Simulated Kalman Filter Algorithm Research Articles

A Tutorial on Population-based Simulated Kalman Filter


 
 
 
 Simulated Kalman Filter (SKF) is an estimation-based optimization algorithm which is established based on the Kalman filtering framework. Even since the SKF algorithm is introduced in 2015, there is no tutorial been published on SKF. One may find that the equations and flowchart of the algorithm is not easy to understand. Hence, this paper provides a tutorial on SKF algorithm that emphasizes on a numerical example for easy and intuitive explanations. This tutorial would be important to those who work on the fundamentals and applications of SKF as well as to students who are new to optimization research.
 
 
 

Fitness-evaluated Adaptive Switching Simulated Kalman Filter Algorithm with Randomness


 
 
 
 The original Simulated Kalman Filter (SKF) is an optimizer that employs synchronous update mechanism. The agents in SKF update their solutions after all fitness calculations, prediction process, and measurement process are completed. An alternative to synchronous update is asynchronous update. In asynchronous update, only one agent does fitness calculation, prediction, measurement, and estimation processes at one time. A recent study shows that the asynchronous SKF outperforms synchronous SKF. In this study, synchronous and asynchronous mechanisms are combined in SKF. At first, the SKF starts with either synchronous or asynchronous update. By evaluating the fitness, if no improved solution is found, the SKF changes its update mechanism. The decision to switch from synchronous to asynchronous or vice versa is made randomly. Using the CEC2014 benchmark test suite, experimental results indicate that the proposed adaptive switching SKF randomness outperforms the original SKF algorithm.
 
 
 

Distance Evaluated Simulated Kalman Filter with State Encoding for Combinatorial Optimization Problems

Simulated Kalman Filter (SKF) is a population-based optimization algorithm which exploits the estimation capability of Kalman filter to search for a solution in a continuous search space. The SKF algorithm only capable to solve numerical optimization problems which involve continuous search space. Some problems, such as routing and scheduling, involve binary or discrete search space. At present, there are three modifications to the original SKF algorithm in solving combinatorial optimization problems. Those modified algorithms are binary SKF (BSKF), angle modulated SKF (AMSKF), and distance evaluated SKF (DESKF). These three combinatorial SKF algorithms use binary encoding to represent the solution to a combinatorial optimization problem. This paper introduces the latest version of distance evaluated SKF which uses state encoding, instead of binary encoding, to represent the solution to a combinatorial problem. The algorithm proposed in this paper is called state-encoded distance evaluated SKF (SEDESKF) algorithm. Since the original SKF algorithm tends to converge prematurely, the distance is handled differently in this study. To control and exploration and exploitation of the SEDESKF algorithm, the distance is normalized. The performance of the SEDESKF algorithm is compared against the existing combinatorial SKF algorithm based on a set of Traveling Salesman Problem (TSP).

Single-solution Simulated Kalman Filter algorithm for global optimisation problems

This paper introduces single-solution Simulated Kalman Filter (ssSKF), a new single-agent optimisation algorithm inspired by Kalman Filter, for solving real-valued numerical optimisation problems. In comparison, the proposed ssSKF algorithm supersedes the original population-based Simulated Kalman Filter (SKF) algorithm by operating with only a single agent, and having less parameters to be tuned. In the proposed ssSKF algorithm, the initialisation parameters are not constants, but they are produced by random numbers taken from a normal distribution in the range of [0, 1], thus excluding them from tuning requirement. In order to balance between the exploration and exploitation in ssSKF, the proposed algorithm uses an adaptive neighbourhood mechanism during its prediction step. The proposed ssSKF algorithm is tested using the 30 benchmark functions of CEC 2014, and its performance is compared to that of the original SKF algorithm, Black Hole (BH) algorithm, Particle Swarm Optimisation (PSO) algorithm, Grey Wolf Optimiser (GWO) algorithm and Genetic Algorithm (GA). The results show that the proposed ssSKF algorithm is a promising approach and able to outperform GWO and GA algorithms, significantly.

Adaptive Beamforming Algorithm Based on a Simulated Kalman Filter

Adaptive beamforming is a technique used to steer the radiation pattern towards the desired signal and cancel out any interference signal by finding the appropriate weights for every element in an array antenna, to achieve maximum signal to interference plus noise ratio (SINR). There are many methods to perform adaptive beamforming and one of the method is to use metaheuristic algorithm, to estimate the weights for individual elements in an array. Over the years, various metaheuristic algorithms have been applied to adaptive beamforming. Some of the metaheuristic algorithms have been modified from the original algorithms to improve the algorithms performance in adaptive beamforming application. A new metaheuristic algorithm named Simulated Kalman Filter (SKF), is inspired by the estimation capabilities of Kalman filter, has not been applied to adaptive beamforming application. Therefore, this research presents the first-time application of SKF algorithm to adaptive beamforming. The SKF algorithm, however, often converge prematurely at local optimum due to lack of exploration, preventing it from finding better solution. A modified version of the SKF algorithm, named Opposition-Based SKF (OBSKF), introduced by K. Zakwan, applies Opposition-Based Learning method to improve the exploration capabilities of SKF algorithm. Moreover, a new modified version of the SKF algorithm named SKF with Modified Measurement (SKFMM) is introduced to further improve the exploration capabilities of SKF algorithm by modifying the measurement-update equation. The SKF, OBSKF and SKFMM is applied to an array antenna with 10 elements arranged linearly with 0.5

PARAMETER-LESS SIMULATED KALMAN FILTER

Simulated Kalman Filter (SKF) algorithm is a new population-based metaheuristic optimization algorithm. In the original SKF algorithm, three parameter values are assigned during initialization, the initial error covariance, P(0), the process noise, Q, and the measurement noise, R. Further studies on the effect of P(0), Q and R values suggest that the SKF algorithm can be realized as a parameter-less algorithm. Instead of using constant values suggested for the parameters, this study uses random values for all three parameters, P(0), Q and R. Experimental results show that the parameter-less SKF managed to converge to near-optimal solution and performs as good as the original SKF algorithm. Keywords: Optimization, Simulated Kalman Filter, parameter-less

Simulated Kalman Filter: A Novel Estimation-Based Metaheuristic Optimization Algorithm

In this paper, a novel population - based metaheuristic optimization algorithm , which is named as Simulated Kalman Filter (SKF) , is introduced for global optimization problem . This new algorithm is inspired by the estimation capability of the well - known Kalman Filter. In principle, state estimation problem is regarded as an optimization problem and each agent in SKF acts as a Kalman Filter. An agent in the population finds solution to optimization problem using a standard Kalman Filter framewo rk, which includes a simulated measurement process and a best - so - far solution as a reference. To evaluate the performance of the SKF algorithm, it is applied to 30 benchmark functions of CEC 2014 for real - parameter single - objective optimization problems. S tatistical analysis is then carried out to rank SKF results to those obtained by other metaheuristic algo rithms. The experimental results show that the proposed SKF algorithm is a promising approach and able to outperform some well - known metaheuristic algo rithms , such as Genetic Algorithm, Particle Swarm Optimization, Black Hole Algor ithm, and Grey Wolf Optimizer.