New approach to online optimal estimation of multisensor biases J.A. Besada Portas, J.Garcı´a Herrero and G. de Miguel Vela Abstract: The paper presents a new approach to multiple sensor bias estimation. It is applied to a practical example: correcting radar biases for ATC applications. A novel procedure to organise and process measurements is proposed and compared with classical approaches, which are shown to achieve inferior performance. It is shown how the exploitation of all available information allowed by the proposed data arrangement improves the accuracy of estimates. Besides, efficient implementations are developed and a cost – benefit analysis of the main alternatives for this problem is presented in the results. 1 Introduction Modern air surveillance systems [1] are composed of sensor networks providing data about all interesting objects (targets) located within their joint covered areas. Sensors are data sources to be merged, so that the data fusion process is becoming an essential aspect of all surveillance systems. It must combine sensor detections with the aim of achieving better inferences than those coming from only a single sensor (in terms of accuracy, reliability, robustness, etc.) [2, 3]. Data fusion needs a correct model of measurement errors, including random and systematic ones. While considerable attention has been given to the problem of optimum state estimation by filtering sequences of sensor measurements, the problem of coherent calibration of a sensor network, usually referred to as multisensor registration, have received less attention. This aspect is recognised as an inevitable requisite for sensor fusion [4], since not-cancelled biases in multisensor measurements degrade the output performance in different degrees. They not only induce biases in the estimators, increasing RMS errors, but also their alternation from different sensors produces track instabilities (‘zig-zag’ effect due to erroneous manoeuvre detection in adaptive tracking filters), and may even produce multiple tracks (continuity faults) when systematic errors are higher than spatial correlation gates. Some of the error sources are static (radar position or orientation errors,…) and could be estimated off-line with test flight data, but some of the causes of systematic errors, such as multipath or propa- gation-induced errors, may vary in time. So an online scheme, updating the estimated parameters while new measurements are received, is needed to guarantee that multisensor data being fused are continuously unbiased. However, a deep analysis is needed of the available approaches for online calibration, stressing the advantages and disadvantages of each one for different applications. This analysis would allow the fusion-systems designer to take appropriate decisions about the convenient algorithm to be selected. The basic problem addressed here will be the proper processing of measurements from all sensors available in the network to obtain online estimation of sensor biases, taking account of the complete model assumed for sensor errors. Alternative methods based on the estimation of systematic components of sensor errors will be presented and analysed to compare their relative performance and computational costs. All methods compared are based on processing differ- ences of measurements taken from pairs of sensors and referred to the same aircraft. However, the organisation of available measurements to extract these pairs or even the number of pairs selected is an aspect not considered in detail in previous works. Usually, the obvious pairing of measurements closest in time has been profusely applied (using each measurement only once), although other alternatives could exploit more information to improve the estimations. Here, generic solutions covering the optimum case are presented and compared with conventional approaches, contributing also with efficient implemen- tations. A cost– benefit analysis of different approaches will be a main goal of the work, reflected in the final results. Although this work analyses systematic errors in a particular scenario of civil air traffic context with a network of available secondary radars, the general ideas are applicable to other scenarios with different types of sensors. The model for measurement errors with radars is presented, and also explicit relations between observations and radar bias parameters through co-ordinate transformations are indicated. General processing architecture is presented with emphasis on the problem of organising the chain of measurement to obtain differences. Also, a procedure to keep linearity in the relations is also presented. The different algorithms to derive bias estimators are detailed: first the general best linear unbiased estimator (BLUE) solution, then proposals for an efficient implementation; and finally particular solutions of the generic solution proposed, corresponding to other conventional approaches. A per- formance analysis is carried out, presenting the analytical predictions based on a statistical models and simulations according to these models. Also, computational cost is q IEE, 2004 IEE Proceedings online no. 20040116 doi: 10.1049/ip-rsn:20040116 The authors are with ETSI Telecomunicacio ´n, Despacho C-315-1, Ciudad Universitaria s/n, 28040 Madrid, Spain J.A. Besada Portas and G. de Miguel Vela are also with Universidad Polite ´cnica de Madrid, Spain J. Garcı ´a Herrero is also with Universidad Carlos III de Madrid, Spain Paper first received 2nd January and in revised form 22nd July 2003 IEE Proc.-Radar Sonar Navig., Vol. 151, No. 1, February 2004 31