Kalman Filter Enhancement for UAV Navigation

This paper proposes two methods to enhance traditional extended Kalman filter for UAV navigation. One is based on using fuzzy rules to choose parameters of an adaptive Kalman filter. The other uses inherent parallelism to speed up iterations in Kalman filter computations. Both methods are described briefly and simulation results are presented. INTRODUCTION Unmanned Aerial Vehicles (UAV), such as spacecraft, aircraft, helicopters, free-flying robots or mobile robots are increasingly applied in various domains, particularly in the military, scientific research, and in certain industries. Therefore it becomes crucial to optimize trajectories, motion, fuel consumption and other performance related aspects of UAVs. In navigation of a UAV, three mutually dependent issues need to be considered: • plan the path dependence on the known information, • determine the position and velocity of the vehicle, and • avoid the unexpected obstacles. In general, obstacles may not be fully known when we plan the path for the UAVs. In this case, the vehicle has to handle an event such as unexpectedly encountering some moving or static obstacles on its way and an original plan may no longer be executable in the new situation. This is especially important when the vehicle operates in the space environment for long periods of time, without frequent communications with the ground station. From this point of view, as well as because of the need of fault-tolerant operation, a new set of requirements emerges calling for autonomous operation of UAVs for long unattended periods of time. For this purpose, our group is currently developing an Autonomous Health Monitoring and Control System (AHMCS), based on the new concept of a High-Fidelity Dynamic Model-Based Simulation (HFDMS). It relies on the use of highly accurate dynamic models to replicate the behavior of the actual system [4]. Figure 1. Basic architecture of the control system. The basic architecture of the entire system is presented in Figure 1. Out of several layers of the control hierarchy, in this paper we consider only the lowest, monitoring layer. The essential function of the control system at this layer is to monitor both the state of the vehicle itself and the state of the actuators. When the vehicle has to change its original path, and revise its motion to achieve the collision-free path during navigation, the environment uncertainty and complexity is a key issue. The position and velocity of the vehicle can be determined, when navigating and guiding an autonomous vehicle, with the Global Positioning System (GPS). It is known, however, that several errors are associated with the GPS measurement [6]. It has superior long-term error performance, but poor short-term accuracy. For many vehicle navigation systems, GPS is insufficient as a standalone position system. actuator Conventional Real-Time Controller Plant Modeling Based Reasonning Nonlinear Robust Control Robust and Dynamic Fault Detection Module Real-time Nonlinear Estimation Optimal Filter Robust and Dynamic Fault Detection Module Real-time Nonlinear Estimation Optimal Filter Desired Objective Disturbances and Uncertainties To ensure high accuracy and fidelity of monitoring, which in principle means detecting any unexpected behavioral changes, in real time, we use Kalman filtering [2]. Kalman filtering is a form of optimal estimation characterized by recursive evaluation, and an internal model of the dynamics of the system being estimated. The dynamic weighting of incoming evidence with ongoing expectation produces estimates of the state of the observed system. We propose to enhance an extended Kalman filter in two ways. First, we apply fuzzy rules to the weighted Kalman filter to increase accuracy. Secondly, we apply parallelization to the extended Kalman filter to achieve high computational speed. In the next sections, we present the principles of both approaches and discuss the simulations. FUZZY ADAPTIVE KALMAN FILTER To ensure high accuracy and fidelity of monitoring, we use data fusion to combine measurements from GPS and Inertial Navigation System (INS). The integration of GPS and INS is ideal for vehicle navigation. In general, the shortterm accuracy of INS is good and the long-term accuracy is poor. The disadvantages of GPS/INS are ideally cancelled. If the signal of GPS is interrupted, the INS enables the navigation system to coast along until GPS signal is reestablished [1]. The requirements for accuracy, availability and robustness are therefore achieved. In this paper, a fuzzy logic adaptive system (FLAS) is used to adjust the exponential weighting of a weighted EKF and prevent the Kalman filter from divergence. The fuzzy logic adaptive controller (FLAC) will continually adjust the noise strengths in the filter’s internal model, and tune the filter as well as possible. The FLAC performance is evaluated by simulation of the fuzzy adaptive extended Kalman filtering scheme of Fig.2. The models and basic implementation equations for the weighted Kalman filter are shown below, for the nonlinear dynamic model and the nonlinear measurement model: where wk ~ N (0,Q) and vk ~ N (0, R). We assume model covariance matrices equal to: where, α≥1, and Q and R are constant matrices.. For α>1, as time k increases, the Rk and Qk decrease, so that the most recent measurement is given higher weighting [5]. If α=1, it is a regular EKF. Corrected position, velocity,etc Predicted measurements Estimated INS errors Pseudo-range