Matthew Lashley

Performance Analysis of Vector Tracking Algorithms for Weak GPS Signals in High Dynamics

This paper explores the ability of vector tracking algorithms to track weak Global Positioning System (GPS) signals in high dynamic environments. Traditional GPS receivers use tracking loops to track the GPS signals. The signals from each satellite are processed independently. In contrast, vector-based methods do not use tracking loops. Instead, all the satellite signals are tracked by a lone Kalman filter. The Kalman filter combines the tasks of signal tracking and navigation into a single algorithm. Vector-based methods can perform better than traditional methods in environments with high dynamics and low signal power. A performance analysis of the vector tracking algorithms is included. The ability of the algorithms to operate as a function of carrier to noise power density ratio, user dynamics, and number of satellites being used is explored. The vector tracking methods are demonstrated using data from a high fidelity GPS simulator. The simulation results show the vector tracking algorithms operating at a carrier to noise power density ratio of 19 dB-Hz through 2 G, 4 G, and 8 G coordinated turns. The vector tracking algorithms are also shown operating through 2 G and 4 G turns at a carrier to noise power density ratio of 16 dB-Hz.

A valid comparison of vector and scalar tracking loops

This paper analyzes the benefits offered by vector tracking loops relative to scalar tracking loops. A method for designing equivalent scalar and vector tracking loops is first introduced. The benefits of vector tracking are then determined by comparing the two equivalent algorithms. The improvements in signal tracking afforded by vector tracking are quantified in different scenarios using covariance analysis and Monte Carlo simulations. The vector tracking algorithms show a maximum improvement in tracking threshold of 6.2 dB with an eleven satellite constellation and a minimum improvement of 2.4 dB with a five satellite constellation. The results presented in this paper demonstrate the amount of improvement vector tracking can provide in different situations. Furthermore, the analysis technique used to design the equivalent tracking loops provides a simple way to compare other attributes of the algorithms, such as their multipath immunity and robustness.

Analysis of deeply integrated and tightly coupled architectures

This paper analyzes the impact that architectural features have on the performance of deeply integrated and tightly coupled algorithms. The effects of two specific architectural features are investigated. The first is the design of the Kalman filter used in the algorithms. The performance degradation caused by using a federated filtering architecture instead of a single, centralized filter is analyzed. The second feature is the usage of scalar and vector tracking loops. The advantage offered by vector tracking loops over scalar tracking loops is quantified. The effects of these two architectural features are determined by analyzing the comparative performance of three different algorithms. One algorithm uses a single Kalman filter to process the GPS signals and the inertial sensor data. The other two algorithms use a federated filtering architecture. One federated algorithm uses scalar tracking loops and the other uses vector tracking loops. Comparing the performance of the three algorithms allows the effects of filter design and tracking loop operation to be isolated. Covariance analysis and Monte Carlo simulations are used to study the performance of the algorithms with different inertial sensor grades and satellite constellations. The analysis reveals that the federated algorithm with vector tracking and the centralized filtering algorithm perform virtually identically. The federated algorithm with scalar tracking loops performs poorer. However, the performance of all three algorithms converge as the carrier to noise power density ratio declines. At low signal powers, all three algorithms provide identical performance. The results quantify how the architectural features of coupled systems affect their performance.

Impact of carrier to noise power density, platform dynamics, and IMU quality on deeply integrated navigation

In this paper, the authors investigate how the Carrier to Noise power density ratio (C/N0), platform dynamics, and differing Inertial Measurement Unit (IMU) quality affect the performance of Deeply Integrated (DI) algorithms. Two different DI algorithms are described in detail and analyzed using a high fidelity GPS simulator. The first algorithm is a Vector Delay/Frequency Lock Loop (VDFLL). The second algorithm is a Deeply Integrated GPS/INS system with differing grades of IMUpsilas. The ability of the algorithms to operate at low C/N0 levels and in high dynamics is investigated empirically with the GPS simulator. The VDFLL algorithm can successfully track the received GPS signals through 2 g, 4 g, and 8 g coordinated turns at 19 dB-Hz. Initial results of the Deeply Integrated GPS/INS algorithm show its operation through the 2 g, 4 g, and 8 g coordinated turn at 16 dB-Hz with a tactical grade IMU.

Comparison of Adaptive Estimation Techniques for Vector Delay/Frequency Tracking

In this paper, several adaptive estimation techniques are applied to a Vector Delay/Frequency Lock Loop (VDFLL) GPS navigation algorithm. The adaptive estimation techniques are used to detect platform maneuvers and to correct the VDFLL’s Kalman filter states for the platform maneuvers. Three different adaptive estimation algorithms are investigated. The first technique is process noise level adjustment. The second is the Variable State Dimension (VSD) approach. The third adaptive algorithm investigated is Input Estimation (IE). The three different techniques are compared through Monte Carlo simulations of a high dynamic flight profile. The mean squared error in the VDFLL’s Kalman filter states is used to determine which adaptive estimation technique performs best.

Split-gate tracking accuracy for phase coded CW radar

In this paper, a phase coded continuous wave (CW) radar system is analyzed. The motivation for the research was to accelerate tracking filter convergence. The main goal of the paper is to express the variance of the range errors as a function of signal to noise ratio and position in the split-gate region. Furthermore, the effect of different signal processing algorithms on the variance of the range errors is investigated. The effects of channel mismatch in the receiver and range gate spacing on the variance of the range errors are also included. Analytical equations that relate the variance of the range errors to signal to noise ratio (SNR) and position within the split gate region are derived using a Taylor series expansion. The analytical equations are consistent with a statistical analysis of a simulation of the radar system in MATLAB. The results of the work are the analytical equations for the variance of the range error as a function of SNR, range gate spacing, and channel mismatch for a split-gate tracker.