Dead reckoning is a method of using vehicle-based sensors to continue carrying out position determination during failure or poor reception of GPS signals. In addition, a comparison to map material takes place called map matching. Modern GPS receivers increasingly offer the option of processing information from vehicle-based sensors and thereby integrating dead reckoning. As a result, positions are given with a higher level of accuracy.
Until recently GPS receivers were used primarily to evaluate signals received from GPS satellites and to present them in the form of time, coordinates, speed and direction. GPS receivers fulfil this task with a high level of accuracy most of the time. However, reception of GPS signals from satellites can be interrupted or interfered with. Visibility to the satellite can be restricted (gaps between buildings, narrow valleys) or even completely interrupted (tunnels, parking garages). Furthermore, disturbances can occur through reflections, multipath reception or signal degradation from accidental or intentional disturbances (jamming). In these cases, either no position at all, or one inadequately extrapolated, could be calculated. In this situation information is relayed to a navigation system. By using dead reckoning and with the support of additional trip information, the system is able to provide positional calculations. For a long time, other applications, such as those in fleet management or the security sector, had only the most recent valid position available to them.
INTEGRATED DEAD RECKONING
So why not use the GPS receiver as an instrument to evaluate additional information? Previously the resources missing from GPS processors worked against the sensible implementation of dead reckoning as an additional method for obtaining more exact position determination. This has changed due to technical developments. Tyco Electronics now has available on its GPS receivers the Vespucci STA2051 processor from STMicroelectronics. Besides the computational-power and storage needs for GPS functions, enough resources remain to fulfil additional tasks. Because dead reckoning uses an odometer signal as its speed indicator — for forward or backward movement it uses a digital signal, and as directional indicator it uses an angular acceleration sensor (gyro) — the corresponding signal inputs must, of course, be available.
The odometer signal consists of digital pulses that correspond to the route that has been covered. However, the number of pulses varies from vehicle to vehicle and can change, for example, even when switching from winter to summer tyres. By adding up the pulses — taking into account the direction of travel (forwards or backwards) — the route that has been covered can be calculated. The gyro delivers an analog signal. Commencing from a bias or open-circuit voltage, the directional changes per unit of time are indicated via a correspondingly higher or lower voltage level. Here too the open-circuit voltage can change, e.g. depending upon temperature. As a result, both measurement values require calibration. Of course the system itself should perform this task. To this end, dead reckoning signals are continually compared with valid positional information, and a closed feedback loop occurs.
Calculation of new positional information, which is based on both GPS and dead reckoning data, then takes place in a so-called "Kalman filter." At this location, the evaluation and combination of this data occurs, including the previous history. Because processed GPS data enters the Kalman filter, i.e. values calculated for longitude, latitude and direction, it is described as a loosely controlled system. The calculation of GPS data has also already occurred via a Kalman filter.
Besides this implementation of a loose system with feedback other loose systems exist without feedback (the dead-reckoning signals are not calibrated), as well as tightly controlled systems with or without feedback. In tightly controlled systems, raw GPS data, i.e. pseudo-ranges and delta ranges, are processed into a single Kalman filter, instead of the GPS data being processed first by their own Kalman filter.
As with many results from series of measurements, the determination of position with GPS is fraught with errors. Multiple variables compose the system. Pure GPS includes longitude, latitude and direction; while dead reckoning deals with, among other things, speed, change of direction and speed of this change. By combining the last system state with up-to-date variables, the new system state is calculated in real time. This means that a recursive procedure is involved. Knowledge of the entire past is not necessary; the last respective state suffices. Therefore this procedure is efficient regarding the storage space required.
By means of a transformation, a probable new state can be predicted from the previous state without new measurement data. This prediction is afflicted with inaccuracies. At the same time, the new measurement values for calculating the new state can be integrated. However this can present measurement uncertainty, as well. The larger these inaccuracies are (in GPS, for example, derived from the number of available satellites) the smaller the weighting of the new measurement. Then the weighting of the prediction will be respectively greater. The equations that are utilised here are linear in nature, and therefore, the Kalman filter is linear. In a statistical sense, therefore, the result is optimal. The average quadratic error in the results remains as minimal as the calculated inaccuracy. Because this error is independent of the initial value the system can in some senses be described as self-learning.
Naturally an important aspect of implementation involves exact knowledge of the dependence each parameter has on each other. For this reason, in addition to theoretical perspectives, extensive field tests are required. This method confirms theoretical observations relatively quickly.
Directional input from GPS becomes inaccurate at low speeds until it loses all meaning at a standstill. This is a fact that must be considered. Therefore below a certain speed, the directional information from the gyro should be taken more strongly into consideration; at standstill the directional information should not be recalculated. At the same time, the standstill state should be used to reset the gyro's open-circuit voltage. Especially in cities where dead reckoning is deployed more often than in open space due to gaps between buildings or tunnels, stops at traffic signals can be used for this purpose. Deviations are therefore reduced.
Clearly the choice of gyro is important. The gyro should deliver similarly reliable results, whether in long, drawn-out curves in highway tunnels, in parking garages or during very slow turns.
In general, test drives have shown that dead reckoning is a very good extension to GPS. During a normal trip GPS alone is indeed reverted to in a large number of situations. But especially within cities the availability of GPS signals is somewhat reduced. Nevertheless even in tunnels or parking garages an exceptionally exact position continues to be available. In order to gather experiences over longer distances a test drive was done with the antenna voltage turned off. In these cases the average deviation from actual position over a travel distance of 5km remained within 150m, which corresponds to 3%.
At Tyco Electronics dead reckoning has already been successfully tested for a year on its GPS receiver A1025. A new addition is the new model Platform A1030 (Picture 4), which is based on STM's GPS processor Vespucci STA2051. Besides the 32bit core ARM7 and GPS correlators, the Vespucci's primary features include integrated flash (256kB) and SRAM (64kB). In order to offer enough room for applications, the A1030, as with the A1025, has been fitted with additional flash (8MB) and SRAM (2MB). The odometer signal uptake occurs via one of the many I/O pins. The integrated 12bit A/D converter serves as connector for the gyro, and the converted values are read in at a scan rate of 20 Hz. The gyro itself sits on an offset board. This offers the advantage of having an independent installation in the vehicle — the gyro should be installed as horizontally as possible — and enables the test of different gyros as well. Essentially nothing stands in the way of a platform with integrated gyro.
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