Distributed Kalman filter for linear system with complex multi‐channel stochastic uncertain parameter and decoupled local filters

In the last few decades, the main problem which has attracted the attention of researchers in the field of aerial robotics is the position estimation or Simultaneously Localization and Mapping (SLAM) of aerial vehicles where the GPS system does not work. Aerial robotics are used to perform many tasks such as rescue, transportation, search, control, monitoring, and different military operations where the performance of humans is impossible because of their vast top view and reachability anywhere. There are many different techniques and algorithms which are used to overcome the localization and mapping problem. These techniques and algorithms use different sensors such as Red Green Blue and Depth (RGBD), Light Detecting and Range (LIDAR), Ultra-Wideband (UWB) techniques, and probability-based SLAM which uses two algorithms Linear Kalman Filter (LKF) and Extended Kalman filter (EKF). LKF consists of 5 phases and this algorithm is only used for linear system problems but on the other hand, EKF algorithm is also used for non-linear system. EKF is found better than LKF due to accuracy, practicality, and efficiency while dealing SLAM problem.

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Rapid SINS Two-Position Ground Alignment Scheme Based on Piecewise Combined Kalman Filter and Azimuth Constraint Information

Sensors ◽

10.3390/s19051125 ◽

2019 ◽

Vol 19 (5) ◽

pp. 1125 ◽

Cited By ~ 1

Author(s):

Lu Zhang ◽

Wenqi Wu ◽

Maosong Wang

Keyword(s):

Kalman Filter ◽

Linear System ◽

State Estimation ◽

Rate Of Convergence ◽

Inertial Navigation System ◽

Alignment Algorithm ◽

Time Consumption ◽

Performance Factors ◽

Constraint Information ◽

Time Invariant

The accuracy and rate of convergence are two important performance factors for initial ground alignment of a strapdown inertial navigation system (SINS). For navigation-grade SINS, gyro biases and accelerometer offsets can be modeled as constant values during the alignment period, and they can be calibrated through two-position ground alignment schemes. In many situations for SINS ground alignment, the azimuth of the vehicle remains nearly constant. This quasi-stationary alignment information can be used as an augmented measurement. In this paper, a piecewise combined Kalman filter utilizing relative azimuth constraint (RATP) is proposed to improve the alignment precision and to reduce the time consumption for error convergence. It is presented that a piecewise time-invariant linear system can be combined into a whole extended time-invariant linear system so that a piecewise combined Kalman filter can be designed for state estimation. A two-position ground alignment algorithm for SINS is designed based on the proposed piecewise combined Kalman filter. Numerical simulations and experimental results show its superiority to the conventional algorithms in terms of accuracy and the rate of convergence.

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On kalman filter for linear system with colored measurement noise

Journal of Geodesy ◽

10.1007/s00190-014-0751-7 ◽

2014 ◽

Vol 88 (12) ◽

pp. 1163-1170 ◽

Cited By ~ 27

Author(s):

Guobin Chang

Keyword(s):

Kalman Filter ◽

Linear System ◽

Measurement Noise

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Fusion of Redundant Aided-inertial Sensors with Decentralised Kalman Filter for Autonomous Underwater Vehicle Navigation

Defence Science Journal ◽

10.14429/dsj.65.8874 ◽

2015 ◽

Vol 65 (6) ◽

pp. 425 ◽

Cited By ~ 1

Author(s):

Vaibhav Awale ◽

Hari B. Hablani

Keyword(s):

Kalman Filter ◽

Inertial Navigation System ◽

Autonomous Underwater Vehicle ◽

Inertial Sensors ◽

Global Estimate ◽

Autonomous Operation ◽

System A ◽

Filter Approach ◽

Local Filters ◽

Navigation Information

<p class="p1">Most submarines carry more than one set of inertial navigation system (INS) for redundancy and reliability. Apart from INS systems, the submarine carries other sensors that provide different navigation information. A major challenge is to combine these sensors and INS estimates in an optimal and robust manner for navigation. This issue has been addressed by Farrell1. The same approach is used in this paper to combine different sensor measurements along with INS system. However, since more than one INS system is available onboard, it would be better to use multiple INS systems at the same time to obtain a better estimate of states and to provide autonomy in the event of failure of one INS system. This would require us to combine the estimates obtained from local filters (one set of INS system integrated with external sensors), in some optimal way to provide a global estimate. Individual sensor and IMU measurements cannot be accessed in this scenario. Also, autonomous operation requires no sharing of information among local filters. Hence a decentralised Kalman filter approach is considered for combining the estimates of local filters to give a global estimate. This estimate would not be optimal, however. A better optimal estimate can be obtained by accessing individual measurements and augmenting the state vector in Kalman filter, but in that case, corruption of one INS system will lead to failure of the whole filter. Hence to ensure satisfactory performance of the filter even in the event of failure of some INS system, a decentralised Kalman filtering approach is considered.</p>

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Vehicle tracking using fractional order Kalman filter for non-linear system

International Conference on Computing, Communication & Automation ◽

10.1109/ccaa.2015.7148423 ◽

2015 ◽

Cited By ~ 2

Author(s):

Harpreet Kaur ◽

J. S. Sahambi

Keyword(s):

Kalman Filter ◽

Linear System ◽

Fractional Order ◽

Vehicle Tracking ◽

Non Linear ◽

Non Linear System

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A new numerical method for 1-D backward stochastic differential equations without using conditional expectations

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2030 ◽

2020 ◽

Vol 28 (2) ◽

pp. 79-91

Author(s):

Aissa Sghir ◽

Sokaina Hadiri

Keyword(s):

Kalman Filter ◽

Linear System ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Numerical Method ◽

Extended Kalman Filter ◽

Backward Stochastic Differential Equations ◽

Conditional Expectations ◽

Non Linear System ◽

Reference Trajectories

AbstractIn this paper, we propose a new numerical method for 1-D backward stochastic differential equations (BSDEs for short) without using conditional expectations. The approximations of the solutions are obtained as solutions of a backward linear system generated by the terminal conditions. Our idea is inspired from the extended Kalman filter to non-linear system models by using a linear approximation around deterministic nominal reference trajectories.

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Simplified Federated Filtering Algorithm With Different States in Local Filters

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4002071 ◽

2010 ◽

Vol 133 (1) ◽

Author(s):

Guoliang Liu ◽

Jian Xie ◽

Shizuo Yan ◽

Wenyi Qiang

Keyword(s):

Kalman Filter ◽

Kalman Filtering ◽

Navigation Systems ◽

Integrated Navigation ◽

Transition Matrices ◽

Filtering Algorithm ◽

Federated Kalman Filter ◽

Federated Filtering ◽

Local Filters ◽

Computation Load

In this paper, to reduce the computation load of federated Kalman filters, a simplified federated filtering algorithm for integrated navigation systems is presented. It has been known that the per-cycle computation load grows roughly in proportion to the number of states and measurements for a single centralized Kalman filter. Hence, the states that have poor estimation accuracies are removed from local filters, so that the per-cycle computation load is reduced accordingly. Local filters and master filter of the federated Kalman filter may have different states, so the transition matrices are required to combine the outputs from the local filters and the master filter properly and to reset the global solution into the local filters and the master filter correctly. An experiment demonstrates that the proposed algorithm effectively reduces the computation load, compared with the standard federated Kalman filtering algorithm.

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