Iterated Unscented Kalman Filter for Passive Target Tracking

SINS (Strap-down Inertial Navigation System) and GPS (Global positioning system) integrated navigation system has been extensively applied in many areas. In-flight alignment (IFA) is one of the key technologies. In this paper, an iterative unscented Kalman filter (IUKF) for SINS/GPS integrated navigation system is proposed to achieve IFA approach. Firstly, the nonlinear error equation of SINS is established, and the difference between the position and velocity of the two navigation systems is taken as the observation variables. Then, an IUKF is proposed to minimize the truncation error caused by Taylor expansion and reduce the influence of initial state value on the system state. Finally, simulation results can prove that the IUKF improves the navigation precision and robustness of system compared with the counterpart of UKF.KeywordsIntegrated navigation systemIterative filterIn-flight alignment

The celestial navigation system is one of the important autonomous navigation system for spacecraft. The basic principle of it is using the extended Kalman filter (EKF) and the measurement of angle between celestial bodies estimate the position and velocity of spacecraft. But the EKF may not converge because of the inaccurate initial state. In this paper, a new Bayesian bootstrap filtering approach is used at the initial stage of the filtering interval to provide EKF with an accurate initial state to overcome the divergence problem. Simulation results demonstrated the high precision of orbit determination even in the presence of large initial states errors.

This study concerns the strapdown inertial navigation system (SINS) initial alignment under marine mooring condition with large initial error. The ten‐dimensional state initial alignment error functions of the SINS with inclusion of non‐linear characteristics have been derived. It is pointed out for the first time that the non‐linear functions are applied to only a subset of the elements of the state vector, that is, the velocities error and the misalignment angles. Then a computationally efficient refinement of the unscented transformation (UT) called marginalised UT (MUT) is investigated in these special non‐linear systems with a linear substructure. A performance comparison between the extended Kalman filter (EKF), the UT‐based Kalman filter (UKF) and the MUT‐based Kalman filter (MUKF) demonstrates that both the UKF and the MUKF can outperform the EKF and the MUKF and can achieve, if not better, at least a comparable performance to the UKF, at a significantly lower expense.

Passive location of the nonlinear systems with fuzzy uncertainty

This paper presents an innovative application of the particle filtering techniques to the vertical gyro problem, which is a highly nonlinear and non Gaussian recursive state estimation problem. The classical approach to recursive state estimation problem of nonlinear and/or non Gaussian systems is based on the extended Kalman filter (EKF), which is a heuristic method based on the linearization of the state dynamics and observations near a nominal path. Depending on the amount of nonlinearities and non Gaussian noise, the EKF often provides a solution far from acceptable. The vertical gyro is an instrument adopted to measure the tilt angles (pitch and roll) of an aircraft with respect to local vertical. It is composed by three orthogonal gyros that are used as process sensors and by three orthogonal accelerometers that are used as aiding sensors. The output of accelerometers is filtered using a proper low-pass filter to allow for the estimation of the local direction of the gravity vector that is assumed the same of the local vertical. In the application to the vertical gyro, Gordon's version of the particle filter was used. The relevant dynamical model is based on non-linear attitude rate equation using Euler angles rather than quaternions. The algorithm, developed in Matlab environment, was first calibrated and tested in simulations, obtaining very appealing performances. Subsequently, it was implemented using real data, acquired by means of an inertial unit produced by Crossbow <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> (model DMU-HDX <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> ), and its results were compared to those provided by the proprietary EKF embedded in the unit. First of all, stationary tests were performed. Sensor data were input to the particle filter that outputs the tilt angles (roll and pitch) with respect to the local geodetic reference. The results were compared to those provided by the internal EKF. Subsequently, the same operation was done using data that were acquired with moving platform. The accuracy of the filter was tested also for degraded operating conditions (lower data rates) and large initial errors. The main advantage of the methodology is that, while the internal filter works with 7 states (quaternions, biases and temperature), the particle filter ensures the convergence with 3 states, and provides acceptable performances with 1000 particles only, appearing promising for a real time application.

Mock circulatory loops (MCLs) have been widely used to test left ventricular assist devices. The hydraulic properties of the mock systemic arterial system are usually described by two alternative four-element windkessel (W4) models. Compared with three-element windkessel model, their parameters, especially the inertial term, are much more difficult to estimate. In this paper, an estimator based on the iterated unscented Kalman filter (IUKF) algorithm is proposed to identify model parameters. Identifiability of these parameters for different measurements is described. Performance of the estimator for different model structures is first evaluated using numerical simulation data contaminated with artificial noise. An MCL is developed to test the proposed algorithm. Parameter estimates for different models are compared with the calculated values derived from the mechanical and hydraulic properties of the MCL to validate model structures. In conclusion, the W4 model with an inertance and an aortic characteristic resistance arranged in series is proposed to represent the mock systemic arterial system. Once model structure is appropriately selected, IUKF can provide reasonable estimation accuracy in a limited time and may be helpful for future clinical applications.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

Wireless sensor networks can be used for the localization and tracking of moving targets. However, the range measurements are noisy and Kalman filters are frequently used to improve the tracking accuracy. Three different tracking algorithms, namely, a standard Kalman filter (SKF), an extended Kalman filter (EKF), and a modified Kalman filter (MKF) are empirically studied in terms of accuracy and latency for a range-based indoor tracking system. The experimental results show that the filtering techniques improve the tracking accuracy when the target is moving rapidly. However, different forms of Kalman filters introduce different levels of latency which affects the real-time tracking performance.

This paper presents four vision-based tracking system architectures for marine surface objects using a fixed-wing unmanned aerial vehicle (UAV) with a thermal camera mounted in a pan/tilt gimbal. The tracking systems estimate the position and velocity of an object in the North-East (NE) plane, and differ in how the measurement models are defined. The first tracking system measures the position and velocity of the target with georeferencing and optical flow. The states are estimated in a Kalman filter. A Kalman filter is also utilized in the second architecture, but only the georeferenced position is used as a measurement. A bearing-only measurement model is the basis for the third tracking system, and because the measurement model is nonlinear, an extended Kalman filter is used for state estimation. The fourth tracking system extends the bearing-only tracking system to let navigation uncertainty in the UAV position affect the target estimates in a Schmidt-Kalman filter. All tracking architectures are evaluated on data gathered at a flight experiment near the Azores islands outside of Portugal. The results show that various marine vessels can be tracked quite accurately.

Tracking a ballistic target in its reentry mode by considering the radar measurements is a highly complex problem in nonlinear filtering. Kalman Filter (KF) is used to estimate the position of target when the measurements are corrupted with noise. If the measurements are nonlinear (radar measurements) then Extended kalman filter (EKF) is used. For obtaining reliable estimate of the target state, filter has to be tuned before the operation which is offline. Tuning an EKF is the process of estimating the process noise covariance matrix (Q) and measurement noise covariance matrix (R). This paper presents a new method of tuning the EKF using different evolutionary algorithms.

This paper proposes a near range, low altitude, target detection, and passive tracking system using a narrow azimuth field of view (AFOV) infrared camera. The technology identifies and tracks infrared-emitting objects such as jet planes and helicopters. Such systems are passive, meaning they do not give out any radiation of their own, unlike radar, so the enemy can’t explore them. This system is used instead of surveillance radars as a gap filler to detect low-flying aircrafts penetrating gaps. Target tracking is often conflicted by the measurement noise and I.R. sensors’ uncertainty. The noise must be illuminated to predict the true path of a moving target. This research analyzes the accuracy of the Extended Kalman Filter (EKF) as a probabilistic prediction method for infrared visual tracking. Various simulations were examined, including maneuvering and non-maneuvering targets. The results show that the Kalman filter, in conjunction with two I.R. searcher cameras, successfully smoothed random deviations from the true path of the targets, enhancing the ability to predict the target trajectory.

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

In this paper, an algorithm of 3-D single observer passive location for fixed emitters based on the extended kalman particle filter (EPF) using the azimuth angle and its changing rate is proposed. EPF is a method of particle filter (PF) using the extended Kalman filter (EKF) as the importance function. The method obtains target emitter's position by the principle of kinematic geometry. The raw location results are rectified and smoothed by EPF algorithm to realize fast and high precision passive target's location. Simulation results show that the performance of algorithm based on EPF is better than EKF's has faster and steady convergence speed, better filtering effect and better location precision.

Object-Oriented Environment for Assessing Tracking Algorithms

Multiple object tracking is one field of study in vision-based navigation. Basically, in many current-research of this study, the common method in object tracking consists two main parts such as object detection and motion prediction, Object detection is highly related to the image processing which has a high tendency in using biggest part of computation resources. But, for the certain purpose, the computation resources should be used in proper way. In this paper, the problem will be limited in the case of football player tracking which needs so many computation resources for the image processing such the motion prediction algorithm that should be significantly reduced this need without decrease the system performance. In this paper, there will be explained the implementation of modified Hungarian algorithm and Kalman Filter as the main core of the motion prediction system in this case. Kalman Filter is the simplest algorithm for motion prediction, but in the case of multiple objects, there should be an additional computing to identify detected object before it will be tracked. Besides that, the system should have an ability to maintain object's identity in many worst case like occlusion, and boundary condition. In this paper, there also be explained the performance and consideration to increase system performance. In the highlight, the implementation result state that multiple point tracking module successfully being implemented as a part of fast multiple object tracking systems for football. The main indicator is identity maintainability which reaches 10% in 800 sample frames. Besides that, the computation parameter could be quantified using statistics that include the threshold value for data association is 2 meters per frame and 6 meters per frame for occlusion threshold. In the computational resources needs analysis, using worst case approximation, the system will need approximately 26 KB memory for computing in each frame. By this result, the conclusion is that the tracking system is proper to be implemented in football player tracking system both from the computation resources need and the performance.