CN107655463A - Electronic compass calibration method based on simulated annealing - Google Patents
Electronic compass calibration method based on simulated annealing Download PDFInfo
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- CN107655463A CN107655463A CN201710860678.0A CN201710860678A CN107655463A CN 107655463 A CN107655463 A CN 107655463A CN 201710860678 A CN201710860678 A CN 201710860678A CN 107655463 A CN107655463 A CN 107655463A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C17/00—Compasses; Devices for ascertaining true or magnetic north for navigation or surveying purposes
- G01C17/38—Testing, calibrating, or compensating of compasses
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
Abstract
The invention provides a kind of electronic compass calibration method based on simulated annealing, belong to intelligent algorithm and non-linear regression technique field.The algorithm of optimal solution is widely searched in simulated annealing as one in solution space, and contrast conditional electronic method for calibrating compass and some common optimization algorithms have a stronger global convergence superiority, is met during use：Initial temperature is sufficiently high；Final temperature is sufficiently low；Cooling is slow enough；Just meet the global convergence characteristic of solution during the sufficiently long condition of heat balance time, i.e., initial parameter it is suitable in the case of, simulated annealing can search out global minima point in solution space.Find to produce under function in appropriate initial parameter and new explanation in actual experiment, the nonlinear fitting solution of electronic compass can be produced under relatively good Time ＆ Space Complexity, precision has reached 10E 3, contrasts conventional calibration method and least square method precision is higher.
Description
Technical field
The invention belongs to intelligent algorithm and non-linear regression technique field, it is proposed that one kind has relatively strong targetedly electronics
The optimization method of compass calibration.
Background technology
Electronic compass is a kind of attitude transducer wide variety of in modern technologies and magnetic force signal transducer.Itself and biography
Attitude transducer of uniting compares low energy consumption, small volume, in light weight, precision is high, and its output signal can be realized digital aobvious by processing
Show, can not only be used for pointing to, its data signal can be with the manipulation of controller unit or offer attitude signal.At present, widely make
Three axle strapdown reluctance type Digital Magnetic Compass, this compass have anti-shake and vibration resistance, course precision it is higher, to interference
There is electronic compensation field, is desirably integrated into control loop progress data link, thus be widely used in Aeronautics and Astronautics,
The fields such as robot, navigation, vehicular autonomous navigation.
However, we usually usually need to carry out school to electronic compass when using electronic compass in routine work practice
It is accurate, if it is desired to high efficiency, high-precision calibration are carried out to electronic compass except direct being parsed using traditional from data
Optimization algorithm is usually needed to use beyond outside method, such as is fitted the methods of least square method, and in such algorithm
How the initial parameter of electronic compass always make us a puzzlement the problem of is determined.Simulated annealing is that a kind of common probability is calculated
Method, for finding Optimum Solution in a big search space, the invention provides a kind of based on simulated annealing
Calibration method solves these problems.
Specifically, patent of the present invention has both sides purpose:One there is provided one kind is carried out based on simulated annealing
The scheme of nonlinear fitting；Two there is provided a kind of calibration method of strong robustness, and electronic compass has the ability to locate under this algorithm
Manage the ability of the input data of whole solution space.
The content of the invention
The present invention provides one kind and is based on simulated annealing (Simulated Annealing, SA), is passed for electronic compass
The method that the three-dimensional data entered is fitted ellipsoid, final algorithm will export an ellipsoid, on this basis to electronics sieve
Disk is calibrated.
Technical scheme：
Electronic compass calibration method based on simulated annealing, step are as follows：
Data are collected, set simulated annealing parameter, nonlinear fitting goes out ellipsoid equation.Next the ellipsoid exported
The scaling coefficient that tri- reference axis of a position offset vector and x, y, z are parsed in equation completes the calibration of electronic compass.
(1) solution procedure of simulated annealing
1. the operation principle of simulated annealing
As its name suggests, the annealing process of solid, i.e., add solid in its principle simulation actual life for simulated annealing
Heat arrives certain high temperature Slow cooling again, as long as cooling procedure is slow enough in theory, solid may finally be under the condition of high temperature
Particle disordered state be cooled to orderly, interior energy minimum state under low-temperature condition.Data are brought into fitting parameter in this algorithm
Corresponding ellipsoid equation simultaneously calculates functional value and handled together, and the ellipsoid equation of output and the error of input data are as simulated annealing
" interior energy " in algorithm, the minimum value of " interior energy " in solution space is solved, represent that now fitting parameter is when reaching minimum value
One of electronic compass input data is preferably fitted.
2. the setting of simulated annealing
Initial data is obtained from electronic compass using three-dimensional 8 word calibration methods, the original electronic compass tables of data collected
The data set of three-dimensional vector group is shown as, in order to avoid the waste of computing capability, first data are pre-processed in the beginning of algorithm,
Deleting duplicated data and it is normalized depending on concrete condition, solution must be carried out at the end of algorithm if being normalized
Reversely normalization, reduction solution is the former order of magnitude, normalizes and is not required what is carried out.
For the three-dimensional vector data of input, meet：
Wherein x, y, z are input three-dimensional coordinate method value,For parameter to be asked；
It is equal to the function of fitting deformation：
Way common in nonlinear optimization is taken,(m is input
Data amount check) it is more low better as error (interior energy) function calibrated, the functional value.Wherein Fm(α) is represented current estimation
ParameterBring m group data (x intom,ym,zm) value.
Set the initial temperature T that simulated annealing needs0(100≤T0≤ 1010), final temperature Tf(Tf<10), arbitrarily
Temperature T iterations Lk(K, LmIt is parameter preset, T is Current Temperatures), the cooling of simulated annealing
Table：New temperature TnewWith old temperature ToldRelation be Tnew=0.95*Told。
The new explanation that setting simulated annealing needs produces function, and tending to use in principle can try one's best throughout solution space
All areas generation function, the function must is fulfilled for having the ability in the continuous iteration of a certain steady temperature jumping out current simultaneously
Very small region to search for other possible extreme points.Calibration for electronic compass uses short annealing function, the function
An any direction in solution space, step-length and temperature is produced to meet：Step=kT (k is constant) new explanation.Due to electronics sieve
The calibration solution space dimension of disk is higher, it should which it is in non-linear relation to prevent using Boltzmann Annealing functions unique step and temperature
Annealing function decline too fast Premature Convergence to prevent step-length.
3. the step of simulated annealing
According to Metropolis importance sampling method and Kirkpatrick combinatorial optimization model, typical mould
The step of intending annealing algorithm can be described as：A parameter T is set as control parameter, target function value f is set to interior energy E, Gu
State at a temperature of some of body is equal to a solution x of object functioni, with being gradually reduced for control parameter T, solid interior
The continuous permutatation of particle, generate new solution xi, the interior energy E of solid is also gradually reduced, i.e. target function value f is also gradually reduced,
It will be eventually reached global minima.
(2) electronic compass is calibrated using the ellipsoid equation of fitting
Assuming that the magnetic vector that electronic compass measures is (xi,yi,zi), then it is not affected by errors magnetic vector and meets spheroid equation：
xi 2+yi 2+zi 2=di 2, it is assumed that the magnetic vector that the electronic compass under error measures is (xm,ym,zm), then (xm,ym,zm) and (xi,
yi,zi) relation can be expressed as：xm=Axi+xoffset,ym=Byi+yoffset,zm=Czi+zoffset.We can from above formula
To find out on the process nature of the calibration of electronic compass being exactly to seek A, B, C, xoffset,yoffset,zoffsetThe value of this six parameters
Process.
Six parameters are exported using simulated annealingAfterwards, by xm=Axi+xoffset,ym
=Byi+yoffset,zm=Czi+zoffsetBring x intoi 2+yi 2+zi 2=di 2And with reference functionDrawn after comparing: Mould can be used
Intend the parameter that annealing algorithm is tried to achieveObtain real magnetic vector (xi,yi,zi)：
Beneficial effects of the present invention：
1. arithmetic accuracy is higher
Although simulated annealing is as the algorithm that optimal solution is found in big search space, it is for higher-dimension search
Space faces this solution space excessively complexity unavoidably and minimum is excessively caused by the problem of iteration speed overfill, and the present invention carries
A kind of possibility scheme for sextuple solution space under the support of certain calculation resources is supplied.
2. algorithm robustness is stronger
The method of traditional calibration electronic compass finds out each dimension to obtain the electronic compass magnetic vector data after error
Span, using corresponding to the intermediate value of the span of each dimension place as the origin of coordinates after error, by each dimension
The length of span compared with gross data span rear scaling to raw footage to offset original each dimension to magnetic
The error of vectorial elongation/diminution effect influences, and is that calibration speed is fast the advantages of this method, shortcoming is easily by indivedual extreme big
The influence of error information and significantly influence calibrate effect.
The algorithm of optimal solution is widely searched in simulated annealing as one in solution space, contrasts conditional electronic compass
Calibration method and some common optimization algorithms have a stronger global convergence superiority, meet during use：Initial temperature is enough
It is high；Final temperature is sufficiently low；Cooling is slow enough；Just meet that the global convergence of solution is special during the sufficiently long condition of heat balance time
In the case that property, i.e. initial parameter are suitable, simulated annealing can search out global minima point in solution space.Actual experiment
It is middle to find in the case where appropriate initial parameter and new explanation produce function, it can be produced under relatively good Time ＆ Space Complexity
The nonlinear fitting solution of electronic compass, precision have reached 10E-3, contrast conventional calibration method and least square method precision is higher.
Brief description of the drawings
Fig. 1 is the electronic compass calibration research approach schematic diagram of the present invention.
Fig. 2 is simulated annealing nonlinear fitting process schematic.
Fig. 3 is that simulated annealing algorithm object function declines process schematic.
Embodiment
Below in conjunction with accompanying drawing and technical scheme, embodiment of the invention is further illustrated.
A kind of electronic compass calibration method based on simulated annealing algorithm, including simulated annealing it is non-linear and you
Two parts are calibrated with electronic compass：
1. it is based on simulated annealing nonlinear fitting
A) T=T is made first0, generate first RANDOM SOLUTION α0And calculate E (α0)；
B) according to cooling table renewal temperature, the temperature T of laststatei, Current Temperatures Tj；
C) old solution is αiWhen produce a new explanation αj, make Δ E=E (αj)-E(αi)；
If d) Δ E≤0, receive new explanation αj, otherwise with probability exp (- Δ E/Tj) receive new explanation αj；
E) in each temperature TjUnder, repeat LkSecondary step c) and step d)；
F) if TjLess than Tf, shut down；Otherwise algorithm goes to step b) and repeated.
2. the calibration of electronic compass
Solution vector is handled after obtaining the nonlinear fitting solution based on simulated annealing, six ginsengs included from it
The abstract representation of error is parsed in number, represents error vector with a new solution vector, the number got to electronic compass afterwards
Electronic compass magnetic vector after being calibrated according to the parameter processing included with this error vector.
Claims (1)
1. a kind of electronic compass calibration method based on simulated annealing, it is characterised in that step is as follows：
(1) solution procedure of simulated annealing
1. the setting of simulated annealing
Initial data is obtained from electronic compass using three-dimensional 8 word calibration methods, the original electron compass data collected is expressed as
The data set of three-dimensional vector group；First the data set of three-dimensional vector group is pre-processed, i.e., deleting duplicated data and regards specific feelings
Condition is normalized；If be normalized, solution must reversely be normalized at the end of algorithm, reduction solution is former number
Magnitude；
For the data set of the three-dimensional vector group of input,
Meet：
Wherein：X, y, z are input three-dimensional coordinate method value,For parameter to be asked；
It is equal to the function of fitting deformation：
WillIt is more low better as the error function of calibration, the functional value；
Wherein, Fm(α) is represented current estimation parameterBring m group data (x intom,ym,zm)
Value；M is the number of input data group；
Set simulated annealing, 100≤T of initial temperature0≤ 1010, final temperature Tf<10, arbitrary temp T iterations
Lk,K and LmIt is parameter preset, T is Current Temperatures, the cooling table of simulated annealing：New temperature TnewWith
Old temperature ToldRelation be Tnew=0.95*Told；
The new explanation that setting simulated annealing needs produces function, tends in principle using as far as possible throughout all areas of solution space
The generation function in domain, the function must are fulfilled for having the ability to jump out current minimum area in the continuous iteration of a certain steady temperature simultaneously
Domain is to search for other possible extreme points；Calibration for electronic compass uses short annealing function, and the function produces one
Any direction, step-length and temperature meet in solution space：Step=kT new explanation, k are constant；
2. the step of simulated annealing
According to Metropolis importance sampling method and Kirkpatrick combinatorial optimization model, simulated annealing
The step of be described as：A parameter T is set as control parameter, target function value f is set to interior energy E, at a temperature of some of solid
State be equal to one of object function solution xi, with being gradually reduced for control parameter T, the particle of solid interior is constantly reset
Row, generate new solution xi, the interior energy E of solid is also gradually reduced, i.e. target function value f is also gradually reduced, and will be eventually reached the overall situation
It is minimum；
(2) electronic compass is calibrated using the ellipsoid equation of fitting
Assuming that the magnetic vector that electronic compass measures is (xi,yi,zi), then it is not affected by errors magnetic vector and meets spheroid equation：xi 2+
yi 2+zi 2=di 2, it is assumed that the magnetic vector that the electronic compass under error measures is (xm,ym,zm), then (xm,ym,zm) and (xi,yi,zi)
Relation be expressed as：xm=Axi+xoffset, ym=Byi+yoffset, zm=Czi+zoffset；The school of electronic compass is found out from above formula
It is exactly to seek A on accurate process nature, B, C, xoffset,yoffset,zoffsetThe process of the value of this six parameters；
Six parameters are exported using simulated annealingAfterwards, by xm=Axi+xoffset, ym=Byi
+yoffset, zm=Czi+zoffsetBring x intoi 2+yi 2+zi 2=di 2, and and reference functionDrawn after comparing： The parameter tried to achieve using simulated annealingObtain real magnetic vector (xi,yi,zi)：
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| CN109858882A (en) * | 2019-01-31 | 2019-06-07 | 山大鲁能信息科技有限公司 | A kind of new college entrance examination cource arrangement method and system based on improved annealing algorithm |
| CN116345495A (en) * | 2023-04-03 | 2023-06-27 | 华能山东发电有限公司烟台发电厂 | Power plant unit frequency modulation optimization method based on data analysis and modeling |
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Cited By (3)
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| CN109858882A (en) * | 2019-01-31 | 2019-06-07 | 山大鲁能信息科技有限公司 | A kind of new college entrance examination cource arrangement method and system based on improved annealing algorithm |
| CN116345495A (en) * | 2023-04-03 | 2023-06-27 | 华能山东发电有限公司烟台发电厂 | Power plant unit frequency modulation optimization method based on data analysis and modeling |
| CN116345495B (en) * | 2023-04-03 | 2023-10-10 | 华能山东发电有限公司烟台发电厂 | Power plant unit frequency modulation optimization method based on data analysis and modeling |
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