18-Geom-B2 Satellite Navigation · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2015 — 3 hours, closed book (approved Casio/Sharp non-programmable calculators only). NINE questions: Q1–Q7 are mandatory (80 marks) and the candidate answers one of Q8/Q9 (20 marks) for a total of 100. This is a theory paper — answers are in essay form, with one short symbolic derivation (Q4 double differencing) and one counting problem (Q5, measurements vs unknowns). All nine questions, including both Q8 and Q9, are solved below for completeness.
Reference texts: Hofmann-Wellenhof, Lichtenegger & Wasle, GNSS — Global Navigation Satellite Systems (Springer, 2008); Leick, Rapoport & Tatarnikov, GPS Satellite Surveying (4th ed., Wiley, 2015); Kaplan & Hegarty, Understanding GPS/GNSS: Principles and Applications (3rd ed., Artech House); Groves, Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems (2nd ed., Artech House, 2013) for Q9; Natural Resources Canada — Canadian Geodetic Survey (CSRS-PPP service, Canadian Active Control System). Canadian frame throughout (NAD83(CSRS), NRCan reference products).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Why integrate. An Inertial Navigation System (INS) built on an Inertial Measurement Unit (IMU) of accelerometers and gyroscopes is self-contained, high-rate and immune to jamming, but its errors drift unboundedly with time. GNSS is the opposite: bounded, absolute accuracy but low-rate and prone to outages and interference. Fusing them — almost always through a Kalman filter that estimates and corrects the INS error states with GNSS aiding — gives a navigation solution that is high-rate, continuous and bounded. The three strategies differ in where in the processing chain the two sensors are combined.
Loosely-coupled.
The GNSS receiver produces its own position/velocity solution, which is fed as measurements into a Kalman filter alongside the INS-derived position/velocity; the filter estimates the INS errors and feeds corrections back. It is the simplest and most modular architecture (the GNSS receiver and INS are independent black boxes) and easy to implement. Its limitation is that the GNSS solution requires at least four satellites; when fewer are visible (urban canyon, foliage) the aiding drops out entirely, and two cascaded filters (receiver + integration) can interact. Sensors: a stand-alone GNSS receiver output plus an IMU. Applications: general-purpose vehicle, marine and aerial navigation, mobile mapping and UAVs where the sky is mostly open.
Tightly-coupled.
The raw GNSS measurements — pseudoranges and Doppler (and carrier phase) — are fed directly into a single integration filter, which also predicts those same measurements from the INS position; the filter works in measurement (range) space. Because it uses individual satellite measurements, it can still aid the INS when fewer than four satellites are available, since even one or two ranges constrain the drift. It is more robust in poor geometry and partial obstruction, at the cost of greater complexity and the need for the receiver’s raw observables and a common time base. Sensors: IMU plus a GNSS receiver providing raw pseudorange/Doppler/carrier observables. Applications: land-vehicle navigation in urban canyons, precise mobile mapping and airborne survey where signal obstruction is frequent.
Deeply- (ultra-tightly-) coupled.
Integration reaches inside the GNSS receiver: the INS-derived velocity is used to aid the receiver’s code and carrier tracking loops (Doppler aiding), narrowing the tracking-loop bandwidth so the receiver can hold lock on weak or dynamic signals; the tracking-loop outputs in turn feed the integration filter. This closed coupling gives the greatest robustness in high dynamics, weak-signal and jamming/interference environments, but is the most complex and requires access to the receiver’s internal correlators. Sensors: IMU tightly interfaced to the GNSS receiver’s baseband/tracking hardware. Applications: high-dynamic and defence platforms — guided munitions, agile aircraft and missiles — and any environment with strong interference where maintaining signal lock is the priority.
Summary of the trade. Moving from loose to tight to deep increases the robustness and the ability to operate with degraded or contested signals, but also increases complexity and the level of access required into the GNSS receiver. The choice is dictated by the operating environment: open-sky mapping is well served by loose coupling; obstructed urban work by tight; high-dynamics or jamming-prone military work by deep.