equivalent rotation quantity method from the gyro output angle increment.
Figure 142212DEST_PATH_IMAGE058
The acceleration integral obtained by subtracting the gravity acceleration g for the northeast speed under the navigation coordinate system is updated,
Figure DEST_PATH_IMAGE059
the longitude and latitude high position is obtained by the velocity integral of the northeast.
(V x) is an antisymmetric array, i.e., satisfies (V x) = - (V x)T. (Vx) is represented by a three-dimensional vector V = [ V ]x Vy Vz]TForming an anti-symmetric array.
The motion metadata includes: velocity increment of moving body in front, side and top three directions
Since the diameter of the vehicle tire is affected by thermal expansion and shows drift of the odometer scale factor, engine sparking and electromagnetic interference cause the sudden output of a large number of pulses of mileage, while the Deep Neural Network (DNN) is good at filtering noise and irrelevant information while extracting useful features from inertial devices, i.e., motion metadata, the method can effectively judge acceleration, deceleration, constant speed and stationary states for eliminating the generation of erroneous motion information caused by drift and abnormal value interference of the devices. The system can estimate the noise generated in the frame, realize dynamic noise reduction, has invariance to the influence of vibration and the like, can predict the abnormal and drifting of the training data more accurately, and improves the stability of the system.
Then, we construct the backbone neural network frameUsing TCN to model f, the spatial and temporal characteristics of the hierarchy can be jointly processed. The receptive field of each cell in the ith layer in TCN is
Figure 207120DEST_PATH_IMAGE060
The kernel size is k × k, the dilation factor is p, and the relationship is shown in equation 5:
Figure 464926DEST_PATH_IMAGE061
(formula 5)
Here, the
Figure 284983DEST_PATH_IMAGE062
In order to expand the nucleus p times later,
Figure 995450DEST_PATH_IMAGE060
the size is i x (k-1) + k, the memory and overfitting are not occupied, and the TCN kernel allows the network to search up and down in a long inertial data sequence while maintaining the input resolution and coverage. The convolution can keep the time sequence without calculating a complex and intensive circulation unit, and supports the unordered parallelization processing in the training period. Furthermore, the two expanded causal convolution layers are fused together by a switched-type residual block z for modeling the bounded non-linearity and the time dependence of the input sequence, as shown in equation 6:
z=tanh(
Figure 129628DEST_PATH_IMAGE005
*
Figure 569837DEST_PATH_IMAGE006
)⊙𝜎（
Figure 639424DEST_PATH_IMAGE007
) (formula 6)
Wherein tanh () and𝜎() Is an activation function, x is a state quantity of system modeling, W represents a weight matrix of a convolution filter, h and g represent filters and gates, k is a layer index, _ is convolution operation, _ is element-by-element multiplication operation. ByWhen the method needs to be applied to a low-resource hardware environment (FLASH and SRAM are limited) and meets the real-time requirement, the NAS finds an ideal neural inertia data sequence from the backbone TCN as a candidate, and models neural architecture search to regard the neural inertia data sequence as a BO problem capable of being processed in a parallelization mode. Defining the search space Q as a neural network weight of w and a hyperparameter of𝛾Directed acyclic graph for neural networks
Figure 699171DEST_PATH_IMAGE063
Indicating that the activation graph edge is E, the vertex is V,𝜆for a random scalar domain, f () is an objective function,𝛿representing operations employing conventional machine learning (including convolution, batch normalization, etc.), the goal is to find a neural network that maximizes the utilization of the device hardware SRAM and FLASH while minimizing latency. The optimization model is shown in formulas 7-12:
Figure 512407DEST_PATH_IMAGE009
(formula 7)
Wherein:
Figure 72701DEST_PATH_IMAGE011
(equation 8)
Figure 313189DEST_PATH_IMAGE012
(formula 9)
Figure 326145DEST_PATH_IMAGE013
(equation 10)
Figure 802125DEST_PATH_IMAGE014
(formula 11)
Figure 623451DEST_PATH_IMAGE064
； (formula 12)
Wherein, the first and the second end of the pipe are connected with each other,
Figure 159474DEST_PATH_IMAGE065
outputting corresponding usage information by the hardware simulation system,
Figure 659726DEST_PATH_IMAGE018
and
Figure 80343DEST_PATH_IMAGE066
the maximum capacity of hardware FLASH and SRAM.
Figure 880809DEST_PATH_IMAGE067
Is a tensrflow model of FLASH,
Figure 463100DEST_PATH_IMAGE068
is to obtain
Figure 716227DEST_PATH_IMAGE069
0The norm of (a) of (b),
Figure 409376DEST_PATH_IMAGE022
the column vector is input for a time t,
Figure 897356DEST_PATH_IMAGE070
pto expand the operation load p times later, the target is set
Figure 509603DEST_PATH_IMAGE071
Thought to seek in competition with each other
Figure 125392DEST_PATH_IMAGE072
As a function of the pareto optimal solution, as follows:
Figure 746866DEST_PATH_IMAGE073
(formula 13)
Handle
Figure 397291DEST_PATH_IMAGE074
The approximation is considered a gaussian process and therefore a search can be made forward in the moment of distribution. In addition, a random scalar field𝜆The method can be set according to different system characteristics, and can guide parallel search so as to enter a pareto optimal area in a gradual change plane. The next group
Figure 446018DEST_PATH_IMAGE075
Using monte carlo sampling, also known as thompson sampling, over the bayes confidence interval, this approach can balance search efficiency and usage efficiency. In addition to accelerating NAS, parallel search can ensure that NAS is not executed in an early network deformation state, maximize information gain in the search process, and generate a periodic coarse-to-fine search space.
It should be noted that, instead of characterizing the error, a form of verifying the mean square error may be used
Figure 549103DEST_PATH_IMAGE076
Finding the mathematically expected form (equation 8); alternatively, a standard RAM model may be used instead
Figure 771006DEST_PATH_IMAGE077
(equation 11), storing the intermediate layer activation map and the tensor in the SRAM; then, since the model delay is proportional to various convolution operations of the processor, floating point arithmetic capability (FLOPS) of the processor is used as an actual arithmetic capability to express the model delay
Figure 541516DEST_PATH_IMAGE078
(equation 10). Finally, when HIL is valid, it can be obtained directly from the operating system implementing the target compiler
Figure 761145DEST_PATH_IMAGE077
、
Figure 351526DEST_PATH_IMAGE079
And
Figure 314803DEST_PATH_IMAGE078
all hardware parameters are standardized by the equipment. And (4) searching the whole neural framework by the upper computer.
The working process of the system is as follows, firstly, a sensor constructed by an IMU and a milemeter sends original triaxial angular velocity, triaxial acceleration and mileage pulse information to an INS/OD combined navigation module for basic attitude calculation, a settlement result is sent to a neural network for real-time mathematical platform correction, the neural network performs memory allocation according to a simplified model and real-time delay information, the model is updated in real time under the condition of an upper computer, errors caused by conditions of drift, mutation and the like in combined navigation are eliminated according to model achievement of deep learning, and the precision and robustness of the system are further improved. And outputting the corrected three-dimensional angle information, the northeast speed and the longitude and latitude height information. A mathematical platform which runs in an upper computer and takes a Bayesian NAS as a core searches a design space according to a hardware simulation model under the condition that the lower computer is not connected and according to an HIL hardware model under the condition that the lower computer is connected, sends a control command to a deep learning machine platform, extracts motion metadata (mainly judging acceleration, deceleration, constant speed and static states) according to training information of combined navigation under a conventional route and road conditions and real information output by an IMU (inertial measurement unit) of the lower computer to judge the precision of navigation data, returns the precision to the Bayesian NAS, and sends a hardware model, correction information and a control command which are updated in real time to the lower computer.
The invention has the following advantages:
(1) the invention introduces a Bayesian NAS scheme, so that the prediction of a neural network is closer to reality, thereby improving the precision, stability and reliability of the system;
since the diameter of the vehicle tire is affected by thermal expansion and shows drift of the odometer scale factor, engine sparking and electromagnetic interference cause the sudden output of a large number of pulses of mileage, while the Deep Neural Network (DNN) is good at filtering noise and irrelevant information while extracting useful features from inertial devices, i.e., motion metadata, the method can effectively judge acceleration, deceleration, constant speed and stationary states for eliminating the generation of erroneous motion information caused by drift and abnormal value interference of the devices. The system can estimate the noise generated in the frame, realize dynamic noise reduction, has invariance to the influences of vibration and the like, can predict the abnormity and drift of the training data more accurately, and improves the stability of the system.
(2) The invention carries out real-time feedback on hardware resources according to two modes (HIL simulation and hardware model simulation) and further optimizes the system capability.
(3) According to the invention, by introducing the scheme of the upper computer, the lower computer inertial navigation system with limited resources also has the deep learning capability, the high-efficiency algorithm is realized on low-cost equipment, the equipment cost of using the deep learning is reduced, the lower computer can only carry out conventional operation, a large amount of convolution operation is handed over to the upper computer for carrying out, and meanwhile, one upper computer can simultaneously support several navigation equipment, and even the capability can be further improved by using a cloud computing mode.
Drawings
FIG. 1 is a flow chart of an inertial navigation method based on Bayesian NAS;
FIG. 2 is a system diagram of an inertial navigation method based on Bayesian NAS;
FIG. 3 is a comparison graph of a first set of navigation trajectories in an embodiment 1 of an inertial navigation method based on Bayesian NAS;
FIG. 4 is a velocity error diagram of the integrated navigation of the first set of INS/OD in embodiment 1 of the inertial navigation method based on Bayesian NAS;
FIG. 5 is a velocity error graph of a Bayesian NAS-based inertial navigation method in embodiment 1, after a Bayesian NAS optimization;
fig. 6 is a comparison diagram of the second group of navigation tracks in the inertial navigation method embodiment 1 based on bayesian NAS.
Reference numerals are as follows:
1. an inertia/mileometer integrated navigation module; 11. An inertial measurement unit; 12. An odometer; 2. A navigation computer; 21. An attitude resolving module; 22. A navigation computer neural network module; 23. A control module; 3. An upper computer; 31. A Bayesian neural architecture search module; 32. A machine learning platform; 33. A hardware simulation module; 34. And (4) designing space.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Example 1
As shown in fig. 1-2, an inertial navigation method based on bayesian NAS includes the following steps:
s1, signal acquisition: the inertia/mileage meter combined navigation module 1 simultaneously outputs the measured angular velocity signal, acceleration signal and mileage pulse signal to the navigation computer 2 and the upper computer 3;
s2, resolving a basic attitude: the navigation computer 2 comprises an attitude calculation module 21, a navigation computer neural network module 22 and a control module 23 which are electrically connected, the attitude calculation module 21 performs basic attitude calculation according to an angular velocity signal, an acceleration signal and a mileage pulse signal to obtain attitude information and motion metadata which are output to the navigation computer neural network module 22, the motion metadata are used for eliminating noise by judging the motion state of the inertia/mileage meter combined navigation module 1, the motion state comprises acceleration, deceleration, constant speed and stillness, the motion metadata comprise speed increment, and the noise comprises drift and abnormal value interference of the inertia/mileage meter combined navigation module 1;
s3, neural architecture search: the upper computer 3 searches and searches for an optimal neural network which improves the utilization rate of hardware SRAM and FLASH of the navigation computer 2 and reduces delay by using a Bayesian neural architecture, and outputs a control command, correction information and a hardware model to the control module 23;
s31, training a machine learning platform: constructing a backbone neural network architecture, using navigation training information including routes and road conditions to train the machine learning platform 32, and enabling the hardware simulation module 33 to establish a hardware simulation model;
in step S31, the method for constructing the backbone neural network architecture is to model f using TCN, and combine and process layered spatial and temporal features:
Figure 736557DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 598858DEST_PATH_IMAGE002
for the receptive field of each cell in the ith layer in the TCN,
Figure 676536DEST_PATH_IMAGE003
the kernel size is k × k, p is the expansion factor,
Figure 177924DEST_PATH_IMAGE004
in order to expand the nucleus p times later,
Figure 391868DEST_PATH_IMAGE002
size i x (k-1) + k;
z=tanh(
Figure 953299DEST_PATH_IMAGE005
*
Figure 518273DEST_PATH_IMAGE006
)⊙𝜎（
Figure 292194DEST_PATH_IMAGE007
）；
wherein z is a switch type residual block, tanh and𝜎is the function of the activation of the function,xw is a weight matrix of a convolution filter, h and g are filter and gates, k is a layer index, [ lambda ] is convolution operation, [ alpha ] is element-by-element multiplication operation;
the two expanded causal convolution layers are fused together by a switched-mode residual block z for modeling the bounded non-linearity and the time dependence of the input sequence;
s32, sending a control command: when the hardware simulation module 33 is communicated with a real-time system timer and the machine learning platform 32 is communicated with the inertia/odometer integrated navigation module 1, the inertia/odometer integrated navigation module 1 outputs an angular velocity signal, an acceleration signal and a mileage pulse signal to the machine learning platform 32, and the Bayesian neural architecture search module 31 searches the design space 34 according to the hardware simulation model and then sends a control command to the machine learning platform 32;
s33, Bayesian optimization: the machine learning platform 32 performs attitude calculation according to the angular velocity signal, the acceleration signal and the mileage pulse signal to obtain attitude information and motion element data, and the machine learning platform 32 performs precision judgment on the angular velocity signal, the acceleration signal and the mileage pulse signal according to the navigation training information and the motion element data and returns the precision condition to the Bayesian neural architecture searching module 31;
s34, the Bayesian neural architecture searching module 31 searches for an optimal neural network by using Bayesian neural architecture searching and Monte Carlo sampling and outputs a control command, correction information and a hardware model to the control module 23;
the Bayesian neural architecture search module 31 finds from the TCN
Figure 750857DEST_PATH_IMAGE008
，
Figure 358556DEST_PATH_IMAGE008
Is an optimal neural network;
Figure 535459DEST_PATH_IMAGE009
；
wherein f is an objective function, fError of the measurementTo characterize the error objective function, ftlaylag is the objective function characterizing the delay, fflashTo characterize the capacity objective function of FLASH, fSRAMTo characterize the objective function of SRAM usage capacity,𝜆is a random scalar domain, and Q is a search space;
Figure 316333DEST_PATH_IMAGE008
to seek in competition with each other
Figure 504869DEST_PATH_IMAGE010
A function of the pareto optimal solution of (a);
Figure 876945DEST_PATH_IMAGE011
；
Figure 275565DEST_PATH_IMAGE012
；
Figure 797813DEST_PATH_IMAGE013
；
Figure 228139DEST_PATH_IMAGE080
；
Figure 177640DEST_PATH_IMAGE064
；
wherein w is the weight of the neural network,𝛾Is a hyper-parameter,
Figure 1240DEST_PATH_IMAGE016
Is directed acyclic graph, E is activation graph edge, V is activation graph vertex,𝛿for convolution and batch normalization, the HIL information is the usage amount information corresponding to the output of the search hardware simulation module 33;
Figure 655075DEST_PATH_IMAGE017
is a tensrflow model of FLASH,
Figure 942837DEST_PATH_IMAGE018
is the maximum capacity of the hardware FLASH,
Figure 328819DEST_PATH_IMAGE019
is the maximum capacity of the hardware SRAM,
Figure 702031DEST_PATH_IMAGE020
is to ask for
Figure 300503DEST_PATH_IMAGE021
0The norm of (a) of (b),
Figure 708351DEST_PATH_IMAGE022
t is the input column vector, theta is the computational load,
Figure 593130DEST_PATH_IMAGE023
the operation load after expanding p times;
monte Carlo sampling is used in a Bayesian upper signal interval;
alternatively, the first and second electrodes may be,
Figure 329005DEST_PATH_IMAGE081
obtaining by using a method for verifying mean square error;
Figure 121380DEST_PATH_IMAGE025
obtaining by using a RAM (random access memory) model, and storing an intermediate layer activation graph and tensor in an SRAM (static random access memory);
Figure 259101DEST_PATH_IMAGE026
obtaining using floating point arithmetic capabilities of a processor;
alternatively, when the HIL information of the hardware emulation module 33 is valid,
Figure 845940DEST_PATH_IMAGE025
、
Figure 69111DEST_PATH_IMAGE027
and
Figure 871369DEST_PATH_IMAGE026
obtaining from an implementing operating system of a target compiler;
steps S2 and S3 may be performed simultaneously;
s4, model control: the control module 23 performs memory allocation, model loading, instruction response and model updating on the navigation computer neural network module 22, and the navigation computer neural network module 22 performs noise filtering, dynamic noise reduction, data anomaly prediction and drift prediction by combining attitude information and motion metadata and then outputs corrected three-dimensional angle information, northeast speed and longitude and latitude height information;
the three-dimensional angle information comprises an attitude angle phi, the speed of the northeast is v, and the longitude and latitude height information is P;
Figure 660334DEST_PATH_IMAGE028
；
Figure 683653DEST_PATH_IMAGE029
；
Figure 394120DEST_PATH_IMAGE030
；
wherein the content of the first and second substances,
Figure 997140DEST_PATH_IMAGE031
in order to be the attitude angle,
Figure 375032DEST_PATH_IMAGE031
the update is obtained by the equivalent rotation metric method from the angular increment of the angular velocity signal,
Figure 506936DEST_PATH_IMAGE032
exp (x) is an exponential function of an antisymmetric matrix, which is the true value of angular velocity,
Figure 829333DEST_PATH_IMAGE033
satisfy the requirement of
Figure 376989DEST_PATH_IMAGE034
；
Figure 140545DEST_PATH_IMAGE035
For the northeast speed of the navigation coordinate system,
Figure 505668DEST_PATH_IMAGE035
integral of acceleration by subtracting acceleration of gravity gThe update is obtained by the user,
Figure 253044DEST_PATH_IMAGE036
is a specific force truth value;
Figure 869970DEST_PATH_IMAGE059
is a longitude and latitude high position, and is characterized in that,
Figure 815929DEST_PATH_IMAGE059
obtained from the northeast speed integral;
Figure 961740DEST_PATH_IMAGE038
；
Figure 990220DEST_PATH_IMAGE039
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 879678DEST_PATH_IMAGE040
is the actual output of the gyroscope,
Figure 945723DEST_PATH_IMAGE041
is the actual output of the accelerometer,
Figure 793594DEST_PATH_IMAGE042
is the white noise of the gyroscope,
Figure 312300DEST_PATH_IMAGE043
is the white noise of the accelerometer and,
Figure 5449DEST_PATH_IMAGE044
and
Figure 660422DEST_PATH_IMAGE045
is a zero offset and is set to zero,
Figure 148035DEST_PATH_IMAGE044
and
Figure 154037DEST_PATH_IMAGE045
is related to temperature;
Figure 244353DEST_PATH_IMAGE046
；
Figure 894777DEST_PATH_IMAGE047
；
wherein the content of the first and second substances,
Figure 677925DEST_PATH_IMAGE048
and
Figure 46589DEST_PATH_IMAGE049
is gaussian white noise;
the inertia/mileometer combined navigation module 1 comprises an accelerometer and a mileometer;
the navigation computer neural network module 22 uses a deep neural network;
the upper computer 3 comprises a Bayesian neural architecture searching module 31 electrically connected with the control module 23, a machine learning platform 32, a hardware simulation module 33 and a design space 34 electrically connected with the Bayesian neural architecture searching module 31, wherein the Bayesian neural architecture searching module 31 uses a Bayesian neural architecture searching and Monte Carlo sampling method, the machine learning platform 32 uses a deep neural network, the machine learning platform 32 is electrically connected with the inertia/odometer combined navigation module 1, and the hardware simulation module 33 is connected with the control module 23 through a real-time system timer;
the motion metadata includes: a forward speed increment, a side speed increment, and a tip speed increment.
And performing a test vehicle navigation test by using an inertial navigation system, and performing a comparison test by using an INS/OD combined navigation method and an inertial navigation method based on Bayesian NAS assistance respectively for the same group of navigation data, wherein the test takes the real-time positioning navigation data of the satellite as a reference after being subjected to smoothing treatment. The test conditions are summarized below:
table 1: test article state table
Figure 878279DEST_PATH_IMAGE082
The test vehicle is two-wheel drive four-wheel IVECO, the odometer is arranged on the left rear wheel of the vehicle, positioning information of 20 groups of different road sections is collected before the test for deep learning, and the road section requirements are as follows: the road runs for 20km and navigates for 2 hours, the road surface comprises asphalt roads and gravel roads, and the route comprises an L shape, an S shape, an O shape and a random shape.
The two sets of positioning data are shown in fig. 3-6, the speed error of the INS/OD combined navigation reaches 0.03m/s, and the maximum speed error after the Bayesian NAS optimization is 0.004 m/s. The fixed precision of the INS/OD combined navigation is 20km, the maximum error reaches 80m, and the maximum positioning error after Bayesian NAS optimization is 15 m.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.

Claims (10)

1. An inertial navigation method based on Bayesian NAS is characterized in that: the method comprises the following steps:
s1, signal acquisition: the inertia/mileometer combined navigation module (1) simultaneously outputs the measured angular velocity signal, acceleration signal and mileage pulse signal to a navigation computer (2) and an upper computer (3);
s2, resolving a basic attitude: the navigation computer (2) comprises an attitude calculation module (21), a navigation computer neural network module (22) and a control module (23) which are electrically connected, wherein the attitude calculation module (21) performs basic attitude calculation according to the angular velocity signal, the acceleration signal and the mileage pulse signal to obtain attitude information and motion metadata which are output to the navigation computer neural network module (22), the motion metadata are used for eliminating noise by judging the motion state of the inertia/milemeter combined navigation module (1), the motion state comprises acceleration, deceleration, constant speed and static, the motion metadata comprise speed increment, and the noise comprises drift and abnormal value interference of the inertia/milemeter combined navigation module (1);
s3, neural architecture search: the upper computer (3) searches for an optimal neural network which improves the utilization rate of hardware SRAM and FLASH of the navigation computer (2) and reduces delay by using a Bayesian neural architecture, and outputs a control command, correction information and a hardware model to the control module (23);
s4, model control: the control module (23) performs memory allocation, model loading, instruction response and model updating on the navigation computer neural network module (22), and the navigation computer neural network module (22) outputs corrected three-dimensional angle information, northeast speed and longitude and latitude height information after performing noise filtering, dynamic noise reduction, data anomaly prediction and drift prediction by combining the attitude information and the motion metadata.
2. The inertial navigation method based on Bayesian NAS of claim 1, wherein: the integrated inertial/odometer navigation module (1) comprises an accelerometer and an odometer;
the navigation computer neural network module (22) uses a deep neural network;
the upper computer (3) comprises a Bayesian neural architecture search module (31) electrically connected with the control module (23), and a machine learning platform (32), a hardware simulation module (33) and a design space (34) electrically connected with the Bayesian neural architecture search module (31), wherein the Bayesian neural architecture search module (31) uses a Bayesian neural architecture search and Monte Carlo sampling method, the machine learning platform (32) uses a deep neural network, the machine learning platform (32) is electrically connected with the inertia/mileometer combined navigation module (1), and the hardware simulation module (33) is connected with the control module (23) through a real-time system timer;
the motion metadata includes: a forward speed increment, a side speed increment, and a top speed increment.
3. The inertial navigation method based on Bayesian NAS of claim 2, wherein:
step S3 includes the steps of:
s31, training a machine learning platform: constructing a backbone neural network architecture, training the machine learning platform (32) by using navigation training information including routes and road conditions, and enabling the hardware simulation module (33) to establish a hardware simulation model;
s32, sending a control command: when the hardware simulation module (33) is communicated with the real-time system timer and the machine learning platform (32) is communicated with the inertia/odometer integrated navigation module (1), the inertia/odometer integrated navigation module (1) outputs the angular velocity signal, the acceleration signal and the mileage pulse signal to the machine learning platform (32), and the Bayesian neural architecture search module (31) searches the design space (34) according to the hardware simulation model and then sends a control command to the machine learning platform (32);
s33, Bayesian optimization: the machine learning platform (32) performs attitude calculation according to the angular velocity signal, the acceleration signal and the mileage pulse signal to obtain the attitude information and the motion metadata, and the machine learning platform (32) performs precision judgment on the angular velocity signal, the acceleration signal and the mileage pulse signal according to the navigation training information and the motion metadata and returns the precision condition to the Bayesian neural architecture searching module (31);
s34, the Bayesian neural architecture search module (31) searches the optimal neural network by using Bayesian neural architecture search and Monte Carlo sampling and outputs a control command, correction information and a hardware model to the control module (23).
4. The inertial navigation method based on the Bayesian NAS of claim 3, wherein: in step S31, the method for constructing the backbone neural network architecture is to model f using TCN, and combine and process layered spatial and temporal features:
Figure 391051DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 58793DEST_PATH_IMAGE002
for the receptive field of each cell in the ith layer in the TCN,
Figure 258830DEST_PATH_IMAGE003
the kernel size is k × k, p is the expansion factor,
Figure 580090DEST_PATH_IMAGE004
in order to expand the nucleus p times later,
Figure 599998DEST_PATH_IMAGE002
size i x (k-1) + k;
z=tanh(
Figure 930485DEST_PATH_IMAGE005
*
Figure 536695DEST_PATH_IMAGE006
)⊙𝜎（
Figure 435381DEST_PATH_IMAGE007
）；
wherein z is a switch type residual block, tanh and𝜎is the function of the activation of the function,xw is a weight matrix of a convolution filter, h and g are filter and gates, k is a layer index, [ lambda ] is convolution operation, [ alpha ] is element-by-element multiplication operation;
the two dilated causal convolution layers are fused together by a switched-mode residual block z for modeling the bounded non-linearity and the time dependence of the input sequence.
5. The inertial navigation method based on the Bayesian NAS of claim 4, wherein: in step S34, the Bayesian neural architecture search module (31) finds the TCN
Figure 4903DEST_PATH_IMAGE008
，
Figure 342343DEST_PATH_IMAGE008
Is the optimal neural network;
Figure 454656DEST_PATH_IMAGE009
；
wherein f is an objective function, fError ofTo characterize the objective function of the error, ftlaye is the objective function characterizing the delay, fflashTo characterize the capacity objective function of FLASH, fSRAMTo characterize the objective function of SRAM usage capacity,𝜆is a random scalar domain, and Q is a search space;
Figure 648877DEST_PATH_IMAGE008
to seek in competition with each other
Figure 846640DEST_PATH_IMAGE010
Is determined as a function of the pareto optimal solution of (a).
6. The inertial navigation method based on the Bayesian NAS of claim 5, wherein:
Figure 722192DEST_PATH_IMAGE011
；
Figure 813645DEST_PATH_IMAGE012
；
Figure 788554DEST_PATH_IMAGE013
；
Figure 67089DEST_PATH_IMAGE014
；
Figure 543069DEST_PATH_IMAGE015
；
wherein w is the weight of the neural network,𝛾Is a hyper-parameter,
Figure 161133DEST_PATH_IMAGE016
Is directed acyclic graph, E is activation graph edge, V is activation graph vertex,𝛿for convolution and batch normalization, the HIL information is corresponding usage information output by a search hardware simulation module (33);
Figure 903348DEST_PATH_IMAGE017
is a TensorFlow model of FLASH,
Figure 75703DEST_PATH_IMAGE018
is the maximum capacity of the hardware FLASH,
Figure 89796DEST_PATH_IMAGE019
is the maximum capacity of the hardware SRAM,
Figure 31207DEST_PATH_IMAGE020
is to ask for
Figure 941394DEST_PATH_IMAGE021
0The norm of (a) of (b),
Figure 460100DEST_PATH_IMAGE022
input column vector at t, and θ is operationThe load is a load of the vehicle,
Figure 153250DEST_PATH_IMAGE023
the operation load after expanding p times;
monte carlo sampling is used during the bayes confidence interval.
7. The Bayesian NAS-based inertial navigation method according to claim 5, wherein:
Figure 73801DEST_PATH_IMAGE024
obtaining by using a method for verifying mean square error;
Figure 154890DEST_PATH_IMAGE025
obtaining by using a RAM (random access memory) model, and storing an intermediate layer activation graph and tensor in an SRAM (static random access memory);
Figure 301837DEST_PATH_IMAGE026
obtained using the floating-point arithmetic capabilities of the processor.
8. The inertial navigation method based on the Bayesian NAS of claim 5, wherein: when the HIL information of the hardware emulation module (33) is valid,
Figure 392153DEST_PATH_IMAGE025
、
Figure 636053DEST_PATH_IMAGE027
and
Figure 560146DEST_PATH_IMAGE026
obtained from the implementing operating system of the target compiler.
9. The inertial navigation method based on the Bayesian NAS of claim 1, wherein: in step S4, the three-dimensional angle information includes an attitude angle Φ, the northeast speed is ν, and the longitude and latitude height information is P;
Figure 50515DEST_PATH_IMAGE028
；
Figure 85467DEST_PATH_IMAGE029
；
Figure 183873DEST_PATH_IMAGE030
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 75606DEST_PATH_IMAGE031
in order to be the attitude angle,
Figure 259462DEST_PATH_IMAGE031
the update is obtained by the equivalent rotation quantity method from the angular increment of the angular velocity signal,
Figure 426001DEST_PATH_IMAGE032
exp (x) is an exponential function of an antisymmetric matrix, which is the true value of angular velocity,
Figure 175651DEST_PATH_IMAGE033
satisfy the requirement of
Figure 441548DEST_PATH_IMAGE034
；
Figure 112701DEST_PATH_IMAGE035
For the speed of the northeast day under the navigation coordinate system,
Figure 879668DEST_PATH_IMAGE035
the update is obtained from the acceleration integral after subtracting the gravitational acceleration g,
Figure 359191DEST_PATH_IMAGE036
is a ratio truth value;
Figure 920622DEST_PATH_IMAGE037
is a longitude and latitude high position, and is characterized in that,
Figure 751175DEST_PATH_IMAGE037
obtained from the northeast velocity integral.
10. The inertial navigation method based on the bayesian NAS as recited in claim 9, wherein:
Figure 793605DEST_PATH_IMAGE038
；
Figure 393214DEST_PATH_IMAGE039
；
wherein the content of the first and second substances,
Figure 594388DEST_PATH_IMAGE040
is the actual output of the gyroscope,
Figure 771291DEST_PATH_IMAGE041
is the actual output of the accelerometer,
Figure 817745DEST_PATH_IMAGE042
is the white noise of the gyroscope,
Figure 537439DEST_PATH_IMAGE043
is the white noise of the accelerometer and,
Figure 643935DEST_PATH_IMAGE044
and
Figure 308135DEST_PATH_IMAGE045
is a zero offset and is set to zero,
Figure 423858DEST_PATH_IMAGE044
and
Figure 732480DEST_PATH_IMAGE045
is related to temperature;
Figure 806615DEST_PATH_IMAGE046
；
Figure 567898DEST_PATH_IMAGE047
；
wherein, the first and the second end of the pipe are connected with each other,
Figure 749962DEST_PATH_IMAGE048
and
Figure 37724DEST_PATH_IMAGE049
is gaussian white noise.
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