Instantaneous Ambiguity Reinitialization and Fast Ambiguity Initialization for L1-L2 GPS Measurements

This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines NL1 and NL2 ambiguities based on the ambiguity functions: Ψ(NL1)NL1NL2 and Ψ(NL2)NL2NL1. These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve NL1 and NL2 ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution (NL1, NL2). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation.

Meter of Two Angular Coordinates with a Space-Time Radiated Signal

The article describes the development of an algorithm of operation of a monopulse meter of two angular coordinates with two receiving channels with using complex space-time emitted signal. The azimuth of the target estimates by using the received space-time signals. The elevation estimates by using the phase monopulse method. Calculations of the Ambiguity Functions (AF) of space-time signals, their anal-ysis to identify the influence of the angular code on the form of AF and measuring precision of angular coordinates. The calculation of discriminating characteristics of the position angle and azimuth meters is performed.

The Myopic Property in Decision Models

We examine conditions under which decisions made in isolation provide an optimal strategy for the multiperiod problem. We focus on investment decisions with constant returns to scale. We first consider the framework of subjective expected utility. Under minimal assumptions (i.e., without assuming utility is concave), we prove that only log utility is myopically optimal when returns are serially correlated. When returns are serially independent, we generalize Mossin’s result [Mossin J (1968) Optimal multiperiod portfolio policies. J. Bus. 41(2):215–229.] that only log and power, including linear and convex, possess the myopic property. Finally, we extend the inquiry when probabilities are uncertain and the decision maker uses the recursive smooth model of ambiguity to identify an optimal strategy. We show that with serial correlation, preferences including ambiguity concerns cannot be myopic and optimal. Without correlation, we identify the exact pairs of utility and ambiguity functions that permit myopic decision rules.