CN109061579A - A kind of robust volume filtering method of band thickness tail noise - Google Patents
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Abstract
The present invention provides a kind of robust volume filtering methods of band thickness tail noise, belong to filter design technology field, for estimating that dynamical system in the state at current time, specifically includes that the movement of construction target and sensor measurement discrete nonlinear equation；Calculate correlation between accuracy, the measurement predictor at current time, the accuracy of current time measurement predictor and the current time measurement predictor and each state vector predicted value of system of each state vector predicted value of current time system, each state vector predicted value of current time system；Current time filter gain and current time statistical distance are calculated later；Finally each state vector predicted value of the system at current time and each state vector evaluated error covariance matrix of system are updated.Method proposed by the invention has better robustness and higher estimated accuracy in the maneuvering target tracking scene under the conditions of making significantly motor-driven and sensor under clutter environment for target and measuring there are outlier interference.
Description
Technical field
The present invention relates to airborne fire control radar target following technical fields, do under clutter environment more particularly to target
It is significantly motor-driven, and in the poor sensor application of some high sample frequencys, reliability, by measurement outlier disturbed condition
Under maneuvering target tracking field, and in particular to a kind of robust volume filtering method of band thickness tail noise.
Background technique
Nonlinear filtering has been widely used in the engineerings such as navigator fix, target following, signal processing and automatic control
In field.After the key of Nonlinear Filtering Problem is namely based on random Nonlinear state space model solving system state
Test probability density function (Probability density function, PDF).Bayesian Estimation theory is nonlinear filtering
Problem provides an optimal frame model, it is by calculating the posteriority PDF of state recursively to solve nonlinear system
The state estimation problem of system.However, being often related to for general nonlinear system, in Bayesian Estimation containing complexity
Multidimensional nonlinear function integral calculating, generally can not Analytical Solution, it is usually the case that be not present optimal nonlinear filtering
Wave device.In order to complete the state estimation task of nonlinear system, it is necessary to take approximate means to obtain the nonlinear filtering of suboptimum
Wave device.Gaussian approximation (Gaussian approximate, GA) is a kind of effective method, based on different numerical approximations
The non-linear Gaussian filter (Gaussian filter, GF) of many suboptimums has been proposed in method at present.
GF assumes that noise model Gaussian distributed, and state still Gaussian distributed after nonlinear transformation.
However in some practical engineering applications, the noise model of system might not Gaussian distributed, it is also possible to have thick tail
Distribution character.Such as in target tracking domain, when target does significantly motor-driven under clutter environment, what target was shown
Model uncertainty can induce the process noise for generating thick tail.And in some sensings poor with high sample frequency, reliability
The measurement noise for generating thick tail can equally be induced by measuring outlier in device application, caused by sensor.Thick tail noise is made an uproar with Gauss
Sound is compared, and since there are outlier interference, causes noise value to increase from the farther away region possibility of mean value, to form thickness
Tail shape.Therefore, Gaussian Profile can not the lower thick tail distribution of accurate simulation outlier interference, so as to cause based on Gauss vacation
And if the GF filtering accuracy designed declines, or even diverging.In order to solve to ask with the linear filtering of thick tail process and measurement noise
State posteriority PDF is approximately that Student ' s t is distributed, and is deduced new robust Student ' s t by topic, Roth et al.
Filter.In order to solve to measure the linear filtering problem of noise, Agamennoni etc. due to tail thick caused by measuring outlier
People proposes a kind of pair of outlier and measures the improved kalman-filter algorithm with robustness.Noise is measured in order to solve the thick tail of band
Multi-sensor information fusion problem, the thick tails of multiple sensors measures noise modeling into Student ' s t points by Zhu et al.
Cloth then proposes a kind of linear robust multisensor method for estimating state.However the above linear robust filter is not
It can be used to solve the problems, such as with thick tail process and measure the nonlinear state Eq of noise.
Summary of the invention
It is an object of the invention to overcome deficiency in the prior art, engineering background of combining closely proposes a kind of band
Robust Student ' the s t volume filter of thick tail noise, do for solving target under clutter environment it is significantly motor-driven, with
And in the poor sensor application of some high sample frequencys, reliability, (the thick tail process of band under by measurement outlier disturbed condition
With measure noise) maneuvering target track question.
The robust volume filtering method of band thickness tail noise of the present invention, for estimate dynamical system in the state at current time,
It specifically includes that
Step 1: the movement of construction target and sensor measurement discrete nonlinear equation；
Step 2: calculating each state vector of current time system according to the estimated value of each state vector of system previous moment
Predicted value；
Step 3: calculating the accuracy of each state vector predicted value of current time system, the accuracy is missed using estimation
Poor covariance matrix characterization；
Step 4: calculating the measurement predictor at current time according to each state vector predicted value of current time system；
Step 5: calculating the accuracy of current time measurement predictor；
Step 6: calculating the accurate of cross-correlation between current time measurement predictor and each state vector predicted value of system
Degree；
Step 7: calculating current time filter gain；
Step 8: calculating current time statistical distance；
Step 9: each state vector predicted value of the system at current time is updated；
Step 10: updating each state vector evaluated error covariance matrix of current time system.
Preferably, in the step 1, the movement of construction target and sensor measurement discrete nonlinear equation
Wherein, xk∈RnIndicate k moment system mode vector, n is state dimension, zk∈RmIndicate k moment external measurement
Vector, m are to measure dimension, and f () and h () respectively indicate state transition function and measure function, wk-1∈RnWith vk∈RmPoint
Not Biao Shi process noise and measure noise, by process noise and measure noise be assumed to be thick tail noise, be modeled as respectively as follows
Stable Student ' s t distribution:
Wherein, St (；μ, Σ, v) expression mean value be μ, Scale Matrixes Σ, freedom degree parameter be v Student ' s t
Distribution.QkAnd v1It is the Scale Matrixes and freedom degree parameter of system noise, R respectivelykAnd v2It is the scale square for measuring noise respectively
Battle array and freedom degree parameter；Original state x0Assuming that obedience mean value isScale Matrixes are P0|0, freedom degree parameter is v3's
Student ' s t distribution, it may be assumed that
And x0, wkAnd vkIt is irrelevant.
Preferably, in the step 2, calculating each state vector predicted value of current time system includes calculating state
Priori mean value
Preferably, in the step 3, the accuracy for calculating each state vector predicted value of current time system includes meter
The priori covariance matrix P of calculation statek|k-1:
Preferably, in the step 4, the measurement predictor for calculating current time includes calculating the priori mean value measured
Preferably, in the step 5, the accuracy for calculating current time measurement predictor includes calculating the elder generation measured
Test covariance matrix
Preferably, in the step 6, calculate current time measurement predictor and each state vector predicted value of system it
Between cross-correlation accuracy include calculating state and measurement priori Cross-covariance
Preferably, in the step 7 and step 8, filter gain is calculated
Statistical distance calculates
Preferably, in the step 9 and step 10, each state vector predicted value of the system at current time is updated
It is updated including state mean value
Updating each state vector evaluated error covariance matrix of current time system includes
Preferably, any step of the step 2 to step 6 includes more using the solution of cube sphere diameter volume criterion
Tie up nonlinear function integral, solved using cube sphere diameter volume criterion be related to contain Student ' s t distribution it is more
Tie up nonlinear function integralThat is I [g]=3rd-STSRCR [μ, Σ, v, g ()],
Wherein input parameter includes μ, Σ, v, and g () exports result are as follows:
Wherein, ejIndicate that j-th of element is 1 unit column vector.
Method proposed by the invention constructs one kind and is based on the approximate cube sphere diameter volume criterion of Student ' s t,
Solves the problems, such as the complex multi-dimensional nonlinear function Integration Solving being distributed containing Student ' s t；Secondly, compared to tradition
Non-linear Gaussian filter, method proposed by the invention for target done under clutter environment it is significantly motor-driven, and
Maneuvering target tracking under the conditions of some sensors poor with high sample frequency, reliability are measured there are outlier interference
There is better robustness and higher estimated accuracy in scene, solve in some practical engineering applications, traditional Gauss filter
Filtering accuracy declines when wave device system noise model and practical mismatch, or even the problem of diverging.
Robust Student ' s t volume filtering algorithm with thick tail noise proposed by the invention has good extension
Property and adaptability, can be widely applied to undertake the tactics function such as fire control, monitoring, early warning, to target following stabilization have higher requirements
Various airborne active phased array radar fire control systems, have a extensive future, application value is huge.
Detailed description of the invention
Fig. 1 is the flow chart of a preferred embodiment of the robust volume filtering method according to the present invention with thick tail noise.
Specific embodiment
To keep the purposes, technical schemes and advantages of the invention implemented clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical solution in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or
Similar label indicates same or similar element or element with the same or similar functions.Described embodiment is this
Invention a part of the embodiment, instead of all the embodiments.The embodiments described below with reference to the accompanying drawings are exemplary,
It is intended to be used to explain the present invention, and is not considered as limiting the invention.Based on the embodiments of the present invention, this field is general
Logical technical staff every other embodiment obtained without creative efforts, belongs to protection of the present invention
Range.The embodiment of the present invention is described in detail with reference to the accompanying drawing.
The technical scheme is that a kind of robust Student ' the s t volume filter of band thickness tail noise, core exist
In the design to filter.Firstly, the present invention is directed to generated thick tail mistake when target does significantly motor-driven under clutter environment
Journey noise, and measured in the poor sensor of some high sample frequencys, reliability by the thick tail for measuring outlier interference and generating
Noise has carried out mathematical modeling；Secondly, the present invention pushes away on the basis of the nonlinear system with thick tail process and measurement noise
It is derived based on the approximate robust nonlinear filter of Student ' s t (Robust Student ' s t based
Nonlinear filter, RSTNF) general structure.Finally, containing Student ' s t points for what is be related in RSTNF
The Multidimensional nonlinear function Integration Solving problem of cloth, the invention proposes the cube sphere diameter appearances based on Student ' s t distribution
Product criterion (Student ' s t spherical-radial cubature rule, STSRCR), and devise on this basis
A kind of robust Student ' s t volume filter (Robust Student ' s t based cubature filter,
RSTCF).As shown in Figure 1, including following key step:
Step 1: the movement of construction target and sensor measurement discrete nonlinear equation；
Step 2: calculating each state vector of current time system according to the estimated value of each state vector of system previous moment
Predicted value；
Step 3: calculating the accuracy of each state vector predicted value of current time system, the accuracy is missed using estimation
Poor covariance matrix characterization；
Step 4: calculating the measurement predictor at current time according to each state vector predicted value of current time system；
Step 5: calculating the accuracy of current time measurement predictor；
Step 6: calculating the accurate of cross-correlation between current time measurement predictor and each state vector predicted value of system
Degree；
Step 7: calculating current time filter gain；
Step 8: calculating current time statistical distance；
Step 9: each state vector predicted value of the system at current time is updated；
Step 10: updating each state vector evaluated error covariance matrix of current time system.
It is specific:
Step 1: it is constructed with thick tail process and the nonlinear system for measuring noise
Consider the Discrete-time Nonlinear Systems of following state space form:
Wherein, xk∈RnIndicate k moment system mode vector (n is state dimension, speed, the position in the direction xyz etc.), zk
∈RmIndicate k moment external measurement vector (m is to measure dimension, radial distance, azimuth, pitch angle of radar etc.).f(·)
State transition function is respectively indicated with h () and measures function.wk-1∈RnWith vk∈RmIt respectively indicates process noise and measurement is made an uproar
Sound.Since there may be a degree of uncertainties for system model, and unreliable sensor may also can generate some amount
Outlier is surveyed, therefore process noise and measurement noise are assumed to be thick tail noise, is modeled as following stable Student ' respectively
S t distribution:
Wherein, St (；μ, Σ, v) expression mean value be μ, Scale Matrixes Σ, freedom degree parameter be v Student ' s t
Distribution.QkAnd v1It is the Scale Matrixes and freedom degree parameter of system noise, R respectivelykAnd v2It is the scale square for measuring noise respectively
Battle array and freedom degree parameter.Original state x0Assuming that obedience mean value isScale Matrixes are P0|0, freedom degree parameter is v3's
Student ' s t distribution, it may be assumed that
And x0, wkAnd vkIt is irrelevant.
Step 2: robust Student ' s t nonlinear filter constructs (theory deduction)
(1) state mean value updates (a) according to the measuring value at k moment, corrects k moment each system mode vector predicted value
(2) state estimation error co-variance matrix updates (accuracy for calculating k moment each system mode vector estimated value)
(3) filter gain calculates
(4) statistical distance calculates
Wherein, the physical quantity being related in above each step is represented sequentially as:
The priori mean value of state(according to k-1 moment each system mode vector estimated value, calculate k moment each system
State vector predicted value)
The priori covariance matrix P of statek|k-1: calculate the accuracy of k moment each system mode vector predicted value
The priori mean value of measurement(according to k moment each system mode vector predicted value, calculate the measurement at the k moment
Predicted value)
The priori covariance matrix of measurementCalculate the accuracy of k moment measurement predictor
The priori Cross-covariance of state and measurementIt calculates between k moment measurement predictor and status predication value
The accuracy of cross-correlation
Step 3: Multidimensional nonlinear function is solved using cube sphere diameter volume criterion and is integrated
Contained using cube sphere diameter volume criterion (3rd-STSRCR) come involved in solution procedure two
The Multidimensional nonlinear function integral of Student ' s t distributionThat is I [g]=3rd-
STSRCR [μ, Σ, v, g ()], wherein 3rd-STSRCR [] indicates 3rd-STSRCR function interface, and input parameter includes μ,
Σ, v, g () export result are as follows:
Wherein, ejIndicate that j-th of element is 1 unit column vector.
Step 4: robust Student ' s t volume filter building
(1) time updates
A) priori mean value computation
B) priori covariance matrix calculates
(2) it measures and updates
C) priori mean value computation is measured
D) priori covariance matrix is measured to calculate
E) state and measurement priori Cross-covariance calculate
F) statistical distance calculates
G) filter gain calculates
H) state mean value updates
I) state estimation error co-variance matrix updates
The method that the invention is proposed is described in detail below by numerical simulation.Consider that target is assisted in two-dimensional surface
Same motor-driven situation of turning, system equation and measurement equation can respectively indicate as follows:
Wherein, state vectorξ and η respectively indicates target in the position in the direction x and y,With
Target is respectively indicated in the speed in the direction x and y, Ω indicates unknown constant rate of turn, T indicate to measure interval (or system from
Dissipate the time).White thickness tail system noise wkWith measurement noise vkIt generates as follows:
Wherein, w.p. indicates occur with certain probability, and w.p.0.05 indicates the probability for outlier occur.Q=diag
{q1M,q1M,q2T } indicate the covariance matrix of system noise, wherein q1=0.1m2s-3, q2=1.75 × 10-4s-3,
Indicate the covariance matrix of measurement noise, wherein σr=10m,
Relatively for justice, all filters are both configured to identical primary condition, and be carried out 200 times it is independent
Monte Carlo l-G simulation test.It is false based on Gauss in order to verify when process all has thick tail distribution with measurement noise profile
And if the filtering accuracy of the non-linear Gaussian filter of tradition designed declines, while in view of implementing high dimension, strong nonlinearity
When target following, first order Taylor is linearized there are huge truncated error, and the non-linear Gauss based on deterministic sampling thought
Filter can approach the Posterior Mean and covariance of any non-linear system status at least with second order Taylor's precision, thus at this
Emphasis is compared the CKF derived using volume transformation, the UKF derived using Unscented transform and this method and is mentioned in emulation
The filtering performance of RSTCF these three filters out.
Each filter root-mean-square error mean value of table 1 compares
Table (1) then gives the comparison result of each filter root-mean-square error mean value.As can be seen that proposed by the invention
RSTCF method than existing CKF and UKF have smaller root-mean-square error, and have the smallest root-mean-square error.When imitative
The true time enters after 70s, and CKF and UKF filtering hair occur to the estimated result of target position, speed and angular speed of turning
Phenomenon is dissipated, the reason of generating this phenomenon is caused to be, CKF and UKF are assuming that process noise and measurement noise obey Gauss
It is designed under the premise of distribution, and Gaussian Profile process to thick tail and can not measure noise and carry out accurate modeling, to lead
Cause CKF and UKF sensitive to the variation of the uncertainty of model and measurement outlier, filtering accuracy decline, final appearance filtering is sent out
It dissipates.And compared to Gaussian Profile, Student ' s t distribution can preferably match thick tail non-gaussian distribution, so being based on
It journey noise and measures noise and obeys Student ' s t distributional assumption and the RSTCF that designs has higher filtering accuracy and more
Good robustness.
Finally it is noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations.
Although the present invention is described in detail referring to the foregoing embodiments, those skilled in the art should understand that: its according to
It is so possible to modify the technical solutions described in the foregoing embodiments, or part of technical characteristic is equal
Replacement；And these are modified or replaceed, technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution
Spirit and scope.
Claims (10)
1. a kind of robust volume filtering method of band thickness tail noise, for estimating dynamical system in the state at current time, spy
Sign is, comprising:
Step 1: the movement of construction target and sensor measurement discrete nonlinear equation；
Step 2: calculating each state vector prediction of current time system according to the estimated value of each state vector of system previous moment
Value；
Step 3: calculating the accuracy of each state vector predicted value of current time system, the accuracy is assisted using evaluated error
Variance matrix characterization；
Step 4: calculating the measurement predictor at current time according to each state vector predicted value of current time system；
Step 5: calculating the accuracy of current time measurement predictor；
Step 6: calculating the accuracy of cross-correlation between current time measurement predictor and each state vector predicted value of system；
Step 7: calculating current time filter gain；
Step 8: calculating current time statistical distance；
Step 9: each state vector predicted value of the system at current time is updated；
Step 10: updating each state vector evaluated error covariance matrix of current time system.
2. the robust volume filtering method as described in claim 1 with thick tail noise, which is characterized in that in the step 1,
Construct target movement and sensor measurement discrete nonlinear equation
Wherein, xk∈RnIndicate k moment system mode vector, n is state dimension, zk∈RmIndicate k moment external measurement vector, m
To measure dimension, f () and h () respectively indicate state transition function and measure function, wk-1∈RnWith vk∈RmIt respectively indicates
Process noise and measurement noise are assumed to be thick tail noise, are modeled as respectively as follows smoothly by process noise and measurement noise
Student ' s t distribution:
Wherein, St (；μ, Σ, v) expression mean value is μ, Scale Matrixes Σ, freedom degree parameter is Student ' the s t point of v
Cloth.QkAnd v1It is the Scale Matrixes and freedom degree parameter of system noise, R respectivelykAnd v2Respectively be measure noise Scale Matrixes and
Freedom degree parameter；Original state x0Assuming that obedience mean value isScale Matrixes are P0|0, freedom degree parameter is v3Student ' s
T distribution, it may be assumed that
And x0, wkAnd vkIt is irrelevant.
3. the robust volume filtering method as claimed in claim 2 with thick tail noise, which is characterized in that in the step 2,
Calculate the priori mean value that each state vector predicted value of current time system includes calculating state
4. the robust volume filtering method as claimed in claim 3 with thick tail noise, which is characterized in that in the step 3,
The accuracy for calculating each state vector predicted value of current time system includes the priori covariance matrix P of calculating statek|k-1:
5. the robust volume filtering method as claimed in claim 4 with thick tail noise, which is characterized in that in the step 4,
The measurement predictor for calculating current time includes calculating the priori mean value measured
6. the robust volume filtering method as claimed in claim 5 with thick tail noise, which is characterized in that in the step 5,
The accuracy for calculating current time measurement predictor includes calculating the priori covariance matrix measured
7. the robust volume filtering method as claimed in claim 6 with thick tail noise, which is characterized in that in the step 6,
The accuracy for calculating cross-correlation between current time measurement predictor and each state vector predicted value of system include calculating state with
The priori Cross-covariance of measurement
8. the robust volume filtering method as claimed in claim 7 with thick tail noise, which is characterized in that the step 7 and step
In rapid eight, filter gain is calculated
Statistical distance calculates
9. the robust volume filtering method as claimed in claim 8 with thick tail noise, which is characterized in that the step 9 and step
In rapid ten, each state vector predicted value of the system at current time is updated to be updated including state mean value
Updating each state vector evaluated error covariance matrix of current time system includes
10. the robust volume filtering method as described in claim 1 with thick tail noise, which is characterized in that the step 2 is extremely
Any step of step 6 includes that Multidimensional nonlinear function integral is solved using cube sphere diameter volume criterion, utilizes cube sphere diameter
Volume criterion integrates to solve the Multidimensional nonlinear function for containing Student ' s t distribution being related toThat is I [g]=3rd-STSRCR [μ, Σ, v, g ()], wherein input parameter includes μ,
Σ, v, g () export result are as follows:
Wherein, ejIndicate that j-th of element is 1 unit column vector.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110083060A (en) * | 2019-04-09 | 2019-08-02 | 河南工业和信息化职业学院 | A kind of optimal output controller control method of discrete linear systems information fusion |
| CN111207744A (en) * | 2020-01-15 | 2020-05-29 | 哈尔滨工程大学 | Pipeline geographical position information measuring method based on thick tail robust filtering |
| CN112990256A (en) * | 2020-12-29 | 2021-06-18 | 北京电子工程总体研究所 | Multi-sensor noise calculation method, information fusion method, storage medium and device |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105703740A (en) * | 2016-01-13 | 2016-06-22 | 中国科学院重庆绿色智能技术研究院 | Gaussian filtering method based on multilayer importance sampling and Gaussian filter |
| CN106646356A (en) * | 2016-11-23 | 2017-05-10 | 西安电子科技大学 | Nonlinear system state estimation method based on Kalman filtering positioning |
| CN106767837A (en) * | 2017-02-23 | 2017-05-31 | 哈尔滨工业大学 | Based on the spacecraft attitude method of estimation that volume quaternary number is estimated |
| CN107290742A (en) * | 2017-06-20 | 2017-10-24 | 武汉理工大学 | Square root volume kalman filter method in a kind of Nonlinear Parameter tracking system |
| CN108303095A (en) * | 2018-02-02 | 2018-07-20 | 哈尔滨工业大学 | Robust volume target cooperative localization method suitable for non-Gaussian filtering |
| CN108304612A (en) * | 2017-12-26 | 2018-07-20 | 南京邮电大学 | The car radar method for tracking target of iterative square root CKF based on noise compensation |
-
2018
- 2018-08-03 CN CN201810876963.6A patent/CN109061579A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105703740A (en) * | 2016-01-13 | 2016-06-22 | 中国科学院重庆绿色智能技术研究院 | Gaussian filtering method based on multilayer importance sampling and Gaussian filter |
| CN106646356A (en) * | 2016-11-23 | 2017-05-10 | 西安电子科技大学 | Nonlinear system state estimation method based on Kalman filtering positioning |
| CN106767837A (en) * | 2017-02-23 | 2017-05-31 | 哈尔滨工业大学 | Based on the spacecraft attitude method of estimation that volume quaternary number is estimated |
| CN107290742A (en) * | 2017-06-20 | 2017-10-24 | 武汉理工大学 | Square root volume kalman filter method in a kind of Nonlinear Parameter tracking system |
| CN108304612A (en) * | 2017-12-26 | 2018-07-20 | 南京邮电大学 | The car radar method for tracking target of iterative square root CKF based on noise compensation |
| CN108303095A (en) * | 2018-02-02 | 2018-07-20 | 哈尔滨工业大学 | Robust volume target cooperative localization method suitable for non-Gaussian filtering |
Non-Patent Citations (3)
| Title |
|---|
| YULONG HUANG 等: "A robust Student"s t based cubature filter", 《2016 19TH INTERNATIONAL CONFERENCE ON INFORMATION FUSION (FUSION》 * |
| YULONG HUANG 等: "Robust Student’s t-Based Stochastic Cubature Filter for Nonlinear Systems With Heavy-Tailed Process and Measurement Noises", 《 IEEE ACCESS 》 * |
| 黄玉龙 等: "带有色厚尾量测噪声的鲁棒高斯近似滤波器和平滑器", 《自动化学报》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110083060A (en) * | 2019-04-09 | 2019-08-02 | 河南工业和信息化职业学院 | A kind of optimal output controller control method of discrete linear systems information fusion |
| CN111207744A (en) * | 2020-01-15 | 2020-05-29 | 哈尔滨工程大学 | Pipeline geographical position information measuring method based on thick tail robust filtering |
| CN112990256A (en) * | 2020-12-29 | 2021-06-18 | 北京电子工程总体研究所 | Multi-sensor noise calculation method, information fusion method, storage medium and device |
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