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.
Precise Point Positioning (PPP). PPP delivers high-accuracy absolute coordinates from a single dual-frequency receiver — no local base station and no reference network. The concept is to replace the broadcast orbit and clock (which limit ordinary single-point positioning) with precise satellite orbit and clock products, computed globally by the IGS (International GNSS Service) from a worldwide tracking network, and then to model every remaining error rigorously rather than differencing it away.
Because there is no second receiver, the satellite and receiver clock errors are not cancelled by differencing; instead PPP uses the ionosphere-free carrier-phase and code combination (removing the first-order ionosphere), estimates the residual tropospheric delay and the receiver clock as unknowns, and corrects the small deterministic effects that matter at the centimetre level — phase wind-up, satellite antenna phase-centre offsets, solid-Earth tides, ocean loading and relativity. The float carrier-phase ambiguities (or, with additional products, fixed integers) are estimated in a sequential (Kalman-filter) solution. PPP therefore needs a convergence period — typically tens of minutes — to separate the ambiguities from position, after which it reaches centimetre-to-decimetre accuracy. Its output is naturally in the global frame (ITRF) at the products’ epoch. In Canada this is offered operationally through NRCan’s CSRS-PPP online service, which returns NAD83(CSRS) or ITRF coordinates.
Network RTK. Network RTK extends single-base real-time kinematic positioning by using a network of permanent reference (CORS) stations instead of one base. A central processing facility continuously collects the reference-station data, fixes the network ambiguities, and models the spatially-correlated errors — distance-dependent ionosphere, troposphere and orbit — as a surface across the whole network. From this model it generates corrections tailored to the rover’s location, streamed to the rover over a mobile data link (NTRIP). Common realizations are the Virtual Reference Station (VRS), where the server synthesizes observations for a “virtual” base beside the rover, and area-correction approaches (MAC/MAX, FKP).
Because the distance-dependent errors are interpolated from many surrounding stations rather than a single base, Network RTK maintains centimetre accuracy over much larger inter-station spacings (tens of kilometres) than single-base RTK, with more uniform accuracy and faster, more reliable ambiguity fixing. It requires a subscription to a correction service and continuous communications. Canadian examples include provincial and commercial CORS networks that broadcast RTK corrections to subscribers.
Contrast. PPP is global, infrastructure-light (one receiver + downloadable products), absolute, but needs convergence time and gives its result in a global frame; Network RTK is regional, infrastructure-heavy (a CORS network + comms), relative to the network datum, but instantaneous and real-time. The emerging PPP-RTK/SSR approach blends the two — broadcasting state-space corrections that give PPP-like operation with RTK-like fast convergence.
