CN110516197A - Weight parameter estimation method is determined in a kind of segmentation in weight unit under error constraints - Google Patents

Weight parameter estimation method is determined in a kind of segmentation in weight unit under error constraints Download PDF

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CN110516197A
CN110516197A CN201910593557.3A CN201910593557A CN110516197A CN 110516197 A CN110516197 A CN 110516197A CN 201910593557 A CN201910593557 A CN 201910593557A CN 110516197 A CN110516197 A CN 110516197A
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data
weight
observation
segmentation
parameter estimation
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CN110516197B (en
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于先文
罗鹏
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Southeast University
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Southeast University
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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
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

Abstract

The invention discloses the segmentations under error constraints in a kind of weight unit to determine weight parameter estimation method.The method comprising the steps of 1, after obtaining and observing data, establishes indirect adjustment model according to the functional relation between observation data and parameter to be estimated；Step 2 is resolved using Classical Least-Squares, obtains the resolved datas such as preliminary correction；Step 3 weighs the segmentation weighting formula that correction substitutes into weight unit under error constraints surely again；Step 4 carries out least square resolving using new power again, obtains correction and resolved data；Step 5 judges whether to terminate iteration, judges that formula is invalid, repeat Step 3: Step 4: step 5, until Rule of judgment is set up, iteration terminates, and exports adjustment result.This method is met 3 σ principle of data processing to the method that data use segment processing by error constraints in weight unit.Easy to operate, process program has adaptive robustness, is suitble to carry out parameter Estimation work to the data containing rough error.

Description

Weight parameter estimation method is determined in a kind of segmentation in weight unit under error constraints
Technical field:
The present invention relates to the segmentations under error constraints in a kind of weight unit to determine weight parameter estimation method, belongs to data processing Technical field.
Background technique:
The main purpose of data processing is to eliminate or weaken the influence of error in observation data, to accurately estimate unknown ginseng Several values obtains the reliable data of high-precision for all trades and professions and provides guarantee.
Important method of the least square method as Data processing has the excellent statistical properties such as unbiasedness, validity, When processing contains only the data of accidental error, least square method is exactly Maximum-likelihood estimation.But least square method is with as follows Defect: (1), when being mixed into rough error in data, the observation correction and parameter estimation result of least-squares estimation all can be by Strong influence；(2) without error in abundant application unit power etc. observation data information.
In view of the above-mentioned problems, previous scholars research and development robust M estimation, and it is tied with least square method It closes, proposes principle of equivalent weight, export the least squares formalism of robust M estimation.Therefore M estimation becomes simple and practical, it passes through In each iteration, the power of each observation is modified using the resulting correction of calculating, and then has adjusted ADJUSTMENT SYSTEM to error With power of energizing, to achieve the purpose that elimination or weaken the influence of error.This method has been high accuracy data processing (such as essence at present Close engineering survey) common method.
But this method is also not without disadvantage.Be mainly shown as: (1) many Modified Equivalent Weight Functions are empirical functions, are not had Corresponding probability statistics principle；(2) many Modified Equivalent Weight Functions are by being manually set empirical, to adapt to different adjustment feelings Condition causes weight function to have certain defect at adaptive aspect；(3) numerous weight functions are not sufficiently using error in weight unit.
On " the Technical Colleges Of Guilin's journal " of the 2nd phase in 1998, paper " Probablity Least Square Method " proposition is taken with error From probability distributing density function be extremal function equivalence weight design method, i.e. Probablity Least Square Method overcomes above-mentioned warp The defect of allusion quotation M estimation method.Constraint of this method based on error in weight unit weighs letter according to error update in rear weight unit is tested Number has certain adaptive ability.But this method, when handling large error, the rate for dropping power is relatively low, so that pollution number It is unobvious according to the differentiation with pollution-free data, reduce the efficiency of parameter Estimation.
With the development of society, in modern surveying work, data volume is become much larger, data type becomes more diversification, therefore There is an urgent need to a kind of energy adaptive abilities by force, observation data information, the apparent data processing method of robust effect is made full use of Meet current demand.
Summary of the invention
The purpose of the present invention is provide the segmentation in a kind of weight unit under error constraints in view of the above problems to weigh surely Method for parameter estimation, for solving the problems, such as technological deficiency existing for existing M estimation method.
Above-mentioned purpose is achieved through the following technical solutions:
Weight parameter estimation method is determined in a kind of segmentation in weight unit under error constraints, and this method comprises the following steps:
Step 1, after obtaining and observing data, established according to the functional relation between observation data and parameter to be estimated indirect Adjustment Models；
Step 2 is resolved using Classical Least-Squares, obtains the resolved datas such as preliminary correction；
Step 3 weighs the segmentation weighting formula that correction substitutes into weight unit under error constraints surely again；
Step 4 carries out least square resolving using new power again, obtains correction and resolved data；
Step 5 judges whether to terminate iteration, judges that formula is invalid, repeat Step 3: Step 4: step 5, until judgement Condition is set up, and iteration terminates, and exports adjustment result.
Further, observation data described in step 1 is mutually indepedent, and observes data amount check n and be greater than parameter to be estimated Number t.
Further, establish indirect adjustment model described in step 1 the following steps are included:
Step 1.1, according to observation dataWith parameter to be estimatedBetween relationship, establish such as lower linear mould Type:
Wherein,V is observation L0Correction, B be sequency spectrum constant matrices, be otherwise known as adjustment Design matrix, and it is determined by the mathematical relationship between observation data and parameter to be estimated,It is observation L0Variance matrix, Q It is observation L0Association's factor battle array, P is observation L0Power battle array, σ0It is error in weight unit；
Step 1.2 writes out error equation according to above-mentioned linear model:
Wherein
L=L0-BX0 (4)
L is observation vector.
Further, the process solved described in step 2 using Classical Least-Squares is as follows:
Further, the process weighed surely again described in step 3 is as follows, and i is currently to rerun number, i=1, 2 ...:
Wherein, j=1,2 ..., n,It isJ-th of diagonal entry, pjjFor j-th of diagonal entry of P,For V(i-1)J-th of observation correction；
Further, the process of solution correction and resolved data described in step 4 is as follows:
Further, judge whether that the process for terminating iteration is as follows described in step 5:
Step 5.1, following formula are judged:
(V(i)-V(i-1))T(V(i)-V(i-1)) < ε (8)
Wherein, ε is a minimum, generally takes ε≤0.0001.
When formula (8) are set up, iteration is exited, exports adjustment result, the step 3 that otherwise reruns and step 4.
Step 5.2, output result:
Wherein,It is parameter estimation resultVariance matrix,It is observation adjustment resultVariance matrix.
The utility model has the advantages that
Weight parameter estimation is determined in segmentation in a kind of weight unit applied to data processing of the present invention under error constraints Method is a kind of design method of M estimation Modified Equivalent Weight Function.Similar to the Huber method and IGG method in M estimation classical way, originally Method has equally carried out segment processing to data, while having made full use of control information in weight unit, and then can obtain accurately Parameter estimation result.
This method has well the utility model has the advantages that (1) has sufficiently used control information in weight unit, in iteration constantly Change itself functional form using error in rear weight unit is tested, current ADJUSTMENT SYSTEM is adapted to continuous adjustment, is had stronger Adaptive ability；(2) data are handled by the way of segmentation, the power that will be greater than 2.5 σ errors is set to 0, meets at data Manage 3 σ principles；(3) this method only needs input observation data and its variance matrix, initial parameter values to be estimated, observes data and wait estimate Count the mathematical relationship between parameter, so that it may carry out parameter Estimation work, easy to operate, process is simple, easy to accomplish.
Detailed description of the invention
Fig. 1 is that weight parameter estimation method techniqueflow chart is determined in the segmentation in a kind of weight unit under error constraints；
Fig. 2 is the area specific example Zhong Ce levelling network schematic diagram.
Specific embodiment
Weight parameter estimation method is determined in a kind of segmentation in weight unit under error constraints, and this method comprises the following steps:
Step 1, after obtaining and observing data, established according to the functional relation between observation data and parameter to be estimated indirect Adjustment Models；
Step 2 is resolved using Classical Least-Squares, obtains the resolved datas such as preliminary correction；
Step 3 weighs the segmentation weighting formula that correction substitutes into weight unit under error constraints surely again；
Step 4 carries out least square resolving using new power again, obtains correction and resolved data；
Step 5 judges whether to terminate iteration, judges that formula is invalid, repeat Step 3: Step 4: step 5, until judgement Condition is set up, and iteration terminates, and exports adjustment result.
Further, observation data described in step 1 is mutually indepedent, and observes data amount check n and be greater than parameter to be estimated Number t.
Further, establish indirect adjustment model described in step 1 the following steps are included:
Step 1.1, according to observation dataWith parameter to be estimatedBetween relationship, establish such as lower linear mould Type:
Wherein,V is observation L0Correction, B be sequency spectrum constant matrices, be otherwise known as adjustment Design matrix, and it is determined by the mathematical relationship between observation data and parameter to be estimated,It is observation L0Variance matrix, Q It is observation L0Association's factor battle array, P is observation L0Power battle array, σ0It is error in weight unit；
Step 1.2 writes out error equation according to above-mentioned linear model:
Wherein
L=L0-BX0 (13)
L is observation vector.
Further, the process solved described in step 2 using Classical Least-Squares is as follows:
Further, the process weighed surely again described in step 3 is as follows, and i is currently to rerun number, i=1, 2 ...:
Wherein, j=1,2 ..., n,It isJ-th of diagonal entry, pjjFor j-th of diagonal entry of P,For V(i-1)J-th of observation correction；
Further, the process of solution correction and resolved data described in step 4 is as follows:
Further, judge whether that the process for terminating iteration is as follows described in step 5:
Step 5.1, following formula are judged:
(V(i)-V(i-1))T(V(i)-V(i-1)) < ε (17)
Wherein, ε is a minimum, generally takes ε≤0.0001.
When formula (8) are set up, iteration is exited, exports adjustment result, the step 3 that otherwise reruns and step 4.
Step 5.2, output result:
Wherein,It is parameter estimation resultVariance matrix,It is observation adjustment resultVariance matrix.
Specific embodiment:
The present embodiment is a certain region adjustment of levelling network case, and Fig. 2 is the levelling network schematic diagram.Wherein, No. 1 point and No. 6 Point is known point, elevation information are as follows: No. 1 point: H01=0m；No. 6 points: H06=6.9991m.And in the case, observation Number n=11, number of parameters t=4 to be estimated.
Observation data are as follows:
1 levelling network of table observes tables of data
Now weight parameter estimation method is determined with the elevation of 2,3,4, No. 5 points for mesh using the segmentation under error constraints in weight unit It marks parameter and carries out adjustment solution (set forth below as a result, its unit is m):
The first step establishes the corresponding indirect adjustment model of the case, i.e. B matrix in building formula (1), and building result is such as Under:
Second step is solved according to technical scheme steps two using Classical Least-Squares, i.e. formula (5), obtains unit Error in powerAre as follows: 0.0059, and the resolved datas such as preliminary correction are as follows:
The preliminary correction table of each observation of table 2
Third step substitutes into error in above-mentioned weight unit and preliminary correction in technical scheme steps three, carries out again It weighs calmly, at this time i=1, result such as the following table 3:
The power of each observation of table 3
4th step carries out parameter Estimation using least square method again, and the result being calculated is as follows:
Each observation correction of table 4 and power
Current iteration calculates to obtain error in weight unit simultaneouslyAre as follows: 0.0067.
5th step, ε=0.0000001 in modus ponens (8), and whether true, and be calculated if judging it:
(V(1)-V(0))T(V(1)-V(0)The > 0.0000001 of)=0.00045 (22)
Obvious current iteration is unsatisfactory for iteration termination condition, therefore need to continue iteration.Next last time iteration knot is provided Fruit:
Correction and equivalence weight when 5 last time iteration of table
The number of iterations i=33 at this time, and be calculated:
(V(33)-V(32))T(V(33)-V(32))=1.52 × 10-10<0.0000001 (23)
Export final result:
The precision of each observation adjusted value of table 6
This parameter Estimation terminates with regard to this.Parameter Estimation can be completed by the above method and observation adjustment works.
The above is only a preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered It is considered as protection scope of the present invention.

Claims (7)

1. weight parameter estimation method is determined in the segmentation in a kind of weight unit under error constraints, which is characterized in that this method includes as follows Step:
Step 1, obtain observe data after, according to observation data and parameter to be estimated between functional relation establish indirect adjustment Model；
Step 2 is resolved using Classical Least-Squares, obtains the resolved datas such as preliminary correction；
Step 3 weighs the segmentation weighting formula that correction substitutes into weight unit under error constraints surely again；
Step 4 carries out least square resolving using new power again, obtains correction and resolved data；
Step 5 judges whether to terminate iteration, judges that formula is invalid, repeat Step 3: Step 4: step 5, until Rule of judgment It sets up, iteration terminates, and exports adjustment result.
2. weight parameter estimation method is determined in the segmentation in weight unit according to claim 1 under error constraints, which is characterized in that Observation data described in step 1 is mutually indepedent, and observes data amount check n and be greater than number of parameters t to be estimated.
3. weight parameter estimation method is determined in the segmentation in weight unit according to claim 1 or 2 under error constraints, feature exists In, establish indirect adjustment model described in step 1 the following steps are included:
Step 1.1, according to observation dataWith parameter to be estimatedBetween relationship, establish such as Linear Model with Side:
Wherein,V is observation L0Correction, B be sequency spectrum constant matrices, the design for the adjustment that is otherwise known as Matrix, and it is determined by the mathematical relationship between observation data and parameter to be estimated,It is observation L0Variance matrix, Q be see Measured value L0Association's factor battle array, P is observation L0Power battle array, σ0It is error in weight unit；
Step 1.2 writes out error equation according to above-mentioned linear model:
Wherein
L=L0-BX0 (4)
L is observation vector.
4. weight parameter estimation method is determined in the segmentation in weight unit according to claim 1 or 2 under error constraints, feature exists In the process solved described in step 2 using Classical Least-Squares is as follows:
5. weight parameter estimation method is determined in the segmentation in weight unit according to claim 1 or 2 under error constraints, feature exists In, the process weighed surely again described in step 4 is as follows, and i is currently to rerun number, i=1, and 2 ...:
Wherein, j=1,2 ..., n,It isJ-th of diagonal entry, pjjFor j-th of diagonal entry of P,For V(i-1)J-th of observation correction.
6. weight parameter estimation method is determined in the segmentation in weight unit according to claim 1 or 2 under error constraints, feature exists In the process of solution correction and resolved data described in step 4 is as follows:
7. weight parameter estimation method is determined in the segmentation in weight unit according to claim 1 or 2 under error constraints, feature exists In, judge whether described in step 5 terminate iteration process it is as follows:
Step 5.1, following formula are judged:
(V(i)-V(i-1))T(V(i)-V(i-1)) < ε (8)
Wherein, ε is a minimum, generally takes ε≤0.0001.
When formula (8) are set up, iteration is exited, exports adjustment result, the step 3 that otherwise reruns and step 4.
Step 5.2, output result:
Wherein,It is parameter estimation resultVariance matrix,It is observation adjustment resultVariance matrix.
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Publication number Priority date Publication date Assignee Title
CN102322863A (en) * 2011-07-26 2012-01-18 武汉大学 Remote sensing satellite multi-satellite combined converse orbit and attitude determination method
CN103869344A (en) * 2012-12-13 2014-06-18 东莞市泰斗微电子科技有限公司 Robust estimation method
US20160109579A1 (en) * 2014-10-16 2016-04-21 Gmv Aerospace And Defence, S.A. Device and method for computing an error bound of a kalman filter based gnss position solution

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