Schuler himself genially but clearly warned here and there in his 1923 paper that he had not proved his principle, and indicated that the general proof was not within the range of his own limitations, thus inviting his readers to be critical of what amounted to interesting suggestions cheerfully offered. Professor Stratton's commentary (Journal, 21, 507), ‘The Schuler pendulum and inertial navigation’, by its scope, clearness and authenticity, could make effectual the remark that Schuler's calculation of acceleration is not correct except in one and the same great circle and possibly a few other special cases. Schuler jumps to the conclusion that it holds for any spherical motion, thus neglecting much of kinematics. The following standard analysis uses the moving trihedral and the intrinsic equations of ordinary differential geometry. There are many other methods having their own advantages.

In this paper, which was presented in a fuller version at an Ordinary Meeting of the Institute held in London on 20 December 1963, Mr. Kurz of the United States Maritime Administration and Mr. Bentkowsky and Captain Quinn, both of the Sperry-Piedmont Company, describe a control console for ships which was developed by the Sperry-Piedmont Company under contract from the Maritime Administration. The console, which has its sea trials early this year, comprises five sub-consoles which cater for navigation aids, communications-radar, steering, position plot, and ship condition. The paper enumerates the advantages that might be expected from such an arrangement.

There are occasions when, because of the density of shipping and/or lack of sea room, ships navigating by radar in thick weather cannot avoid passing within a distance of two miles, the least distance usually considered desirable. In such a situation a simple plan of procedure and of avoiding action, if possible to devise, should greatly reduce strain on the navigator and so increase the safety of navigation generally. Also, if such a plan came to be generally followed, safety would be further enhanced, because each navigator would know what the others were likely to do.

Recently I was asked to assist the engineers in my company (a Canadian electronics firm) devise a method for using radiation from the Sun to check the alignment of heavy ground radar sets to within very fine tolerances. The degree of accuracy would have to be better than five minutes of arc in azimuth for search antennas, and three minutes of arc in elevation angle for height finding antennas. Solar radiation in the microwave region of the radio frequency spectrum would be used as a reference. The antenna reflector would be rotated in azimuth and elevation until maximum solar radiation was reflected into the waveguide horn and thence to the radar receiver. The moment peak detector current was obtained, the antenna would be locked in position and the exact G.M.T. noted. Normal astro-navigation calculation methods and tables would then be used to calculate the Sun's true azimuth and elevation angle, which would be compared with that measured by the antenna to determine its accuracy.

Since none of the engineers had previous navigation experience, they had run into difficulties when they tried to devise a method for calculating the Sun's position to within the requisite accuracy limits.

The first difficulty was the fact that most antenna calibrations would be performed by field technicians having no knowledge of astro-navigation tables and calculation methods. They would be at extremely remote radar stations across Canada and thus would not have an opportunity to ask questions if our instructions proved ambiguous.

It has been acknowledged that the Doppler is beneficial to the GNSS positioning of smartphones. However, analysis of Doppler precision on smartphones is insufficient. In this paper, we focus on the characteristic analysis of the raw Doppler measurement from Android smartphones. A comprehensive investigation of the Doppler was conducted. The results illustrate that the availability of Doppler is stable and higher than that of carrier measurements, which means that the Doppler-smoothed code (DSC) method is more effective. However, there is a constant bias between the Doppler and the code rate in Xiaomi MI8, which indicates that extra processing of the DSC method is necessary for this phone. Additionally, it is demonstrated that the relationship between the Doppler and C/N0 can be expressed as an exponential function, and the fitting parameters are provided. The numerical experiment in car-borne and hand-held scenes was conducted for evaluating the performance of the Doppler-aided positioning algorithm. For positioning, the improvement reaches 37 ⋅ 69%/37 ⋅ 14%/26 ⋅ 61% in the east, north and up components, respectively, after applying the Doppler aiding. For velocity estimation, the improvement reaches 29 ⋅ 62%/39 ⋅ 63%/29 ⋅ 37% in the three components, respectively.

Mr. Bell and Professor Stratton have in the October Journal shed interesting light on the nature of inertial navigation as applied to navigation around a planet. It is a pity that Mr. Bell has repeated that in such inertial systems vehicle position and velocity are deduced from measurement of acceleration. This idea is certainly misleading so far as understanding error propagation in these systems is concerned, if not actually wrong.

Captain Wylie's extensive and detailed criticisms of the Sailing and Steering Rules in the new Collision Regulations (Journal, 26, 365) were published in the January number of Navigation, the journal of the French Institute of Navigation, with an editorial note by Professor Hugon. The note and Captain Wyile's reply are given below.

A simple scheme is presented for mapping the 2D probability density for an observer's position, defined by any number of lines of position (LOPs) on the surface of the Earth, assuming that the LOPs result from uncorrelated observations that have normally distributed errors. Although the mapping can be used to determine the position fix corresponding to the LOPs (which is consistent with other methods), its intended use is computing the total probability that the observer is located within (or outside) some specified area of interest, such as a zone of avoidance around a navigational hazard. Numerical experiments with areas where the average total interior probability is known, such as the triangles and polygons formed by nearly convergent LOPs, show that the method provides correct answers. The numerical experiments also revealed that theoretical probabilities associated with commonly used error ellipses are overstated for navigational solutions based on small numbers of LOPs.

The authors give a personal account of the use of astro navigation during the years before GPS became the primary aid for oceanic navigation. The paper also contains an account of the support provided by The Nautical Almanac (NA) together with its associated tables and computer programs which ease the tedium of sight reduction while leaving the satisfaction to be found in successful astro observations at sea.

An early version of Section 2 of this paper formed part of a presentation made at the Symposium After Longitude – Modern Navigation in Context which took place at the UK National Maritime Museum from 22–23 March 2012.

MR. J. A. Lee by his commentary (Journal, 22, 267) rightly suggests that instead of saying in my par. 1 (Journal, 21, 504), as I did after quoting Mr. Carr and Sq. Leader Scott, R.A.F. (Journal, 20, 406, sec. 2, par. 1) my words ‘—and from this deducing velocity and position of the vehicle,’ I could better have simply continued their words, ‘From this acceleration we can then, by successive mathematical integrations, deduce first velocity and secondly the displacement of the vehicle.’ Furthermore, it was superfluous and careless of me to add my quite worthless opinion as to soundness and virtue of expression on their part, but I comfort myself, and I hope also Mr. Lee, with the knowledge that there is no evidence that my opinions have ever previously had any effect whether for good or ill. To the extent, if any, that I can understand Mr. Lee's learned commentary, I believe I quite agree with him and am especially grateful for the clear definition given in his final sentence. If, however, an answer has been given to the question I raised as to the connection of Schuler's 1923 paper with inertial navigation, I am not presently aware of this.

It is generally accepted nowadays that, to obtain full value for anti-collision purposes from the use of radar by a ship proceeding in poor visibility, it is necessary to plot, or to compute in some other way, the raw data which may be obtained from the radar. It is also usually conceded that, for this to be done effectively in frequented areas, without the aid of mechano/electronic devices, a great deal of time and expertise is demanded from the radar observer and a great deal of responsibility thereby rests upon his shoulders.

To reduce the load of work and the possibility of human error and to give the observer more time to use his intelligence in appraising the situation and keeping it under review, radar engineers are already pressing forward the development of automatic devices which, in one way or another, produce computed informatioa in the form ultimately needed.

Many discussions have taken place regarding the feasibility of plotting when using radar in reduced visibility and it soon becomes apparent that there is confusion in what each of us considers by the term ‘plotting’.

These notes are to suggest definitions of the various stages of plotting and to consider the conditions under which each is necessary.

Radar plotting can be divided into three stages:

(a) Record plotting

(b) Deductive plotting

(c) Forecast plotting.

Reference to a chart of the Thames Estuary will show that the dominant feature of the submarine morphology is the series of elongated banks, of which the Barrow, Sunk and Long Sand are the most important. Between these banks, and with the same north-east to south-west trend, are the navigable channels of the Swin, Barrow and Black Deep (Fig. 1).

The alignment of the channels suggests that they originated as a result of tidal-stream scour of a fairly uniform sheet of fine silt and sand. In each tidal period, streams enter the estuary from the north and flow on the flood in a south-westerly direction parallel to the Essex coast. After about six hours they slacken, turn and flow out of the estuary in the reverse direction. This continuous flood and ebb stream action, with a maximum velocity varying from 2·3 to 2·9 knots depending on whether the tide is neap or spring, has apparently scoured out channels to depths which exceed 10 fathoms in places. If the channels largely arose in this way, the banks represent the modified remnants of the initial surface. These banks are constantly being extended seaward as more riverine silt is emptied into the estuary by the Thames, Medway and the rivers of Essex. The distal end of Long Sand alone has grown almost ½ mile in the past 100 years (see Figs. 1 and 4).

The collision avoidance of a pair of uniformly moving bodies is considered in three dimensions. The relative motion of the bodies yields an expression relating the time to closest approach, the minimum range, the current range and its rate of change, other variables being unobservable. A Boolean relation is then proposed that is satisfied whenever the minimum range and time to closest approach simultaneously fall below given thresholds. The relation is further studied, in particular with regard to the issue of false and premature alarms. An airborne collision avoidance system is a possible application.