Mamoun F. Abdel-Hafez

Observability of an integrated GPS/INS during maneuvers

An observability analysis of a GPS/INS system during manoeuvers is presented based upon a perturbation model with respect to the Earth-centered-Earth-fixed (ECEF) coordinate system. Analysis is performed on two types of manoeuvers, linear acceleration and steady turn. These manoeuvers could be used for in-flight INS alignment using GPS. During the constant linear acceleration without rotation relative to the Earth, the linear system model is shown to be time-invariant. The observability analysis for the time invariant linear system model shows that linear acceleration does not change the number of observable modes but rather the structure of the observable space. For a nonconstant linear acceleration or a steady turn, the perturbation linear system becomes time varying. For this time-varying system, three types of observability are considered, complete, differential, and instantaneous observability. Instantaneous observability is the strongest properties and means that the state of the system at any time may be determined instantaneously from observation of the output and its derivatives. Instantaneous observability is important for fast in-flight INS alignment. It is shown that the number of instantaneously observable moded is increased by at least 2 during a maneuver. Hence, some linear combinations of the attitude angles become instantaneously observable.

The Autocovariance Least-Squares Technique for GPS Measurement Noise Estimation

In this paper, the autocovariance least-squares (ALS) technique is proposed to estimate the Global Positioning System (GPS) pseudorange measurement noise-covariance matrix. The large GPS measurement noise magnitude can be attributed to signal interference, jamming , or other factors, such as signal multipath. The proposed method makes use of the dynamics of the system measured by an inertial measurement unit (IMU) and the propagated residual of a GPS/IMU estimation filter to form a bank of statistics used to estimate the GPS measurement noise covariance. The method is used along an ultratightly coupled GPS/IMU filter to first estimate the measurement noise covariance matrix and then use this covariance matrix to obtain a high-accuracy and high-integrity state estimate. Simulated scenarios of different levels of noise magnitude are applied, and the proposed method is used to estimate the GPS pseudorange noise-covariance matrix.

An Instrumentation System Applied to Formation Flight

As part of a NASA dryden autonomous formation flight program for improved drag reduction of multiple F/A-18 aircraft, a new instrument, the formation flight instrumentation system (FFIS), for the precise estimation of the relative position, velocity, and attitude between two moving aircraft without the aid of ground-based instruments, was developed. The FFIS uses a global position system (GPS) receiver and an inertial navigation sensor (INS) instrumentation package on each aircraft combined with a wireless communication system for sharing measurements between vehicles. An extended Kalman filter structure blends the outputs of each GPS/INS in a distributed manner so as to maximize the accuracy of the relative state estimates. Differential carrier phase GPS measurements are used to provide high accuracy relative range measurements to the filtering algorithm. A multiple hypothesis Wald test for estimating the integer ambiguity between the two moving vehicles was developed as part of this project. The FFIS was tested in a hardware-in-the-loop simulation (HIL Sim) before being tested in actual F-18 flight tests. Test results validated the FFIS performance. Flight test results showed that the Wald test accurately estimates the integer ambiguity and that relative range estimates using least squares provide accurate position estimates with a mean of approximately 7 cm and a standard deviation of 13 cm

On the development of an inertial navigation error-budget system

Abstract This paper targets the development of an inertial navigation error-budget system for performance validation before actual field operation. The paper starts by studying the various errors that an inertial measurement unit (IMU) incorporates. A systematic approach of error modeling is proposed. The error models are integrated in time and added to the true measurement of the IMU to obtain the observed measurements. Simulation results are presented to show the contribution of the errors to the final measurement of the IMU. The IMU error model is blended with a GPS measurements’ model and the performance of a GPS/IMU extended Kalman filter (EKF) to IMU errors is shown. The simulated IMU errors are essential to study IMU quality effect on an inertial navigation systems (INS) state estimate accuracy.

Real-Time Implementation of GPS Aided Low-Cost Strapdown Inertial Navigation System

This work details the study, development, and experimental implementation of GPS aided strapdown inertial navigation system (INS) using commercial off-the-shelf low-cost inertial measurement unit (IMU). The data provided by the inertial navigation mechanization is fused with GPS measurements using loosely-coupled linear Kalman filter implemented with the aid of MPC555 microcontroller. The accuracy of the estimation when utilizing a low-cost inertial navigation system (INS) is limited by the accuracy of the sensors used and the mathematical modeling of INS and the aiding sensors’ errors. Therefore, the IMU data is fused with the GPS data to increase the accuracy of the integrated GPS/IMU system. The equations required for the local geographic frame mechanization are derived. The direction cosine matrix approach is selected to compute orientation angles and the unified mathematical framework is chosen for position/velocity algorithm computations. This selection resulted in significant reduction in mechanization errors. It is shown that the constructed GPS/IMU system is successfully implemented with an accurate and reliable performance.

Detection of Bias in GPS Satellites' Measurements: A Probability Ratio Test Formulation

A sequential and multihypothesis probability ratio test is proposed for detecting and identifying a bias fault in GPS pseudorange measurements. Initially, a measurement residual variable that is only a function of the measurement noise and the possible bias fault is constructed. The probability of this residual given a certain bias hypothesis is then obtained. Subsequently, an error variable is constructed for each hypothesis based on the ratio of the probability of that hypothesis to the probability of a base hypothesis. The propagation of the error variables with time is monitored for all hypotheses. If a hypothesis is associated with the true bias on the satellite measurement, then the corresponding error variable will remain around zero in mean. Otherwise, in case of a wrong hypothesis, the associated error variable will diverge away from zero. Error bounds for declaring false hypotheses are formulated in this brief. The advantage of the proposed method is that false hypotheses are continuously removed from the hypothesis set when their error variables exceed the error bound. Therefore, the size of the hypothesis set will reduce with time, ending up with only the correct bias hypothesis. This will result in a monotonic reduction in the computational time of the method. Finally, an ultratightly coupled filter structure is used to test the performance of the proposed method and the obtained results will be presented.

Enhancement in Li-Ion Battery Cell State-of-Charge Estimation Under Uncertain Model Statistics

Accurate battery state-of-charge (SOC) estimation in real time is desired in many applications. Among other methods, the extended Kalman filter (EKF) allows for high-accuracy real-time tracking of the SOC. However, an accurate SOC model is needed to guarantee convergence. Additionally, knowledge of the statistics of the process noise and the measurement noise is needed for high-accuracy SOC estimation. In this paper, two methods, namely, the multiple-model EKF (MM-EKF) and the autocovariance least squares technique, are proposed for estimating the SOC of lithium-ion (Li-ion) battery cells. The first method has the advantage of minimizing the EKF algorithms dependence on the correct assumptions of the measurements noise statistics, thus, minimizing the impact of model mismatch. The MM-EKF assumes a number of hypotheses for the unknown measurement noise covariance. An EKF is assigned for each assumed measurement noise covariance. The SOC estimate is then obtained by probabilistically summing up the estimates of the hypothesized EKFs. On the other hand, the second method assumes that the measurement noise is unknown and determines its value from the statistics of the EKF. Given an initial and possibly wrong assumption of the measurement noise covariance, the method accounts for possible correlation in the measurement innovations. The estimated measurement noise covariance is subsequently used to obtain an optimal SOC estimate. The proposed methods are evaluated and compared with the conventional EKF method on experimental test data obtained from a 3.6-V Li-ion battery cell.

Optimization of Intelligent Approach for Low-Cost INS/GPS Navigation System

Due to the inherent highly nonlinear vehicle state error dynamics obtained from low-cost inertial navigation system (INS) and Global Positioning System (GPS) along with the unknown statistical properties of these sensors, the optimality/accuracy of the classical Kalman filter for sensor fusion is not guaranteed. Therefore, in this paper, low-cost INS/GPS measurement integration is optimized based on different artificial intelligence (AI) techniques: Neural Networks (NN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) architectures. The proposed approaches are aimed at achieving high-accuracy vehicle state estimates. The architectures utilize overlapping windows for delayed input signals. Both the NN approaches and the ANFIS approaches are used once with overlapping position windows as the input and once with overlapping position and velocity windows as the input. Experimental tests are conducted to evaluate the performance of the proposed AI approaches. The achieved accuracy is presented and discussed. The study finds that using ANFIS, with both position and velocity as input, provides the best estimates of position and velocity in the navigation system. Therefore, the dynamic input delayed ANFIS approach is further analyzed at the end of the paper. The effect of the input window size on the accuracy of state estimation is also discussed.

Attitude and Flapping Angles Estimation for a Small-Scale Flybarless Helicopter Using a Kalman Filter

Unmanned aerial helicopters are essential for use in environments that are inaccessible for fixed wing aerial vehicles. Flybarless helicopters are famous for their high agility and maneuverability, which makes them suitable platforms in many challenging applications. This paper is concerned with the problem of estimating the attitude and flapping angles of a flybarless, small-scale, single-rotor helicopter. This paper utilizes a nonlinear model for the Maxi Joker 3 helicopter. A dynamic-model-based Kalman filter is designed and implemented to estimate both the attitude and the flapping angles of the helicopter. Results of a simulation scenario are shown to validate the performance of the proposed approach. The results demonstrate high-accuracy flapping angles estimation with errors not exceeding, |Amax|,0.3° in longitudinal flapping angles and 0.1° in lateral flapping angles. An experimental test is also conducted to demonstrate the performance of the method.

Non-Linear Autoregressive Delay-Dependent INS/GPS Navigation System Using Neural Networks

Autoregressive neural network fusion architecture is presented for low-cost global positioning system (GPS) and inertial measurement unit (IMU) measurements integration. The proposed intelligent fusion architecture is a non-linear method that takes into account the variable delay between GPS measurement epochs. This delay is due to possible operation of the GPS/IMU integrated system in urban canyon environments. To verify the performance of the proposed method, a simulation environment is constructed. In the simulation environment, the vehicle’s truth model is known and GPS/IMU measurements are simulated with a number of GPS measurements outages. The performance of the proposed fusion architecture is evaluated against the truth state of the vehicle. Subsequently, the proposed method is used in an experimental setup to estimate the state of a vehicle that is driven through a number of chosen paths. The performance of the fusion architecture is compared against a commercial off-the shelf solution.