CN109840643B - Performance evaluation method of composite navigation fusion algorithm - Google Patents
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Abstract
The invention belongs to the technical field of navigation information processing, and particularly relates to a performance evaluation method of a composite navigation fusion algorithm.
Description
Technical Field
The invention belongs to the technical field of navigation information processing, and particularly relates to a composite navigation fusion algorithm performance evaluation method based on log least square FAHP-FCE.
Background
Inertial/land-based/satellite hybrid navigation is one of the commonly used navigation methods for ballistic missiles. The precision and reliability of the composite navigation system of the ballistic missile depend on the performance of the fusion algorithm thereof under the conditions of all-time, all-weather and complex electromagnetic interference. Before the fusion algorithm is put into use, the performance of the algorithm is evaluated, and a basis is provided for designing and determining system parameters meeting the performance requirements of the composite navigation system and optimizing the system parameters. Meanwhile, an algorithm verification platform is provided for the navigation system, which is beneficial to system parameter optimization, functional design and improvement, saves the test cost and shortens the development cycle of the system. Therefore, the evaluation of the performance of the fusion algorithm becomes a precondition and a necessary basis for improving the performance of the composite navigation system.
The performance evaluation of the fusion algorithm of the composite navigation system is a process of synthesizing a system performance evaluation result by a certain distinguishing and synthesizing method aiming at the performance of the filtering algorithm, such as fusion precision, real-time performance, reliability, stability, algorithm complexity and the like. The composite navigation system fusion algorithm has a plurality of influencing factors, each factor has relevance, the performance evaluation is a multi-level and multi-level processing process, the detection, interconnection, correlation, estimation and synthesis of data and information of a multi-source navigation sensor are involved, and quantitative judgment results are difficult to give.
At present, few people research performance evaluation methods aiming at a composite navigation system fusion algorithm, but domestic and foreign scholars already put forward a plurality of evaluation methods applied to other systems, wherein a fuzzy hierarchical analysis method is most representative, and has been widely concerned by domestic and foreign scholars and drawn forth a plurality of novel methods. Among a plurality of fuzzy evaluation methods, the FAHP method (fuzzy LLSM) of log least squares decomposes factors which are difficult to distinguish and influence the performance of a fusion algorithm, constructs a multi-level system to form a judgment index, then constructs a fuzzy judgment matrix according to the judgment index, and finally solves each index weight vector of the fusion algorithm of the composite navigation system. However, only the weight vector of each evaluation index of the composite navigation system fusion algorithm is obtained, and a comprehensive evaluation method is still required to be searched for further comprehensive evaluation of the system. The Fuzzy Comprehensive Evaluation (FCE) method is a quantitative Comprehensive evaluation method which converts qualitative evaluation into quantitative Comprehensive evaluation according to Fuzzy mathematical membership theory. The method has the characteristics of clear result and strong comprehensive judgment capability. The fuzzy LLSM method and the FCE method are combined, the fuzzy LLSM method is used for determining the index weight vector of the composite navigation system fusion algorithm, the fuzzy relation matrix is obtained by judging the index by using the membership function, and the weighting average fuzzy operator is used for synthesizing the weight vector and the fuzzy relation matrix, so that the comprehensive evaluation result of the algorithm performance can be obtained, and the performance evaluation of the fusion algorithm of the inertia/land-based/satellite composite navigation system can be quantized.
Disclosure of Invention
The invention aims to provide a performance evaluation method of a composite navigation fusion algorithm, which can solve the problems that the fusion algorithm performance influence factors of an inertia/land-based/satellite composite navigation system carried by a ballistic missile are numerous and quantitative evaluation is difficult.
The technical scheme of the invention is as follows:
a performance evaluation method of a composite navigation fusion algorithm comprises the following steps:
step 1, a composite navigation system performance multi-level index system;
establishing an evaluation sub-target and an evaluation level discourse domain set of U and V respectively
U＝{u1,u2,u3},V＝{V1,V2,...,V5}
Wherein u isiFor the ith sub-object in the first layer of the index system, ui＝{ui1,ui2,..., u ip1,2,3, and p is the index number in the second layer of the index system;
W＝{W1,W2,W3W andi＝{wi1,wi2,...,wip}
Wiand wijSatisfies the following conditions:
wherein, { W1,W2,W3The complexity evaluation (u) of the fusion algorithm is respectively1) Evaluation of localization effect (u)2) And algorithm stability assessment (u)3) The weight assignment of (2); { wi1,wi2,...,wipAre { u } respectively1,u2,u3Assigning a weight of a p-th index in a next layer;
Wherein the matrix element rijkThe j-th index of the ith sub-target is represented as the degree of membership to the k-th evaluation level, wherein j is 1,2,3 … m, and k is 1,2,3 … n;
and 4, selecting a weighted average fuzzy operator for comprehensive judgment.
The hierarchical structure of the multi-level index system comprises a target layer, a criterion layer and a measure layer; wherein, the criterion layer can be divided into fusion algorithm complexity evaluation (u)1) Evaluation of localization effect (u)2) And algorithm stability assessment (u)3) Waiting for 3 primary evaluation criteria, wherein the 3 criteria respectively comprise a plurality of secondary indexes; the measure layer is composed of the index model and the quantization result in the criterion layer.
The evaluation level discourse domain set V has the following assignments: very good (V)1) Has a quantization interval of [90,100 ]](ii) a Preferably (V)2) Has a quantization interval of [80,90 ]](ii) a Medium (V)3) Has a quantization interval of [60,80 ]](ii) a Poor (V)4) Has a quantization interval of [50,60 ]](ii) a Very poor (V)5) Has a quantization interval of [50,0 ]]。
The step 4 is
Constructing a first-level fuzzy evaluation set:
wherein ". smallcircle" is a "weighted average" type blurring operator; wiIs the sub-target { u1,u2,u3The set of weights of; riIs the sub-target { u1,u2,u3A membership subset of { C };
a secondary fuzzy comprehensive evaluation model:
wherein, b1,b2,...bnSet of secondary evaluations generated for the set of discourse domains V according to the evaluation level, bi1,bi2,...binA set of first level evaluations for the ith sub-target.
The invention has the following remarkable effects: the technical scheme includes that a FAHP method and an FCE method based on log least squares are combined, the FAHP method is used for solving a fusion algorithm performance evaluation index weight vector which is accurate and high in evaluation resolution, the FCE method is used for evaluating a constructed index model by means of a membership function to obtain a fuzzy relation matrix, and then the weight vector and the fuzzy relation matrix are synthesized. The method solves the problems that the performance influence factors of the fusion algorithm of the inertia/land-based/satellite composite navigation system carried by the ballistic missile are numerous and quantitative evaluation is difficult to carry out.
(1) Aiming at the problems that the performance evaluation of the fusion algorithm of the inertia/land-based/satellite composite navigation system has a plurality of influencing factors, each factor has correlation and the performance evaluation is relatively complex, the invention effectively solves the problems of a plurality of index factors and difficult quantization by constructing a multi-level index system structure.
(2) The method provided by the invention effectively utilizes the advantages that both the FAHP method and the FCE method are good at processing the problems of fuzziness and inaccuracy, and establishes a relation between qualitative analysis and quantitative analysis. Meanwhile, the fuzzy evaluation method has stronger comprehensive evaluation capability, and the accurate index weight is determined by using the FAHP method to form advantage complementation, so that the fuzzy evaluation is more scientific.
(3) The method provided by the invention can solve the problems of non-uniqueness of weight and ambiguity in the performance evaluation of the fusion algorithm of the composite navigation system, and the uniqueness of the normalized fuzzy weight vector is ensured by giving out the restrictive condition of the fuzzy judgment matrix, namely meeting the requirement that at least one expert gives out the importance judgment between any two indexes; in addition, further utilize CSCF method to carry on defuzzification to the fuzzy weight vector, thus get the non-fuzzy weight value that can be used for FCE method to be integrated directly.
Drawings
FIG. 1 is a multi-level structure diagram of the fusion algorithm evaluation index of the present invention;
FIG. 2 is a functional block diagram of the method of the present invention;
1. a log least squares (FAHP) method; FCE process; 3. and (5) index model.
Detailed Description
The invention is further illustrated by the accompanying drawings and the detailed description.
The execution steps of the evaluation method provided by the invention can be summarized as follows:
step 1, constructing a multi-level structure system
According to factors and related relations contained in the performance of a composite algorithm of the composite navigation system, a key judgment criterion is decomposed, and a judgment sub-target, an index and an evaluation level domain set are constructed, so that a multi-level index system structure is formed. The set of the evaluation sub-targets and the evaluation level discourse domain is respectively U and V:
U＝{u1,u2,u3},V＝{V1,V2,...,V5} (1)
in the formula uiIs the ith sub-object in the first layer (highest layer) and is determined by p indexes in the second layer, i.e. ui＝{ui1,ui2,...,uip},i＝1,2,3。
As shown in fig. 1, the hierarchical structure includes three layers, a target layer (1), a criterion layer (2), and a measure layer (3). Wherein, the criterion layer can be divided into fusion algorithm complexity evaluation (u)1) Evaluation of localization effect (u)2) And algorithm stability assessment (u)3) And 3 primary evaluation criteria are adopted, and the 3 criteria respectively comprise a plurality of secondary indexes. The two-level performance evaluation indexes related to the algorithm complexity criterion areTime complexity (u)11) Spatial complexity (u)12) (ii) a The index related to the positioning effect criterion has positioning absolute error (u)21) Relative error of positioning (u)22) Positioning speed (u)23) And positioning effectiveness (u)24) (ii) a The algorithm stability criterion includes convergence (u)31) Fault tolerance capability (u)32) And robustness (u)33). The specific index models and the quantitative results jointly form a secondary performance evaluation measure layer (3).
It is worth proposing that the measure layer (3) has relatively independent mathematical models and quantized result output, so that the built multilayer structure evaluation index system model can describe the performance evaluation result of the fusion algorithm more accurately.
The evaluation level discourse domain set V in the formula (1) has an assignment table as follows:
TABLE 1 evaluation set quantization interval value-assigning table
| Set of evaluation ratings | Very good (V)1) | Preferably (V)2) | Medium (V)3) | Poor (V)4) | Very poor (V)5) |
| Quantization interval | [90,100] | [80,90] | [60,80] | [50,60] | [50,0] |
And determining a performance sub-target and a weight distribution set of the evaluation index of the composite algorithm of the composite navigation system by using a fuzzy LLSM method. The steps are summarized as follows:
2.1) constructing a fuzzy weight vector solving model by using a fuzzy LLSM method, and determining conditions according to the uniqueness of a triangular fuzzy weight vector, namely ensuring that at least one expert judges the importance of any two indexes;
2.2) calculating a normalized fuzzy weight vector.
And 2.3) carrying out defuzzification treatment on the fuzzy weight vector by using a CFCS (computational fluid dynamics) method to obtain a non-fuzzy normalized weight vector.
According to the steps, the weight distribution set W of the sub-targets and the weight distribution set W of the indexes can be obtained respectivelyi：
W＝{W1,W2,W3W andi＝{wi1,wi2,...,wip} (2)
in the formula, WiAnd wijSatisfies the following conditions:
wherein, { W1,W2,W3The complexity evaluation (u) of the fusion algorithm is respectively1) Evaluation of localization effect (u)2) And algorithm stability assessment (u)3) The weight assignment of (2); { wi1,wi2,...,wipAre { u } respectively1,u2,u3The weight assignment of the p index in the next layer.
To time complexity (u)11) Spatial complexity (u)12) Absolute error of positioning (u)21) Relative error of positioning (u)22) Positioning speed (u)23) Positioning effectiveness (u)24) Astringency (u)31) Fault tolerance capability (u)32) And robustness (u)33) Respectively constructing index models by indexes, obtaining a normalized index model value through Monte Carlo simulation for a plurality of times, substituting the normalized index model value into a unitary linear membership function, and determining a sub-target set uiThe degree of membership of each index in the index set V is related to the evaluation set V, so as to derive a membership matrix R of a sub-target leveliComprises the following steps:
wherein the matrix element rijkAnd j is 1,2,3 … m, and k is 1,2,3 … n.
Because complex uncertain factors still exist in the performance evaluation of the fusion algorithm of the composite navigation system, the factors belong to different levels, the weights need to be determined layer by layer from low to high and are evaluated comprehensively, and meanwhile, the integrity and consistency of the evaluation need to be kept, so that the secondary fuzzy comprehensive evaluation needs to be further introduced on the basis of the primary fuzzy comprehensive evaluation to obtain a secondary comprehensive evaluation result.
Step 4, selecting weighted average fuzzy operator to carry out comprehensive evaluation
Constructing a first-level fuzzy evaluation set as follows:
wherein ". smallcircle" is a "weighted average" type blurring operator; wiIs the sub-target { u1,u2,u3The set of weights of; riIs the sub-target { u1,u2,u3A membership subset of. bi1,bi2,...binA set of first level evaluations for the ith sub-target.
In order to further obtain high-level comprehensive evaluation, secondary fuzzy comprehensive calculation is required to be carried out, and the following secondary fuzzy comprehensive evaluation model is established:
wherein, b1,b2,...bnA set of secondary assessments is generated for the set of discourse domains V in terms of an assessment rating.
Thus, on the basis of the primary fuzzy evaluation, the normalized evaluation results obtained by the primary fuzzy comprehensive evaluation are combined into a matrix R which is used as a membership matrix from a factor set U to an evaluation set V, and an evaluation set b is calculated according to a formula (6)1,b2,...bnAnd the multi-stage comprehensive evaluation is completed by the layer-by-layer evaluation.
The method combines the characteristics of the performance evaluation of the fusion algorithm of the composite navigation system, ensures the uniqueness of the weight vector by deeply analyzing the FAHP method and the FCE method based on the log least square and controlling the number of experts judging the importance of any two indexes of the fusion algorithm, and defuzzifies the fuzzy weight vector determined by the fuzzy LLSM method, so that the weight vector can be directly weighted and integrated by using the FCE method to form advantage complementation. By taking the performance evaluation of the fusion algorithm of inertia/land-based/satellite composite navigation carried by ballistic missiles as an example, the quantitative evaluation of the performance of the fusion algorithm of the composite navigation system is realized, and the evaluation method is simple to apply and easy to realize in engineering.
Claims (1)
1. A performance evaluation method of a composite navigation fusion algorithm is characterized by comprising the following steps:
step 1, a composite navigation system performance multi-level index system;
establishing an evaluation sub-target and an evaluation level discourse domain set of U and V respectively
U＝{u1,u2,u3},V＝{V1,V2,...,V5}
Wherein u isiIs the first layer of the index systemi sub-targets, ui＝{ui1,ui2,...,uip1,2,3, and p is the index number in the second layer of the index system;
step 2, determining a composite algorithm performance sub-target weight distribution set W of the composite navigation system and a weight distribution set W of the evaluation indexi
W＝{W1,W2,W3W andi＝{wi1,wi2,...,wip}
Wiand wijSatisfies the following conditions:
wherein, { W1,W2,W3The complexity evaluation (u) of the fusion algorithm is respectively1) Evaluation of localization effect (u)2) And algorithm stability assessment (u)3) The weight assignment of (2); { wi1,wi2,...,wipAre { u } respectively1,u2,u3Assigning a weight of a p-th index in a next layer;
step 3, constructing a membership matrix
Wherein the matrix element rijkThe j-th index of the ith sub-target is represented as the degree of membership to the k-th evaluation level, wherein j is 1,2,3 … m, and k is 1,2,3 … n;
step 4, selecting a weighted average fuzzy operator to carry out comprehensive judgment;
the hierarchical structure of the multi-level index system comprises a target layer, a criterion layer and a measure layer; wherein, the criterion layer can be divided into fusion algorithm complexity evaluation (u)1) Evaluation of localization effect (u)2) And algorithm stability assessment (u)3)3 primary evaluation criteria, wherein the 3 criteria respectively comprise a plurality of secondary indexes; the measure layer is formed by the index model and the quantization result in the criterion layer;
the evaluation level discourse domain set V has the following assignments: very good (V)1) Has a quantization interval of [90,100 ]](ii) a Preferably (V)2) Has a quantization interval of [80,90 ]](ii) a Medium (V)3) Has a quantization interval of [60,80 ]](ii) a Poor (V)4) Has a quantization interval of [50,60 ]](ii) a Very poor (V)5) Has a quantization interval of [50,0 ]]；
The step 4 is
Constructing a first-level fuzzy evaluation set:
wherein the content of the first and second substances,
a "weighted average" type blurring operator; wiIs the sub-target { u1,u2,u3The set of weights of; riIs the sub-target { u1,u2,u3A membership subset of { C };
a secondary fuzzy comprehensive evaluation model:
wherein, b1,b2,...bnSet of secondary evaluations generated for the set of discourse domains V according to the evaluation level, bi1,bi2,...binA first-level evaluation set is the ith sub-target;
the step 2 is to determine the weight distribution of the performance sub-targets and the evaluation indexes of the composite algorithm of the composite navigation system by using a fuzzy LLSM method, and specifically comprises the following steps:
2.1) constructing a fuzzy weight vector solving model by using a fuzzy LLSM method, and determining conditions according to the uniqueness of a triangular fuzzy weight vector, namely ensuring that at least one expert judges the importance of any two indexes;
2.2) calculating a normalized fuzzy weight vector;
2.3) carrying out defuzzification processing on the fuzzy weight vector by using a CFCS (computational fluid dynamics) method to obtain a non-fuzzy normalized weight vector;
and 3, constructing a membership matrix, and respectively constructing index models for time complexity, space complexity, positioning absolute error, positioning relative error, positioning speed, positioning effectiveness, convergence, fault tolerance and robustness indexes.
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| EP0595570A2 (en) * | 1992-10-26 | 1994-05-04 | General Electric Company | Navigation module for a semi-autonomous vehicle |
| CN103528587A (en) * | 2013-10-15 | 2014-01-22 | 西北工业大学 | Autonomous integrated navigation system |
| CN106682416A (en) * | 2016-12-24 | 2017-05-17 | 合肥城市云数据中心股份有限公司 | Sewage enterprise water pollution source assessment method based on multi-index evaluation algorithm |
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