Imperfect Detection Probability Research Articles

Comparing contemporary models to traditional indices to estimate abundance of desert bighorn sheep

AbstractAerial surveys for large ungulates produce count data that often underrepresent the number of animals. Errors in count data can lead to erroneous estimates of abundance if they are not addressed. Our objective was to address imperfect detection probability by developing a framework that produces realistic and defensible estimates of bighorn sheep (Ovis canadensis) abundance. We applied our framework to a population of desert bighorn sheep (O. c. nelsoni) in the Great Basin, Nevada, USA. We captured and marked 24 desert bighorn sheep with global positioning system (GPS)‐collars and then conducted helicopter surveys naïve to the locations of collared animals. We developed a Bayesian integrated data model to leverage information from telemetry data, helicopter survey counts, and habitat characteristics to estimate abundance while accounting for availability and perception probability (i.e., detection given availability). Distance to ridgeline, terrain ruggedness, tree cover, and slope influenced perception probability of sheep given they were viewable from the helicopter. There was also annual variation in perception probability (2018: median = 0.64, credible interval [CrI] = 0.37–0.87; 2019: median = 0.81, CrI = 0.49–0.97). The abundance estimates from the integrated data model decreased from 2018 (594; 95% CrI = 537–656) to 2019 (487; 95% CrI = 436–551). In addition, accounting for availability and imperfect perception resulted in greater estimates of abundance compared to traditional directed search methods, which were 340 for 2018 and 320 for 2019. Our modeling framework can be used to generate more defensible population estimates of bighorn sheep and other large mammals that have been surveyed in a similar manner.

Liming and spring salamander abundance

AbstractEnvironmental acidification is affecting ecosystems around the globe, and as a result, managers are using limestone applications to mitigate the effects of acid rain and acid mine drainage. Limestone applications attempt to reverse acidification by increasing stream pH; however, liming can have variable effects on stream biota. We examined the effects of liming on spring salamander (Gyrinophilus porphyriticus) abundance in West Virginia, USA, from 10 June to 1 September 2013. We used multiple methods (i.e., leaf litterbags, visual encounter surveys, area constrained flip and search) to sample spring salamanders within 11 different streams in the Monongahela National Forest. Using N‐mixture models, which allow for estimation of abundance from count data and account for imperfect detection probabilities, we examined the effects of direct application liming (DAL) on spring salamander abundance. Direct application liming at a higher lime frequency did not have a significant effect on salamander abundance; however, we observed differences in spring salamander size in areas near the DAL site. These results have influenced management of limed streams and will enlighten managers to the effects of high frequency liming on salamander communities and other stream organisms, and will provide insights on how to mitigate potential impacts as a result of liming practices.

Estimation of demographic parameters of some plant species accounting for imperfect detection probabilities

AbstractDetection probability (p) in plants is imperfect in natural conditions due to several factors. This imperfect detectability is rarely accounted for in the estimation of demographic parameters, such as survival probabilities (S) or transition rates between different life states or size classes (ψ), which may result in inaccurate quantitative information about plant populations. In this study, we used previously collected data of five plant species belonging to different families with contrasting life forms and habitats (Flaveria chlorifolia,Mammillaria hernandezii,Neobuxbaumia macrocephala,Govenia lagenophora, andCastilleja tenuiflora), data simulations, multi‐state models (a demographic tool that explicitly accounts forp), and direct estimation of survival and transition rates (i.e., assuming perfect detection) to identify in which species, states, or demographic parameters the bias caused by ignoring our imperfect detectability is more severe. Detection was imperfect (p < 1) for all our study species. In general, ignoring detection probabilities yielded underestimated survival and transition rates in all five species. Biases caused by assuming perfect detection were also large and significant, mainly in inconspicuous life states and size classes, such as seedlings and dry individuals. In contrast, considering detection probabilities resulted in fewer underestimated survival and transition rates, with smaller and mostly nonsignificant biases. Intriguingly, some transitions were overestimated even when accounting for detection probabilities. Our findings highlight the importance of considering that detection of most plant species is imperfect in the field, even in species that are apparently conspicuous, to avoid incorrect inferences about plant populations.

Density surface and excursion sets modeling as an approach to estimating population densities

AbstractEffective species management and conservation require knowledge of species distribution and status. We used point‐transect distance sampling surveys of the endangered palila (Loxioides bailleui), a honeycreeper currently found only on the Island of Hawai'i, USA, to generate robust estimates of total abundance and simultaneously model the distribution, abundance, and spatial correlation of the species as a density surface model (DSM). Point‐transect distance sampling is a widely applied method to estimate bird densities accounting for imperfect detection probability. For the DSM we used a generalized additive model framework and soap film smoothers to control the effects of boundary features. This modeling approach allowed us to account for imperfect detection and propagate detection probability uncertainty. We compared the uncertainty in palila abundance estimates using standard point‐transect distance sampling to estimates from the DSM. The DSM, accounting for both distance‐sampling‐derived detection probability variance and the generalized additive model density estimate variance, did not improve population estimator precision; however, it provided insight into the species' distribution, density, and uncertainty. We also applied excursion sets analysis to objectively identify areas where the species occurs in high densities. The 2017 global population of <2,000 individuals was limited to an excursion area of 1,500 ha. Our findings can help management and regulatory agencies by simultaneously mapping a species' distribution and density, improving survey protocols, and providing information important to species conservation.

A hierarchical N-mixture model to estimate behavioral variation and a case study of Neotropical birds.

Understanding how and why animals use the environments where they occur is both foundational to behavioral ecology and essential to identify critical habitats for species conservation. However, some behaviors are more difficult to observe than others, which can bias analyses of raw observational data. To our knowledge, no method currently exists to model how animals use different environments while accounting for imperfect behavior-specific detection probability. We developed an extension of a binomial N-mixture model (hereafter the behavior N-mixture model) to estimate the probability of a given behavior occurring in a particular environment while accounting for imperfect detection. We then conducted a simulation to validate the model's ability to estimate the effects of environmental covariates on the probabilities of individuals performing different behaviors. We compared our model to a naïve model that does not account for imperfect detection, as well as a traditional N-mixture model. Finally, we applied the model to a bird observation data set in northwest Costa Rica to quantify how three species behave in forests and farms. Simulations and sensitivity analyses demonstrated that the behavior N-mixture model produced unbiased estimates of behaviors and their relationships with predictor variables (e.g., forest cover, habitat type). Importantly, the behavior N-mixture model accurately characterized uncertainty, unlike the naïve model, which often suggested erroneous effects of covariates on behaviors. When applied to field data, the behavior N-mixture model suggested that Hoffmann's woodpecker (Melanerpes hoffmanii) and Inca dove (Columbina inca) behaved differently in forested versus agricultural habitats, while turquoise-browed motmot (Eumomota superciliosa) did not. Thus, the behavior N-mixture model can help identify habitats that are essential to a species' life cycle (e.g., where individuals nest, forage) that nonbehavioral models would miss. Our model can greatly improve the appropriate use of behavioral survey data and conclusions drawn from them. In doing so, it provides a valuable path forward for assessing the conservation value of alternative habitat types.

Breeding expansion of sandhill cranes in Quebec

AbstractSandhill cranes (Antigone canadensis) were broadly extirpated from much of their historical range in North America at the beginning of the twentieth century. Various conservation‐related legislation, such as the United States Migratory Bird Treaty Act, have assisted with population recovery. The eastern population of sandhill cranes has been growing rapidly since the 1980s and is thought to have expanded its geographic range to Quebec, Canada. Understanding the colonization and habitat use by the species in previously unoccupied breeding areas is necessary to develop and apply management measures. Using a dynamic occupancy modeling approach, we investigated the recent colonization and extirpation patterns of sandhill cranes in Quebec from 2004–2019. We combined data from 3 data sets (helicopter surveys, breeding bird atlas surveys, and eBird) to increase the spatial coverage and the number of species occurrence records while accounting for imperfect detection probability. Detection probability was highest for the helicopter survey (0.70), whereas the 2 other data sets had relatively low detection levels (0.10–0.26). Based on a simulation study, we found that excluding the eBird data from the analysis produced more biased estimates than excluding the atlas and helicopter survey data sets. Throughout the study, sandhill cranes seemed to have completed their colonization of western Quebec and only recently started to nest in eastern areas. Initial occupancy increased with wetland cover and colonization probability increased weakly with the cover of agricultural areas, suggesting that in our study area sandhill cranes rely essentially on natural wetlands during the breeding season.

Use of occupancy modelling to identify sample sizes and waterbodies with fish exceeding mercury consumption advisory thresholds.

Identifying waterbodies where fish methylmercury concentrations are elevated is critical for development of consumption guidelines. However, mercury concentrations vary among waterbodies and fishes due to a suite of environmental conditions and detection of elevated mercury concentrations is imperfect, resulting in inaccurate consumption guidelines. Occupancy models may be a useful approach for addressing these issues but have not been used for these purposes. Our objectives were to use occupancy modeling to (1) estimate number of samples needed to detect mercury levels surpassing >0.30 mg/kg wet weight in fish at a waterbody (2) identify individual fish-level factors associated with detection probability, and (3) identify environmental-level factors linked to elevated mercury levels in fish at a waterbody. Mercury concentrations were estimated from >500 largemouth bass Micropterus salmoides and walleye Sander vitreus from 30 waterbodies throughout Iowa, USA to identify individuals with concentrations > or <0.30 mg/kg. Probability of detecting mercury concentrations >0.30 mg/kg varied between species and increased with fish length; consequently, more samples were needed to detect elevated mercury concentrations in small versus large fish. The probability of a waterbody having fish with elevated mercury levels increased with the percent grassland and declined with percent agriculture in the watershed, providing prioritization metrics for mercury surveillance programs. Our results demonstrate that occupancy models can be a valuable tool for mercury surveillance due to their ability to estimate necessary sample sizes and identify fish sizes and waterbodies with elevated mercury concentrations while accounting for imperfect detection probabilities.

Decline of Leach’s Storm Petrels Hydrobates leucorhous at the largest colonies in the northeast Atlantic

Leach’s Storm Petrel Hydrobates leucorhous has undergone substantial population declines at North Atlantic colonies over recent decades, but censusing the species is challenging because it nests in burrows and is only active at colonies at night. Acoustic playback surveys allow birds present in nest sites to be detected when they respond to recordings of vocalisations. However, not all birds respond to playback on every occasion, response rate is likely to decline with increasing distance between the bird and the playback location, and the observer may not detect all responses. As a result, various analysis methods have been developed to measure and correct for these imperfect response and detection probabilities. We applied two classes of methods (calibration plot and hierarchical distance sampling) to acoustic survey data from the two largest colonies of breeding Leach’s Storm Petrels in the northeast Atlantic: the St Kilda archipelago off the coast of northwest Scotland, and the island of Elliðaey in the Vestmannaeyjar archipelago off the southwest of Iceland. Our results indicate an overall decline of 68% for the St Kilda archipelago between 2000 and 2019, with a current best estimate of ~8,900 (95% CI: 7,800–10,100) pairs. The population on Elliðaey appears to have declined by 40 –49% between 1991 and 2018, with a current best estimate of ~5,400 (95% CI: 4,300–6,700) pairs. We also discuss the relative efficiency and precision of the two survey methods.

Towards an Optimization of Sample Plot Size and Scanner Position Layout for Terrestrial Laser Scanning in Multi-Scan Mode

A novel approach is presented to model the tree detection probability of terrestrial laser scanning (TLS) in forest inventory applications using a multi-scan mode. The traditional distance sampling framework is further extended to account for multiple scan positions at a single sample plot and to allow for an imperfect detection probability at distance r = 0. The novel methodology is tested with real world data, as well as in simulations. It is shown that the underlying detection model can be parameterized using only data from single scans. Hereby, it is possible to predict the detection probability also for different sample plot sizes and scanner position layouts in a multi-scan setting. Simulations showed that a minor discretization bias can occur if the sample size is small. The methodology enables a generalized optimization of the scanning layout in a multi-scan setting with respect to the detection probability and the sample plot area. This will increase the efficiency of multi-scan TLS-based forest inventories in the future.

Combining species distribution modeling and distance sampling to assess wildlife population size: A case study with the northern yellow-cheeked gibbon (Nomascus annamensis).

Population size and distribution data for wildlife species play an important role in conservation and management, especially for endangered species. However, scientists seriously lack data on the population status of many species. The northern yellow-cheeked gibbon (Nomascus annamensis) is found in southern Lao PDR, central Vietnam, and northeastern Cambodia. The population of the species has significantly declined due to hunting, habitat loss, and the wildlife trade. To examine the population size and distribution of N. annamensis, we conducted a field survey in Song Thanh Nature Reserve, Quang Nam Province, central Vietnam from February to April 2019 using the audio point count method. We combined Distance Sampling and Ecological Niche Modeling to estimate the population of the gibbons. Results showed that the total suitable area for the gibbons was about 302.32 km2 , with the two most important variables of the habitat model being the distance-to-villages and forest type. We detected 36 gibbon groups through field surveys and estimated 443 (95% CI, 278-707) gibbon groups in Song Thanh Nature Reserve. Our results indicate that the gibbon population in Song Thanh Nature Reserve is the largest known population of N. annamensis in Vietnam. In addition, our study was the first to combine species distribution modeling with distance sampling to estimate gibbon density and population size. This approach might be useful in surveying and monitoring gibbon populations because it takes imperfect detection probability into account in estimating gibbon population density while estimating the area of potential habitat using environmental variables.

Estimating Reproduction and Survival of Unmarked Juveniles Using Aerial Images and Marked Adults

Methods for estimating juvenile survival of wildlife populations often rely on intensive data collection efforts to capture and uniquely mark individual juveniles and observe them through time. Capturing juveniles in a time frame sufficient to estimate survival can be challenging due to narrow and stochastic windows of opportunity. For many animals, juvenile survival depends on postnatal parental care (e.g., lactating mammals). When a marked adult gives birth to, and provides care for, juvenile animals, investigators can use the adult mark to locate and count unmarked juveniles. Our objective was to leverage the dependency between juveniles and adults and develop a framework for estimating reproductive rates, juvenile survival, and detection probability using repeated observations of marked adult animals with known fates, but imperfect detection probability, and unmarked juveniles with unknown fates. Our methods assume population closure for adults and that no juvenile births or adoptions take place after monitoring has begun. We conducted simulations to evaluate methods and then developed a field study to examine our methods using real data consisting of a population of mule deer in a remote area in central Nevada. Using simulations, we found that our methods were able to recover the true values used to generate the data well. Estimates of juvenile survival rates from our field study were 0.96, (95% CRI 0.83–0.99) for approximately 32-day periods between late June and late August. The methods we describe show promise for many applications and study systems with similar data types, and our methods can be easily extended to unmanned aerial platforms and cameras that are already commercially available for the types of images we used.Supplementary materials accompanying this paper appear online.

Quantifying imperfect camera-trap detection probabilities: implications for density modelling

Abstract ContextData obtained from camera traps are increasingly used to inform various population-level models. Although acknowledged, imperfect detection probabilities within camera-trap detection zones are rarely taken into account when modelling animal densities. AimsWe aimed to identify parameters influencing camera-trap detection probabilities, and quantify their relative impacts, as well as explore the downstream implications of imperfect detection probabilities on population-density modelling. MethodsWe modelled the relationships between the detection probabilities of a standard camera-trap model (n=35) on a remotely operated animal-shaped soft toy and a series of parameters likely to influence it. These included the distance of animals from camera traps, animal speed, camera-trap deployment height, ambient temperature (as a proxy for background surface temperatures) and animal surface temperature. We then used this detection-probability model to quantify the likely influence of imperfect detection rates on subsequent population-level models, being, in this case, estimates from random encounter density models on a known density simulation. Key resultsDetection probabilities mostly varied predictably in relation to measured parameters, and decreased with an increasing distance from the camera traps and speeds of movement, as well as heights of camera-trap deployments. Increased differences between ambient temperature and animal surface temperature were associated with increased detection probabilities. Importantly, our results showed substantial inter-camera (of the same model) variability in detection probabilities. Resulting model outputs suggested consistent and systematic underestimation of true population densities when not taking imperfect detection probabilities into account. ConclusionsImperfect, and individually variable, detection probabilities inside the detection zones of camera traps can compromise resulting population-density estimates. ImplicationsWe propose a simple calibration approach for individual camera traps before field deployment and encourage researchers to actively estimate individual camera-trap detection performance for inclusion in subsequent modelling approaches.

Response of wild bee communities to beekeeping, urbanization, and flower availability

Wild bees provide pollination services and are currently declining at the global scale. A potential cause for this decline is competitive interactions with domestic honey bees. Urban beekeeping, a fairly new activity, is rapidly gaining popularity. In contrast with agricultural and natural areas, the extent of competition between honey bees and wild bees in urban areas is unclear. The objectives of this study were to quantify the impact of honey bees, urbanization, and the availability of floral resources on wild bee communities. We hypothesized that honey bees exert negative impacts on wild bees, that floral resources favor wild bee communities and mitigate the negative impacts of competition with honey bees, and that the influence of heat islands, used as a proxy for urbanization, varies between wild bees with their functional traits (nesting behavior). We tested these hypotheses with a data set of 19,077 wild bee specimens collected using colored pan-traps at 25 urban sites in 2012 and 2013. We investigated community and population patterns after accounting for imperfect detection probability. We found no evidence of competition between wild and domesticated bees. Our analyses indicate mixed effects of urban heat islands across species and positive effects of floral resources. We conclude that cities can allow the coexistence of urban beekeeping and wild bees under moderate hive densities. However, it will remain crucial to further investigate the competitive interactions between wild and honey bees to determine the threshold of hive densities beyond which competition could occur.

Estimating population size with imperfect detection using a parametric bootstrap

We develop a novel method of estimating population size from imperfectly detected counts of individuals and a separate estimate of detection probability. Observed counts are separated into classes within which detection probability is assumed constant. Within a detection class, counts are modeled as a single binomial observation X with success probability p where the goal is to estimate index N. We use a Horvitz–Thompson‐like estimator for N and account for uncertainty in both sample data and estimated success probability via a parametric bootstrap. Unlike capture–recapture methods, our model does not require repeated sampling of the population. Our method is able to achieve good results, even with small X. We show in a factorial simulation study that the median of the bootstrapped sample has small bias relative to N and that coverage probabilities of confidence intervals for N are near nominal under a wide array of scenarios. Our methodology begins to break down when P(X=0)&gt;0.1 but is still capable of obtaining reasonable confidence coverage. We illustrate the proposed technique by estimating (1) the size of a moose population in Alaska and (2) the number of bat fatalities at a wind power facility, both from samples with imperfect detection probabilities, estimated independently.

Multi-target Tracking and Track Management Algorithm Based on UFIR Filter With Imperfect Detection Probability

This paper proposes an unbiased finite impulse response filter and track management algorithm for multi-target tracking (MTT) with imperfect detection probability. Targets cannot be detected under MTT for various reasons, including sensor failure and screening by other targets. Despite the temporary missed detection, the proposed MTT algorithm robustly tracks targets under MTT conditions by replacing the missed detection with recently detected target measurement. The track is deleted on the track table when consecutive detection failure exceeding missing horizon occurs. Computational time for the proposed MTT algorithm is significantly less than that for existing MTT algorithm based finite impulse response filters due to the proposed track update and track management algorithm. Simulation and experimental vehicle and pedestrian tracking results verify outstanding tracking accuracy and shorter calculation times for the proposed algorithm.

Analyzing patterns in population dynamics using repeated population surveys with three types of detection data

• We generalize distance sampling with multiple observers and time to detection. • Standard distance sampling can misrepresent population trends in some configurations. • Estimating availability to detection is made easier by combining multiple data types. • That new framework increases the number of parameters and the computing time. To facilitate the use of population counts as an index of population change, we describe a generalization of the distance sampling methodology to analyze, in addition to distance to the observer, two other ways to estimate imperfect detection probability: multiple observers and time-to-detection, in a flexible manner, meaning that not all sites or years need to have distance information or be surveyed in the same way every year. We also account for the effect of partially-observed individual covariates, to account for the effect of group size on detection probability. Finally, we separate the probability of availability to detection from the probability of detection itself. We perform a thorough, illustrated assessment of the pros and cons of this framework with simulations and real case studies. First, we compare to simple linear models, illustrating the magnitude of the bias caused by imperfect detection. Second, we compare to standard distance sampling, illustrating the bias caused by variation in the probability of availability to detection. However, the availability to detection was weakly identifiable, meaning that the ability to separate it from detection probability, and therefore debias the trend estimate, depended on the data configuration. Combining distance with multiple observers and with time-to-detection solved the weak identifiability in an applied case study. We recommend using both the type of analysis we showcase, and a simple regression of the population count against time. Discrepancies between results from simple and complex analyses can help identify sources of bias in the former and loss of precision in the latter within the logistical constraints of local wildlife management schemes.

A century of climate and land-use change cause species turnover without loss of beta diversity in California's Central Valley.

Climate and land-use changes are thought to be the greatest threats to biodiversity, but few studies have directly measured their simultaneous impacts on species distributions. We used a unique historic resource-early 20th-century bird surveys conducted by Joseph Grinnell and colleagues-paired with contemporary resurveys a century later to examine changes in bird distributions in California's Central Valley, one of the most intensively modified agricultural zones in the world and a region of heterogeneous climate change. We analyzed species- and community-level occupancy using multispecies occupancy models that explicitly accounted for imperfect detection probability, and developed a novel, simulation-based method to compare the relative influences of climate and land-use covariates on site-level species richness and beta diversity (measured by Jaccard similarity). Surprisingly, we show that mean occupancy, species richness and between-site similarity have remained remarkably stable over the past century. Stability in community-level metrics masked substantial changes in species composition; occupancy declines of some species were equally matched by increases in others, predominantly species with generalist or human-associated habitat preferences. Bird occupancy, richness and diversity within each era were driven most strongly by water availability (precipitation and percent water cover), indicating that both climate and land-use are important drivers of species distributions. Water availability had much stronger effects than temperature, urbanization and agricultural cover, which are typically thought to drive biodiversity decline.

Testing infrared camera surveys and distance analyses to estimate feral horse abundance in a known population

ABSTRACTWe tested the use of high‐resolution infrared (IR) camera technology and distance sampling analyses to estimate abundance of feral horses (Equus caballus) during 2015–2016 in the McCullough Peaks Herd Management Area, Wyoming, USA. Infrared technology is becoming more common in ungulate population monitoring. The quality of IR cameras now allows ungulate species to be differentiated. Imperfect detection is a common problem in aerial surveys, so we tested the use of distance sampling analyses to account for imperfect detection probability. We conducted 2 aerial surveys in a sagebrush ecosystem with a demographically closed horse population. True abundance was known to within ±4 animals as a result of intensive, ground‐based monitoring of each animal, all of which are uniquely identifiable. After truncation of our data, the most supported detection function was a uniform function with a detection probability equal to 1.0 out to 255 m. Our analyses yielded results that were within 10% of true abundance, but the coefficient of variation (CV) was large (36–58%) assuming a small sampling fraction. However, our truncated surveys covered approximately 95% of the herd management area. By including a finite population correction factor in our calculations of variance estimates, CVs (8–13%) were dramatically reduced. We found the combination of IR surveys and distance sampling analysis to be a useful method to estimate feral horse abundance in sagebrush vegetation type, which had limited cover to obscure horses. Repeated testing in sagebrush ecosystems as well as further testing in other habitat types and under differing conditions will inform how general our approach can be. © 2018 The Wildlife Society.

Occupancy and Detection of Clinch Dace Using Two Gear Types

Abstract The Clinch Dace Chrosomus sp. cf. saylori, discovered in 1999, is an undescribed headwater fish species of global conservation concern with a limited distribution in two counties in southwest Virginia. Highly efficient sampling gears are key to monitoring headwater fish assemblages in Appalachia, including those containing Clinch Dace. Additional information is needed regarding the habitat requirements of the species to understand responses to future mining and logging activities in the region. An occupancy modeling framework is useful to account for incomplete detection, with multiple sampling gears in presence–absence surveys for cryptic or rare species. We detected Clinch Dace at 13 of 70 sites. Occupancy corrected for imperfect detection probability did not differ from naïve occupancy estimates and was 0.19. Clinch Dace occurred in streams with higher substrate embeddedness and catchment forest cover. Backpack electrofishing had a 55% higher probability of detecting Clinch Dace in a 50-m subreach than minnow traps. Appropriate management actions for this species may focus on preserving forested cover in occupied watersheds and monitoring the future impact of surface mining activities that increase total dissolved solids. Sampling protocols for the imperiled Clinch Dace can incorporate both gears and adjust sampling effort to maximize species detection in specific habitats and with specific research goals.

Probability hypothesis density filter with imperfect detection probability for multi-target tracking

Probability hypothesis density (PHD) filter is an effective means to track multiple targets in that it avoids explicit data association between measurements and targets. However, the PHD filter cannot be directly applied to track targets in imperfect detection probability conditions. Otherwise, the performance of almost all the PHD-based filters significantly decreases. Aiming at improving the estimate accuracy as for target states and their number, a multi-target tracking algorithm using the probability hypothesis density filter is proposed, where a novel multi-frame scheme is introduced to cope with estimates of undetected targets caused by the imperfect detection probability. According to the weights of targets at different time steps, both the previous weight array and state extraction identifier of individual targets are constructed. When the targets are undetected at some times, the states of the undetected targets are extracted based on previous weight arrays and state extraction identifiers of correlative targets. Simulation results show that the proposed algorithm effectively improves the performance of the existing relevant PHD-based filters in imperfect detection of probability scenarios.