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Processing of GNSS signals from more than one frequency band enhances the accuracy and integrity of a position solution in both standalone and differential positioning. The modern GPS program and newly launched GNSS systems such as GALILEO, BeiDou allow civilians to access signals from multiple frequencies in the L-band spectrum. While there are some advantages in triple-frequency processing in carrier phase applications, in general most of the standalone kinematic receivers get benefit from dual-frequency signals for ionosphere error correction. In implementing a dual-frequency receiver, it is necessary to select a combination of frequencies leading to an optimum performance of the existing civilian signals. In the current research work, we have analyzed the performance of dual-frequency receiver in terms of combined signal observation noise, sensitivity and robustness using analytical models by taking the combination of GPS L1, L2C and L5 signals as an example. Further, we have investigated the benefits of common Doppler estimate-based two-frequency signal tracking to reduce the noise in linear combination of observations. Through analytical and experimental results, it is confirmed that the L1/L5 signal combination in GPS system has low observation noise, which is suitable to use in high accuracy and precise positioning applications using standalone dual-frequency receiver. Further, it is shown that common Doppler estimate-based dual-frequency signal tracking has improved receiver tracking loop performance in terms of observation noise and multipath in linear combination of observations and enhanced receiver sensitivity and robustness. In GPS system, L1/L5 signals processed using common Doppler estimate-aided two-frequency signal tracking architecture, it is possible to effectively mitigate ionosphere delay and other receiver observation errors, to achieve less than 1 m position accuracy using unambiguous code phase observations. Proposed analysis is applicable of finding an optimal two-frequency signal combination in multi-frequency GNSS system and suitable signal processing architecture to obtain high accuracy and precise ionosphere-free position solution using code phase observations in standalone dual-frequency receiver.

In traditional federated receiver, all the tracking channels work independently, and there is no interaction among them. However, in vectorized receiver, stronger channels aid others in their tracking. Such architecture makes a receiver to be of interest for positioning in urban canyons and harsh environments. On the other hand, the combination of GPS and GLONASS as the only augmented global constellations is utilized to increase the availability of the receivers which is defined as the percentage of the epochs with enough number of tracked satellites for solving the positioning equation. We report about the software implementation of a GPS-combined-GLONASS Vectorized Receiver (GGVR) and performance assessment of this architecture in signal attenuation and blocking incidents. We also compare the GGVR performance with a GPS-combined-GLONASS Federated Receiver (GGFR). Experimental tests in different case studies are included. The results show that in the static blocking situation, the GGVR can reacquire the signal immediately after the momentary outage while the GGFR must return to acquisition stage. For two dynamic case studies, one in a suburban road and one in an urban canyon, the position results on the road are the same, but in an urban environment, the GGFR has only 88% availability in contrast to 100% availability of the GGVR.

Snapshot techniques are based on computing a position using only a set of digital signal samples captured over some milliseconds. Existing techniques require, in addition to the satellite ephemerides, a rough knowledge of the position and/or time at which the snapshot was captured. We propose a new method to instantaneously compute a snapshot position and time solution without any reference time or position. The method is based on the addition of a fifth unknown to the instantaneous Doppler equations, which accounts for a time difference between the reference time and the measurement time. Using this new system of equations at different initialization times separated by some hours, time uncertainties of days or weeks can be solved. The algorithm has been implemented in a snapshot GPS software receiver in MATLAB, proving that position accuracies of a few meters with time uncertainties of several weeks can be obtained in a few seconds.

This paper describes the main ideas of a GNSS SDR receiver and its implementation. Aims of the development, advantages, and some specific details are discussed. Particular attention is paid to the issue of security in GNSS receivers used for special purposes and some strategies of tracking. The idea of a snapshot receiver is briefly mentioned.

The first triangulation activity on Danish ground was carried out by the astronomer Tycho Brahe who resided on the island Hven. He wanted to determine the longitude difference of his observatory Uraniborg to Copenhagen. A by-product was a map of his island made in 1579. In 1761 the Royal Danish Academy of Sciences and Letters initiated a mapping project which should be based on the principle of triangulation. Eventually 24 maps were printed in varying scales, predominantly in 1:120 000. The last map was engraved in 1842. The Danish GradeMeasurement initiated remeasurements and redesign of the fundamental triangulation network. This network served scientific as well as cartographic purposes in more than a century. Only in the 1960s all triangulation sides were measured electronically. A combined least-squares adjustment followed in the 1970s

Geodetic networks can be described by discrete models. The observations may be height differences, distances, and directions. Geodesists always make more observations than necessary and estimate the solution by using the principle of least squares. Contemporary networks often contain several thousand points. This leads to so large matrix problems that one starts thinking of using continous network models. They result in one or more differential equations with corresponding boundary conditions. The Green’s function works like the covariance matrix in the discrete case. If we can find the Green’s function we also can study error propagation through large networks. Exactly this idea is exploited for error propagation studies in large geodetic networks. To solve the boundary value problems we have used the FEMLAB software. It is a powerful tool for this type of problems. The M-file was created by Daniel Bertilsson. Modifying the code is so simple that a student can do it. We demonstrate some results obtained this way.

This paper analyzes strengths and shortcomings of the existing aids for GNSS receiver development. A new set of tools is presented that provides to the developer debugging and optimization capabilities not supplied so far by existing tools. The proposed tools are simple and therefore very affordable, but never the less they are very functional. The first results are presented from the application of the proposed tools in a GNSS receiver debugging.

A receiver for the Global Positioning System (GPS) signals provides information on its position and time. The position is given in an Earth-Centered and Earth-Fixed coordinate system. This means that a static receiver keeps its coordinates over time, apart from the influence of measurement errors. The system time (GPST) counts in weeks and seconds of week starting on January 6, 1980. Each week has its own number. Time within a week is counted in seconds from the beginning at midnight between Saturday and Sunday (day 1 of the week). GPST is maintained within the system itself. Universal Time Coordinated (UTC) goes at a different rate which is connected to the actual speed of the rotation of the Earth. At present 14 seconds have to be added to UTC to get GPST. The GPS has 6 orbital planes with at least 4 satellites. At the moment GPS consists of 29 active satellites. They complete about 2 orbits/day. 1 The Transmitted GPS Signals Satellite positioning systems exploit Spread Spectrum (SS) techniques. SS came alive in 1980s and is popular for applications involving radio links in hostile environments. SS is an RF communications system in which the baseband signal bandwidth is intentionally spread over a larger bandwidth by injecting a higher-frequency signal. As a direct consequence, energy used in transmitting the signal is spread over a wider bandwidth and appears as noise. The ratio (in dB) between the spread baseband and the original signal is called processing gain. Typical SS processing gains run from 10 dB to 60 dB, see [1]. To apply an SS technique, simply inject the corresponding SS code somewhere in the transmitting chain before the antenna. That injection is called the spreading operation. The effect is to diffuse the information in a larger bandwidth. Conversely, you can remove the SS code by a despreading operation, at a point in the receive chain before data retrieval. The effect of a despreading operation is to reconstitute the information in its original bandwidth. Obviously, the same code must be known in advance at both ends of the transmission channel. In GPS, SS modulation is applied on top of a BPSK modulation, see below. Intentional or un-intentional interference and jamming signals are rejected because they do not contain the SS code. This characteristic is the real beauty of SS. Only the desired signal, which has the code, will be seen at the receiver when the despreading operation is exercised. In GPS the codes are digital sequences that must be as long and as random as possible to appear as “noise-like” as possible. But in any case, they must remain reproducible. Otherwise, the receiver will be unable to extract the message that has been sent. Thus, the sequence is “nearly random”. Such a code is called a pseudorandom number (PRN) or sequence. The PRN sequences applied in GPS are Gold sequences. These sequences are generated by feedback shift registers, and they are inserted at the data level. This is the direct sequence form of spread spectrum (DSSS). The PRN is applied directly to data entering the carrier modulator. All GPS satellites use the same carrier frequencies: On L1 1575.42 MHz and L2 1227.60 MHz. In a modernized GPS there will be a new civilian frequency L5 (then the military might remove L2 from civilian use). Each satellite has two unique spreading sequences or codes. The first one is the coarse acquisition code (C/A) and the other one is the encrypted precision code (P(Y)). The C/A code is a sequence of 1 023 chips. (A chip corresponds to a bit. It is simply called a chip to emphasize that it does not hold any information.) The code is repeated each ms giving a chipping rate of 1.023 MHz. The P code is a longer code ( . 2 35 10 : . chips) with a chipping rate of 10.23 MHz. It repeats itself each week starting at the beginning of the GPS week. The C/A code is only modulated onto the L1 carrier while the P(Y) code is modulated onto both the L1 and the L2 carrier. The purpose of PRN codes is twofold: They spread the signals and they provide for measuring the travel time between satellite and receiver. The system keeps all C/A code starts aligned in all active satellites. In the rest of this presentation we focus on the L1 signal. Each satellite transmits a continuous signal with at least three components: – a carrier wave with frequency f1 = 1575.42 = 154 × 10.23 MHz – an individual PRN code which is a sequence of −1 and +1 each of length 1 millisecond – a data bit sequence which carries information from which the satellite’s position can be computed. The length of one navigation bit is 20 milliseconds. The PRN code and the data bits are combined through modulo-2 adders. The result is modulated onto the carrier signal using the binary phase shift keying (BPSK) method: The carrier is instantaneously phase shifted by 180° at the time of a chip change. When a navigation data bit transition occurs, the phase of the resulting signal is also phase shifted 180°. So the signal transmitted from satellite k is ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) . s t P C t D t f t P P t D t f t P P t D t f t cos sin sin 2 2 2 2 2 2 k C k k L

The European navigation satellite system Galileo is moving ahead. We describe the open service signal L1 OS transmitted from the satellites. Compared to GPS some new features are introduced: Binary offset carrier modulation, coherent adaptive sub-carrier modulation, pilot signals, and tiered codes. These features make the GPS and Galileo signals live together on the same frequencies, and they make Galileo signals in general more robust

So far we have been dealing with absolute observations. By this we understand that for distance measurements the unit of length is exactly unity and for direction measurements all directions are measured relative to true north.

We describe the technique of block elimination. It is used for explaining Schreiber’s device. We use the technique to derive the equations for sequential least-squares problems. In so doing we derive the basic equations for the Kaiman filter. Finally we study the influence of changing the weight of observations. We bring a list of matrix identities as several steps rely on these.

Knowledge of the probability density function of the observables is not needed to routinely apply a least-squares algorithm and compute estimates for the parameters of interest. For the interpretation of the outcomes, and in particular for statements on the quality of the estimator, the probability density has to be known

In the spring of 1991 the first author conceived the plan of establishing a fundamental network in Lithuania by means of GPS. In July 1992 the financial support for the plan was provided. The Danish Government payed for GPS receivers, personal computers, and other materials needed while the Lithuanian Government agreed to subsidize the renovation of the survey ground marks, the observational campaign, and calculations.

Studies of error propagation in geodetic networks of an absolute type have already been carried through by several authors using various mathematical techniques. The geodetic elasticity theory relies on a continuation of the actual, discrete network. The traditional observation and normal equation matrices are substituted by partial differential equations with corresponding boundary conditions. The continuous approach only reflects the global error behaviour opposed to the discrete case, and produces only asymptotic results. An advantage of the method is that we may directly profit from existing mathematical knowledge. The fundamental solution of the partial differential equations acts as a formal covariance function and yields the best linear unbiased estimates for estimable functions of the adjustment parameters. Levelling networks and networks with distance and azimuth measurements are studied in this framework.

The geodetic elasticity theory is broadly outlined. It relies heavily on the structure matrix which mainly is defined as weight per area unit.