Contact email:
ALeick@mtu.edu 



Alpha
GPS
& Geodesy offers online courses on the mathematical and geodetic
foundation of GPS/GNSS (Global Positioning System / Global
Navigation Satellite System). The depth of coverage and the
mathematical presentation provide the detailed knowledge
necessary to understand techniques and algorithms for positioning at
all levels of accuracy. These courses are available for
credit and noncredit
through Michigan Technological University (MTU). GNSS=f(GPS, GLONASS, Galileo, Beidou, QZSS, IRNSS, WAAS, EGNOS, GAGAN, MSAS, SDCM) 

Course Delivery
Students access the
courses via the CANVAS Learning Management System. The lecture
videos are
fully supported with graphics and audio. There
are many Mathcad solutions with audio that use real data to amplify
key topics. All
solutions are original implementations, including complete GPS
Precise Point Positioning and GPS baseline solutions using actual
pseudorange and carrier phase observations. Selected Mathcad
implementations,
i.e. worksheets with source code, are available to students for further experimentation and indepth development beyond
class requirements. There is no commercial GPS/GNSS or geodetic
software used.
Students’
progress and understanding of the material is assessed by multiple
choice tests. The test questions are in form of images which makes
it possible to incorporate mathematical expressions and graphics to address the details of the
material to be tested. Courses that are taken for credit require
additional laboratory work. 

Credit OptionsCourses labeled
GPS XXX are a unique series offered by Alpha GPS
&
Geodesy. They are available for noncredit, and anybody can enroll
at any time during the year. If enrollment takes place during a
regular MTU
semester, the course terminates at the end of the following
semester. There is an implicit understanding that students are familiar with
collegelevel calculus, statistics, and matrix operations. The students are free to decide how
much effort they wish to put into these courses. If a minimum total
score is achieved, a letter of completion can be requested. For registration
please check
GPSGAP Studies at
Michigan
Technological University. Courses labeled SU XXXX are available for credit through Michigan Technological University as part of the Integrated Spatial Technology MS Program. Students not currently enrolled at Michigan Technology University (MTU) can enroll as nondegree student to get college credit. Tuition, semester schedule, prerequisites, grading and other matters strictly follow MTU rules. For more information visit the MTU website. To register as a nondegree student at MTU please click here. Prior contact with the instructor is recommended. 

Textbook (all courses)
Alfred Leick, Lev Rapoport, Dmitry Tatarnikov 

Courses
GPS 101 Mathematics Refresher
(noncredit,
MTU, no course fee if taken concurrently with another GPS
XXX course): Real number systems and operations, basic functions,
linear algebra with emphasis on matrices, eigenvalues, eigenvectors,
differentiation, integration, elements of vector calculus, spherical
trigonometry, interpolation, solution of linear and nonlinear
equation systems, quadratic forms, minimization of multidimensional
functions, basic univariate distributions and functions thereof,
multivariate normal distribution.
GPS
401 Adjustments with Observation Equations
(noncredit,
MTU):
Errors, stochastic and mathematical models,
quadratic forms, linearization and variancecovariance propagation
of multidimensional nonlinear functions, leastsquares algorithm of
observation equations, position estimation using surveying and GPS
vector measurements that are nonlinear functions of parameters;
review of statistics and linear algebra. Equivalent of 1 Cr
GPS
402 Adjustment Algorithms
(noncredit,
MTU):
Error ellipses and ellipsoids, propagation of
estimated quantities, a priori information on parameters, adjustment
of implicitly related observations and parameters, mixed model,
condition equation model, sequential solutions, testing conditions
on nonlinear parametric functions. Equivalent of 1Cr. Recommended
prerequisite GPS 401.
GPS 403 Quality Control with Adjustments
(noncredit,
MTU):
Geometry of leastsquares, definition of
network coordinate systems, singularities, probability regions,
minimal and inner constraints, invariant quantities, multivariate
normal distribution, relevant statistical tests, type I/II errors,
internal and external reliability, absorption of errors, blunder
detection, decorrelation, inversion of patterned and large matrices,
numerical aspects; Kalman filtering. Equivalent of 1 Cr.
Recommended prerequisite GPS 401.
GPS 441 ThreeDimensional Geodetic Model
(noncredit,
MTU):
Conventional celestial and terrestrial
references frames, precession, nutation, polar motion, geodetic
datum, geoid, ellipsoid of revolution, geodetic coordinates, height
systems, 3D geodetic model and model observations, reduction of
observations, observation equations, partial derivatives, 3D network
adjustments, heightcontrolled 3D networks, GPS vector observations,
review of spherical trigonometry and spherical harmonic expansions.
Prerequisite: GPS 401, GPS 403, Equivalent of 1 Cr
Recommended prerequisite GPS 401.
GPS 442 Ellipsoidal Surface Model
(noncredit,
MTU):
Geodesic line on the ellipsoidal surface,
geodesic curvature, differential equations of the geodesic, direct
and inverse solutions, 2D network adjustment on the ellipsoidal
surface, partial derivatives, reduction of observations, traditional
horizontal and vertical networks in surveying and geodesy; indepth
review of differential geometry. Equivalent of 1 Cr.
Recommended prerequisite GPS 441.
GPS 443 Conformal Mapping Model
(noncredit,
MTU):
Conformal mapping of the ellipsoidal surface,
meridian convergence, point scale factor; State Plane Coordinate
systems, Transverse Mercator, Equatorial Mercator, Lambert Conformal
with one or two standard parallels, polar azimuthal, and UTM;
reduction of observations, computations on the conformal map and
relation to the surface of the earth; review of complex variables.
Equivalent of 1 Cr.
Recommended prerequisite GPS 401, 441.
GPS 490 GNSS Receiver Antennas
(noncredit,
MTU, instructor is D. Tatarnikov):
Basics of
electromagnetic waves, polarization, antenna angular response
pattern and gain, polarization properties of GNSS user antennas,
phase pattern, phase center variations and antenna calibrations,
carrier phase multipath, reflections from the underlying terrain,
antenna down/up ratio, basics of transmission lines, antenna
mismatch and frequency response, cable losses, noise propagation and
signaltonoise ratio. Equivalent of 1Cr
GPS 570 Fundamentals of Satellite Positioning
(noncredit,
MTU):
ITRF and ICRF references frames and
transformations, tectonic plate motions, precession, nutation, polar
motion, rotational and atomic time scales, GPS time, normal orbits,
Kepler's laws and equation, topocentric satellite motions,
visibility, perturbation of satellite orbits, solar radiation
pressure, impact of asymmetry of gravity field and earth's
flattening; GPS, GLONASS and Galileo satellite systems. Equivalent
of 1 Cr.
Recommended prerequisite GPS 401, 441.
GPS 571 Precise Point Positioning
(noncredit),
MTU:
Pseudorange and carrier phase observables,
satellite time, relativity, broadcast and precise ephemerides, range
iteration, receiver and satellite clock errors; singularities,
tropospheric refraction and absorption, impact of the ionosphere,
solid earth tides, ocean loading, satellite antenna offset, phase
windup correction, closed form solutions; Kalman filter; timing,
mapping of the spatial and temporal variation of the troposphere and
ionosphere. Equivalent of 1 Cr.
Recommended prerequisite GPS 401, 441, 570.
GPS 572 Precise Relative Positioning
(noncredit,
MTU):
Differencing observables in space and time,
commonmode error reduction, geometryfree solutions, widelaning,
closedform solutions, cycle slips, constraint solutions, integer
ambiguity estimation, LAMBDA, antenna calibration, multipath on
pseudoranges and carrier phases, spatial vector networks,
differential corrections, global data collection and maintenance,
GPS services. Equivalent of 1 Cr.
Recommended prerequisite GPS 401, 441, 571.
