State Estimation Method for GNSS/INS/Visual Multi-sensor Fusion Based on Factor Graph Optimization for Unmanned System

With the development of unmanned driving technology,intelligent robots and drones,high-precision localization,navigation and state estimation technologies have also made great progress.Traditional global navigation satellite system/inertial navigation system(GNSS/INS)integrated navigation systems can provide high-precision navigation information continuously.However,when this system is applied to indoor or GNSS-denied environments,such as outdoor substations with strong electromagnetic interference and complex dense spaces,it is often unable to obtain high-precision GNSS positioning data.The positioning and orientation errors will diverge and accumulate rapidly,which cannot meet the high-precision localization requirements in large-scale and long-distance navigation scenarios.This paper proposes a method of high-precision state estimation with fusion of GNSS/INS/Vision using a nonlinear optimizer factor graph optimization as the basis for multi-source optimization.Through the collected experimental data and simulation results,this system shows good performance in the indoor environment and the environment with partial GNSS signal loss.

Personnel Localization Method in Transformer Substation Based on Factor Graph

A SINS/GNSS location method based on factor diagram is proposed to meet the requirement of accurate location of substation construction personnel. In this paper, the inertial autonomous positioning, carrier motion information acquisition and satellite positioning technologies are integrated. The factor graph method is adopted to abstract the measurement information received by inertial navigation and satellite into factor nodes, and the state information into variable nodes, so as to construct the SINS/GNSS construction personnel positioning fusion factor graph model. The Gauss-Newton iterative method is used to implement the recursive updating of variable nodes, and the optimal estimate of the location information of the construction personnel is calculated, which realized the high precision location of the construction personnel. The factor graph method is verified by pedestrian navigation data. The results show that the factor graph method can continuously and stably output high-precision positioning results, and realize non-equidistant fusion of SINS and GNSS. The positioning accuracy is better than Kalman filter algorithm, and the horizontal positioning accuracy is less than 1 m. Therefore, the factor graph method proposed can provide accurate location information for substation construction personnel.

Blind receiver for OFDM systems via sequential Monte Carlo in factor graphs

Estimation and detection algorithms for orthogonal frequency division multiplexing (OFDM) systems can be de-veloped based on the sum-product algorithms, which operate by message passing in factor graphs. In this paper, we apply the sampling method (Monte Carlo) to factor graphs, and then the integrals in the sum-product algorithm can be approximated by sums, which results in complexity reduction. The blind receiver for OFDM systems can be derived via Sequential Monte Carlo (SMC) in factor graphs, the previous SMC blind receiver can be regarded as the special case of the sum-product algorithms using sampling methods. The previous SMC blind receiver for OFDM systems needs generating samples of the channel vector assuming the channel has an a priori Gaussian distribution. In the newly-built blind receiver, we generate samples of the virtual-pilots instead of the channel vector, with channel vector which can be easily computed based on virtual-pilots. As the size of the vir-tual-pilots space is much smaller than the channel vector space, only small number of samples are necessary, with the blind de-tection being much simpler. Furthermore, only one pilot tone is needed to resolve phase ambiguity and differential encoding is not used anymore. Finally, the results of computer simulations demonstrate that the proposal can perform well while providing sig-nificant complexity reduction.

Self-dual Codes Defined on Factor Graphs

A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.

Factor graph based navigation and positioning for control system design:A review

Navigation and positioning is an important and challenging problem in many control engineering applications.It provides feedback information to design controllers for systems.In this paper,a bibliographical review on factor graph based navigation and positioning is presented.More specifically,the sensor modeling,the factor graph optimization methods,and the topology factor based cooperative localization are reviewed.The navigation and positioning methods via factor graph are considered and classified.Focuses in the current research of factor graph based navigation and positioning are also discussed with emphasis on its practical application.The limitations of the existing methods,some solutions for future techniques,and recommendations are finally given.

Modified attitude factor graph fusion method for unmanned helicopter under atmospheric disturbance

The Unmanned Aerial Helicopter(UAH)has attracted increasing attention in the military and civil areas with the unique flight performance.The significant impact on the attitude measurement performance of UAHs by the strong airflow disturbance is an essential factor threatening flight safety.To improve the attitude measurement performance of UAHs under atmospheric disturbance,an attitude fusion method over the factor graph is applied and provides the plug-and-play capability.Based on the relationship between position,velocity and attitude,a new attitude correction algorithm for the Modified Attitude Factor Graph Fusion(MAFGF)navigation method is designed and constructed through the fused position and velocity information.Finally,results of simulation and experiment are given to show the effectiveness of the proposed method.

Factor-graph-based iterative channel estimation and signal detection algorithm over time-varying frequency-selective fading channels

The problem of soft-input so,output （ SISO ） detection for time-varying frequency-selec- tive fading channels is considered. Based on a suitably-designed factor graph and the sum-product al- gorithm, a low-complexity iterative message passing scheme is proposed for joint channel estima- tion, equalization and decoding. Two kinds of schedules （parallel and serial） are adopted in message updates to produce two algorithms with different latency. The computational complexity per iteration of the proposed algorithms grows only linearly with the channel length, which is a significantly de- crease compared to the optimal maximum a posteriori （MAP） detection with the exponential com- plexity. Computer simulations demonstrate the effectiveness of the proposed schemes in terms of bit error rate performance.

FRACTIONAL (g, f)-FACTORS OF GRAPHS

This paper presents a new proof of a charaterization of fractional (g, f)-factors of a graph in which multiple edges are allowed. From the proof a polynomial algorithm for finding the fractional (g, f)-factor can be induced.

K_(1,p)~k-FACTORIZATION OF COMPLETE BIPARTITE GRAPHS

In this paper, it is shown that a sufficient condition for the existence of a K 1,p k factorization of K m,n , whenever p is a prime number and k is a positive integer, is (1) m≤p kn,(2) n≤p km,(3)p kn-m≡p km-n ≡0(mod( p 2k -1 )) and (4) (p kn-m)(p km-n) ≡0(mod( p k -1)p k×(p 2k -1)(m+n)) .

ON(g,f)-FACTORIZATIONS OF GRAPHS

Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g less than or equal to f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)less than or equal to d(F)(x)less than or equal to f(x) for all x is an element of V(G). If G itself is a (g, f)-factor, then it is said that G is a (g, f)-graph. If the edges of G can be decomposed into some edge disjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, one sufficient condition for a graph to be (g, f)-factorable is given.

ORTHOGONAL (g,f)-FACTORIZAFIONS OF BIPARTITE GRAPHS

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.

Extracting Sub-Networks from Brain Functional Network Using Graph Regularized Nonnegative Matrix Factorization

Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.

[0, ki ]1m -FACTORIZATIONS ORTHOGONAL TO A SUBGRAPH

Let G be a graph, k(1), ... , k(m) be positive integers. If the edges of graph G can be decomposed into some edge disjoint [0, k(1)]-factor F-1, ..., [0, k(m)]-factor F-m, then we can say (F) over bar = {F-1, ..., F-m}, is a [0, k(i)](1)(m) -factorization of G. If H is a subgraph with m edges in graph G and / E (H) boolean AND E(F-i) / = 1 for all 1 less than or equal to i less than or equal to m, then we can call that (F) over bar is orthogonal to H. It is proved that if G is a [0, k(1) + ... + k(m) - m + 1]-graph, H is a subgraph with m edges in G, then graph G has a [0, k(i)](1)(m)-factorization orthogonal to H.

On the Factorizations of (mg, mf)-graph

Let G be an (mg, mf)-graph, where g and f are integer-valued functions defined on V(G) and such that 0≤g(x)≤f(x) for each x ∈ V(G). It is proved that(1) If Z ≠ , both g and f may be not even, G has a (g, f)-factorization, where Z = {x ∈ V(G):mf(x)-dG(x)≤t(x) or dG(x)-mg(x)≤ t(x), t(x)=f(x)-g(x)>0}.(2) Let G be an m-regular graph with 2n vertices, m ≥ n. If (P1, P2,..., Pr) is a partition of m, P1 ≡m (mod 2), Pi≡0 (mod 2), i=2,..., r, then the edge set E(G) of G can be parted into r parts E1,E2,..., Er of E(G) such that G[Ei] is a Pi-factor of G.

A Neighborhood Condition for Graphs to Have Special [a,b]-Factor

Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, .

On the ｛P_2,P_3｝-Factor of Cubic Graphs

Ler G = （ V, E） be a finite simple graph and Pn denote the path of order n. A spanning subgraph F is called a { P2, P3 }-factor of G if each component of F is isomorphic to P2 or P3. With the path-covering method, it is proved that any connected cubic graph with at least 5 vertices has a { P2, P3 }-factor F such that｜P3（F）｜P2（F）｜, where P2（F） and P3（F） denote the set of components of P2 and P3 in F, respectively.

INDEPENDENT-SET-DELETABLE FACTOR-CRITICAL POWER GRAPHS

It is said that a graph G is independent-set-deletable factor-critical （in short, ID-factor-critical）, if, for everyindependent-set I which has the same parity as ｜V（G）｜, G - I has a perfect matching. A graph G is strongly IM-extendable, if for every spanning supergraph H of G, every induced matching of H is included in a perfect matching of H. The κ-th power of G, denoted by G^κ, is the graph with vertex set V（G） in which two vertices are adjacent if and only if they have distance at most k in G. ID-factor-criticality and IM-extendability of power graphs are discussed in this article. The author shows that, if G is a connected graph, then G^3 and T（G） （the total graph of G） are ID-factor-critical, and G^4 （when ｜V（G）｜ is even） is strongly IM-extendable; if G is 2-connected, then D^2 is ID-factor-critical.

融合自适应周期与兴趣量因子的轻量级GCN推荐

推荐系统在成熟的数据挖掘技术推动下,已能高效地利用评分数据、行为轨迹等显隐性信息,再与复杂而先进的深度学习技术相结合,取得了很好的效果.同时,其应用需求也驱动着对基础数据的深度挖掘与利用,以及对技术要求的减负成为一个研究热点.基于此,提出一种利用GCN(graph convolutional network)方法进行深度信息融合的轻量级推荐模型LG_APIF.该模型结合行为记忆,通过艾宾浩斯遗忘曲线模拟用户兴趣变化过程,采用线性回归等相对轻量的传统方法挖掘项目的自适应周期等深度信息;分析用户当前的兴趣分布,计算项目的兴趣量,以获取用户的潜在兴趣类型;构建用户-类型-项目三元组的图结构,并结合减负后的GCN技术来生成最终的项目推荐列表.实验验证所提方法的有效性,通过与8个经典模型在Last.fm,Douban,Yelp,MovieLens数据集中的对比,表明该方法在Precision,Recall及NDCG指标上都得到良好改善,其中,Precision平均提升2.11%,Recall平均提升1.01%,NDCG平均提升1.48%.

(g,f)-FACTORS WITH SPECIAL PROPERTIES IN BIPARTITE (mg,mf)-GRAPHS

Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible.