JOINT DETECTION AND TRACKING USING MULTI-STATIC DOPPLER-SHIFT MEASUREMENTS Branko Ristic ISR Division DSTO Melbourne Australia branko.ristic@dsto.defence.gov.au Alfonso Farina SELEX - Sistemi Integrati Via Tiburtina km 12 Rome Italy afarina@selex-si.com ABSTRACT The problem is to establish the presence and subsequently to track a target using multi-static Doppler shift measurements. The assump- tion is that in the surveillance volume of interest a single transmitter of known frequency is active with multiple spatially distributed re- ceivers collecting and reporting Doppler-shift frequencies. The mea- surements are affected by additive noise and also contaminated by false detections. The paper develops a Bernoulli particle filter for this application and analyzes its performance by simulations. Index Terms— Bayesian estimation, random sets, nonlinear fil- tering, particle filter 1. INTRODUCTION The problem of position and velocity estimation of a moving object using measurements of Doppler-shift frequencies at several separate locations has a long history [1, 2, 3]. Renewed interest in this prob- lem is driven by applications, such as passive surveillance, and the technological improvements in wireless sensor networks [4, 5, 6]. The problem can be cast in radar or sonar context. In the radar con- text, for example, the transmitters (or illuminators) are typically the commercial digital audio/video broadcasters, FM radio transmitters or GSM base stations, whose transmitting frequencies are known. The radar receivers can typically measure the multi-static range, an- gle and Doppler-shift. The current trend in surveillance, however, is to use many low cost, low power sensors, connected in a network [7]. In line with this trend, this paper investigates the possibility of tracking a moving target using low-cost radars that measure Doppler frequencies only. Existing literature is mainly focused on observability of the tar- get state from the Doppler-shift measurements [4, 5] and geometry- based localisation algorithms [8, 3, 6]. In this paper we cast the problem in the nonlinear filtering framework [9]. Moreover, we model target existence by a two-state Markov chain which allows an automatic detection of target presence or absence from the surveil- lance volume. Finally, we allow for both false detections and miss- detections of the target. The optimal solution for the joint detection and tracking using multi-static Doppler-shifts is thus formulated as a Bernoulli filter in the random set Bayesian estimation framework [10]. This filter is implemented as a particle filter and its perfor- mance investigated by a numerical example. c Commonwealth of Australia The paper is organised as follows. Section 2 describes the prob- lem. Section 3 presents the Bernoulli filter and explains its particle filter implementation. Section 4 illustrates the Bernoulli-particle fil- ter performance by a numerical example, and finally the conclusions of the study are drawn in Section 5. 2. PROBLEM FORMULATION The state of the moving object in two-dimensional surveillance area at time t k is represented by the state vector x k =  x k ˙ x k y k ˙ y k  ⊺ . (1) where ⊺ denotes matrix transpose. Target position is determined by p k =[x k y k ] ⊺ ∈ R 2 , while its velocity by v k =[˙ x k ˙ y k ] ⊺ ∈ R 2 . Target motion is modelled by a nearly constant velocity (CV) model: x k+1 = F k x k + u k (2) where F k is the transition matrix and u k ∼N (u; 0, Q k ) is white Gaussian process noise. We adopt: F k = I2 ⊗  1 T k 0 1  , Q k = I2 ⊗ q  T 3 k 3 T 2 k 2 T 2 k 2 T k  , (3) where ⊗ is the Kroneker product, T k = t k+1 - t k is the sampling interval and q is the level of power spectral density of the corre- sponding continuous process noise [11, p.269]. We refer to k as to the discrete-time index. In order to model target appearance/disappearance we introduce a binary random variable ǫ k ∈{0, 1} referred to as the target ex- istence (the convention is that ǫ k =1 means that target exists at scan k, and vice versa). Dynamics of ǫ k is modelled by a two-state Markov chain with transitional probability matrix (TPM) Π whose elements are [Π]ij = P {ǫ k+1 = j - 1|ǫ k = i - 1} for i, j ∈{1, 2}. We adopt a TPM as follows: Π=  (1 - p b ) p b (1 - ps) ps  (4) where p b := P {ǫ k+1 =1|ǫ k =0} is the probability of target “birth”and ps := P {ǫ k+1 =1|ǫ k =1} the probability of target “survival”. These two probabilities together with the initial target existence probability q0 = P {ǫ0 =1} are assumed known. Target Doppler-shift measurements are collected by spatially distributed sensors (e.g. multi-static Doppler-only radars), as illus- trated in Fig.1. A transmitter T at known position t =[x0 y0] ⊺ , 3881 978-1-4673-0046-9/12/$26.00 ©2012 Crown ICASSP 2012