Rigorous approach to bore-sight self-calibration in airborne laser scanning

TLDR: A rigorous method for estimating some of the calibration parameters in airborne laser scanning (ALS), namely the three bore-sight angles and the range-finder offset, which is shown to be not only accurate but also very robust in terms of convergence.

Abstract: We present a rigorous method for estimating some of the calibration parameters in airborne laser scanning (ALS), namely the three bore-sight angles and the range-finder offset. The technique is based on expressing the system calibration parameters within the direct-georeferencing equation separately for each target point, and conditioning a group of points to lie on a common surface of a known form such as a plane. However, the assumed a priori information about q chosen planar features is only their form not the spatial orientation or position. Thus, the 4·q plane parameters are estimated together with the calibration parameters in a combined adjustment model that makes use of GPS/INS-derived position and orientation as well as LiDAR range and encoder angle as observations. To make the approach practical when working with voluminous ALS and GPS/INS data, the contribution of each laser point to the normal equations is formed sequentially. The discussions focus on practical examples with data from a continuously-rotating scanner that reveal the conditions under which almost complete de-correlation between the estimated parameters occurs. In such a case, all bore-sight angles are determined with accuracy that is several times superior to the system noise level. Given sufficiently strong geometry, the presented method is shown to be not only accurate but also very robust in terms of convergence. When appropriate, the method is applicable for calibration of additional systematic effects such as laser-beam encoder offsets or scale factor with minimal modification to the functional model.

Figures

Table 5 Adjustment's radius of convergence

Table 1 Characteristics of used data sets

Fig. 2. Images and color-coded reliefs of the two test fields with highlighted planar features: (a) soccer field, (b) urban area (only plane nos. 2–12 were used in the adjustment while the plane nos. 13–16 served for control purposes).

Fig. 6. Histogram of residuals for the urban data (withoutΔρ estimate), for observations in x and z positions, orientation in pitch and range. Note that for the other observables, the histogram of y is similar to x, heading is similar to pitch while roll and encoder-angle histograms show less zeros.

Fig. 7. Magnitude of residuals (left vertical axes) by point index and the indication of the planes that the points belong to (right vertical axes). Due to similarities, the residuals are plotted only in x and z positions, pitch and range. The vertical line indicates the change in the flying height and the higher altitude exhibits an expected increase in noise level.

Table 2 Influence of plane geometry and range-finder correction on bore-sight estim

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Rigorous approach to bore-sight self-calibration in airborne laser scanning" ?

The authors present a rigorous method for estimating some of the calibration parameters in airborne laser scanning ( ALS ), namely the three bore-sight angles and the range-finder offset. 

Q2. What is the pre-requisite to the model input?

Together with the target coordinates and GPS/INS trajectory, the point-cloud classification is the only pre-requisite to the model input. 

Q3. What is the method for establishing detailed terrain models from airborne platforms?

Airborne Laser Scanning (ALS) is a very effective and accurate method for establishing detailed terrain models from airborne platforms. 

Q4. How is the separation between the instruments determined?

The lever-arm separation between the individual instruments is determined to better than 1 cm by laboratory calibration and is independent of system installation. 

Q5. What is the main factor for judging the accuracy of the method?

The sensitivity of the adjustment concerning the approximate calibration values is another important fac-tor for judging method's robustness and applicability. 

Q6. What is the significance of the range-finder parameter?

As can be seen from the table, the inclusion of the range-finder parameter has a serious influence on the bore-sight estimate and the Δρ magnitude appears significant when considering the sigma-to-value ratio. 

Q7. What is the argument that a better de-correlation could be achieved by determining?

One might argue that a better de-correlation could be achieved by determining the plane parameters by some independent means (Filin, 2003), which would correspond to sacrificing the practical benefits of this approach.