Standard Kalman Filter Algorithm Research Articles

State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

State space model representation is widely used for the estimation of nonobservable (hidden) random variables when noisy observations of the associated stochastic process are available. In case the state vector is subject to constraints, the standard Kalman filtering algorithm can no longer be used in the estimation procedure, since it assumes the linearity of the model. This kind of issue is considered in what follows for the case of hidden variables that have to be non-negative. This restriction, which is common in many real applications, can be faced by describing the dynamic system of the hidden variables through non-negative definite quadratic forms. Such a model could describe any process where a positive component represents “gain”, while the negative one represents “loss”; the observation is derived from the difference between the two components, which stands for the “surplus”. Here, a thorough analysis of the conditions that have to be satisfied regarding the existence of non-negative estimations of the hidden variables is presented via the use of the Karush–Kuhn–Tucker conditions.

Trajectory tracking analysis of airborne data link antenna

With the development of weapons and equipment and changes in combat concepts, airborne data links have become more and more widely used in war communications. Whether their system performance is stable and reliable has gradually become a key indicator for measuring the combat effectiveness of the Air Force. This article mainly introduces the airborne data link to provide graphical information for combatants, solves the problem that people’s information cannot be shared synchronously, expands the transmission scale of data information, and greatly improves the situational awareness of the battlefield. This paper mainly studies the link between the airborne data link between the computer and the aircraft, and makes a substantial analysis of the trajectory tracking, which is helpful for the combatants to be familiar with the trajectory direction and internal structure, and provide clear trajectory information for the fighters Interpretation, you can see at a glance the graphics, and the information obtained by the combatants is consistent. This paper mainly uses the standard Kalman filter algorithm to study the basic characteristics of the target ballistic group motion, and based on the HLA-simulated development of GBR radar integration and completed the system test to verify the accuracy of the simulation signal processing. The experimental results of this paper show that the information acquisition rate of combatants under the airborne data link has been increased by 40%, and the consistency of simultaneous information acquisition has been improved by 90%. This is the future development direction of the theater.

Acoustic Robust Velocity Measurement Algorithm Based on Variational Bayes Adaptive Kalman Filter

Acoustic Doppler velocity logs or acoustic Doppler current profilers, herein referred to as Doppler sonar, are important types of oceanographic instruments, which have been extensively used over the past 30 years. The precision of Doppler sonar is an important technical specification, which is a statement of velocity random error that partially or entirely averages out over a long period of time. This article focuses on acoustic robust velocity processing algorithm based on variational Bayes adaptive Kalman (VBAK) filter, known as the real-time estimation of velocity statistical characteristics, which may be contaminated by some unknown and nonstationary noise. It aims to solve the problem that the precision of the Doppler sonar is prone to be affected by the marine environment. The theory, simulation, and experimental results are compared with the standard Kalman filter algorithm. It shows that the VBAK algorithm may obtain a reasonable estimate of velocity even in the case of steep slope over 15° and the precision is effectively improved.

Measured accuracy improvement method of velocity and displacement based on adaptive Kalman filter

PurposeThis paper aims to investigate the effect of unknown noise parameters of Kalman filter on velocity and displacement and to enhance the measured accuracy using adaptive Kalman filter with particle swarm optimization algorithm.Design/methodology/approachA novel method based on adaptive Kalman filter is proposed. Combined with the displacement measurement model, the standard Kalman filtering algorithm is established. The particle swarm optimization algorithm fused with Kalman is used to obtain the optimal noise parameter estimation using different fitness function.FindingsThe simulations and experimental results show that the adaptive Kalman filter algorithm fused with particle swarm optimization can improve the accuracy of the velocity and displacement.Originality/valueThe adaptive Kalman filter algorithm fused with particle swarm optimization can serve as a new method for optimal state estimation of moving target.

State of Charge Estimation for Lithium-Ion Battery in Electric Vehicle Based on Kalman Filter Considering Model Error

The state of charge (SOC) is one of the crucial states for battery management. The Kalman filter (KF) family algorithms are promising for SOC estimation. Based on the KF theory, a sufficiently accurate system model is the precondition for a better performance of the algorithm. Thus, we manage to improve the algorithm by estimating the battery model error. In this paper, the sources that may cause model errors are analyzed. Then, in order to estimate the unknown error term, the bias term characterizing the model error is adjoined to the original state vector to form a new state vector, and the KF is utilized to estimate the new state vector. It is a joint estimation algorithm for both SOC and the model error. Subsequently, by decoupling this joint estimation algorithm, a battery model error observer has been built. Finally, to verify the robustness of the proposed method against the battery model error, different types of errors such as open circuit voltage drift and voltage sensor drift are injected. The results indicate that the improved SOC estimation algorithm has better robustness and accuracy against the model mismatch compared with the standard KF algorithm.

A Novel Laser ranging method based on adaptive Kalman filter technology

AbstractAiming at the problem of ranging accuracy of laser radar, a laser ranging method based on adaptive Kalman filter is proposed. According to the pulsed laser ranging method and acceleration model based on Wiener process, the standard Kalman filter algorithm is established. In order to solve the problem that the statistical characteristics of laser ranging noise are inconsistent with the actual noise, the autocovariance least squares method is used to estimate the noise parameters. The Monte Carlo method is used to simulate ranging results of laser radar and evaluate the performance of different methods. The adaptive Kalman filtering algorithm using autocovariance least squares method can better adjust the noise parameters and improve the distance measurement accuracy than the traditional Kalman filter algorithm. The experiment of the actual static ranging is carried out. The experiment results show that the SD of laser ranging is reduced from 10.9 to 4.8 mm by using proposed method.

Investigation of optical current transformer signal processing method based on an improved Kalman algorithm

This paper explores the problem of signal processing in optical current transformers (OCTs). Based on the noise characteristics of OCTs, such as overlapping signals, noise frequency bands, low signal-to-noise ratios, and difficulties in acquiring statistical features of noise power, an improved standard Kalman filtering algorithm was proposed for direct current (DC) signal processing. The state-space model of the OCT DC measurement system is first established, and then mixed noise can be processed by adding mixed noise into measurement and state parameters. According to the minimum mean squared error criterion, state predictions and update equations of the improved Kalman algorithm could be deduced based on the established model. An improved central difference Kalman filter was proposed for alternating current (AC) signal processing, which improved the sampling strategy and noise processing of colored noise. Real-time estimation and correction of noise were achieved by designing AC and DC noise recursive filters. Experimental results show that the improved signal processing algorithms had a good filtering effect on the AC and DC signals with mixed noise of OCT. Furthermore, the proposed algorithm was able to achieve real-time correction of noise during the OCT filtering process.

An Improved GPS Dynamic Positioning Filtering Algorithm

According to the characteristics of the GPS receiver, this paper introduces an improved GPS positioning system filtering algorithm. Firstly, this paper establishes the state equation of the system according to the motor carrier's "current" statistical model, and then we establishes the measurement equation of the system based on the characteristics that GPS receiver can output the location and speed information, and lastly we get a standard Kalman filter algorithm model and a detailed description of the derivation of the algorithm. Algorithm simulation results show that the improved algorithm can greatly improve accuracy.

Recurrent neural network and extended Kalman filter in SLAM problem

The work presented in this paper is aimed at evaluating of the systematic bias error in mathematical model of mobile robot on the process of simultaneous localization and mapping during navigation in unknown environment. We have developed approach using a recurrent neural network and extended Kalman filter. Simulation results show that the proposed algorithm is very effective compared with standard Kalman filter algorithm and adaptive algorithm based on Kalman filter and feedforward neural network. Moreover, the proposed algorithm enables a non-constant biased error in vehicle model.

Square Root Iterative Filter: Theory and Applications to Econometric Models

This paper provides a new algorithm for estimating state space dynamic models and, as an example, it considers the estimation of time-varying parameter models. The novel elements of the algorithm are: a simple, easily implementable, square root method which is shown to solve the numerical problems affecting the standard Kalman filter algorithm and the related information filter and smoothing algorithms;an iterative framework, where information and covariance filters and smoothing are sequentially run in order to estimate all the parameters of the model; four different algorithms to consistently estimate the distribution of the estimated parameters, which are described and then compared by performing appropriate Montecarlo experiments.

Two algorithms for parameter estimation in groundwater flow problems

Abstract Groundwater movement is often described by equations based on Darcy's law and the equation of continuity. These equations contain a number of lumped parameters, representing the properties of the soil. These parameters are not known and have to be estimated from field measurements (e.g., pumping tests) or from calculations. In this paper the situation is considered that groundwater movement can be described by one lumped parameter. Two algorithms are developed to estimate that parameter. Both are based upon an optimal-state estimation with a standard Kalman filter algorithm. The two algorithms are applied to an example with generated data. The estimation methods may be extended to cases with more than one parameter.

Kalman filtering with no a priori information about noise--White noise case: Identification of covariances

Kalman filtering in the presence of white process and measurement noises having unknown means and covariances is considered. Only stationary linear discrete stochastic systems are considered. It is shown that the identification of noise covariances can be done without the knowledge of noise means. This means that the problem of identifying the noise statistics can be decomposed into two separate subproblems, namely, 1) identification of noise covariances and 2) identification of noise means, and that these two subproblems can be solved in that order. A procedure for identifying noise covariances is developed in this paper. It is a nontrivial extension of Mehra's results to the case where the process and measurement noises have unknown means, and are correlated with each other. This procedure, like Mehra's, can be used either in a nonrecursive mode, or in a batch-recursive mode. Solution of subproblem 2), and the standard Kalman filter algorithm are not discussed since they are well known in the literature.