Scientific Computing

Positive train control in dark territory

With the spectre of the Positive Train Control mandate looming over small railroads, it’s not only the short-line railroads impacted. Long-distance rural lines can have considerable dark territory. Such railroads may have substantial cost added to their capital budget by PTC. Without radio contact, such railroads have been limited in dark territory to restricted speed 10-25 mph instead of the 49 mph they might otherwise run in dark territory.

Possible solutions for radio contact in rural areas

  • microwave links - much too expensive for distance, terrain vs. low train count
  • leased (dedicated) phone line - same as microwave–too expensive
  • PSTN/POTS - use a typical “interconnect” for two-way radio.

The latter option may be much more economically feasible for many rural railroads. This option has not been evaluated for compliance with federal railroad regulations. Railroads in the Rocky Mountains, with vast individual tower coverage areas, have long used DTMF selective calling of dispatch to avoid dispatchers being overwhelmed with constant train chatter.

CONOPS of POTS-linked rural dark territory railroad radio: dispatch has multiple phone lines, all ringing for the same number dedicated to inbound radio calls. Different branches dispatched by distinct dispatchers could obviously have separate phone numbers. The caller ID of the individual interconnect into dispatch identifies the approximate subdivision the train is on (not for legal purposes but for convenience). Cell phones could be used in place of POTS if more economical.

Train to dispatch: train keys up mic, dials dispatch phone number like a standard two-way radio interconnect call. Train engineer uses standard radio message protocol to talk to dispatch, then train hangs up via DTMF. Can use single frequency for network to keep any other trains advised, although dark territory and long distances imply long blocks.

Dispatch to train: dispatch calls phone number of interconnect they believe train is in range of. Train engineer answers via DTMF, uses standard radio protocol to talk. Dispatch hangs up phone, train engineer sends DTMF to close link if phone line hangup not detected.

Besides the typical radio base station tower and antenna, selected with sufficient overlap in 49 mph-desired territory, the Zetron Model 30 is about $600. Cost of power and phone connection trenching might be mitigated by sharing with cellular towers or power utility company where feasible. Naturally, a more advanced interconnect could be used to control and monitor railroad switches and the like, also enhancing railway safety. In regions hauling relatively benign cargo with a single train per day, some in the industry have felt PTC requirements were too stringent. If it’s not too late, some waivers might be obtained for a time at least by using ideas as above, pending compliance with all applicable regulations.

HP50g vs. TI-89

I tried honestly to use the HP 50g, and here are a few objections that put me back to the TI-89. The low resolution (blocky/grainy) HP 50g display detracts from its usefulness as a high-end graphing calculator. Low resolution limits length of equations and number of equations on the screen. One of the major reasons for having a high-end calculator is to allow entering long equations on the screen.

That being said, the HP 50g has a dedicated core of aficionados. HP 50g advocates will present a list of counterpoints–and their arguments have merits.

Given the feature set and the inevitable eventual sunsetting of the 15+ year old TI-89 series, a new user considering what high-end calculator to purchase should look to the TI Nspire CX CAS.

In closing, I will give strong admonition to students. DO NOT rely heavily on calculators in math courses. This will only cause suffering in later courses. Even if the last math class in college will be Calculus I or II, you will never gain the true richness of understanding if constantly using a calculator for homework.

A better approach is to do the problems manually, and on occasion check with the calculator.

Solving problems of legacy Auroral video

Legacy auroral video acquisition has been plagued with several problems including

  1. camera sensitivity
  2. data storage
  3. video time synchronization
  4. software instability

An example of such a system was deployed last winter to Poker Flat Research Range. The results of this work won “Honorable Mention” at the CEDAR 2011 Workshop. A two camera system observed the aurora from Poker Flat Research Range (Chatanika, AK) and Ester, AK.

Notice the hardware synchronization connections on the camera are not being used. This makes the system reliant on the vagaries of software timing of the OS, which in Windows case can account for order 100 ms. When one wants 33 ms cadence video, this means such video will be roughly syntonized, but poorly synchronized.

Timing error due to non-hardware synchronization: error for a single frame, the error will accumulate in general due to error bias, quickly leading the cameras to be taking pictures at different times (no video frame overlap in time).

Error source Description Error magnitude [s]
camera FPGA Non-TCXO 100 ppm crystal timebase inside camera 10-6
PC time NTP error 10-3
software trigger Start time error due to SDK 10-1

The software trigger error is not predictable and can reach up to 1/2 second. Aurora has apparent motion of kilometers per second, and so a camera designed for 10..100 m scale width observations needs to have timing error commensurate with the physical phenomenon. Hopes of a tomographic solution are dashed if the pictures are taken at times distant enough such that the feature of interest changes on timescale less than the error.

imager block diagram

Observational Solution for Auroral Tomography: the ill-conditioned, ill-posed nature of the high-resolution auroral tomography problem dictates attention to detail of all aspects of cross-site registration. We will have to ensure:

  1. images are accurately registered.
  2. Absolute and relative timing are synchronized to at least 2 orders of magnitude better than the frame cadence (< 1 % timing error)
  3. If the data writing becomes overwhelmed, the system should discard a bit of video and recover rather than stutter the recording.

Notes

Plant, G., Semeter, J., Marshall, R., Dahlgren, H., Goenka, C., and Hampton, D. (2011). A high-speed tomographic imaging system for studying dynamic aurora. In Instruments or Techniques for Ionospheric or Thermospheric Observation. CEDAR Workshop, Santa Fe, NM. ITIT-06.

Mathematics of Auroral Viewing

When you view the aurora, whether by camera or by being outside with your eyes, what you see is a line integral of the line-of-sight brightness of the optically thin aurora. Mathematically, this is

I = ∫_0 ∞ p(ℓ) dℓ

where:

  • I is the intensity seen by your eye or camera pixel
  • p(ℓ) is the volume intensity rate of the aurora at each differential point along ℓ

Volume emission rate of aurora is created when particles (electrons or ions) strike the cold gas of the ionosphere, typically N_2, N_2+ or O. As altitude increases above a couple hundred kilometers, oxygen starts to become the dominant gas instead of nitrogen. This affects the color of the aurora, and is part of why aurora appears as green below red.

Unfortunately, many of the images taken of aurora with digital cameras have incorrect white balance, and completely non-physical colors are seen. Yes, there is purple aurora, but it is quite faint and below the green emissions in altitude. So a sky full of purple, yellow, and orange is not believable, it’s an artifact of incorrect white balance.

That’s a big part of why it’s good to save auroral photos in RAW format from your camera so you can fix the images in post-processing.

Mars Radar Sounder mission article list

Autofocus Correction of Phase Distortion Effects on SHARAD Echoes

GPR missions on mars

Mars high resolution Shallow Radar (SHARAD) for the MRO 2005 mission

SHARAD design and operation

SHARAD, a shallow radar sounder to investigate the red planet

Subsurface Radar Sounding of the Jovian Moon Ganymede

SolarSystem2012: The Planetary Science Decadal Survey

The SHAllow RADar (SHARAD) Onboard the NASA MRO Mission

Satellite Radar Calibration article list

Martian Surface Reflectivity seen by MARSIS

Mars Express Scientific Overview After One Martian Year in Orbit

The SHAllow RADar (SHARAD) Experiment, a subsurface sounding radar for MRO

Analysis of spacecraft antenna systems: Implications for STEREO/WAVES

MARSIS Ionospheric Calibration

MARSIS Calibration Plan

Calibration of the SHARAD Instrument

MARSIS, a radar for the study of the Martian subsurface in the Mars Express mission

MARSIS Data Inversion Approach

Analysis of spacecraft antenna systems: Implications for STEREO/WAVES

RHEOMETRY: calibration of spacecraft via scale model

Cassini model rheometry

Radar Sounding of Mars with MARSIS

An exploratory survey of the attenuation of radio signals by the ionosphere of Mars

In-flight calibration of the Cassini-Radio and Plasma Wave Science (RPWS) antenna system for direction-finding and polarization measurements

Wire-grid modeling of Cassini spacecraft for the determination of effective antenna length vectors of the RPWS antennas

Analysis of sounding antennas of the Mars express MARSIS experiment

Simulation of a surface-penetrating radar for Mars exploration

Radio Wave Propagation Handbook for Communication on and Around Mars

MARSIS Subsurface Measurements article list

A simple inversion model for the estimation of subsurface features of Mars poles

Applying non-iterative phase errors compensation method to restore radar subsurface image

Exploring the Martian subsurface of Athabasca using MARSIS radar data:

Fast radar signal simulator for SAR ground penetrating applications

GLRT-detection performance in subsurface sounding

GPR Missions on Mars

(MARSIS): subsurface performances evaluation

Mars ionosphere data inversion by MARSIS surface and subsurface signals analysis

Mars surface models and subsurface detection performance in MARSIS

Radar Soundings of the Subsurface of Mars

Radar subsurface sounding over the putative frozen sea in Cerberus Palus, Mars

Subsurface sounding in Northern hemisphere for Mars by MARSIS: Mars express mission

Subsurface sounding of Mars: multi-pulse detection of water-related interfaces

Surface echo reduction by clutter simulation, application to the Marsis data

Surface echo reduction by clutter simulation, Application to the Marsis data

The subsurface investigation by (MARSIS)

Subsurface Investigations by MARSIS in Mars Express Mission

Subsurface imaging method (SSIM) based on phase compensation of radar echoes

Structure of the basal unit of the North Polar Plateau of Mars, from MARSIS

The subsurface investigation by Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS)

Radio-Transparent Deposits in the Elysium Region of Mars as Observed by MARSIS and SHARAD Radar Sounders

MARSIS Antenna characterization article list

The Lightweight Deployable Antenna for the MARSIS Experiment on the Mars Express Spacecraft

Analysis of Sounding Antennas of the Mars Express MARSIS Experiment

Analysis of the Lenticular Jointed MARSIS Antenna Deployment

MARSIS antenna flight deployment anomaly and resolution.

MARSIS antenna deployment testing and analysis

Various methods of calibration of the STEREO/WAVES antennas

Numerical Computation of Radar Echoes Measured by MARSIS During Phobos Flybys

MARSIS: Mars Advanced Radar for Subsurface and Ionosphere Sounding (SP-1240)

The System and Implementation aspects of MARSIS

Probing the Subsurface of Mars with MARSIS on Mars Express

Surface εr reconstruction of Phobos

MARSIS at Phobos: Real Data Processing Compared with Simulations Results

MARS EXPRESS AND MARSIS

Mars Express Science Overview

An Inflatable L-band Microstrip SAR Array

RECENT ADVANCES IN RADAR TECHNOLOGY AND TECHNIQUES FOR AFFORDABLE PLANETARY REMOTE SENSING

Numerical Computation of Radar Echoes Measured by MARSIS During Phobos Flybys

Various methods of calibration of the STEREO/WAVES antennas

MARSIS expected results

Radar signal simulation: Surface modeling with the Facet Method

Mars and Venus the Express Way

THE DIGITAL ELECTRONIC SUBSYSTEM OF MARSIS

MARSIS Ionospheric Measurements article list

MARSIS Ionospheric measurements:

An exploratory survey of the attenuation of radio signals by the ionosphere of Mars

An Imaging HF GPR Using Stationary Antennas:

Areas of enhanced ionization in the deep nightside ionosphere of Mars 

Attenuation of radio signals by the ionosphere of Mars (withers)

Comparison between MARSIS & SHARAD results

Dayside ionosphere of Mars: Empirical model based on data from the MARSIS instrument 

Doppler analysis for data inversion and image processing in the MARSIS experiment

Doppler analysis for data inversion and image processing in the MARSIS experiment 

Dual-spacecraft observation of large-scale magnetic flux ropes in the Martian ionosphere 

Electromagnetic Features of Ground Penetrating Radars for the Exploration of Martian Subsurface

EMI in orbiting sounding radar from ripple in solar arrays

Exploring the Martian subsurface of Athabasca using MARSIS radar data

GPR Missions on Mars

In situ observations of the ionized environment of Mars: the antenna impedance measurements

Ionosphere compensation and stepped frequency processing in the MARSIS experiment

Mars Express: The Scientific Payload

Mars Ionosphere preliminary impact analysis on SHARAD radar signal

MARSIS Data Inversion Approach

MARSIS data inversion approach: Preliminary results

MARSIS Radar Signal Simulation

Modeling the Configuration of HF Electrical Antennas for Deep Bistatic Subsurface Sounding

Nightside ionosphere of Mars: Radar soundings by the Mars Express spacecraft 

Overlapping ionospheric and surface echoes observed by the Mars Express radar sounder near the Martian terminator 

Radar subsurface sounding over the putative frozen sea in Cerberus Palus, Mars

Sharad Design and Operation

Sounding Data with SHARAD & MARSIS

Subsurface sounding in Northern hemisphere for Mars by MARSIS: Mars express mission

The Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS): concept and performance

The Mars express MARSIS sounder instrument

Transterminator ion flow in the Martian ionosphere 

Two years of MARSIS observations

Electron densities in the upper ionosphere of Mars from the excitation of electron plasma oscillations

Dayside Induced (akalin)

Radar Absorption due to a corotating interaction region encounter with Mars detected by MARSIS

An Overview of Radar Sounding of the Martian ionosphere from the Mars Express spacecraft