The size order of the state vector of a continuous-time homogeneous Markov system with fixed size

2001 ◽  
Vol 38 (03) ◽  
pp. 635-646
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Convergence Rate ◽  
Continuous Time ◽  
State Vector ◽  
The State ◽  
Specific Time ◽  
Fixed Size ◽  
Geometric Characteristics ◽  
Markov System ◽  
Selection Of

The variation of the state vectors p (t) = (p i (t)) of a continuous-time homogeneous Markov system with fixed size is examined. A specific time t 0 after which the size order of the elements p i (t) becomes stable provides a criterion of the system's convergence rate. A method is developed to find t 0 and a quickly evaluated lower bound for t 0. This method is based on the geometric characteristics and the volumes of the attainable structures. Moreover, a condition concerning the selection of starting vectors p (0) is given so that the vector functions p (t) retain the same size order for every time greater than a given time t.

The size order of the state vector of a continuous-time homogeneous Markov system with fixed size

2001 ◽  
Vol 38 (3) ◽  
pp. 635-646
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Convergence Rate ◽  
Continuous Time ◽  
State Vector ◽  
The State ◽  
Specific Time ◽  
Fixed Size ◽  
Geometric Characteristics ◽  
Markov System ◽  
Selection Of

The variation of the state vectors p(t) = (pi(t)) of a continuous-time homogeneous Markov system with fixed size is examined. A specific time t0 after which the size order of the elements pi(t) becomes stable provides a criterion of the system's convergence rate. A method is developed to find t0 and a quickly evaluated lower bound for t0. This method is based on the geometric characteristics and the volumes of the attainable structures. Moreover, a condition concerning the selection of starting vectors p(0) is given so that the vector functions p(t) retain the same size order for every time greater than a given time t.

The size order of the state vector of discrete-time homogeneous Markov systems

2001 ◽  
Vol 38 (2) ◽  
pp. 357-368 ◽  
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Discrete Time ◽  
State Vector ◽  
The State ◽  
Order Problem ◽  
Markov Systems ◽  
Markov System

The size order problem of the probability state vector elements of a homogeneous Markov system is examined. The time t0 is evaluated, after which the order of the state vector probabilities remains unchanged, and a formula to quickly find a lower bound for t0 is given. A formula for approximating the mode of the state sizes ni(t) as a function of the means Eni(t), and a relation to evaluate P(ni(t) = x+1) by means of certain terms which constitute P(ni(t) = x) are derived.

The size order of the state vector of discrete-time homogeneous Markov systems

2001 ◽  
Vol 38 (02) ◽  
pp. 357-368 ◽  
Author(s):  
I. Kipouridis ◽  
G. Tsaklidis
Keyword(s):  
Lower Bound ◽  
Discrete Time ◽  
State Vector ◽  
The State ◽  
Order Problem ◽  
Markov Systems ◽  
Markov System

The size order problem of the probability state vector elements of a homogeneous Markov system is examined. The time t 0 is evaluated, after which the order of the state vector probabilities remains unchanged, and a formula to quickly find a lower bound for t 0 is given. A formula for approximating the mode of the state sizes n i (t) as a function of the means En i (t), and a relation to evaluate P(n i (t) = x+1) by means of certain terms which constitute P(n i (t) = x) are derived.

The evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size

1996 ◽  
Vol 33 (01) ◽  
pp. 34-47 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Euclidean Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Fixed Size ◽  
Markov System

In order to describe the evolution of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space in the course of time, and we find the value of the volume asymptotically. Then, using the concept of the volume of the attainable structures, we provide a method to evaluate the ‘age' of the system in continuous and discrete time. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures.

scholarly journals Strapdown inertial navigation systems readings correction based on navigational data of other sensors and systems with intelligent selection of the priority adjuster

2020 ◽  
Vol 224 ◽  
pp. 02024
Author(s):  
P.M. Trefilov ◽  
M.V. Mamchenko ◽  
A.V. Korol’kov
Keyword(s):  
State Vector ◽  
Inertial Navigation ◽  
Physical Nature ◽  
The State ◽  
Coupled Systems ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Navigation Data ◽  
Selection Of ◽  
Strapdown Inertial Navigation

Strapdown inertial navigation systems (SINS) are one of the main components of the navigation systems of the drones and aircraft (including autonomous ones), but their readings need to be instanly corrected due to the constant accumulation of errors. This paper comprises the review of existing approaches to using one or more sensors or systems to correct the navigation data of SINS algorithms (herein after – correctors) using integrated information processing. A common disadvantage of the analysed approaches is the lack of flexibility concerning the types and the number of SINS correctors used, as well as the growth of computational burden due to the use of the measurement vectors of all the correctors in the process of forming the state vector of the system. This article proposes the use of the original adaptive scheme based on the selection of the least noisy data, taking into account environmental conditions, for the integrated processing of the SINS and the correctos’ navigation parameters. The essence of the approach is that the state vector is estimated on the basis of the most reliable corrector. This allows reducing the correlation of errors in the correctors’ measurement of navigational parameters, since only the measurement vectors (or vector) with best navigational data signal/noise ratio (received from the corresponding correctors) are used in forming the state vector. Furthermore, the proposed navigational data fusion scheme has a modular structure and greater flexibility in comparison with the loosely coupled systems, and also implies the use of an arbitrary number of correction sensors and systems regardless of the physical nature of their measurements.

The stress tensor and the energy of a continuous time homogeneous Markov system with fixed size

1999 ◽  
Vol 36 (1) ◽  
pp. 21-29 ◽  
Author(s):  
George M. Tsaklidis
Keyword(s):  
Velocity Field ◽  
Euclidean Space ◽  
Stress Tensor ◽  
Continuous Time ◽  
Suitable Model ◽  
Fixed Size ◽  
Markov System

The set of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, is considered as a continuum and the evolution of the HMS in the Euclidean space corresponds to its motion. Taking account of the velocity field of the HMS, a suitable model of continuum–defined by its stress tensor–is proposed in order to explain the motion of the system. The adoption of this model (equivalently of its stress tensor) enables us to establish the concept of the energy of a structure of the HMS.

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