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18-Geom-B2 Satellite Navigation · December 2014

Question 7 of 9: Multipath Error and Its Mitigation

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Exams, December 2014 — 3 hours, closed book (approved Casio/Sharp non-programmable calculators only). NINE questions: questions 1–7 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 two short symbolic derivations (Q2 DOP, Q4 double differencing). 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); 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) for Q9; Natural Resources Canada — Canadian Geodetic Survey (CSRS-PPP service, Canadian Active Control System). Canadian frame throughout (NAD83(CSRS), NRCan reference products).

Question 7: Multipath Error and Its Mitigation (10 marks)

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.

What multipath is. Multipath is the error caused when a satellite signal reaches the antenna not only along the direct line of sight but also via one or more reflected paths — from the ground, water, buildings, vehicles or other surfaces near the antenna. The reflected replicas arrive slightly delayed and phase-shifted and combine with the direct signal, distorting the correlation peak the receiver tracks and biasing the measured range.

groundantennaSVdirect (true ρ)buildingreflected (multipath, extra path Δρ)
Multipath: the antenna receives the direct signal plus one or more reflected replicas from nearby surfaces; the delayed, phase-shifted reflections distort the tracked correlation peak and bias the measured range.

Multipath affects the code (pseudorange) far more than the carrier phase: code multipath can reach several metres (tens of metres in severe reflective environments), whereas carrier-phase multipath is limited to a few centimetres (at most a quarter-wavelength, ≈ 5 cm on L1). Crucially, multipath is site- and antenna-specific: it is uncorrelated between separate stations, so — unlike the atmosphere or clocks — it does not cancel in differential or double-differenced positioning. It is often the limiting error source in high-precision static work.

Mitigation measures.

No single measure eliminates multipath entirely; good site selection combined with a choke-ring antenna, an appropriate mask angle, and a modern multi-frequency receiver reduces it to the level acceptable for precise surveying.