The relationship between spherical and hyperbolic positioning

Deffenbaugh, Max; Bellingham, James; Schmidt, Henrik

doi:10.1109/oceans.1996.568293

Cited by 34 publications

(35 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the ULPS the MR is not synchronized with the beacons, so only the increments of distances between the receptions of the signals are measured taking one of the signal as reference (hyperbolic trilateration [10]). …”

Section: B Ulps Dynamicsmentioning

confidence: 99%

“…In this case, the IB emits simultaneously an ultrasonic signal and a RF one as synchronization between the IB and the MR in order to measure the absolute distance from the IB to the MR. The distance between an IB placed on and the MR located on the position at time can be expressed as: (10) The vector of measurements from M IBs at time can be expressed as: (11) Differentiating the expression in regards to the state vector, the dynamic model of the IB measurements is obtained:…”

Section: Ib Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

Fusion of data from ultrasonic LPS and isolated beacons for improving MR navigation

Gualda

Ureña

García

et al. 2014

2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

View full text Add to dashboard Cite

This paper presents an improved navigation system for Mobile Robots (MR) in extensive areas using different Ultrasonic Local Positioning Systems (ULPS) and the complement of Isolated Beacons (IB) in regions without LPS coverage. Each single LPS has a high accuracy in positioning but a limited coverage area. The proposal of this paper is the use of a set of additional Isolated Beacons to cover areas between LPSs and then reducing the number of them needed. When the MR is on a place where the positioning data from the ULPS is available, it can obtain its position with high accuracy. On the other hand, if the MR is outside of a LPS coverage area it can measure the distance to one of the IBs and fuse this information with the one of the MR odometer using an H-infinity filter to estimate its position. The complete system has been tested in some scenarios with simulated data and the results show the improvement of the MR navigation error when the IBs are used.1

show abstract

Section: B Ulps Dynamicsmentioning

confidence: 99%

Section: Ib Dynamicsmentioning

confidence: 99%

Fusion of data from ultrasonic LPS and isolated beacons for improving MR navigation

Gualda

Ureña

García

et al. 2014

2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

View full text Add to dashboard Cite

show abstract

“…LBL systems measure travel-times between an array of transponders and a moving pinger. With multiple travel time, or range measurements, a least squares algorithm can be used to estimate the position of the pinger using either a hyperbolic or spherical solution ( [14], [15]). …”

Section: Introductionmentioning

confidence: 99%

Acoustic Positioning and Tracking in Portsmouth Harbor, New Hampshire

et al. 2007

View full text Add to dashboard Cite

Portsmouth Harbor, New Hampshire, is frequently used as a testing area for multibeam and sidescan sonars, and is the location of numerous ground-truthing studies. Having the ability to accurately position underwater sensors is an important aspect of this type of work. However, underwater positioning in Portsmouth Harbor is challenging. It is relatively shallow, approximately one kilometer wide with depths of less than 25 meters. There is mixing between fresh river water and seawater, which is intensified by high currents and strong tides. This causes a very complicated spatial and temporal sound speed structure. Solutions that use the time-of-arrival of an acoustic pulse to estimate range will require very precise knowledge of the travel paths of the signal in order to separate out issues of multipath arrivals. An alternative solution is to use the phase measurements between closely spaced hydrophones to measure the bearing of an acoustic pinger. By using two bearing measurement devices that are widely separated, the intersection of the two bearings can be used to position the pinger. The advantage of this approach is that the sound speed only needs to be known at the location of the phase measurements. Both time-of-arrival and phase difference systems may encounter difficulties arising from horizontal refraction due to spatially varying sound speed. To ascertain which solution would be optimal in Portsmouth Harbor, the time-of-arrival and phase measurement approaches are being examined individually. Initial field tests have been conducted using a 40 kHz signal to look at bearing accuracy. Using hydrophones that are spaced 2/3 wavelengths apart, the bearing accuracy was found to be 1.25°for angles up to 20°from broadside with signal to noise ratios (SNR) greater than 15dB. The results from the closely spaced hydrophones were used to resolve phase ambiguities, allowing finer bearing measurements to be made between hydrophones spaced 5 wavelengths apart. The fine bearing measurements resulted in a bearing accuracy of 0.3°for angles up to 20°from broadside with SNR greater than 15dB. Field tests planned for summer 2007 will include a more detailed investigation of how the environmental influences affect each of the measurement types including range, signal to noise ratio, currents, and sound speed structure.

show abstract

“…Some studies (see [6]- [9] and references therein) have focused on the statistical performance analysis of these location techniques. In general, an analysis of this kind makes a number of assumptions about the nature of the available TOA and TDOA parameters.…”

Section: Introductionmentioning

confidence: 99%

“…When the receiver clock offset is modeled as an additional deterministic unknown parameter, it has been demonstrated in [7] that both approaches (circular and hyperbelic on TDOA measurements) yield identical estimates, although their authors considered only the special case in which all TOA estimates are uncorrelated and have equal variance. On the other hand, it is demonstrated in [9] that the Cramér-Rao (CRB) bounds for position accuracy using TDOA measurements approach those of the spherical navigation system as the variance in the clock-offset approaches zero and those of the hyperbolic positioning system as the variance of the clock offset approaches infinity. Note that clock-offset variance includes both the inacuracies of the local clock, as well as the incuracies in the common transmit time of the BSs.…”

Section: Introductionmentioning

confidence: 99%

Average Performance Analysis of Circular and Hyperbolic Geolocation

Urruela

Sala

Riba³

2006

IEEE Trans. Veh. Technol.

View full text Add to dashboard Cite

Abstract-A comparative performance analysis of four geolocation methods in terms of their theoretical root mean square positioning errors is provided. Comparison is established in two different ways: strict and average. In the strict type, methods are examined for a particular geometric configuration of base stations (BSs) with respect to mobile position, which determines a given noise profile affecting the respective time-of-arrival (TOA) or timedifference-of-arrival (TDOA) estimates. In the average type, methods are evaluated in terms of the expected covariance matrix of the position error over an ensemble of random geometries, so that comparison is geometry independent. Exact semianalytical equations and associated lower bounds (depending solely on the noise profile) are obtained for the average covariance matrix of the position error in terms of the so-called information matrix specific to each geolocation method. Statistical channel models inferred from field trials are used to define realistic prior probabilities for the random geometries. A final evaluation provides extensive results relating the expected position error to channel model parameters and the number of base stations.

show abstract

The relationship between spherical and hyperbolic positioning

Cited by 34 publications

References 1 publication

Fusion of data from ultrasonic LPS and isolated beacons for improving MR navigation

Fusion of data from ultrasonic LPS and isolated beacons for improving MR navigation

Acoustic Positioning and Tracking in Portsmouth Harbor, New Hampshire

Average Performance Analysis of Circular and Hyperbolic Geolocation

Contact Info

Product

Resources

About