Triangulation, Trilateration, or Multilateration? (EE Tip #125)

Local Positioning System (LPS) and GPS (not just the US system) both use several transmitters to enable a receiver to calculate its geographical position. Several techniques are possible, each with its advantages and drawbacks. The important thing in all these techniques is the notion of a direct path (line of sight, or LoS). In effect, if the transmitter signal has not taken the shortest path to the receiver, the distance between them calculated by the receiver will be incorrect, since the receiver does not know the route taken by the radio signal.

Three mathematical techniques are usually used for calculating the position of a receiver from signals received from several transmitters: triangulation, trilateration, and multilateration. The last two are very similar, but should not be confused.

Triangulation

Triangulation (Figure 1) is a very ancient technique, said to date from over 2,500 years ago, when it was used by the Greek philosopher and astronomer Thales of Miletus to measure (with surprising accuracy) the radius of the Earth’s orbit around the Sun.

Triangulation

Figure 1—Triangulation: you are at A, from where you can see B and C. If you know their geographical positions, you can find your own position with the help of a compass.

It allows an observer to calculate their position by measuring two directions towards two reference points. Since the positions of the reference points are known, it is hence possible to construct a triangle where one of the sides and two of the angles are known, with the observer at the third point. This information is enough to defi ne the triangle completely and hence deduce the position of the observer.

Using triangulation with transmitters requires the angle of incidence (angle of arrival, or AoA) of a radio signal to be measured. This can be done using several antennas placed side by side (an array of antennas, for example, Figure 2) and to measure the phase difference between the signals received by the antennas.

Antenna array

Figure 2—An antenna array makes it possible to measure the angle of incidence of a radio signal, and hence its direction.

If the distance between the antennas is small, the incident front of the signal may be considered as straight, and the calculation of the angle will be fairly accurate. It’s also possible to use a directional antenna to determine the position of a transmitter. The antenna orientation producing the strongest signal indicates the direction of the transmitter. All you then have to do is take two measurements from known transmitters in order to be able to apply triangulation.

Trilateration

This technique requires the distance between the receiver and transmitter to be measured. This can be done using a Received Signal Strength Indicator (RSSI), or else from the time of arrival (ToA)—or time of flight (ToF) Figure 3—of the signal, provided that the receiver and transmitter are synchronized — for example, by means of a common timebase, as in GPS.

Arrival time

Figure 3—The length of the arrows corresponds to the arrival time at receiver P of the signals broadcast by three transmitters A, B, and C. It forms a measurement of the distances between the transmitters and the receiver.

Thus, when receiving a signal from a single transmitter, we can situate ourselves on a circle (for simplicity, let’s confi ne ourselves to two dimensions and ideal transmission conditions) with the transmitter at the center. Not very accurate. It gets better with two transmitters — now there are only two positions possible: the two points where the circles around the two transmitters intersect. Adding a third transmitter enables us to eliminate one of these two possibilities (Figure 4).

Trilateration

Figure 4—2-D trilateration. In 3-D, another transmitter has to be added in order to determine a position unambiguously.

When we extend trilateration to three dimensions, the circles become spheres. Now we need to add one more transmitter in order to fi nd the position of the receiver, as the intersection of two spheres is no longer at two points, but is a circle (assuming we ignore the trivial point when they touch). This explains why a GPS needs to “see” at least four satellites to work.

Multilateration

Using a single receiver listening to the signals (pulses, for example) from two synchronized transmitters, it is possible to measure the difference between the arrival times (time difference of arrival, or TDoA) of the two signals at the receiver. Then the principle is similar to trilateration, except that we no longer fi nd ourselves on a circle or a sphere, but on a hyperbola (2D) or a hyperboloid (3D). Here too, we need four transmitters to enable the receiver to calculate its position accurately.

The advantage of multilateration is that the receiver doesn’t need to know at what instant the signals were transmitted—hence the receiver doesn’t need to be synchronized with the transmitters. The signals, and hence the electronics, can be kept simple. The LORAN and DECCA systems, for example, work like this.—Clemens Valens, “Geolocalization without GPS,” Elektor, February 2011.

Wireless Data Links (Part 2): Transmitters and Antennas

If you built your own ham radio “back in the day,” you’ll recall the frustration of putting it together with components that were basic at best.

But as columnist George Novacek points out in the second installment of his series examining wireless data links: “Today you can purchase excellent, reasonably priced low-power gear for data communications off the shelf.”

Transmitter and receiver

Photo 1: SparkFun Electronics’s WRL-10524 transmitter and WRL-10532 receiver are low cost, basic, and work well.

Part 2 of Novacek’s series, appearing in the March issue, looks at transmitters and antennas.

In one section, Novacek expands upon the five basic data-transmitter modules—a data encoder, a modulator, a carrier frequency generator, an RF output amplifier, and an antenna:

Low-power data transmitters often integrate the modulator, the carrier frequency generator, and the amplifier into one circuit. A single transistor can do the job. I’ll discuss antennas later. When a transmitter and a receiver are combined into one unit, it’s called a transceiver.

Modulation may not be needed in some simple applications where the mere presence of a carrier is detected to initiate an action. A simple push button will suffice, but this is rarely used as it is subject to false triggering by other transmitters working in the area in the same frequency band.

Digital encoder and decoder ICs are available for simple devices (e.g., garage door openers) or keyless entry where just an on or off output is required from the receiver. These ICs generate a data packet for transmission. If the received packet matches the data stored in the decoder, an action is initiated. Typical examples include Holtek Semiconductor HT12E encoders and HT12D decoders and Freescale Semiconductor MC145026, MC145027, and MC145028 encoder and decoder pairs. For data communications a similar but more advanced scheme is used. I’ll address this when I discuss receivers (coming up in Part 3 of this series).

Novacek’s column goes on to explain modulation types, including OOK and ASK modulation:

OOK modulation is achieved by feeding the Data In line with a 0-to+V-level  datastream. ASK modulation can be achieved by the data varying the transistor biasing to swing the RF output between 100% and typically 30% to 50% amplitude. I prefer to add a separate modulator.

The advantage of ASK as opposed to OOK modulation is that the carrier is always present, thus the receiver is not required to repeatedly synchronize to it. Different manufacturers’ specifications claim substantially higher achievable data rates with ASK rather than OOK.

For instance, Photo 1 shows a SparkFun Electronics WRL-10534 transmitter and a WRL-10532 receiver set for 433.9 MHz (a 315-MHz set is also available), which costs less than $10. It is a bare-bones design, but it works well. When you build supporting circuits around it you can get excellent results. The set is a good starting point for experimentation.

The article also includes tips on a transceiver you can purchase to save time in developing ancillary circuits (XBee), while noting a variety of transceiver, receiver, and transmitter modules are available from manufacturers such as Maxim Integrated, Micrel, and RF Monolithics (RFM).  In addition, the article discusses design and optimization of the three forms of antennas: a straight conductor (monopole), a coil (helical), and a loop.

“These can be external, internal, or even etched onto the PCB (e.g., keyless entry fobs) to minimize the size,” Novacek says.

Do you need advice on what to consider when choosing an antenna for your design?  Find these tips and more in Novacek’s March issue article.

Wireless Data Links (Part 1)

In Circuit Cellar’s February issue, the Consummate Engineer column launches a multi-part series on wireless data links.

“Over the last two decades, wireless data communication devices have been entering the realm of embedded control,” columnist George Novacek says in Part 1 of the series. “The technology to produce reasonably priced, reliable, wireless data links is now available off the shelf and no longer requires specialized knowledge, experience, and exotic, expensive test equipment. Nevertheless, to use wireless devices effectively, an engineer should understand the principles involved.”

Radio communicationsPart 1 focuses on radio communications, in particular low-power, data-carrying wireless links used in control systems.

“Even with this limitation, it is a vast subject, the surface of which can merely be scratched,” Novacek says. “Today, we can purchase ready-made, low-power, reliable radio interface modules with excellent performance for an incredibly low price. These devices were originally developed for noncritical applications (e.g., garage door openers, security systems, keyless entry, etc.). Now they are making inroads into control systems, mostly for remote sensing and computer network data exchange. Wireless devices are already present in safety-related systems (e.g., remote tire pressure monitoring), to say nothing about their bigger and older siblings in remote control of space and military unmanned aerial vehicles (UAVs).”

An engineering audience will find Novacek’s article a helpful overview of fundamental wireless communications principles and topics, including RF circuitry (e.g., inductor/capacitor, or LC, circuits), ceramic surface acoustic wave (SAW) resonators, frequency response, bandwidth, sensitivity, noise issues, and more.

Here is an article excerpt about bandwidth and achieving its ideal, rectangular shape:

“The bandwidth affects receiver selectivity and/or a transmitter output spectral purity. The selectivity is the ability of a radio receiver to reject all but the desired signal. Narrowing the bandwidth makes it possible to place more transmitters within the available frequency band. It also lowers the received noise level and increases the selectivity due to its higher Q. On the other hand, transmission of every signal but a non-modulated, pure sinusoid carrier—which, therefore, contains no information—requires a certain minimum bandwidth. The required bandwidth is determined by the type of modulation and the maximum modulating frequency.

“For example, AM radios carry maximum 5-kHz audio and, consequently, need 10-kHz bandwidth to accommodate the carrier with its two 5-kHz sidebands. Therefore, AM broadcast stations have to be spaced a minimum of 20 kHz apart. However, narrowing the bandwidth will lead to the loss of parts of the transmitted information. In a data-carrying systems, it will cause a gradual increase of the bit error rate (BER) until the data becomes useless. At that point, the bandwidth must be increased or the baud rate must be decreased to maintain reliable communications.

“An ideal bandwidth would have a shape of a rectangle, as shown in Figure 1 by the blue trace. Achieving this to a high degree with LC circuits can get quite complicated, but ceramic resonators used in modern receivers can deliver excellent, near ideal results.”

Figure 1: This is the frequency response and bandwidth of a parallel resonant LC circuit. A series circuit graph would be inverted.

Figure 1: This is the frequency response and bandwidth of a parallel resonant LC circuit. A series circuit graph would be inverted.

To learn more about control-system wireless links, check out the February issue now available for membership download or single-issue purchase. Part 2 in Novacek’s series discusses transmitters and antennas and will appear in our March issue.

Small, Self-Contained GNSS Receiver

TM Series GNSS modules are self-contained, high-performance global navigation satellite system (GNSS) receivers designed for navigation, asset tracking, and positioning applications. Based on the MediaTek chipset, the receivers can simultaneously acquire and track several satellite constellations, including the US GPS, Europe’s GALILEO, Russia’s GLONASS, and Japan’s QZSS.

LinxThe 10-mm × 10-mm receivers are capable of better than 2.5-m position accuracy. Hybrid ephemeris prediction can be used to achieve less than 15-s cold start times. The receiver can operate down to 3 V and has a 20-mA low tracking current. To save power, the TM Series GNSS modules have built-in receiver duty cycling that can be configured to periodically turn off. This feature, combined with the module’s low power consumption, helps maximize battery life in battery-powered systems.

The receiver modules are easy to integrate, since they don’t require software setup or configuration to power up and output position data. The TM Series GNSS receivers use a standard UART serial interface to send and receive NMEA messages in ASCII format. A serial command set can be used to configure optional features. Using a USB or RS-232 converter chip, the modules’ UART can be directly connected to a microcontroller or a PC’s UART.

The GPS Master Development System connects a TM Series Evaluation Module to a prototyping board with a color display that shows coordinates, a speedometer, and a compass for mobile evaluation. A USB interface enables simple viewing of satellite data and Internet mapping and custom software application development.
Contact Linx Technologies for pricing.

Linx Technologies
www.linxtechnologies.com

Infrared Communications for Atmel Microcontrollers

Are you planning an IR communications project? Do you need to choose a microcontroller? Check out the information Cornell University Senior Lecturer Bruce Land sent us about inexpensive IR communication with Atmel ATmega microcontrollers. It’s another example of the sort of indispensable information covered in Cornell’s excellent ECE4760 course.

Land informed us:

I designed a basic packet communication scheme using cheap remote control IR receivers and LED transmitters. The scheme supports 4800 baud transmission,
with transmitter ID and checksum. Throughput is about twenty 20-character packets/sec. The range is at least 3 meters with 99.9% packet receive and moderate (<30 mA) IR LED drive current.

On the ECE4760 project page, Land writes:

I improved Remin’s protocol by setting up the link software so that timing constraints on the IR receiver AGC were guaranteed to be met. It turns out that there are several types of IR reciever, some of which are better at short data bursts, while others are better for sustained data. I chose a Vishay TSOP34156 for its good sustained data characteristics, minimal burst timing requirements, and reasonable data rate. The system I build works solidly at 4800 baud over IR with 5 characters of overhead/packet (start token, transmitter number, 2 char checksum , end token). It works with increasing packet loss up to 9000 baud.

Here is the receiver circuit.

The receiver circuit (Source: B. Land, Cornell University ECE4760 Infrared Communications
for Atmel Mega644/1284 Microcontrollers)

Land explains:

The RC circuit acts a low-pass filter on the power to surpress spike noise and improve receiver performance. The RC circuit should be close to the receiver. The range with a 100 ohm resistor is at least 3 meters with the transmitter roughly pointing at the receiver, and a packet loss of less then 0.1 percent. To manage burst length limitations there is a short pause between characters, and only 7-bit characters are sent, with two stop bits. The 7-bit limit means that you can send all of the printing characters on the US keyboard, but no extended ASCII. All data is therefore sent as printable strings, NOT as raw hexidecimal.

Land’s writeup also includes a list of programs and packet format information.

Infrared Communications for Atmel Microcontrollers

Are you planning an IR communications project? Do you need to choose a microcontroller? Check out the information Cornell University Senior Lecturer Bruce Land sent us about inexpensive IR communication with Atmel ATmega microcontrollers. It’s another example of the sort of indispensable information covered in Cornell’s excellent ECE4760 course.

Land informed us:

I designed a basic packet communication scheme using cheap remote control IR receivers and LED transmitters. The scheme supports 4800 baud transmission,
with transmitter ID and checksum. Throughput is about twenty 20-character packets/sec. The range is at least 3 meters with 99.9% packet receive and moderate (<30 mA) IR LED drive current.

On the ECE4760 project page, Land writes:

I improved Remin’s protocol by setting up the link software so that timing constraints on the IR receiver AGC were guaranteed to be met. It turns out that there are several types of IR reciever, some of which are better at short data bursts, while others are better for sustained data. I chose a Vishay TSOP34156 for its good sustained data characteristics, minimal burst timing requirements, and reasonable data rate. The system I build works solidly at 4800 baud over IR with 5 characters of overhead/packet (start token, transmitter number, 2 char checksum , end token). It works with increasing packet loss up to 9000 baud.

Here is the receiver circuit.

The receiver circuit (Source: B. Land, Cornell University ECE4760 Infrared Communications
for Atmel Mega644/1284 Microcontrollers)

Land explains:

The RC circuit acts a low-pass filter on the power to surpress spike noise and improve receiver performance. The RC circuit should be close to the receiver. The range with a 100 ohm resistor is at least 3 meters with the transmitter roughly pointing at the receiver, and a packet loss of less then 0.1 percent. To manage burst length limitations there is a short pause between characters, and only 7-bit characters are sent, with two stop bits. The 7-bit limit means that you can send all of the printing characters on the US keyboard, but no extended ASCII. All data is therefore sent as printable strings, NOT as raw hexidecimal.

Land’s writeup also includes a list of programs and packet format information.

Great Plains Super Launch

Contributed by Mark Conner

The Great Plains Super Launch (GPSL) is an annual gathering of Amateur Radio high-altitude ballooning enthusiasts from the United States and Canada. The 2012 event was held in Omaha, Nebraska from June 7th to the 9th and was sponsored by Circuit Cellar and Elektor. Around 40 people from nine states and the Canadian province of Saskatchewan attended Friday’s conference and around 60 attended the balloon launches on Saturday.

Amateur Radio high-altitude ballooning (ARHAB) involves the launching, tracking, and recovery of balloon-borne scientific and electronic equipment. The Amateur Radio portion of ARHAB is used for transmitting and receiving location and other data from the balloon to chase teams on the ground. The balloon is usually a large latex weather balloon, though other types such as polyethylene can also be used. A GPS unit in the balloon payload calculates the location, course, speed, and altitude in real time, while other electronics, usually custom-built, handle conversion of the digital data into radio signals. These signals are then converted back to data by the chase teams’ receivers and computers. The balloon rises at about 1000 feet per minute until the balloon pops (if it’s latex) or a device releases the lifting gas (if it’s PE). Maximum altitudes are around 100,000 feet and the flight typically takes two to three hours.

Prepping for the launch – Photo courtesy of Mark Conner

On Thursday the 7th, the GPSL attendees visited the Strategic Air and Space Museum near Ashland, about 20 minutes southwest of Omaha. The museum features a large number of Cold War aircraft housed in two huge hangars, along with artifacts, interactive exhibits, and special events. The premiere aircraft exhibit is the Lockheed SR-71 Blackbird suspended from the ceiling in the museum’s atrium. A guided tour was provided by one of the museum’s volunteers and greatly enjoyed by all.

Friday featured the conference portion of the Super Launch. Presentations were given on stabilization techniques for in-flight video recordings, use of ballooning projects in education research, lightweight transmitters for tracking the balloon’s flight, and compressed gas safety. Bill Brown showed highlights from his years of involvement in ARHAB dating back to his first flights in 1987. The Edge of Space Sciences team presented on a May launch from Coors Field in Denver for “Weather and Science Day” prior to an afternoon Colorado Rockies game. Several thousand students witnessed the launch, which required meticulous planning and preparation.

EOSS ready for launch – Photo courtesy of Mark Conner

Saturday featured the launch of five balloons from a nearby high school early that morning. While the winds became gusty for the last two launches, all of the flights were successfully released into a brilliant sunny June sky. All five of the flights were recovered without damage in the corn and soybean fields of western Iowa between 10 and 25 miles from launch. The SABRE team from Saskatoon, Saskatchewan took the high flight award, reaching over 111,000 ft during their three-hour flight.

The view from one of the balloons. Image credit: “Project Traveler / Zack Clobes”.

The 2013 GPSL will be held in Pella, Iowa, on June 13-15. Watch the website superlaunch.org for additional information as the date approaches.

Elektor Weekly Wrap-Up: Receiver Project, Arduino-Based Design, & More

It’s officially summertime when Elektor’s special summer issue hits the newsstands. This year the team put together an attention-grabbing issue—complete with a redesigned layout—that’s packed with articles on projects such as a wearable distance-measuring device for swimmers, a music-making application with an Arduino, an “e-smog” detector, an innovative two-transistor regenerative receiver project, and more.

The two-transistor regenerative receiver

Editor-in-Chief Wisse Hettinga presents the issue in the following short video.

The 2012 summer issue is now available.

Elektor's 2012 summer issue

In other news, the Elektor team announced a new book on BASCOM-AVR is in the pipeline.

AVR microcontrollers are popular, easy to use and extremely versatile. Elektor magazine already produced a wealth of special applications and circuit boards based on ATmega and ATtiny controllers. These were mostly finished projects. In this book however the programming of these controllers is the foremost concern. BASCOM is an ideal tool for this. After a minimal preparation phase, you can start right away putting your own ideas into practice.

BASCOM and AVR microcontrollers — it’s an unbeatable team! Whatever you want to develop, in most cases the ATmega has everything you need on board. Ports, timers, A/D converters, PWM outputs and serial interfaces, RAM, flash ROM and EEPROM: everything is in plentiful supply, and with BASCOM their use is child’s play. More challenging peripherals like LCDs, RC5 and I2C can be used as well with just a handful of instructions. A wide hardware platform is available, too. Whether you’re using Atmel’s STK500 kit, the Elektor ATM18 or your own board, you can instantly turn the examples from this book into practice. For less exacting tasks controllers from the ATtiny are series used. That way, you can realize your own projects quickly and with little expense.

The companion CD-ROM with this book provides sample programs and software including BCAVRDMO, AVR STUDIO, LCDTOOLS, and TERMINAL.EXE.

Elektor members can preorder the book now.

CircuitCellar.com is an Elektor International Media publication.